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https://pdglive.lbl.gov/DataBlock.action?node=B130W%2B&home=sumtabB	${{\mathit \Xi}_{{c}}{(2970)}^{+}}$ WIDTH VALUE (MeV) EVTS DOCUMENT ID TECN COMMENT $\bf{ 20.9 {}^{+2.4}_{-3.5}}$ OUR AVERAGE Error includes scale factor of 1.2. $28.1$ $\pm2.4$ ${}^{+1.0}_{-5.0}$ 916 2016 BELL ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \Upsilon}}$ regions $14.8$ $\pm2.5$ $\pm4.1$ $244$ $\pm39$ 2014 BELL ${{\mathit e}^{+}}{{\mathit e}^{-}}$ ${{\mathit \Upsilon}{(1S)}}$ to ${{\mathit \Upsilon}{(5S)}}$ $27$ $\pm8$ $\pm2$ $756$ $\pm206$ 2008 J BABR ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}$ 10.58 GeV $18$ $\pm6$ $\pm3$ $78$ $\pm13$ 2008 BELL ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}{{\mathit \Upsilon}{(4S)}}$ • • We do not use the following data for averages, fits, limits, etc. • • $43.5$ $\pm7.5$ $\pm7.0$ $405$ $\pm51$ 2006 BELL See KATO 2014 References: YELTON 2016 PR D94 052011 Study of Excited ${{\mathit \Xi}_{{c}}}$ States Decaying into ${{\mathit \Xi}_{{c}}^{0}}$ and ${{\mathit \Xi}_{{c}}^{+}}$ Baryons KATO 2014 PR D89 052003 Search for Doubly Charmed Baryons and Study of Charmed Strange Baryons at Belle AUBERT 2008J PR D77 012002 Study of Excited Charm-Strange Baryons with Evidence for New Baryons ${{\mathit \Xi}_{{c}}{(3055)}^{+}}$ and ${{\mathit \Xi}_{{c}}{(3123)}^{+}}$ LESIAK 2008 PL B665 9 Measurement of Masses of the ${{\mathit \Xi}_{{c}}{(2645)}}$ and ${{\mathit \Xi}_{{c}}{(2815)}}$ Baryons and Observation of ${{\mathit \Xi}_{{c}}{(2980)}}$ $\rightarrow$ ${{\mathit \Xi}_{{c}}{(2645)}}{{\mathit \pi}}$ CHISTOV 2006 PRL 97 162001 Observation of New States Decaying into ${{\mathit \Lambda}_{{c}}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{+}}$ and ${{\mathit \Lambda}_{{c}}^{+}}{{\mathit K}_S^0}$ ${{\mathit \pi}^{-}}$	2022-10-01T07:10:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8681676387786865, "perplexity": 8557.50623641588}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335573.50/warc/CC-MAIN-20221001070422-20221001100422-00353.warc.gz"}
https://techbase.kde.org/index.php?title=Getting_Started/Build/Windows/emerge&diff=prev&oldid=36727	# Difference between revisions of "Getting Started/Build/Windows/emerge" emerge is a tool to build the KDE sources and its third party requirements on MS Windows. It is the easy way to build KDE on MS Windows. ## Introduction Emerge is a tool that can build the different parts of KDE and its dependencies under windows. We created this tool to automate and simplify the build process under windows. We try to build all packages that we offer in the KDE installer with emerge. That has some advantages for us: • it is easy for people to join us: Before emerge it was quite some work to set a system up for development. There were some quirks, which were documented in some mailing lists, but you had to remember them or you ran into an already solved problem again, etc. Now to get a development machine you need a windows computer, need to install python and subversion and do the emerge checkout. Then execute emerge to build what you want to build. This is easy for developers coming from windows to KDE, and also for KDE developers coming to windows. • it is easy for us to do (nightly/continuous/release/reproducable/...) builds: With emerge you can build the whole software stack (lowlevel libs, qt, kdelibs, things above that) with only one command. You can start that build, and some hours later you can check if it worked, or if something broke. So we can spot problems easier and earlier. We can also start with a "naked" windows computer without any other installed software and bootstrap kde on it. That ensures, that no hidden dependencies on some pieces of software sneak in, because then the builds on a "naked" computer would break and show the problem. • it is easier to collaborate: We can test the same emerge build description for a package on different windows versions/computers before we do binary releases. People can also add build descriptions for new packages to the subversion repository. This emerge tool was inspired by the Gentoo emerge tool. ## Set up the environment ### Root directory Create a directory if possible in your harddrive's root e.g. C:\kderoot or D:\kderoot (You will need this PATH later). This directory will contain the whole kde installation later. We will refer to it as %KDEROOT%. ### Python interpreter emerge.bat invokes an emerge.py script written in Python programming language, so you first need to install a Python Interpreter. The python installation directory will be added to the PATH later by %KDEROOT%\etc\kdesettings.bat script. ### Subversion client The latest source code for windows emerge and the rest of KDE is stored in a repository created and managed using the Subversion version control tool. You need a Subversion client for the first checkout. There are at least two applications: • a command line client, available at subversion.tigris.org (required by emerge to get the source code from KDE Subversion repository), aimed at developers or power users accustomed with the command line, • GUI program like TortoiseSVN, optional, useful for displaying differences between various versions of files in the repository in a graphical way. Note 1: If you experience problems with the checkout of Qt (subversion doesn't work correctly) please remove any other subversion binaries out of the path that you do have. The different versions of the Apache portable runtime (APR) are incompatible! Note 2: Make sure to use a copy of Subversion that was built on Windows so that checked-out files do not use UNIX line endings. If you check out with UNIX line endings, the patch program will fail when attempting to apply a patch whose line endings don't match the system's. ### Check out the emerge tool The source code of the emerge tool and the recipes for creating KDE packages are located at svn://anonsvn.kde.org/home/kde/trunk/kdesupport/emerge, which is an URL based on Subversion-specific svn protocol. You need to check out the source code from the emerge Subversion directory into a new directory, which in this example we will call %KDEROOT%. #### Check out using the 'svn' command • Option 1: With the svn command line tool, you can accomplish this with the following commands: cd %KDEROOT% • if you will only use anonymous (read-only) access to the KDE svn repository: svn co svn://anonsvn.kde.org/home/kde/trunk/kdesupport/emerge • or, if you plan to use write access (commit) to the KDE svn repository • via https: svn co --username yourusername https://svn.kde.org/home/kde/trunk/kdesupport/emerge • via a puTTY tunnel using your existing account & OpenSSH private key: svn co svn+putty://svn.kde.org/home/kde/trunk/kdesupport/emerge This would result with: Error validating server certificate for 'https://svn.kde.org:443': - The certificate is not issued by a trusted authority. Use the fingerprint to validate the certificate manually! Certificate information: - Hostname: svn.kde.org - Valid: from Wed, 11 May 2005 09:08:21 GMT until Sat, 09 May 2015 09:08:21 GMT - Issuer: SVN, KDE e.V., Nuernberg, Bavaria, DE - Fingerprint: xx:xx:xx:xx:xx:xx:xx:xx:xx:xx:xx:xx:xx:xx:xx:xx:xx:xx:xx:xx (R)eject, accept (t)emporarily or accept (p)ermanently? enter p here to permanently accept the certificate: Authentication realm: <https://svn.kde.org:443> KDE SVN account A emerge\kdeenv.bat A emerge\portage A emerge\portage\kdesupport [....] The password and cache for the certificates is saved in %APPDATA%\Subversion\auth directory. #### Check out using the TortoiseSVN • Option 2: If you use TortoiseSVN: 1. right-click on your %KDEROOT% folder and select SVN Checkout... command from the context menu, 2. paste svn://anonsvn.kde.org/home/kde/trunk/kdesupport/emerge URL into the URL of repository text box (replace with https://svn.kde.org/home/kde/trunk/kdesupport/emerge for read-write access) 3. add \emerge to the folder name in the Checkout directory box and click OK to continue 4. if you picked the read-write access, you will be asked for accepting the SSL certificate of the SVN server (click "Premanent") and then for username and password. For convenience select "Save authentication" checkbox too (the password and cache for the certificates will be saved in %APPDATA%\Subversion\auth directory). After the checkout you should have the directory %KDEROOT%\emerge. If you don't, you move your emerge directory to that location. ### Configure the emerge tool 1. Create the directory %KDEROOT%\etc. 2. Copy the file %KDEROOT%\emerge\kdesettings-example.bat as %KDEROOT%\etc\kdesettings.bat and change its contents according to your needs. The options are described in the rem lines in the file itself. The kdesettings.bat script will be called by the main kdeenv.bat script. Note 1: Be sure that you neither have the msys/bin nor the cygwin/bin in your path. If so you have to definitely remove it. Note 2 from a user: The applications gimp, inkscape and graphviz are also a problem. To make sure that there's nothing wrong I stripped my path to contain only what I needed to build. ## Running emerge To use emerge you need to start a console window and point that to %KDEROOT%\emerge. For example: C: cd \%KDEROOT%\emerge Then you have to execute kdeenv.bat This tells emerge about your environment settings (e.g. paths). It will load your configuration from %KDEROOT%\etc\kdesettings.bat. It should not give any error messages, otherwise emerge will not work as expected. The output should look similar to this one (of course with your paths): C:\kderoot\emerge>kdeenv.bat kdesettings.bat executed KDEROOT : C:\kderoot KDECOMPILER : mingw KDESVNDIR : C:\kderoot\svn PYTHONPATH : C:\python25 C:\kderoot\emerge> Now you should be able to use emerge. Type emerge --help to get some help on usage. ## Setting up a compiler Currently emerge supports both the MinGW and MS Visual C++ (msvc) compilers. We did not add dependencies for the compilers, so you have to make sure to install a compiler by yourself. There are three ways to set up a compiler for emerge. We assumed you have set KDECOMPILER variable properly in the %KDEROOT%\etc\kdesettings.bat. In the following sections you can find information on how to install or reuse an existing compiler. ### Install the MinGW compiler with emerge Let emerge install the MinGW compiler: To install the MinGW ("Minimalist GNU for Windows") compiler with emerge, type emerge mingw and wait until it is finished. If you encounter an error like Assertion failed: hunk, file ../patch-2.5.9-src/patch.c, line 354 try to edit line 51 of file mingw-x.y.z.py (%KDEROOT%\emerge\portage\dev-util\mingw) by adding the --binary after -p1 parameter. The line should then look like this: cmd = "cd %s && patch -p1 --binary < %s" % \ This is probably because the different line break types (Linux vs Dos) in the files and the bug in patch.exe. Althought this is an ugly hack and should be fixed somewhere else, it works for the current versions of patch (2.5.9) and mingw (3.4.5). ### Point to an existing MinGW installation • Point emerge to an existing MinGW installation: This option is not recommended for now, because it only adds one more point of failure, and does not gain something in comparison to the option above. NOTE from a user: be sure that path to \mingw\bin has been set correctly, by default it is pointing to: %KDEROOT%\mingw\bin which does not apply to most installations. If you see an error about cc1plus not being found, either add MinGW's \libexec\gcc\mingw32\3.4.5 to your PATH (in command line set PATH=%PATH%;path\to\directory) variable or copy the contents of this directory to MinGW's bin directory. The prior is preferred. Under Vista, the mingw directory may need to be moved to c:\ in order to compile properly. ### Point to an existing MS Visual C++ installation You need to point emerge to an existing msvc installation. To do that, execute vcvarsall.bat before running %KDEROOT%\emerge\kdeenv.bat. In recent versions this is run automatically for you from kdeenv.bat if configured properly in kdesettings.bat. Check your kdesettings.bat file to know if you need to run this manually or not. Notes related to Vista: • Note that for debug builds MS Visual Studio 2005 Service Pack 1 is required due to the use of manifest files and using pre-built packages for some dependecies. • Notes related to Vista: If you open the command prompt under Vista by right clicking and running as administrator, you don't get the UAC issues with Vista trying to unsuccesfully run patch as an installer in a seperate environment. You may want run Visual Studio with administrative rights anyway under Vista, as this is recommended by Microsoft (perhaps Visual Studio 2008 would not force you to do that...). ## What emerge does emerge will fetch Windows versions of numerous UNIX-like utilities and libraries from the Internet, putting them in kderoot\bin, then get the Win32 support files, then Subversion, then Perl and the Qt libraries, etc. Then emerge compiles the Qt libraries, this takes hours. emerge package performs the separate actions --fetch, --unpack, --compile, --install, --manifest, and --qmerge. ## emerge command line options and settings There are some options that can be used when building with emerge. Command line switch Command line argument Description -v EMERGE_VERBOSE This option sets the verbosity level. Currently the highest verbosity level is 3 (-v -v -v). A verbosity level of 0 should give no output and equals to -q. You can set EMERGE_VERBOSE=3 instead in the environment of the commandline or within your kdesettings.bat file. --nocopy EMERGE_NOCOPY This very useful option suppresses copying the sources from the local subversion tree to a directory within the build directory. It shouldn't be used while packaging; in the other cases it reduces the amount of harddisk used though and removes the copying time. You can set EMERGE_NOCOPY=True or =False instead. --offline This option suppresses the update step of the local tree - which needs some time. Be aware though that you have to have existing sources already if you want to use this option. -t EMERGE_BUILDTESTS This option enables or disables KDE4 buildtests for KDE modules. Other packages will not change. Use EMERGE_BUILDTESTS=True or =False. --buildtype= Debug This option enables full debugging mode for the build. Recommended if you plan to debug the runtime or provide more valuable feedback to developers about software defects. You can also change the 'set EMERGE_BUILDTYPE=RelWithDebInfo' line in the kdesettings.bat file. ## Emerge works, now what? • Once you have emerge --help working, try emerge --print-installable to get a list of valid package names. If you're unsure which are the packages you want, try selecting one from the main "kde" group (e.g. kdegames). ## Hints ### Updating packages • Once you have packagename built, type emerge --unmerge packagename --noclean --target=svnHEAD packagename to update packagename from the subversion and compile it without removing the build dir. ### Altering locale and country settings • To change locale for all users within the KDE environment, edit KDEROOT/share/config/kdeglobals file and add: [Locale] Country= Language= Replace ** with your lowercase alpha-2 country code, e.g. pl for Poland. You can edit your \$HOME/.kde/share/config/kdeglobals file instead to alter your local settings, not for all users. ## Notes emerge can mostly cooperate with the kdewin-installer but we're currently still working on some packages which are packaged in a wrong way. It is not recommended to use another layout then installer for directory_layout in the kdesettings.bat anymore (see that file for more detailed information). emerge creates lots of files in \kderoot\tmp during build. After a package is successfully installed (check \kderoot\etc\portage\installed or the directory \kderoot\manifest\), you can delete its temporary directory. Windows emerge is derived from the Gentoo portage system, but we are currently not enforcing compatibility. If you have questions about that please contact us at the channel #kde-windows on irc.freenode.net. ## Vista issues • jstaniek 12:02, 15 January 2008 (CET): UAC has infamous heuristics that make programs like patch.exe treat as installers and try to run them with admin rights (!). This heuristics can be tricked by renaming patch.exe to something like pch.exe (example) but we did not want to add item to our infrastructure. Instead it is possibleto turn off the heuristics (see the screenshot here in the security blog calling the heuristics 'severe hole in the design of UAC'). If you happen to disable the UAC, as many annoyed users and devs do (msvc demands admin rights anyway!), patch.exe should already work for you as in older Windows. Alternatively you may want to disable UAC for admins only, but this makes no sense if you are the only user of your machine and use only the admin account. • MBitter 15:50, 12 September 2008 (CET): Another workaround for the Vist-Bug is to create a file patch.exe.manifest in the bin directory with the following content: <?xml version="1.0" encoding="UTF-8" standalone="yes"?> <assembly xmlns="urn:schemas-microsoft-com:asm.v1" manifestVersion="1.0"> <assemblyIdentity version="1.0.0.0" processorArchitecture="X86" name="patch.exe" type="win32"/> <trustInfo xmlns="urn:schemas-microsoft-com:asm.v3"> <security> <requestedPrivileges> <requestedExecutionLevel level="asInvoker" uiAccess="false"/> </requestedPrivileges> </security> </trustInfo> </assembly> This page was last edited on 23 December 2008, at 03:11. Content is available under Creative Commons License SA 4.0 unless otherwise noted.	2021-05-08T14:46:02	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6678699254989624, "perplexity": 5440.109468753968}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988882.7/warc/CC-MAIN-20210508121446-20210508151446-00434.warc.gz"}
https://www.cosmos.esa.int/web/planet-eslab-2023/poster-abstract	# Poster abstracts ## Planetary formation and evolution Tracing the late formation and early evolution of young Sub-Neptune progenitors Saugata Barat (University of Amsterdam) Sub-Neptunes and super-Earths correspond to the most common population exoplanets, yet there are several burning questions regarding their formation and their early evolution. In this context the 23 Myr old V1298 Tau system, composed of three Neptunes/Sub-Neptunes transiting exoplanets, represents a unique opportunity to probe the early conditions of what are most likely super-Earth progenitors. We present observational campaigns dedicated to probe the atmospheres of the V1298 Tau planets to trace fossil records of their formation, though the determination of their mass, their elemental abundances and metallicity, and ongoing evolution though their atmospheric dynamics and escape. We find that the planets in this system have lower masses and much lower metal abundances than initially thought, and that atmospheric escape is occurring at lower rates than expected. Our puzzling findings challenges planet formation paradigms for small planets and we discuss our results in the context of planet formation, comparative exoplanetology with other young and mature systems, as well as within the same system. Dynamic Disk Temperature and its Effect on Pebbles and Planet Formation Areli Castrejon (University of Groningen, Kapteyn Astronomical Institute) To date, thousands of exoplanets have been discovered; a sizeable amount of these planets lie in the intermediate mass range (1-10 Earth masses). The predominant theory to grow these planets is the pebble accretion paradigm. In this formulation, larger particles denoted as pebbles, feel drag from the gaseous disk and are accreted onto growing protoplanets. The efficiency of pebble accretion allows planetary embryos to grow quickly, before the disk dissipates. The evolution of the pebble surface density is highly dependent on the temperature structure chosen. We follow an evolving temperature structure with and without a dust sublimation front. We find that the temperature evolution cannot be ignored in calculating the pebble dynamics and this has implications for the growth of planets. A dynamic temperature leads to a longer-lived pebble surface density. The sustained surface density results in a large population of intermediate mass planets, in-line with observations. Planet across space and time (PAST) III. Morphology of the Planetary Radius Valley as a Function of Stellar Age and Metallicity Di-Chang Chen (Nanjing University), Di-Chang Chen, Jia-Yi Yang, Ji-Wei Xie, Ji-Lin Zhou, Subo Dong Over 5,000 exoplanets have been identified and thousands of candidates are to be confirmed. What are the differences between planetary systems in different Galactic environments, and how do they evolve with time? To address these questions, we conduct a research project, dubbed Planets Across Space and Time (PAST). Here we present some first results of PAST series. We revisit the kinematic method for classification of Galactic components and extend the applicable range from ~ 100 pc to ~ 1, 500 pc from the sun in order to cover most known planet hosts. Furthermore, we revisit the Age-Velocity dispersion Relation (AVR), which allows us to derive kinematic age with a typical uncertainty of 10-20% for an ensemble of stars. Applying the above revised methods, we present catalogs of kinematic properties as well as other basic stellar parameters for 2174 host stars of 2872 planets and 35,835 Kepler stars. Using the above kinematic catalogs, we perform a systematical investigation into the planetary radius valley morphology in the Galactic context, i.e., thin/thick galactic disks, stellar age and metallicity abundance ([Fe/H] and [alpha/Fe]). Did planet formation occur only recently? Evidences from kinematics and chemical properties of exoplanet host stars from GAIA DR3 Swastik Chowbay (Indian Institute of Astrophysics), Swastik Chowbay, Ravinder K Banyal et al In this study, we examine the kinematic and chemical features of the largest number of 2627 exoplanets harbouring stars whose parameters have been uniformly determined. We combine photometric, astrometric, and spectroscopic data from the most recent Gaia DR3 to examine the various populations of exoplanets harbouring stars. Using spectroscopic data, we determined that stars hosting massive planets are metal-rich and $\alpha$-poor in comparison to stars hosting small planets. Kinematic analysis reveals that the host stars of small planets and giant planets differ in all aspects of galactic space velocity and orbital parameters. In addition, we find that small planet hosting stars have a marginally higher eccentricity and $Z_{max}$ (an indication of an older population) than their larger counterparts. Our spectroscopic and kinematic studies suggest that the small and giant planetary systems likely belong to population of stars with different ages, giants being younger than the small ones. Using the PARSEC isochrone grids and isochrone fitting methods, we also estimated the ages of stars bearing exoplanets. All together, three analyses show that gas giants may have stared forming after the interstellar medium was enriched by Type Ia supernovae, which occurred late in the history of Milky Way. At the same time, a large spread seen in various age indicators of small planet hosting stars implies that they formed throughout the GCE. Despite the fact that several previous studies hinted at similar conclusions, they were not robust because to smaller sample sizes and/or inhomogeneous stellar parameter estimations. Due to the fact that our investigation was conducted on the largest sample of stars that host exoplanets, our results are currently the most credible. On the formation history of nearby Sun-like stars (and their planetary systems) Philippe Gondoin (ESA exoplanet team) Nearby Sun-like stars are prime targets for the detection and characterization of exo-planets and possibly exo-Earths. Understanding their formation history and determining the age of these stars (and their planetary systems) is thus essential.The present study addresses the formation history of nearby solar-type stars using the emission reversal in the cores of their Ca II H&K Fraunhofer lines as an age indicator. A representative sample of nearby (< 65pc) main-sequence G-type stars with near-solar metallicity and known magnetic activity levels is built from a catalogue of chromospheric activity indices (Gomes da Silva et al. 2021) derived from high-resolution spectra obtained with the HARPS spectrograph between 2003 and 2019, as compiled in the AMBRE project. I used an empirical age-activity relationship derived from stellar rotation period measurements in intermediate-age open clusters (Gondoin 2020) to infer the age distribution of these sample stars. A unique testbed for the formation and evolution of small exoplanets: TOI-270 Maximilian Guenther (European Space Agency (ESA)), Laurel Kaye, Thomas Mikal-Evans, ASTEP, NGTS, SPECULOOS, TESS and TFOP science teams The nearby exoplanet system TOI-270 provides an unparalleled opportunity to observationally probe hypotheses for planet formation and evolution. The system hosts one super-Earth and two sub-Neptunes near mean-motion resonances and transiting a bright (K-mag 8.25) M3V dwarf. Strangely, M-dwarf systems harbouring only super-Earths or only sub-Neptunes are ubiquitous. However, for still unknown reasons, systems with multiple planets spanning the radius valley are rare - and we know merely a handful of systems bright enough for precise mass measurements and atmospheric studies. To this end, TOI-270's planets are exceptionally favourable for detailed transit timing variation (TTV) and transmission spectroscopy observations. First, with the planets orbiting near low-order resonances (5:3 and 2:1), our extensive observing campaign with eight different observatories since 2018 yields clear TTV signals for planets c and d, with amplitudes of around 10 min and a super-period of circa 3 yr. Using dynamical models, we can thus significantly constrain their radii, mass ratios, and eccentricities. This adds to complementary radial velocity (RV) mass measurements from HARPS and ESPRESSO. Second, via HST and JWST transmission spectroscopy we can characterise and compare the atmospheres of two sub-Neptunes formed from the same protoplanetary nebula and test hypotheses like photoevaporation, core-powered mass-loss, and gas-poor formation. As one of the best-constrained small planet systems, TOI-270 can thus serve as a unique observational testbed for formation and evolution theories. Studying exoplanet orbits & dynamics with allesfitter Maximilian Guenther (European Space Agency (ESA)), Tansu Daylan The orbits and dynamics of exoplanet systems can unveil their tales of formation, migration, star-planet interactions, and atmospheric properties. TESS, CHEOPS, and soon PLATO deliver an unprecedented wealth of new photometric data on this matter, while ground-based follow-up and radial velocity instruments add valuable insights. Here, I will present how we can unite and untangle all this data on exoplanets' orbits and dynamics using allesfitter. This open-source python software enables flexible and robust inference of stars and exoplanets from photometric and radial velocity data. Allesfitter offers a rich selection of orbital and transit/eclipse models, accommodating multiple exoplanets, multi-star systems, transit-timing variations, and phase curves. It can also help mitigate and/or study stellar variability, star spots, and stellar flares. I will highlight some of allesfitter's science output on examples of exoplanet dynamics (e.g., TOI-270 and TOI-216) and orbital phase curves (e.g., WASP-18 and WASP-121). With TESS' extended mission, CHEOPS in full swing, and PLATO on the horizon, a wealth of new data face us, allowing TTV and phase curve studies of dozens of such systems over many years. Young planets are key: HIP 67522 b and TOI-4562 b Alexis Heitzmann (Queen Mary University of London) et al. A search of accreting protoplanets through high-angular resolution H alpha observations Nuria Huélamo (CAB (CSIC-INTA)) Protoplanets embedded in disks are expected to accrete material from their surrounding media. As a result of this process, they can emit in accretion tracers like the H alpha line. In this work, we show the result from SPHERE/ZIMPOL observations to detect accreting protoplanets around five stars with (pre-)transitional disks. They were obtained in the H_alpha line and the adjacent continuum, combining spectral and angular differential imaging techniques to increase the contrast in the innermost regions close to the star. We do not detect any point-like source around any of the stars. When we compare our detection limits with different planetary models, we estimate an average upper limit to the accretion luminosity of < 10^-4 Lsun at 200 mas, which is 2 orders of magnitude higher that that previously estimated from the extrapolation of the L_Halpha - L_acc stellar relationship. We explain the lack of protoplanet detections as a combination of different factors, like e.g. episodic accretion, extinction from the circumstellar and circumplanetary disks, and/or a majority of low-mass, low-accreting planets. The JWST will help to shed light on the accretion process of planets at the earliest stages of their formation. Large impacts on the early Earth: Where does the reducing power go? Jonathan Itcovitz (Institute of Astronomy, University of Cambridge), Auriol S.P. Rae, Thomas M. Davison, Gareth S. Collins, Oliver Shorttle Reduced surface environments are required for many prebiotic chemical pathways. Large impacts onto Hadean Earth have been suggested as scenarios able to generate such environments on a global scale. Physical and chemical processes that occur shortly after impact can, however, limit the reducing power that is available at planet surface. Here, we present impact simulations and chemical calculations that demonstrate the efficient loss of reducing power from the post-impact planetary surface. This loss occurs via the dynamic escape of impactor core material, or the sinking of this material to the planet core, during impact, and through interactions between the atmosphere and the impact-generated melt phase. We suggest that post-impact surface environments are sufficiently reduced that species important to prebiotic chemistry can form (e.g., HCN, HCCCN). Additionally, the formation of a reduced impact-generated melt phase allows for reducing power to be stored in the planet mantle, where it can degas to the surface on geologic timescales. Giant planet formation around host stars of different masses Heather Johnston (University of Leeds), Dr Olja Panic, Dr Beibei Liu We carry out a pebble-driven planet formation simulations to investigate the formation of giant planets around intermediate-mass stars, in the stellar mass range between 1.5 M_sun and 3 M_sun. We find that the massive giant planets are preferred to emerge in the circumstances when the disks have larger sizes, metallicities, and/or higher disk accretion rates. As these properties are only enhanced with stellar mass, an alternative physical scenario is needed to explain the decline of giant planet frequency from 2 to 3 M_sun. We propose that FUV/EUV photoevaporation in this stellar mass range plays a role in actively removing the disc, and slowing down planet formation. This photoevaporation mechanism is only dominant after the first 2Myr, meaning that, in this scenario, giant planets form predominantly later than the first couple of Myr of disc evolution. This is not in contradiction with the ~2Myr disc lifetimes found observationally, because only a small fraction of stars (long-lived discs) end up becoming giant planet hosts. Constraints on the timing of cometary bombardment relative to Earth's growth Sarah Joiret (CNRS - Laboratoire d'Astrophysique de Bordeaux) Isotopic signatures of Xe are different in the mantle and in the atmosphere of the Earth. While mantle Xe is chondritic (Peron Moreira, 2018; Broadley et al., 2020), atmospheric Xe would have evolved from the so-called primordial U-Xe, which is a mixture of ~ 80% chondritic Xe and ~ 20% cometary Xe (Marty et al., 2017). This naively suggests that the cometary bombardment only happened after the Earth was fully formed. The bombardment of comets is thought to have been triggered by the giant planet instability (Gomes et al., 2005) early in the history of the solar system. The timing of this instability is still uncertain (Morbidelli et al., 2018), but recent simulations seem to favour a very early instability (Clement et al., 2018). We present our ongoing project to constrain the timing of cometary bombardment relative to Earth's growth, using numerical simulations on one hand, and laboratory isotopic measurements of meteorites on the other hand. Giant Exoplanets around M dwarf Stars Shubham Kanodia (Carnegie Institution for Science, Earth and Planets Lab) In this presentation, we describe the new Giant Exoplanets around M dwarf Stars (GEMS) survey initiated to to understand giant planets transiting around M dwarf stars. This survey will try to understand giant planet formation, by shedding light on big planets around small stars. We will perform a systematic search for these planets in the TESS full frame images, and continue our radial velocity follow up to confirm these planets and measure their masses. As part of this ongoing effort, we have confirmed about half the known Jovian planets around M dwarf stars and plan to triple this sample in three years. This increased sample will be crucial to estimate the TESS detection sensitivity, and thereby quantify the occurrence of these planets as a function of stellar and orbital parameters. Next, we describe how the existence of some of these planets stretches our understanding of planet formation, and necessitates revisiting the mass budget of class II protoplanetary disks. Finally, we discuss how these planets around cool stars with large transit depths are excellent targets for atmospheric characterisation for JWST and ARIEL, especially for equilibrium temperatures conducive to the existence of methane in planetary atmospheres. Through this presentation, we hope to encourage dialogue about planet formation, tidal evolution, atmospheric characterization and RV mass measurements in a hitherto (largely) unexplored regime of planets. The Possible Formation of Jupiter from Supersolar Gas Olivier Mousis (Aix Marseille Université, Institut Origines, CNRS, CNES, LAM, Marseille, France), Artyom Aguichine, and Jonathan Lunine More than two decades ago, the Galileo probe performed in situ measurements of the composition of Jupiter's atmosphere and found that the abundances of C, N, S, P, Ar, Kr, and Xe were all enriched by factors of 1.5-5.4 times their protosolar value. Juno's measurements recently confirmed the supersolar N abundance and also found that the O abundance was enriched by a factor 1-5 compared with its protosolar value. Here, we aim at determining the radial and temporal evolution of the composition of gases and solids in the protosolar nebula (PSN) to assess the possibility that Jupiter's current composition was acquired via the direct accretion of supersolar gases. To do so, we model the evolution of a 1D Î±-viscous accretion disk that includes the radial transport of dust and ice particles and their vapors, with their sublimation and condensation rates, to compute the composition of the PSN. We find that the composition of Jupiter's envelope can be explained only from its accretion from PSN gas (alpha <= 10-3), or from a mixture of vapors and solids (alpha > 10-3). The composition of the PSN at 4 au, namely between the locations of the H2O and CO2 icelines, reproduces the one measured in Jupiter between 100 and 300 kyr of disk evolution. Our results are found to be compatible with both the core accretion model, where Jupiter would acquire its metallicity by late accretion of volatile-rich planetesimals, and the gravitational collapse scenario, where the composition of proto-Jupiter would be similar to that of the PSN. An unbiased NOEMA 2.6 to 4 mm survey of the GG Tau ring Thi Phuong Nguyen (Korea Astronomy and Space Science Institute), A. Dutrey, E. Chapillon, S. Guilloteau , J. Bary, T. L. Beck, A. Coutens , O. Denis-Alpizar, E. Di Folco, P. N. Diep , L. Majumdar , J.-P. Melisse, C.-W. Lee , V. Pietu, T. Stoecklin , and Y.-W. Tang We will present the chemical content of the protoplanetary disk (PPD) surrounding GG Tau A, a well-known triple T Tauri system. Using NOEMA, we detected 17 molecules in the circumbinary disk of GG Tau A, with H2S and CCS were detected for the first time in a PPD. We analysed the data with a radiative transfer code to derive molecular densities and the abundance relative to 13CO, which we compare to those of the TMC1 cloud and LkCa 15 disk. The analysis confirms that sulphur chemistry is not yet properly understood. The D/H ratio, derived from DCO+/HCO+, DCN/HCN, and DNC/HNC ratios, points towards a low temperature chemistry. The detection of the rare species such as H2S and CCS confirms that GG Tau is a good laboratory to study the protoplanetary disk chemistry. Protoplanetary disks components contained in pristine carbonaceous chondrites Josep M. Trigo-rodríguez (Institute of Space Sciences (CSIC-IEEC)), Jordi Ibáñez-Insa An overview of the rock-forming materials of carbonaceous chondrites will be presented. The intention is summarizing the different approaches to study them and infer valuable clues on the size, composition and properties of the materials forming protoplanetary disks. Signatures of violent dynamical histories in the architectures of planetary systems Diego Turrini (INAF), Angelo Zinzi The dynamical history of planetary systems is recorded by their architectures through the dynamical excitation of the orbits of their planets. Studies have shown the existence of an anti-correlation between the number of planets in a system, i.e. its planetary multiplicity, and the eccentricity of their orbits. Such a trend suggests more violent dynamical histories for planetary systems currently observed to host fewer planets than for systems, like the Solar System, hosting a larger number of them. Orbital eccentricity, however, is only one piece in the mosaic of planetary architectures. Here we show how information on the dynamical past of planetary systems can be more reliably extracted from their architectures using the simple metric provided by the Normalized Angular Momentum Deficit (NAMD). The NAMD metric, already used in the study of the Solar System, offers a fast and efficient way to quantify and compare the global dynamical excitation of planetary systems even when their architectures are quite different. Its use confirms that the eccentricity-multiplicity anti-correlation reflects the underlying dynamical excitation-multiplicity anti-correlation. Using well-studied systems like Trappist-1 and the Solar System itself as reference benchmarks, the NAMD can be used to build a global 'dynamical excitation' scale that makes it easier to ascertain whether the dynamical history of planetary systems are governed by chaos or order. ## planetary system architecture, dynamics, stability Planetary Orbit Eccentricity Trends (POET). I. The Eccentricity-MPetallicity Trend for Small Planets Revealed by the LAMOST-Gaia-Kepler Sample Dongsheng An (Nanjing University), Dong-Sheng An, Ji-Wei Xie , Yuan-Zhe Dai , and Ji-Lin Zhou Orbital eccentricity is one of the basic planetary properties, whose distribution may shed light on the history of planet formation and evolution. Here, in a series of works on Planetary Orbit Eccentricity Trends (dubbed POET), we study the distribution of planetary eccentricities and their dependence on stellar/planetary properties. In this paper, the first work of the POET series, we investigate whether and how the eccentricities of small planets depend on stellar metallicities (e.g., [Fe/H]). Previous studies on giant planets have found a significant correlation between planetary eccentricities and their host metallicities. Nevertheless, whether such a correlation exists in small planets (e.g. super-Earth and sub-Neptune) remains unclear. Here, benefiting from the large and homogeneous LAMOST-Gaia-Kepler sample, we characterize the eccentricity distributions of 244 (286) small planets in single (multiple) transiting systems with the transit duration ratio method. We confirm the eccentricity-metallicity trend that eccentricities of single small planets increase with stellar metallicities. Interestingly, a similar trend between eccentricity and metallicity is also found in the radial velocity (RV) sample. We also found that the mutual inclination of multiple transiting systems increases with metallicity, which predicts a moderate eccentricity-metallicity rising trend. Our results of the correlation between eccentricity (inclination) and metallicity for small planet support the core accretion model for planet formation, and they could be footprints of self (and/or external) excitation processes during the history of planet formation and evolution The COPAINS Survey: directly imaging planetary and sub-stellar companions to accelerating stars Mariangela Bonavita (The Open University), C. Fontanive, R. Gratton, K. Muzic The last decade of direct imaging (DI) searches for sub-stellar companions has uncovered a widely diverse sample that challenges the current formation models, while highlighting the intrinsically low occurrence rate of wide companions, especially at the lower end of the mass distribution. These results clearly show how blind surveys, crucial to constrain the underlying planet and sub-stellar companion population, are not an efficient way to increase the sample of DI companions. It is therefore becoming clear that efficient target selection methods are essential to ensure a larger number of detections. In this poster I will present the results of the COPAINS Survey conducted with SPHERE/VLT, searching for sub-stellar companions to stars showing significant proper motion differences between different astrometric catalogues. With 10 companions detected, including 2 new BDs and two new potentially planetary-mass companions, and a sub-stellar companions detection rate of~20%, significantly higher than any blind survey, COPAINS is the most successful DI survey to date. This poster also introduces FORECAST (Finely Optimised REtrieval of Companions of Accelerating STars), a tool which allows to check the agreement between position and mass of the detected companions with the measured astrometric signatures, and was one of the key factor contributing to the success of the survey. Planetary systems architecture and Earth-like planet prediction Jeanne Davoult (Universität Bern), Lokesh Mishra, Yann Alibert The detection of Earth-like planets is both one of the major goals of planetology and at the same time one of the most challenging. Earth-like planets are small and habitable zones, depending on the mass of the central star, can be far from the star, making difficult the detection of such planets and implying a lot of observation time with the current detection methods. Understanding the formation pathway and the architecture of planetary systems harboring an Earth-like planet could facilitate their detection. In this work, a way to identify systems, which are likely to harbor an Earth-like planet, is presented. This can help the selection of targets and can be used to optimize observational surveys. Using correlations in synthetic planetary systems, between planets themselves, or between planets and stellar parameters, the occurrence of Earth-like planets among systems is studied and typical architectures of systems hosting an Earth-like planet are defined. A random forest classifier is then used to classify system, and infer whether a planetary system harbors an Earth-like planet or not, based on its observable characteristics (e.g. properties of already observed planets). The same classifier allows identifying correlations between planets in the same system. Analysis of Serendipitous Ion Tail Crossings of Comet 73P/Schwassmann-Wachmann 3 Samuel Grant (University College London), Prof. Geraint Jones, Prof. Antoinette Galvin Volatile gases ejected from beneath a comet's surface are ionized when in the inner Solar System, transported by the solar wind through the Solar System, and are partially visible as an ion tail. In-situ encounters with cometary plasma provide unique information on the composition and behaviour of the comet, sometimes at significant distance from the comet nucleus. Serendipitous ion tail encounters by spacecraft occur surprisingly frequently, but are often missed due to the ambiguity of in-situ plasma measurements. Comet 73P/Schwassmann-Wachmann 3 now consists of an extended debris field along its orbit - a dust trail - having undergone fragmentation multiple times in the past few decades. In May-June 2006, fragments of comet 73P passed sunward of spacecraft ACE and Wind, both stationed at Sun-Earth L1. A flux of cometary pickup ions was recognised by Gilbert et al. (ApJ 815, 12, 10pp, 2015) in the ACE/SWICS and Wind/STICS datasets. Here, we use a method that provides relatively accurate information on serendipitous spacecraft-comet encounters to show that these detected ions most likely originated in the extended coma of the debris field trailing behind the larger fragments of 73P, rather than associated with the nucleus fragments themselves. This method uses the solar wind velocity measurements made by the spacecraft to extrapolate the flow of the solar wind back to the Sun, so that the likelihood of the solar wind flow transporting material from the comet to the spacecraft can be measured. In August 2011, Comet C/2010 X1 (Elenin) passed directly sunward of spacecraft STEREO-B. During this period, there was a flux in water-group cometary ions detected by STEREO-B/PLASTIC, identified as an ion tail encounter by Galvin et al. (AGU Fall Meeting 2013, abstract P31A-1789, 2013). Using proton velocities measured by STEREO-B/PLASTIC, a previously unknown ion tail crossing of comet 73P fragment AM is identified 3 weeks after the comet Elenin tail crossing, using the same method as for the ACE and Wind encounter. Encounters with recently fragmented comets such as 73P provide opportunities to measure pristine interior material indirectly through the transportation of cometary ions via the solar wind. Towards completing extrasolar systems with the TROY project Jorge Lillo-Box (Center for Astrobiology (CAB)), O. Balsalobre-Ruza In this poster I will provide an overview of the status of our TROY project aiming at detecting and constraining the presence of co-orbital planets/bodies in extrasolar systems. Co-orbitals do exist in our Solar System in the form of small (max- 400 km in size) asteroids trapped in the Lagrangian points of six out of the eight planets. However, planet formation theories allow their formation up to planetary sizes and dynamical stability confirms these 1:1 resonances are indeed stable in the long-term. Exploring these configurations has remained in the to-do list of the exoplanet exploration. With the TROY project we aim at filling this gap from an observational point of view with strong implications in planet formation and evolution. The first conclusions of the project will be presented. The KOBE experiment: filling the habitable zone desert in late K-dwarfs Jorge Lillo-Box (Center for Astrobiology (CAB)), A. Castro-González The absence of confirmed planets within the habitable zone of late-type K-dwarfs (effective temperatures in the range 3800-4600 K) is potentially due to an observational bias. While missions like Kepler (and ground-based RV surveys like HARPS) have focused on Solar-like stars, other surveys like CARMENES, MEarth, TRAPPIST or SPECULOOS are focusing on the lowest mass potential planet hosts, M-dwarfs. However, K-dwarfs represent a unique opportunity in the astrobiological context. These stars are more quite in terms of extreme radiation than their lower-mass counterparts and have less activity RV noise than the G-dwarfs. Their habitable zones are neither too far to difficult planet detection (like G-dwarfs) nor too close to have the HZ planet tidally locked (like M-dwarfs). The KOBE experiment is a RV survey using the CARMENES instrument at Calar Alto observatory to monitor 50 late K's and proof this apparent observational gap. In this poster, we will present the first results of the survey. Modelling of solar and stellar brightness variations Nina-Elisabeth Nemec (Universität Göttingen) An update on the young V1298 Tau system as observed by CHEOPS, HST and Spitzer Hinna Shivkumar (University of Amsterdam), Hinna Shivkumar, Jean-Michel Désert, Saugata Barat, Georgia Mraz, Bob Jacobs, Vatsal Panwar, James Sikora, John Livingston, Trevor David, Lorenzo Pino, Erik Petigura Young planets form a unique bridge between planet-forming protoplanetary disks and mature planets. In order to infer the internal and atmospheric structure of these young inflated planets, it becomes important to have high-precision measurements of their mass and radius. The V1298 Tau system, only a mere 23 Myrs old, is a keystone multi-planetary system hosting four transiting planets. Since the planets orbit a highly variable star, constraining the mass of the planets using radial velocities becomes a challenge. In such a scenario, using transit-timing variations (TTVs) provides another avenue to constrain the mass of the planets. In this poster, I will present high-precision transit observations of the first three planets in the V1298 Tau system using the CHEOPS telescope. I will provide an insight into the data analysis methodology used to encounter the unique systematics of CHEOPS. I will also briefly discuss the decorrelation methods used to tackle stellar variability evident in the observations. Finally, I will present the improvement in the transit parameters of the three young planets, place these observations in the context of HST and Spitzer observations of this system, and how these observations will help in constraining the mass of the planets using TTV models. Furthermore, I will discuss the implications of these measurements in terms of formation and early evolution of sub-Neptune planets. Planets Across Space and Time (PAST) IV: The Occurrence and Architecture of Kepler Planetary Systems as a Function of Kinematic Age Revealed by the LAMOST-Gaia-Kepler Sample Jia-Yi Yang (Nanjing University), Jia-Yi Yang, Di-Chang Chen, Ji-Wei Xie, Ji-Lin Zhou, Subo Dong, Zi Zhu, Zheng Zheng, Chao Liu, Weikai Zong, Ali Luo One of the fundamental questions in astronomy is how planetary systems form and evolve. Measuring the planetary occurrence and architecture as a function of time directly addresses this question. In the fourth paper of the Planets Across Space and Time (PAST) series, we investigate the occurrence and architecture of Kepler planetary systems as a function of kinematic age by using the LAMOST-Gaia-Kepler sample. To isolate the age effect, other stellar properties (e.g., metallicity) have been controlled. We found the following results. (1) The fraction of stars with Kepler-like planets (FKep) is about 50% for all stars; no significant trend is found between FKep and age. (2) The average planet multiplicity (Np) exhibits a decreasing trend ( 2σ significance) with age, which decreases from Np 2.6–2.7 for stars younger than 1 Gyr to Np 1.8–20 for stars older than 8 Gyr. (3) The number of planets per star (η=FKep × Np) shows a more pronounced decreasing trend (3σ significance), which decreases from η 1.4–1.5 for young stars to η 0.9–1.0 for old stars. (4) The median mutual orbital inclination of the planets (σi,k) increases from 2.2 to 3.9 degree as stars aging, and the Solar System also fit such a trend. The nearly independence of FKep 50% on age implies that planet formation is robust and stable across the Galaxy history. The age dependence of Np and σi,k demonstrates planetary architecture is evolving, and planetary systems generally become dynamically hotter with fewer planets as they age. Investigating Possible Orbital Variations from Exoplanet Transit Databases Li-Chin Yeh (National Tsing Hua University / Institute of Computational and Modeling Science ), Ing-Guey Jiang A huge number of mid-transit times from ExoClock and TESS projects are employed to investigate the possible non-linear transit timing variations of exoplanets by performing data-model fitting with both the fixed orbit and the orbital variation models. Several exoplanets in favor of orbital decay are found. Their tidally evolutionary orbits are also studied and presented. ## Stellar/solar activity and interaction with planet; Exoplanet ground-based observations The HADES RV Programme with HARPS-N@TNG-HADES: THE HArps-n red Dwarf Exoplanet Survey Laura Affer (INAF - Osservatorio Astronomico di Palermo), Affer Laura & the HADES Team Many efforts to detect Earth-like planets around low-mass stars are currently devoted to almost every extra-solar planet search. M dwarfs stand as ideal targets for Doppler radial velocity searches as their lower masses and luminosities make low-mass planets orbiting within their habitable zones more easily detectable than those around higher-mass stars. Nonetheless, the statistics of the frequency of this kind of planet hosted by low-mass stars remains poorly constrained. Our M-dwarf radial velocity monitoring with HARPS-N within the HARPS-N Red Dwarf Exoplanet Survey Radial Velocity (HADES) project started in 2012 and is contributing to the widening of the current statistics through the in-depth analysis of accurate radial velocity observations in a narrow range of spectral sub-types from M0 to M3, to investigate the planetary population around a well-defined class of host stars. The HADES project is the result of a collaborative effort between the Italian Global Architecture of Planetary Systems (GAPS) Consortium, the Institut de Ciències de l'Espai de Catalunya (ICE), and the Instituto de Astrofísica de Canarias (IAC). Two photometric programs regularly and almost simultaneously follow up the sample of M stars to characterize the stellar activity, to highlight periods that are due to chromospheric inhomogeneities modulated by stellar rotation and differential rotation, and thus to distinguish from the periodic signals those due to activity and to the presence of planetary companions. We present the complete analysis of the HADES survey and the results obtained concerning the statistical, activity, and characterization part and the planet revealing part, around M dwarfs. Modelling the Effects of Stellar Magnetic Fields on (Exo)Planetary Magnetosphere - Atmosphere systems with Implications for Habitability Sakshi Gupta (Indian Institute of Science Education and Research Kolkata), Sakshi Gupta, Arnab Basak and Dibyendu Nandy The long-term evolution of stellar magnetic activity governs the environment of the orbiting planets impacting their habitability. We perform three-dimensional magnetohydrodynamic simulations followed by a detailed parameter space study to understand the effect of variation in stellar wind magnetic field and intrinsic magnetosphere on the planetary magnetic field topology and atmospheric mass loss rate. We find that the relative strength of the planetary magnetic field with respect to that of stellar wind plays a critical role in determining the steady-state magnetospheric configuration and atmospheric erosion. Either strengthening the stellar wind magnetic field or weakening the planetary magnetospheric strength results in stellar field accumulation in front of the planet, similar to that of an imposed magnetosphere. We explore the formation of Alfvén wings on the planetary night-side wake region at different magnetic activity levels. We identify reconnection processes and wind conditions that lead to the bifurcation of the current sheet in the magnetotail. With increasing stellar wind magnetic field strength, the day-side reconnection point approaches the planet, thereby increasing the mass-loss rate. Our model results are in line with analytic theory. Our study has far-reaching implications in the context of star-planet interaction and (exo)planetary habitability. Astrospheres of Planet-Hosting Cool Stars and the Cosmic Ray Transport Within Konstantin Herbst (Christian-Albrechts-Universität zu Kiel), L. R. Baalmann, F. Effenberger, N. E. Engelbrecht, S. E. S. Ferreira, K. Scherer, R. D. T. Strauss Thanks to dedicated long-term missions like Voyager and GOES over the past 50 years, much insight has been gained into the activity of our Sun, the solar wind, its interaction with the interstellar medium, and, thus, the formation, the evolution, and the structure of the heliosphere. With the help of multi-wavelength observations by the Hubble Space Telescope, Kepler, and TESS, we could detect a variety of extrasolar planets and exomoons and study the characteristics of their host stars and thus became aware that other stars drive bow shocks and astrospheres. Although features like, e.g., stellar winds, so far can not be measured directly, over the past years, several techniques have been developed to indirectly derive properties like stellar mass-loss rates and wind speeds, information that can be used as direct input to existing astrospheric modeling codes. Here we present our astrospheric modeling efforts (3D (magneto-)hydrodynamic) of Proxima Centauri and LHS1140. In the case of the heliosphere, the propagation of Galactic cosmic rays (GCRs) and their relevance in the context of planetary habitability is well understood; however, it is poorly studied when it comes to M stars. Here we further show our latest 1D and 3D transport model efforts of the GCR flux at Proxima Centauri b and LHS1140 b and briefly discuss the possible impact of turbulence. PLATOspec an UV optimized, high-resolution spectrograph in the southern hemisphere for exoplanet research. Petr Kabath (Astronomical Institute of the Czech Academy of Sciences), Eike W. Guenther, Leonardo Vanzi, Artie Hatzes, Rafael Brahm, Jan Janík After the discovery phase of exoplanet research, the aim is now to understand their structure and evolution. Two new satellite missions are now on the horizon: PLATO and ARIEL. PLATO aims to discover planets down to the size of the Earth, and out to the habitable zone in a solar-like star. In contrast to previous missions, PLATO will not only detect the planets but also characterise them by determining their radii, and ages precisely. An integral part of the mission is the mass-determination using RV-measurements obtained with ground-based telescopes. Unfortunately, many solar-like stars are too active to detect an Earth-like planet in the habitable zone. It is thus necessary to characterise the stars first. Particularly important is to find out how active the stars are, because low-mass planets in wide orbits can only be detect in inactive stars. It is thus necessary to monitor the PLATO targets in the CaII HK-lines before taking many ultra-high precision RV-measurements of them. Furthermore, almost all low-mass planets are in systems. Perhaps many of them even have outer gas-giants. We also need to know if this is the case, and we must exclude binaries. These are the two first aims of the PLATOspec project. PLATOspec is a new, fibre-fed high resolution Echelle spectrograph at the ESO1.5m telescope that will be dedicated to PLATO follow-up observations. The ARIEL mission aims to study the atmospheres of 1000 hot and warm planets. To select the best targets for ARIEL, it is necessary to determine not only the radii of the planets but also their masses. This is necessary, because the extend of the atmosphere of a planet, and thus the strength of the signal from the atmosphere, depends on it. Characterizing warm, and hot planets with extended atmospheres is the third science goal of PLATOspec. Hydrodynamical modelling of the escaping atmospheres of planets around evolved stars Thomas Konings (Insitute of Astronomy, KU Leuven), Leen Decin Planets that orbit low- to intermediate stars will experience vigorous star-planet interactions when their host star evolves through the giant branches, including the Asymptotic Giant Branch (AGB) phase. Alongside the evolution of the orbit, the physical and chemical state of the planet's atmosphere will be affected by the intense radiation and outflow of the AGB star. Until now, the description of atmospheres of planets around evolved stars was limited to analytical expressions that varied from Bondi-Hoyle-Lyttleton accretion of stellar wind material to an energy-limited approximation of hydrodynamical atmospheric mass loss. To properly assess the photoevaporative mass loss of such planets, one needs a numerical approach where heating due to photoionization is computed self-consistently during the integration of the hydrodynamical equations. We present here hydrodynamic models of gaseous planets around a Sun-like AGB star that take into account AGB stellar radiation. Subsequently, we estimate the impact of stellar wind ram pressure on the outflow of the planetary atmosphere. Radar Blackouts at Mars: Evidence for a low altitude ionisation layer Mark Lester (University of Leicester), Beatriz Sanchez-Cano, Dikshita Meggi, Simon Joyce, Katerina Stergiopoulou, Hermann Opgenoorth, Robert Lillis, Olivier Witasse, Roberto Orosei, and Marco Cartacci Radars in orbit around Mars such as MARSIS on Mars Express and SHARAD on Mars Reconnaissance Orbiter provide evidence for the nature of the surface and some sub-surface layers. The MARSIS instrument also operates in a topside sounding mode, the Advanced Ionospheric Sounder (AIS) mode, which also receives surface reflections and we now investigate the impact of the solar energetic particles on the surface reflection during ionospheric sounding observations made by MARSIS. We present observations during December 2014 when MARSIS AIS was making observations on the nightside as Mars Express moved towards periapsis and then towards the dayside. Nightside AIS observations clearly demonstrate a similar loss of the surface signal to that seen in the MARSIS sub-surface mode. In addition there is evidence of a reflection from an enhanced layer created by the electrons which is responsible for the attenuation in the signal. The critical frequency is of order 1 MHz, which is equivalent to a peak electron density of order 1010 m-3, at an altitude of about 100 km. These characteristics are similar to our previous modelling work of the impact of the solar energetic electrons. Mass Constraints of Young Proto-sub-Neptunes: Disentangling V1298 Tau's Planetary and Stellar Activity Radial Velocity Signals with MAROON-X James Sikora (Anton Pannekoek Institute for Astronomy, University of Amsterdam), Jason Rowe, Saugata Barat, Jacob Bean, Jean-Michel Désert, Adina Feinstein, Emily Gilbert, Gregory Henry, David Kasper, Déreck-Alexandre Lizotte, Michael Matesic, Vatsal Panwar, Andreas Seifahrt, Hinna Shivkumar Planets orbiting young stars (<100 Myr) serve as important windows into the early stages of planet formation and evolution. When coupled with known ages and insolation fluxes, bulk density measurements of young planets can be used to infer the core compositions and masses of their primordial H/He-dominated atmospheres. Additionally, precise mass constraints of such planets provide the unique opportunity to test initial planet formation theories and theories of atmospheric mass loss processes. The 20-30 Myr old T-Tauri star, V1298 Tau (V = 10 mag), hosts 4 super-Neptune to Jupiter-sized transiting planets. Depending on the assumed stellar activity and planet masses, they are expected to evolve into super-Earths/sub-Neptunes that bound the radius valley. Here we present a joint analysis of high-precision photometry (K2, TESS) and high-precision radial velocities (MAROON-X, HARPS-N, CARMENES) carried out in order to constrain the masses of these young planets and compare with formation and evolution theories of gas-rich planets. A new tool for precise radial velocity measurements Michaela Vítková (Masaryk University), Jana Köhler, Mathias Zechmeister, Marek Skarka One of the most cost-effective, accurate, and cheap methods for radial velocity measurements is the usage of the gas absorption cell (e.g., Iodine cell) method. We present new open-access software for processing spectra obtained with gas cells, the python-based program Viper (Velocity and IP EstimatoR), and recent results obtained with it. It can be used for data obtained with gas cell from multiple instruments (e.g., OES, TCES, CRIRES+) and new can be easily added. When this method was tested on Ondrejov Echelle Spectrograph data, the achieved rms improved 6 times compared to a classic cross-correlation method. Viper is still under development. One of the new features we are currently working on is employing telluric lines that allow us to use Viper for the analysis without a gas cell. ## Ionospheres, magnetospheres, plasma environment Impact of the precipitation of magnetospheric electrons on the composition of Triton's atmosphere Benjamin Benne (Laboratoire d'Astrophysique de Bordeaux), Bilal Benmahi, Michel Dobrijevic, Thibault Cavalié, Jean-Christophe Loison, Kevin Hickson, Mathieu Barthélémy, Jean Lilensten Introduction Triton is the biggest satellite of Neptune. It was only visited by Voyager 2 in 1989. During this mission, a surprisingly dense ionosphere was observed (Tyler et al. 1989), denser than the one of Titan despite being three times farther from the Sun. Thus, an additional source of ionization seems required. As energetic electrons were detected in Neptune's magnetosphere by the LECP instrument on board Voyager 2 (Krimigis et al. 1989), they could provide the needed additional power to Triton's atmosphere (Krasnopolsky et al. 1993). Therefore, we coupled a photochemical model of Triton's atmosphere with an electron transport code to study how these electrons could impact Triton's atmospheric chemistry. Methodology We used the most recent photochemical model of Triton's atmosphere from Benne et al. (2022) and coupled it with the electron transport code TRANS (see Gronoff et al. (2009a) and references therein). The photochemical model produces an initial atmosphere that is used by TRANS to compute the propagation of magnetospheric electrons inside it. The input precipitation is based on the work of Strobel et al. (1990), using data from the LECP instrument presented in Krimigis et al. (1989). We also tested a modified precipitation flux following the recommendations of Sittler & Hartle (1996), whose calculations suggest that the precipitation of low energy electrons may be strongly inhibited. The outputs of TRANS are then used in the photochemical model to compute the reactions rates of the electron impact-ionization and -dissociation reactions. Iterations between the two codes are performed until steady state is reached. Once the nominal composition of Triton's atmosphere is determined, we ran a Monte Carlo simulation to study the impact of chemical uncertainties on our results. Results Benne et al. (2022) used the ionization profile from Strobel et al. (1990) to take into account the precipitation of magnetospheric electrons but failed to match the electronic number density profiles measured by Voyager 2 from nearly one order of magnitude, even with chemical uncertainties. Coupling this model to TRANS allows us to find results that are in close agreement with those observations. It also permits us to better understand the impact of the different input parameters (input precipitation, magnetic field strength, field line incidence, orbital mean) on the atmospheric chemistry. With this work, the electronic number density maximum is not due to electronic precipitation but to the ionization by EUV photons, in contrast to the results of Benne et al. (2022), Krasnopolsky & Cruikshank (1995) and Strobel & Summers (1995). Seasonal variation of neutral gases in Titan's ionosphere Maélie Coutelier (LATMOS / CNRS), Thomas Gautier, Koyena Das, Joseph Serigano With 13 years of observations, the Ion and Neutral Mass Spectrometer (INMS) onboard the Cassini spacecraft has observed the upper atmosphere of Titan through two seasons: winter and spring. The complex atmosphere is mainly composed of N2, CH4, H2 and Ar, but a lot more carbon and nitrogen bearing trace species have been observed by INMS and other instruments. Using data from the closed source neutral mode of INMS instrument, we studied the abundance and variation of neutral species in Titan ionosphere, between 1500 and 950 km of altitude. We will present an ongoing effort on the reanalysis of the entire INMS Titan's observation dataset. We recalibrated INMS data by taking into account the dead time correction, the ram pressure enhancement, the saturation correction, the increase of pressure in the chamber with the decreases of altitude, the sensitivity and the contamination by thruster firing (Cui et al., 2009,2012). In addition, species entering the instrument were ionized and fragmented into ions inside INMS chamber, making difficult the identification of different species in such complex mass spectra. To retrieve the molecular mixing ratios we used a Monte-Carlo sampling on the fragmentation pattern to deconvolve the signal. To obtain a complete mass spectrum (m/z 1 to 99), we stacked INMS data, which increases the incertitude on the altitude. We used the mass spectra deconvolution code developed by Gautier et al., (2020), also employed by Serigano et al., (2020) when they treated Saturn INMS data. This enabled the retrieval of vertical and seasonal variation of Titan's atmosphere major components. Our results show the strong influence of the solar activity on the gases mixing ratio variations (Shebanits et al, 2017 ; Westlake et al., 2014). We also derived the N2 and CH4 density from our results (Muller Wodarg et al., 2008). Utilising light ion measurements to derive mixing ratios of heavier neutral species in Saturn's ionosphere and addressing open questions with light ion chemistry Joshua Dreyer (Swedish Institute of Space Physics (IRFU), Uppsala University), Erik Vigren, Fredrik L. Johansson, J. Hunter Waite During Cassini's Grand Finale in 2017, the number densities of electrons and light ions in Saturn's ionosphere were measured in situ. Light ion chemistry and density measurements can be utilised to derive mixing ratios for heavier neutral species, such as water and methane, which we compare to recent estimates and measurements from other studies. Furthermore, we show that electron data from the Langmuir Probe and light ion densities from the Ion and Neutral Mass Spectrometer (INMS) correlate very well after correcting the INMS timestamps as outlined in Dreyer et al. (2022, PSJ). This may serve cross-calibration purposes and be of further use to constrain the abundance of heavier ions and address open questions in regard to light ion chemistry. BepiColombo 2nd Mercury flyby: ion composition measurements from the Mass Spectrum Analyzer Lina Hadid (LPP /CNRS - École Polytechnique), MSA/MPPE Team On June 23rd 2022, BepiColombo performed it’s second gravity assist maneuver (MFB2) at Mercury. Just like the first encounter which took place on October 1 2021, the spacecraft approached the planet from dusk-nightside to dawn-dayside to an extremely close distance within about 200 km altitude above the planet’s surface. This distance is closer than the two orbiters of BepiColombo will orbit the planet after the orbit insertion in 2025. Eventhough BepiColombo is in a so-called “stacked configuration” during cruise, meaning that the instruments cannot yet be fully operated, the instruments can still make interesting observations. Particularly, despite their limited field-of-view, the particle sensors will allow us to get a hint on the ion composition and the dynamics very close to the planet. In this presentation, we will present the first observations of the Mass Spectrum Analyzer (MSA) at Mercury during MFB2. MSA is part of the low energy sensors of the Mercury Plasma Particle Experiment (MPPE, PI: Y. Saito), which is a comprehensive instrument package for plasma, high-energy particle and energetic neutral atom measurements (Saito et al. 2021), onboard the Mercury Magnetospheric Orbiter (Mio). MSA is a time-of-ﬂight spectrometer that provides information on the plasma composition and the three-dimensional ion distribution functions up to a somewhat larger energy ~ 38 keV/q and masses from ~ 1-60 amu (Delcourt et al. 2016). We will focus on the ion composition during 1) the closest approach which occurred around 09:44 UT and on the outbound orbit in the 2) foreshock region between ~10:00 UT and ~ 10:30 UT. Solar Orbiter's Crossing of Comet Leonard's Ion Tail Geraint Jones (UCL Mullard Space Science Laboratory, UK), Samuel Grant, Timothy Stubbs, Christopher Owen, et al. In December 2021, ESA's Solar Orbiter spacecraft crossed the ion tail of comet C/2021 A1 Leonard, around 44.5 million km downstream of the nucleus. This event was predicted by co-author S. Grant. Here, we provide an overview of the circumstances of this fortuitous ion tail crossing, including how it had been predicted, and the relative geometry of the comet, tail, and Solar Obiter spacecraft. Comet Leonard was imaged extensively from the ground and also by some spacecraft. We show the results of our initial analysis of these Earth- and space-based images, and how they provide context for the Solar Orbiter tail crossing observations by the spacecraft's suite of in situ instruments. An overview is also provided of some of the data returned by the spacecraft, including the detection of the suspected weakened bow shock of the comet. We briefly discuss the implications of the results of the crossing in the context of other, similar events, and for the ESA Comet Interceptor mission, due for launch in 2029. Exploring Plasma Asymmetries in Venus' Magnetosheath Sebastián Rojas Mata (Swedish Institute of Space Physics, Kiruna), Gabriella Stenberg Wieser, Yoshifumi Futaana Venus is a prime target for studying how magnetized plasma flows interact with atmospheric bodies in our Solar System or around other stars. Though similarly sized to Earth, it lacks an intrinsic magnetic field, leading to a close coupling of its magnetosphere to the solar wind. Conversely, while Venus and Mars share such coupling typical at unmagnetized planets, their different sizes cause other dissimilar interactions with the space plasma environment. Comparative analyses between these planets therefore enable us to investigate the physics of planetary magnetospheres. Here we focus on the proton plasma in Venus' magnetosheath, the intermediary region through which the solar wind transfers momentum and energy to the planet. Using data taken by Venus Express' (VEX's) Ion Mass Analyser (IMA) instrument, we statistically characterize the asymmetries in proton bulk parameters between different electromagnetic hemispheres of the dayside magnetosheath. Investigating such details of Venus' induced magnetosphere, especially when compared to similar studies at Earth and Mars, helps us understand how factors like spatial scale, turbulence, or pick-up ions influence planetary magnetosheaths. NIRwave: A wave-turbulence-driven solar wind model constrained by Parker Solar Probe observations Simon Schleich (University of Vienna), Sudeshna Boro Saikia, Udo Ziegler, Manuel Güdel, Michael Bartel Stellar winds represent one of the essential phenomena shaping exoplanet atmospheres over evolutionary timescales. However, as the winds of solar analogues are very weak, we need to characterise them and the effects they have on exoplanet atmospheres through model descriptions of the solar wind. We present NIRwave, a solar wind model based on coupling the general MHD code NIRVANA to an explicit wave-turbulence-driven heating mechanism. Our model is constrained by observational data from the Parker Solar Probe (PSP). The adapted heating mechanism is based on the interaction and subsequent dissipation of counter-propagating Alfvén waves in the solar corona, accounting for a turbulent heating rate as a driving mechanism of the solar wind. The solar magnetic field is assumed to be an axisymmetric dipole. NIRwave is able to successfully reproduce the characteristic bimodal structure of the solar wind. Despite implementing simplified conditions representing the coronal magnetic field and initial parameters of the simulation domain, the parameters characterising our steady-state solution agree with previously established results and empirical constraints. In a comparison to a polytropic wind model based on the unmodified version of NIRVANA, we find that our NIRwave model is in better agreement with the observational constraints derived by us. As this model relies on simplified assumptions about the nature of the solar wind, it could be utilised to derive the wind parameters of a wide range of solar-type stars, including targets of upcoming exoplanet missions such as Ariel and PLATO. Ionopause detections in the Martian ionosphere Katerina Stergiopoulou (University of Leicester), Beatriz Sánchez-Cano, Mark Lester, Dikshita Meggi, Simon Joyce, David Andrews The ionopause boundary at unmagnetised planets, such as Mars and Venus, separates the planetary ionospheres from the solar wind plasma. It is not always present in the Martian ionosphere and the conditions under which it is formed are not as well defined as in the Venus case. In this study we use MAVEN LPW observations to probe the dayside ionosphere of Mars and describe the structure of the ionopause and its formation and variability drivers. We identify the boundary as the location where we see electron density and temperature gradients as well as increased electron temperature fluctuations. Utilising several years of electron density and temperature measurements, we perform a statistical analysis of the ionopause detections with respect to their height and solar zenith angle, and we compare our findings with what is known about the ionopause at Venus to better understand the processes resulting in the ionopause formation at Mars. What is more, through observations from additional MAVEN and Mars Express instruments, we investigate how various factors, including the crustal fields and the upstream solar wind conditions, alter the characteristics of the ionopause formation. Detecting solar energetic particle events and Forbush Decreases on Mars with an Error Detection and Correction counter Shayla Viet (Norwegian University of Science and Technology (NTNU)), Shayla B.T. Viet, Elise W. Knutsen, Franck Montmessin, Olivier Witasse, Beatriz Sanchez-Cano, Mark Lester, Robert F. Wimmer-Schweingruber The objective of this project was to detect and investigate space weather events around Mars over a longer continuous time period by using data from Mars Express which has been in orbit around Mars for almost 20 years. Monitoring space weather events is becoming increasingly important as we expand our presence at Mars, both on the surface and in orbit. In addition, we are becoming more and more dependent in our daily lives on Earth on satellites, which may be damaged by radiation. Mars is less protected than Earth from space weather events as the planet has a thinner atmosphere and no global intrinsic magnetic field, making radiation a challenge. In this project an algorithm was created to detect space weather events at Mars from data from an algorithm called Error Detection and Correction (EDAC). EDAC counters exist on all spacecraft, and monitor memory errors in onboard computers. The EDAC software is often active even when other instruments are turned off, providing engineers long uninterrupted timeseries. Charged energetic particles from Galactic Cosmic Rays (GCRs) and transient solar energetic particle (SEP) events are able to trigger an EDAC algorithm by penetrating the spacecraft and cause bit-flips on the physical memory cells in the onboard computers, which triggers the EDAC counter into incrementing. By obtaining a daily count rate from an EDAC on the Mars Express and correcting for the long-term variations of the GCR background radiation caused by the solar cycle modulation, numerous SEP events and Forbush Decreases, which are rapid and temporary declines of GCR intensity, in Mars orbit from Jan 2005 to Feb 2022 were identified. ## habitability & exobiology Introducing the concept of â€œastrobiological time-analogsâ€: Ecological successions throughout the desiccation of hypersaline lagoons on Earth and the wet-to-dry transition on early Mars Alberto Fairén (Centro de Astrobiología), Nuria Rodríguez, Laura Sánchez-García, Esther Uceda, Daniel Carrizo, Patricia Rojas, Ricardo Amils, and Jose Luis Sanz Early Mars most likely had a diversity of environments in terms of pH, redox conditions, temperature, geochemistry, and mineralogy. Field research in terrestrial analog environments contribute to understand the habitability of this diversity of environments on Mars in the past, because terrestrial analogues are places on Earth characterized by environmental, mineralogical, geomorphological, or geochemical conditions similar to those observed on present or past Mars. So far, analogs have been referred to terrestrial locations closely similar to any of the geochemical environments that have been inferred on Mars, i.e., they are "site-analogs" that represent snapshots in time: one specific environmental condition at a very specific place and a very specific time. Because of this, each individual field analog site cannot be considered an adequate representation of the changing martian environmental conditions through time. Here we introduce the concept of "astrobiological time-analog", referred to terrestrial analogs that may help understand environmental transitions and the related possible ecological successions on early Mars. As Mars lost most of its surface water at the end of the Hesperian, this wet-to-dry global transition can be considered the major environmental perturbation in the geological history of Mars, and therefore merits to be the first one to be assigned a "time-analog" for its better understanding and characterization. At the end of the Hesperian, several paleolakes on Mars were characterized by episodic inundation by shallow surface waters with varying salinity, evaporation, and full desiccation repeatedly over time, until the final disappearance of most surface water after the wet-to-dry transition. We show here that similar conditions can be tested through time in the terrestrial analog Tirez lagoon. Tirez was a small and seasonal endorheic athalassohaline lagoon that was located in central Spain. In recent years, the lagoon has totally dried out, offering for the first time the opportunity to analyze its desiccation process as a "time-analog" to similar events occurred during the wet-to-dry transition on early Mars. To do so, here we describe (i) the microbial ecology of Tirez when the lagoon was still active 20 years ago, with prokaryotes adapted to extreme saline conditions; (ii) the composition of the microbial community in the dried lake sediments today, in many case groups that thrive in sediments of extreme environments; and (iii) the molecular and isotopic analysis of the lipid biomarkers that can be recovered from the sediments today. We conclude that Tirez was habitable for a wide range of prokaryotes before and after its complete desiccation, in spite of the repeated seasonal dryness; and our results may inform about research strategies to search for possible biomarkers in Mars after all the water was lost. Our 25 yearlong analyses of the ecological transitions in the Tirez lagoon represent the first terrestrial astrobiological "time-analog" for desiccating saline lakes on early Mars. Habitable zones in stellar binaries with circumbinary giant planets Nikolaos Georgakarakos (New York University Abu Dhabi), Siegfried Eggl, Ian Dobbs-Dixon Several stellar binary systems are known to host circumbinary planets. The so-called dynamically informed habitable zones are a valuable tool for evaluating the potential of a planet to have liquid water on its surface because they take into consideration the orbital evolution of the system as well as the actual stellar radiation received by the planet. In this work, we present an analytic method for calculating dynamically informed habitable zones in circumbinary systems and we explore whether such systems, which already have a planet, can host additional potentially habitable worlds. We apply our methodology to some of the Kepler circumbinary systems; more specifically to Kepler-34 and Kepler-38. We demonstrate that the presence of the known giant planets is not prohibitive for the existence of potentially habitable worlds. Should the debate on the life in the clouds of Venus include acidophilic fungi? Grzegorz P. Slowik (Institute of Materials and Biomedical Engineering, University of Zielona Gora, Poland), Anna Olewicz (Department of Immunology, Poznan University of Medical Sciences Poznan, Poland) Venus and Earth are the most similar planets in the Solar System in terms of relative radius, accelaration of gravity and mean density [1]. Although present-day Venus is characterized by a very strong greenhouse effect, 3D-climate models suggest that this planet could have had hospitable climate and ocean of water on its surface [2]. The conditions supporting life include the presence of elements C, H, N, O, P, and S and solvents [3]. The lower cloud layer of Venus comprises favorable components for microbial life, including moderate temperatures, pressures, and the presence of micron-sized sulfuric acid aerosols [4]. Fungi metabolic versatility is well established, including metabolic pathways for sulfur assimilation [5]. Biofilms are the most abundant form of life in extreme environments including highly acidic ones, and acidophilic fungi are known components of biofilms, the most successful life strategy on the Earth. [6]. Fungi are also characterized by incredible ecological plasticity, remarkably tolerant to water-stress conditions, and possess outstanding ability to tolerate and even thrive in the most extreme environments [7]. References: [1] Taylor, Fredric W., Håkan Svedhem, and James W. Head. Venus: the atmosphere, climate, surface, interior and near-space environment of an Earth-like planet. Space Science Reviews 214 (2018):1-36. [2] Way MJ, Del Genio AD, Kiang NY, Sohl LE, Grinspoon DH, Aleinov I, Kelley M, Clune T (2016) Was Venus the first habitable world of our solar system? Geophys Res Lett 43:8376-8383. https://doi.org/ 10.1002/2016GL069790 3. Noam R. Izenberg, Diana M. Gentry, David J. Smith, Martha S. Gilmore, David H. Grinspoon, Mark A. Bullock, Penelope J. Boston, and Grzegorz P. Słowik. The Venus Life Equation Astrobiology 2021 21:10, 1305-1315 4. Sanjay S. Limaye, Rakesh Mogul, David J. Smith, Arif H. Ansari, Grzegorz P. Słowik, and Parag Vaishampayan. Venus' Spectral Signatures and the Potential for Life in the Clouds Astrobiology 2018 18:9, 1181-1198 5. Linder T. Assimilation of alternative sulfur sources in fungi. World J Microbiol Biotechnol. 2018;34(4):51. doi: 10.1007/s11274-018-2435-6. 6. . Hujslová M, Bystrianský , Benada O, Gryndler M. Fungi, a neglected component of acidophilic biofilms: do they have a potential for biotechnology? Extremophiles. 2019 May;23(3):267-275. doi: 10.1007/s00792-019-01085-9. 7. Coleine C, Stajich JE, Selbmann L. Fungi are key players in extreme ecosystems. Trends Ecol Evol. 2022 Jun;37(6):517-528. doi: 10.1016/j.tree.2022.02.002. Investigation into possible anaerobic communities near Gale crater, an experimental Bayesian approach Dylan Verburg (TU Delft), supervisor: Ralph Lindeboom The 14th of July 2013, a methane peak was observed in the Gale crater. This methane peak has been investigated in non-biological context before. This study applies exoplanet research strategies and knowledge about biological methane production on Earth to investigate the complementary biological context. Thermodynamic calculations show methanogenesis and sulphate reduction to be viable catabolic reactions under Mars temperatures and concentrations. Experiments into methane and hydrogen sulfide gas, as well as biomass growth, were conducted on organisms gathered from Boom clay porewater. These experiments show that methane and hydrogen sulfide gas production are sparsely affected by the introduction of modified Phylosilicate Martian Regolith Analog (P-MRA) and Martian Atmosphere Analog (MAA). Biomass growth is not consistent between the tests. Comparison with the ADM1 kinetic model shows that only methane gas can be compared. Biomass and sulphur gas production is inconsistent between experiments and the kinetic model. Using the modified ADM1 model, a Monte Carlo (MC) approach was used to assess the correlation between the observed methane peak and the kinetic model results. Based on this, 78% of the simulations showed a significant correlation. Using Bayesian inference, the posterior probability of the methane peak being biological in origin is higher than the prior probability of an anaerobic community being active around the Gale crater. This goes for all prior probabilities of an active anaerobic community existing, and all prior probabilities of the methane being produced abiotically below 0.78. Impact-induced Formation of Prebiotic Molecules on Terrestrial Planets Andrea Zorzi (Stanford University), Laura K. Schaefer New chemical species can form from reactions induced by shock-heating upon formation of an impact vapor plume and its interaction with the background atmosphere of a rocky planet. Previous studies have assumed chemical equilibrium in computing the abundance of chemical species: such a simplified model can underestimate those concentrations by a factor of 10 in high temperature shock conditions. A more accurate description of the plume/atmosphere interaction demands a coupled hydrodynamics and kinetics calculation. We present a new model extending the work of Ishimaru et al. (2010) by considering an atmosphere on the target planet. We assess the production of prebiotic molecules (HCN, CH4, NH3) for different impact scenarios, varying kinetic energy of the impactor, atmospheric surface density and composition. We find that prebiotic species are produced on Earth-like planets with a N2-CH4 atmosphere, with increasing abundance when: i) the atmospheric surface density increases; ii) the impact energy decreases; iii) the amount of methane in the pre-existing atmosphere increases. The presence of oxygen in today's inner solar system planets prevents the production of HCN. On Titan, impacts can constitute an additional sink for methane. Our findings provide necessary but not sufficient conditions for prebiotic chemistry to start, to assess the astrobiological potential of impacts on terrestrial worlds. ## Atmospheres Modelling Jupiter's Atmosphere; More Simplistic Models for More Applicable Results Charlotte Alexander (University of Oxford), Patrick Irwin There are many current cloud models of Jupiter, typically involving several cloud and haze layers, that are able to successfully reproduce visible observations of the planet. However it is often difficult to differentiate between these models due to the high amount of degeneracy between the parameters in the models. This leads to several models being able to reproduce observations equally successfully, despite different values for model parameters, leading to an inability to conclude on the most realistic atmospheric set up for Jupiter's clouds. By introducing a new method [1], utilising two viewing angles, it helps to break some of the degeneracy of the problem. We were able to show that some previous models such as [2], which are highly successful at reproducing one viewing angle observations, are unable to fit to a high viewing angle simultaneously to a nadir observation, as successfully as a single observation. Therefore utilising the dual viewing angle technique allows us to derive a model which can reduce the degeneracy between the parameters, due to pre-determining some parameters before a retrieval. Hence we aim to find a model which is able to fit the two angle observations comparatively, or better, than the models derived for single viewing angles. A uniform main cloud pressure for all latitudes in the study (50°S-50°N) has been inferred using the techniques outlined in [3]. From this point fitting for other parameters including the refractive imaginary index, can be done using the Non-Linear Optimal Estimator for Multivariate Spectral Analysis (NEMESIS) algorithm [4], in order to build a cloud model. Expansion of the above technique to specific features such as the Great Red Spot will also be done to see how the cloud structure varies between the GRS and other regions being parameterised. Hence cloud structure can be determined globally whilst eliminating some of the degeneracy which in the past had lead to a difficultly discerning the most realistic cloud model for Jupiter. These models can then be tested using the highly detailed observations of Jupiter that have been taken by JWST in its first year of operation, particular the GRS, adding to the validation of the model that is determined by application of this technique. Therefore this work will detail the steps undertaken and the models retrieved in order to reduce some of the degeneracy in the atmospheric modelling of Jupiter at no expense to the atmospheric fit retrieved. [1] Pérez-Hoyos, et al., (2020), Icarus, 352:114031 [2] Braude, et al., (2020), Icarus, 338:113589 [3] Irwin, et al., (2008), JQSRT, 109:1136-1150 [4] Irwin, et al., (2022), JGR:Planets, 127, e2022JE007189 The evolution of atmospheric escape as seen through the helium 1083nm triplet Andrew Allan (Leiden Observatory, Leiden University), Aline Vidotto, Carolina Villarreal D'Angelo, Leonardo dos Santos Atmospheric escape has traditionally been observed in Lyman-alpha transits, but more recently detections using the metastable helium triplet 1083nm line were obtained. Given its ability to be observed from the ground, the 1083nm helium line offers more possibilities for studying atmospheric escape. One issue however is that the formation of this line is strongly dependent on the specific high-energy flux received by the planet. Previous studies have shown that the extreme-UV band both drives atmospheric escape and populates the triplet state, whereas lower energy mid-UV radiation depopulates the triplet state through photoionisations. The goal of our own work is to understand how the observability of escaping helium evolves as the planet ages. For that, we couple our one-dimensional hydrodynamic non-isothermal model of atmospheric escape with a ray tracing technique in order to predict the physical nature and observability of escaping helium as the planet ages. In our models, we consider the evolution of the stellar high-energy radiation and the evolution of the planet gravitational potential, both of which contribute to a decline in the rate of atmospheric escape. We show also how the assumed fraction of helium to hydrogen as well as often neglected helium heating and cooling processes affect both the escape hydrodynamics and the helium observations. Modelling Atmospheric Erosion for Terrestrial Planets in the Solar System Maria Luisa Alonso Tagle (BIRA-IASB), M. L. Alonso Tagle, R. Maggiolo, H. Gunell, J. De Keyser, G. Cessateur, G. Lapenta, V. Pierrard, A. C. Vandaele Since the Great Oxidation Event, the oxygen escape rate on Earth has changed over time mainly due to solar evolution. Two solar agents drive the Earth's atmospheric erosion rate: the solar wind and the EUV radiation. The first one affects the non-thermal processes by changing the plasma conditions, and the second one affects both types of processes: by increasing the atmospheric temperature, and by modifying the ion production rate. Hence EUV radiation affects atmospheric parameters, such as the exobase distance and neutral density, which influence the escape rate. In this work, we describe a model that uses in-situ measurements and physical considerations to estimate the effect of solar evolution on the atmospheric loss rate. Physical assumptions are made to describe the contribution of the solar wind pressure on each erosion mechanism. The main objective is to reproduce earlier solar conditions to constrain oxygen loss over geological time scales. Seven different mechanisms are studied, to determine the fundamental factors that have a significant impact on the oxygen escape rate in the past Earth. We discuss the effects of the exospheric parameters and solar wind drivers on the oxygen erosion rate. We examine their relevance for total oxygen loss and their influence on the stability of our atmosphere. The LIFE space mission: characterizing atmospheres of terrestrial exoplanets and searching for habitable worlds and biosignatures Daniel Angerhausen (ETH Zürich), and the LIFE Initiative In this poster we will give a general introduction and overview to the LIFE (Large Interferometer for Exoplanets) mission concept. We will summarize the status and prospects of LIFE in context of the ESA Voyage 2050 Senior Committee Report, present it's science objectives and show ways to contribute to the initiatives efforts. HCN photochemistry in HD 209458 b and WASP-76 b Robin Baeyens (Anton Pannekoek Institute for Astronomy, University of Amsterdam) Photochemistry is an important phenomenon that shapes the atmospheric composition of hot Jupiters. This has been illustrated plain and clear through the detection of SO2, a photochemically produced molecule in the atmosphere of WASP-39 b. In addition, several high-resolution spectroscopy detections of HCN have been reported, which could be linked to the elemental C/O ratio of the planet. However, given the known photochemical origin of HCN, this interpretation requires accurate photochemical modelling. Here, I present recent results of pseudo-2D photochemical kinetics models of HD 209458 b and WASP-76 b, providing predictions of the HCN abundance, as well as implications carried by the recent HCN detections. Investigating Thermal Contrasts Between Jupiter's Belts, Zones, and Polar Regions with VLT/VISIR Deborah Bardet (School of Physics and Astronomy, University of Leicester, Leicester, UK), Padraig T. Donnelly, Leigh N. Fletcher, Arrate AntuÃ±ano, Michael T. Roman, Glenn S. Orton, Sandrine Guerlet, Henrik Melin, Jake Harkett Concerning the Jovian polar regions, the analysis of VISIR imaging shows a large region of mid-infrared cooling poleward ~67°S, co-located with the reflective aerosols observed in methane-band imaging by JunoCam, suggesting that they play a key role in the radiative cooling at the poles, and that this cooling extends from the upper troposphere into the stratosphere. These VISIR observations also reveal thermal contrasts across polar features, such as numerous cyclonic and anticyclonic vortices, as well as evidence of high-altitude heating by auroral precipitation. Comparison of zonal mean thermal properties and high-resolution visible imaging from Juno allows us to study the variability of atmospheric properties as a function of altitude and jet boundaries, particularly in the cold southern polar vortex. To investigate the radiative processes and influence of auroral precipitation on the southern cold vortex, a radiative-convective model tailored for Jupiter's atmosphere (Guerlet et al., 2020), with an updated polar aerosol distribution from Juno mission results, will be used to determine the aerosol distribution needed to reproduce the thermal structure of the cold polar vortex of Jupiter. Water-Hydrogen Demixing and the Atmospheric Water Abundance of Uranus and Neptune Marina Cano Amoros (DLR-German Aerospace Center), Nadine Nettelmann, Nicola Tosi Understanding the atmospheric water abundance of solar and extrasolar giant planets can reveal important insights into their internal structures. Recent water abundance measurements from JUNO at Jupiter showed that the atmosphere is less enriched in water than what the gravity data implies for the deep interior, yielding an inhomogeneous and H-He dominated interior [1]. For the ice-rich outer planets Uranus and Neptune, interior models constrained by the observed gravitational harmonics J2 and J4 also indicate that their interiors are composed of a H/He-rich envelope but atop an ice-rock-rich interior. The transition occurs at pressures of a few (tens) of GPa. However, formation theories can explain such a highly inhomogeneous composition profile [2] only if specific conditions are assumed [3]. Alternatively, the phase separation of the two major constituents water and molecular hydrogen has been proposed as an explanation for their current structures [4]. In this scenario, water would rain out to deeper levels and deplete the atmosphere in water over time. Here, we follow up on the possibility of demixing in the H-He-H2O system. We employ a water-hydrogen phase diagram constrained by experimental data up to 3 GPa [4]. We show that demixing can occur over a wide range of assumed initial bulk water abundances and that this process may have started already billions of years ago, with higher ice abundances leading to colder interiors and earlier onsets of demixing. Our models suggest similar atmospheric water abundances for both planets. However, a major uncertainty arises from the poorly known phase diagram at pressures beyond 3 GPa. To account for uncertainties we adopt a Monte Carlo approach implemented within the TATOOINE code for exoplanet structure modelling [5]. Acknowledgements: MC and NT acknowledge support from the Research Unit 2440/2 funded by the DFG (Deutsche Forschungsgemeinschaft). NN acknowledges support through NASA's Juno Participating Scientist Program under grant 80NSSC19K1286. References: [1] Miguel Y., Bazot M., Guillot T. et al., AA 662:A18 (2022) [2] Helled R., Nettelmann N., Guillot T., SSRv 216:38 (2020) [3] Frelikh R. and Murray-Clay R.A., AJ 154:98 (2017) [4] Bailey E. and Stevenson D.S., PSJ 2:64 (2021) [5] Baumeister P., Padovan S., Tosi N. et al., ApJ 889:42 (2020) Quantifying trace gases in the lower atmosphere of Titan using Huygens GCMS Koyena Das (LATMOS-CNRS), Thomas Gautier, Joseph Serigano, Cyril Szopa, Sarah M. Hörst, Maélie Coutelier, Sandrine Vinatier, Melissa G. Trainer In Titan, the two major gases nitrogen (N2) and methane (CH4) are ionized and/or photolyzed at high altitudes by the sunlight and the energetic particles from Saturn's magnetosphere, resulting in rich atmospheric chemistry and a wide variety of carbon and nitrogen-bearing atmospheric compounds. In the present work, we focus on studying the vertical profiles of trace species in the lower atmosphere to obtain a better insight into the atmospheric processes taking place on Titan. To do so, we reanalyzed the data from the Gas Chromatograph Mass Spectrometer (GCMS) on the Huygens probe which executed its mission on 14th January 2005. The GCMS instrument sampled for nearly three and a half hours from a height of 146 km. It recorded data for two and a half hours in the atmosphere of Titan, then landed on the surface and kept on recording for another hour, after which the signal was lost. We analyzed the measurements made by direct sampling of the atmosphere. These mass spectra obtained at different altitudes and pressure levels have been recalibrated to account for deadtime and saturation corrections to the measurements and considered ion cross-section and transfer cross-section measurements from Cassini-Ion and Neutral Mass Spectrometer calibrations. We then analyzed the corrected mass spectra using Monte-Carlo deconvolution simulations. The simulations allow us to vary the peak intensities of fragmentation patterns of known species, which usually bears uncertainties on this kind of data, and then use a least-square fitting to deconvolve the mixed signals. This is the first time mixing ratios of high-altitude trace gases could be quantified using this GCMS data. Currently, we are working with 10 species and developing their vertical profiles in the atmosphere. In the future, we plan to extend this study to develop a sub-surface model of Titan which will help us understand the outgassing of methane that was observed by the probe upon its touchdown on the surface. Looking above the cloud deck of GJ 3470b Spandan Dash (University of Warwick), Dr. Matteo Brogi, Dr. Siddharth Gandhi Characterisation of cooler atmospheres of super-Earths and Neptune sized objects at low-resolution is often thwarted by the presence of clouds, hazes and aerosols which effectively flatten the transmission spectra. High-Resolution Spectroscopy (HRS) presents an opportunity to overcome this limitation by having the ability to detect molecular species whose spectral line cores extend above the level of clouds in these atmospheres. We analyse High-Resolution observations of the warm Neptune GJ 3470b taken over two transits using CARMENES (R ~ 80400) and look at the possibility of H2O signatures in these transits. We find that our custom pipeline can provide an unambiguous detection of H2O using two transits when they have an injected signal equivalent to the level of what has been observed using HST WFC3 + Spitzer at low resolution. Using a Bayesian retrieval tool on the two observed transits to put simultaneous constraints on the abundance of H2O and the cloud top-deck pressure selects for low abundance and deep cloud deck (clear atmosphere) models, which is in slight dissonance with published results from low resolution. Applications of Approximate Bayesian Computation (ABC) within Exoplanet Atmospheric Studies Jack Davey (University College London (UCL)), Ingo Waldmann, Ahmed Al-Refaie While Approximate Bayesian Computation (ABC) and other likelihood free (LF) methods for Bayesian inference have been adopted in many areas of scientific research including cosmology, they have seen limited application in exoplanetary science. Cosmologists have been dealing with the problem of intractable likelihoods for a number of years and have implemented these techniques in order to bypass the need to define a likelihood function. With the launch and first observations of the James Webb Space Telescope (JWST), there is a strong expectation that assumptions in the likelihood could bias results of atmospheric retrievals on exoplanet transmission spectra so the need for LF methods is evident now more than ever. Here, we implement ABC with the atmospheric retrieval code TauREx3 (using the PyMC library) with the aims of revealing and mitigating the effects of non-gaussianity in spectral data sets. To this end we will study effects due to non-gaussian noise in simulated data sets of hot Jupiter spectra. This will allow us to identify any biases on specific parameters and we will then go on to perform a reanalysis of Hubble and JWST early release science observations to identify any non-gaussian bias in retrievals performed with these data. Perturbation of exoplanetary spectra in cool stars transit spectroscopy Pierre Drossart (Institut d'Astrophysique de Paris / CNRS, Sorbonne Université), Emilie Panek (IAP), Andrea Chiavassa (OCA), Jean-Philippe Beaulieu (IAP), Matteo Brogi (U. Warwick) The interference between the molecular lines in cool stars (K or M spectral types) and a transiting planet observed by transit spectroscopy can produce important biases in the molecular retrieval of the planetary composition, in particular for CO or H2O molecules which are present in K or M stars (Drossart et al. COSPAR 2022). Here we present a deeper analysis of the effect on realistic model of star WASP 43 limb profile, including Doppler shift variation during transit and stellar limb darkening (Chiavassa & Brogi, 2019). This work constitutes a template for future stellar corrections to be taken into account in the frame of JWST and Ariel retrievals of transiting planet spectroscopy in the case of K or M star presenting molecular absorptions coincident with the planetary absorptions. Laboratory measurements of ferric chloride as a major contributor to the anomalous UV absorption in the Venusian atmosphere Joanna Egan (University of Leeds), Alexander James, James Manners, Daniel Marsh, John Plane In-situ probe measurements and remote sensing have revealed that Venus has a highly organised cloud system. Comparisons between models of the expected spectrum and observations reveal unexplained absorption in the near-UV to blue region of the spectrum. While many candidates for this â€œunknown absorberâ€ have been proposed over the years, none have been conclusively demonstrated to match the physical and optical behaviour observed (Pérez-Hoyos et al., 2018, JGR Planets, 123). One such candidate is ferric chloride (Krasnopolsky, 2017, Icarus, 286; Zasova et al., 1981, ASR, 1). Attempts to reliably determine its suitability have been hampered by the scarcity of representative spectra available. The FeCl3 absorbance spectrum generally used in the literature is measured in ethyl acetate (Aoshima et al., 2013, Polymer Chemistry, 4), and therefore may not be representative of the absorption produced by ferric chloride in the Venusian clouds. We present absorption spectra of ferric chloride in sulphuric acid, measured using UV-Vis spectrometry. This change of solvent produces an environment more closely aligned to that on Venus, where ferric chloride, if present, may exist as an impurity in the micron-sized sulphuric acid cloud droplets (Petrova, 2018, Icarus, 306). We also utilise 1D multiple scattering radiative transfer modelling to estimate the concentration of ferric chloride required to explain the observed absorbance. The unknown absorption was first observed close to 100 years ago, yet the mystery of its cause remains unsolved. More representative spectra of ferric chloride and a greater understanding of its behaviour in the atmosphere of Venus are critical to advancing the identification of the unknown absorber. As the absorber is located towards the top of the clouds and absorbs in the near-UV to blue region, it is responsible for large amounts of absorption of incident sunlight, and therefore has a significant impact on the Venusian energy budget. Accurate atmospheric modelling of the planet therefore requires an understanding of the absorber which can only be achieved once it has been conclusively identified. Surprising Decrease in the Martian He Bulge during PEDE-2018 and Changes in Upper Atmospheric Circulation Meredith Elrod (University of Maryland College Park / NASA GSFC), Stephen Bougher, Kali Roeten Using the Neutral Gas and Ion Mass Spectrometer (NGIMS) on the Mars Atmosphere Volatile and Evolution spacecraft (MAVEN) we analyzed data from Mars Year (MY) 32, 34, and 35 to examine the He bulge during the northern winter solstice (Ls ~180-240) specifically focusing on the effects from the planet encircling dust event (PEDE-2018). He collects on the dawn/nightside winter polar hemisphere of the terrestrial planets (Earth, Mars, and Venus). The seasonal migration of the Martian He bulge has been observed and modeled (Elrod et al., 2017, Gupta et al., 2021). The MAVEN orbit precesses around Mars allowing for a variety of latitude and local time observations throughout the Martian year. MY32, 34 and 35 had the best possible opportunities to observe the He bulge during northern winter (Ls ~180-240). NGIMS observations during MY 32 and MY 35 revealed a He bulge on the nightside to dawn in alignment with modeling and previous publications. However, in MY 34, during the PEDE, the He bulge was not present indicating the PEDE directly impacted upper atmospheric circulation. Updates in modeling indicate changes in circulation and winds can cause He to shift further north and dawn-ward than MAVEN was able to observe. The temperature increases in the thermosphere on the nightside during the dust storm along with changes in gravity waves and eddy diffusion occurring during this event could account for this circulation change. Ground-based, high-resolution spectroscopy of exoplanet WASP-18b: Atmospheric composition and dynamics Vanessa Emeka-Okafor (University of Warwick) We present high-resolution dayside thermal emission observations of the ultra-hot Jupiter WASP-18b using IGRINS on Gemini South. Using standard algorithms, we remove the stellar and telluric signatures and extract the planet signal via cross-correlation with model spectra. Our results demonstrate that ground-based, high-resolution spectroscopy at infrared wavelengths can provide meaningful constraints on the compositions and climate of highly irradiated planets. We detect the atmosphere of WASP-18b at a signal-to-noise ratio (SNR) of 5.9 using a full chemistry model, measure H2O (SNR=3.3), CO (SNR=4.0), and OH (SNR=4.8) individually and confirm previous claims of a thermal inversion layer. We use a Bayesian inference framework to retrieve abundance, temperature, and velocity information. For this ultra-hot Jupiter, thermal dissociation processes likely play an important role. Retrieving abundances constant with altitude and allowing the temperature-pressure profile to freely adjust results in a moderately super-stellar carbon-to-oxygen ratio (C/O=0.75^{+0.14}{-0.17}) and metallicity ([M/H]=1.03^{+0.65}{-1.01}). Accounting for undetectable oxygen produced by thermal dissociation leads to C/O=0.45^{+0.08}{-0.10} and [M/H]=1.17^{+0.66}{-1.01}. A retrieval that assumes radiative-convective-thermochemical-equilibrium and naturally accounts for thermal dissociation constrains C/O<0.34 (2-sigma) and [M/H]=0.48^{+0.33}_{-0.29}, in line with the chemistry of the parent star. Looking at the velocity information, we see a tantalizing signature of different Doppler shifts at the level of a few km/s for different molecules, which might probe dynamics as a function of altitude and location on the planet disk. Our work also elucidates potential pitfalls with commonly employed retrieval assumptions when applied to UHJ spectra. Overall, our study highlights the potential of ground-based, high-resolution spectroscopy to uncover the atmospheric composition and dynamics of highly irradiated exoplanets, shedding light on their formation and evolution. Temperate exoplanets observable with Ariel : an update with new targets from TESS Therese Encrenaz (Paris Observatory), A. Coustenis, B. Edwards, K. Molaverdikhani, M. Ollivier, G. Tinetti In 2018 and 2022, we have published an analysis of the observability of temperate planets (with an equilibrium temperature of about 300-550 K) with ARIEL [1, 2]. This presentation is an update of this analysis which uses new targets identified in particular from the TESS database [3] and investigates their observability with ARIEL. Using the parameters of these new targets, and an atmospheric mean molecular weight of 2.3 g/mol (corresponding to a hydrogen-rich atmosphere), and using the ArielRad code [4], we give an estimate of the number of transits (T2) needed for these objects to be observed in the Tier 2 mode of the space mission, i. e. with a S/N @ 7 . The Tier 2 spectroscopic mode (R @ 10 for 1.1 µm < l < 1.95 µm, R = 50 for 1.95 µm < l < 3.9 µm, R @ 15 for 3.9 µm < l <7.8 µm) will allow us to infer constrains about the atmospheric composition of these targets. Preliminary results of this study are given below: 1) Using the candidate list of Edwards and Tinetti (2022) [3], we find 22 targets with T2 < 35, observable during the lifetime of ARIEL. 2) 7 among these targets, with a mass above 5 terrestrial masses, are presumably hydrogen-rich planets and should be observable with Ariel in the Tier 2 mode. In particular, the big Neptune TOI-3884 b, with T2 = 1, is expected to be observable also in the Tier 3 mode. 3) 8 other targets, with a mass between 1.5 and 5 terrestrial masses, will be observable in the Tier 2 mode if they have a hydrogen-rich atmosphere. The Ariel observation will thus allow us to determine whether they are sub-Neptunes or super-Earths. A promising case is LC 98-59 c and d for which the value of T2 is low (T2 = 7 and 6 respectively). 4) The 7 remaining candidates are exo-Earths, mostly from the TRAPPIST-1 system. Because their atmospheric mean molecular weight is expected to be as high as 18 g/mol (in the case of a H2O-rich atmosphere) or even more (in case of a CO/N2/CO2-rich atmosphere), they are not expected to be observable with Ariel in the Tier 2 mode. In the future, we plan to re-evaluate the observability of the candidates using different values of the atmospheric mean molecular weight. For the most favorable cases, we plan to calculate their synthetic spectra for different atmospheric compositions, considering also the possible effect of clouds. References : [1] Encrenaz et al., Exp. Astr. 46, 31 (2018) [2] Encrenaz et al., Exp. Astr. 53, 375 (2022). [3] Edwards, B. and Tinetti, G. Astron. J., 164, id.15, 25 pp. (2022) [4] Mugnai, L. V. et al. 2021b, Astron. J, 161, 284 (2021) The atmosphere of ultra-hot Neptune LTT 9779 b survived thanks to an unusually slow spinning and X-ray faint star Jorge Fernandez (University of Warwick), Peter Wheatley, George King I present XMM-Newton observations of the sun-like star LTT 9779 together with a study of the X-ray evaporation of its transiting planet, LTT 9779 b, the first ultra-hot Neptune in the middle of the Neptune desert. The presence of LTT 9779 b so close to its star is puzzling, as the intense XUV flux it receives from its star should have stripped it of its H/He-rich atmosphere. I find that only an X-ray faint host star is able to explain both our observations as well as the survival of its atmosphere under photoevaporation. This is consistent with both an unusually slow rotation of the star for its age, and a low measured X-ray flux. LTT 9779 b is a super-Neptune (4.7 Earth radii, 28 Earth masses) that is consistent with the presence of a H/He envelope that constitutes 8% of its mass. The planet, with an age of 2 Gyr, orbits its solar-mass host star every 19 hours. This planet lies in the Neptune desert, a region of the planet radius - orbital period parameter space with very few short-period Neptune-sized planets. These planets are thought to undergo substantial evaporation due to X-ray and extreme ultraviolet radiation (together, XUV) from their host stars which heats up the upper atmosphere, driving a hydrodynamic wind that can completely strip them of their volatile-rich envelopes down to a barren rocky core. LTT 9779 b is truly unique: the only planet with an orbital period of less than a day with both measured mass and radius that maintains a significant atmosphere. In order to find feasible evaporation pasts that can explain its current state, I simulated the XUV history of its host star by modelling its spin period evolution, as the two quantities are linked through the rotation-activity relation, where faster rotators produce higher X-ray fluxes. I confirm that the XUV history expected for a solar-mass star should have already stripped LTT 9779 b of its envelope, ruling out this scenario. I then modelled a low-level XUV history that matches the measured upper limits for both its spin period and its X-ray luminosity, which I estimated using XMM-Newton measurements. I thus find that the planet's envelope can survive through 2 Gyr of irradiation under these conditions, starting out as a 6.5 Earth radii planet that has evolved to its current state through photoevaporation. The Solar System planets as testing ground for exoplanets: a contribution from the Ariel Consortium Working Groups Gabriella Gilli (Instituto de Astrofísica de Andalucia (IAA/CSIC)), G. Gilli, P. Machado, P. Drossart, T. Encrenaz, M. Rengel, D. Quirino, C. Gapp, M. Lopez-Puertas, E. Marcq, K. Molaverdikhani, J. Leconte, S. Robert, F. Oliva, A. Piccialli, A. Sanchez-Lopez, M. Lefevre, A. Spiga, P. Wolkenberg, A. Coustenis, A. Migliorini, L. Lara, F. Brasil, J. Dias, J. Silva, D. Turrini, A. C. Vandaele The adopted ESA M4 mission Ariel (Atmospheric Remote-sensing Infrared Exoplanet Large-survey) is scheduled for launch in 2029. During its 4-year nominal mission, the space telescope aims to study 1) what exoplanets are made of; 2) how they formed and 3) how they evolve, by observing a diverse sample of about 1000 planets simultaneously in the visible and infrared wavelengths [1]. Within the ARIEL Mission Consortium, several Science Working Groups (WG) were formed in 2019 to help prepare the RedBook, defining the science cases, and to contribute to address the 3 fundamental questions above. Among those WGs, "Synergies between Solar System planets and exoplanets" was set-up to foster collaboration between the scientific community working on Solar System (SS) Planets atmospheres and the new growing community of the Ariel Science Team. The planetary exploration and research with a focus on comparative planetology has played an important role in our understanding of climate on Earth. Although optimal ARIEL targets are hot and warm giant planets close to their host star, a long-term scientific objective is characterising the whole range of exoplanets, including potentially habitable ones. We show an overview of on-going studies and future projects foreseen by WG members, mostly focused on using our Solar System planets as proxies to develop and test tools to support ARIEL science cases. For instance: • Jupiter is taken as a benchmark for gas Giant planets to study physico-chemical processes that could help to better understand hot-Jupiters and interpret observations of a whole category of exoplanets. The measured composition and isotope ratios can help to test planet formation mechanisms in other systems [2,3]. We also take into account recent efforts that are being carried out with JWST observations, and future efforts with JUICE. In addition, Uranus and Neptune are considered as a subcategory of ice giants planets that are more representative of colder objects. • To search for new Ariel targets, the TESS database has been used to investigate the observability of "temperate" exoplanets (with temperatures ranging between 350 K and 500 K) [4]. • General Circulation Models (GCMs) developed for Solar System planets have been applied to specific cases of known rocky exoplanets (e.g., Trappist-1c, LP 890-9c), under the hypothesis that their atmosphere evolved into a modern Venus. As a first step, our goal is to study the impact of atmospheric dynamics on the phase curve, as if they were observed by JWST [5, 6]. • GCMs and convection-resolving models will be also used to study the terrestrial exoplanets cloud characteristics (spatial coverage, altitude range, temporal variability) for different surface pressure and atmospheric dynamical regime to help retrievals and analyse the data through the observation of phase curves of exoplanets [7]. • We also plan to use Earth resolved spectra to craft observations of Earth-like planets with different percentages of surface/cloud endmembers in the field of view. By integrating these observations into a single pixel, it is possible to derive the percentages needed to identify each endmember in the resulting spectrum. Even if not directly related to the science that ARIEL will be doing, such an analysis can provide a good framework to understand what we expect to see in these objects [8,9]. • We retrieved a transmission spectrum of the atmosphere of Venus, using high resolution observations performed with FIRS instrument at Dunn telescope, during the solar transit in June 2012, the last one before 2117. This event was a unique opportunity to assess the feasibility of the atmospheric characterisation of Earth-size exoplanets near the habitable zone with the transmission spectroscopy technique and provide an invaluable proxy for the atmosphere of such a planet. Our aim is to produce a valuable template of a transit of Venus-like planets around Sun-like stars in a unique calibration opportunity. References: [1] Tinetti et al. RedBook, [2] Gapp, C. (2021). Master's thesis: 'Characterization of Jupiter's atmosphere using far infrared spectra measured with PACS onboard the Herschel Space Observatory'. Georg-August-Universitaet Goettingen, Germany [3] Gapp, Rengel, Hartogh et al. in preparation [4] Encrenaz et al. 2021, Experimental Astronomy [5] Quirino et al. MNRAS, under review [6] Quirino, D (2022). Master's Thesis: 'Modelling Venus-like exoplanetary atmospheres with a GCM: planetary parameters impact on the large-scale circulation and observational prospects'. Faculty of Sciences, University of Lisbon, Portugal, [7] Turbet et al. 2016A&A...596A.112T, [8] Oliva et al. EPSC Abstracts. Vol. 11, EPSC2017-531, 2017, [9] Oliva et al. EGU 2017, Geophysical Research Abstracts Vol. 19, EGU2017-17016, 2017 Current challenges in Giant planet atmospheric modelling Sandrine Guerlet (Laboratoire de Meteorologie Dynamique / CNRS), Aymeric Spiga, Deborah Bardet, Gwenaël Milcareck, Alexandre Boissinot, Ehouarn Millour The atmospheres of the four giant planets of the Solar System present a rich and varied meteorological activity. The dominant flow, well documented in their troposphere thanks to cloud tracking, consists of jet streams encircling these planets alternatively (depending on the latitude) from east to west or from west to east. The number and speed of these jets vary greatly depending on the planets, reaching 27 jets for Jupiter and only three for Uranus and Neptune, and reaching +400 m/s at the equator on Saturn and -400 m/s at the equator on Neptune. Various waves, cyclones, anticyclones, giant storms and other polar vortices, imaged from the ground or from space (Juno, Cassini, HST, ...), complete this picture. Above the troposphere, all have a stratosphere, a region where the temperature increases with altitude. In this region, anomalies observed in the temperature and composition fields (mainly by infrared spectroscopy) indicate the presence of seasonal circulation cells on Saturn as well as periodic oscillations in temperature and zonal wind at the equator of Jupiter and Saturn. These observations have motivated the development of general circulation models adaptable to each giant planet, in order to better understand the organization of the flow in these fluid planets and the processes underlying the observed phenomena. Our model, named DYNAMICO-PCM, solves the Navier-Stokes equations on the rotating sphere on an icosahedral grid with a fairly high spatial resolution (typically 1°). The model extends from the troposphere (a few bars) to the stratosphere (a few microbars) and takes into account radiative and seasonal exchanges, including the effect ring shadowing on Saturn and radiative forcing by polar hazes (related to auroral/ion chemistry) on Jupiter. We will present a review of the atmospheric modeling work recently carried out in the LMD planetary science team. Among the main results obtained, let us quote the reproduction of the equatorial oscillation of Saturn and its seasonal circulation cells, forced by the activity of planetary waves; and the forcing of realistic jet streams in the Jupiter model thanks to the addition of a sub-grid scale parametrization of convective plumes. Challenges that remain to be addressed as well as comparisons to observations will be presented. Machine learning as a tool to determine exoplanet properties Thomas Hajnik (University of Vienna / Department of Astrophysics), Thomas Hajnik, Andreas Schanz, Sudeshna Boro Saika Characterization of exoplanetary atmospheres and interiors requires information on planetary properties such as mass, radius, and density. However, precise measurements of these fundamental properties are not always possible, as a result of which the masses and radii of these planets are often unknown. We propose a data driven machine learning method to estimate missing exoplanet properties by applying clustering algorithms to a subset of the currently known exoplanet populations, containing approximately 4000 exoplanets. We applied the Uniform Manifold Approximation Projection (UMAP, McInnes et al., 2018) algorithm, together with a range of clustering techniques, such as Gaussian Mixture Models, K-means and HDBSCAN, to a custom data set, created by merging the NASA exoplanet archive and the exoplanet.eu catalogue. This enables us to create the most complete parameter set, that current observations allow. We show that a combination of different clustering algorithms and trained UMAP models is able to infer estimates on planetary radii and masses, when provided with a large enough training sample. Based on this method, we can provide estimates for radii and masses of Hot Jupiters. Our results deviate from ground truth by 0.06 Jupiter radii and 0.23 Jupiter masses on average. This is achieved for a test data set containing three host star properties (mass, radius, effective temperature) and only the orbital period of the planet. The results show that data-driven methods are a promising approach for parameter estimation in exoplanets, which can be very useful in the target characterization of upcoming missions such as PLATO and Ariel. Improving Exoplanet Atmospheric Retrievals with a Learning-Based Model for Pressure-Temperature Profiles Björn S. Konrad (ETH Zürich), T. D. Gebhard, D. Angerhausen, E. Alei, S. P. Quanz, and B. Schölkopf Atmospheric retrievals are commonly used to infer exoplanet properties (e.g., the chemical composition of the atmosphere) from an observed spectrum. A retrieval framework requires a forward model (calculates the spectrum corresponding to a set of model parameters) and a Bayesian inference scheme (samples the space of model parameters in search of the best combination). One important component of the forward model is the pressure-temperature (PT) profile, which describes the thermal structure of the atmosphere. Retrievals typically employ parametric functions to describe the atmospheric PT structure (e.g., polynomials in Konrad et al. 2022). While being versatile, such parametric forward models are not physical. Thus, we have no guarantee that the retrieved PT structure describes a physically possible atmospheric state. Furthermore, parametric forward models require large parameter numbers (more than 4), which slows down the atmospheric retrieval routine. We employ a new Machine Learning (ML) approach to parameterize the PT structure of exoplanet atmospheres in retrieval studies. This new approach requires fewer parameters (only two) and is trained on physically accurate PT profiles. We train our ML model on the PyAtmos data set (Bell at al. 2018, Chopra et al. 2018), which consists of more than 100000 physically and chemically self-consistent PT profiles of Earth-like planets around a solar-type star, which were calculated with Atmos (a one-dimensional coupled photochemistry-climate model; Arney et al. 2016, Meadows et al. 2018). To prove the applicability of the ML PT Model, we run atmospheric retrievals on a low resolution (R=50) MIR thermal emission spectrum of an Earth-twin exoplanet. We find that employing our ML PT model speeds up the retrieval significantly over the baseline retrieval with a polynomial PT model (by roughly 50%). The retrieved values for most planetary and atmospheric parameters are comparable. However, the retrieval that employs the ML PT model provides better estimates for the atmospheric PT structure than the polynomial baseline. These retrieval runs show the potential of ML-base PT models for atmospheric retrievals. Such models provide a physically accurate description of atmospheric PT profiles while requiring less parameters than the commonly used parametric PT models. References: Arney, G., Domagal-Goldman, S. D., Meadows, V. S., et al. 2016, Astrobiology, 16, 873 Bell, A., Chopra, A., Fawcett, W., et al. 2018, in 5th Workshop on Challenges in Machine Learning (NeurIPS) Chopra, A. et al. 2018, About the FDL PyATMOS dataset Konrad, B. S., Alei, E., Quanz, S. P., et al. 2022, A&A, 664, A23 Meadows, V. S., Arney, G. N., Schwieterman, E. W., et al. 2018, Astrobiology, 18, 13 Atmospheric Retrieval of Terrestrial Solar System Planets for LIFE Björn S. Konrad (ETH Zürich), Eleonora Alei, Daniel Angerhausen, Sascha P. Quanz, and the LIFE collaboration Context: A long-term goal of exoplanet research is to characterize the atmospheres of a sizable sample of temperate terrestrial exoplanets. Such studies will build our knowledge about the diversity of terrestrial worlds and enable the discovery of habitable or even inhabited worlds. To achieve this goal, missions capable of measuring the spectra of temperate terrestrial exoplanets have been proposed (LUVOIR/HabEx - optical & near-infrared; Large Interferometer For Exoplanets (LIFE)[1] - mid-infrared (MIR)). The MIR thermal emission measured by LIFE provides exclusive probes to important molecules (e.g. the potential bioindicators CH4, O3). Further, the MIR observations can provide constraints on a planet’s pressure-temperature (PT) profile, radius, and surface conditions. Methods & Results: We present results from our recent atmospheric retrieval studies. We investigated a cloud-free Earth- [2] and, to our knowledge for the first time, a cloudy Venus-twin [Konrad et al., subm.] exoplanet around a sun-like star at 10 pc. We simulate the MIR planet emission spectra with petitRADTRANS (1D radiative transfer model) [3] and use LIFESim [4], to estimate the wavelength-dependent noise expected for exoplanet observations with LIFE. Our retrieval suite uses the atmospheric model petitRADTRANS and the MultiNest algorithm [5] for parameter estimation. We retrieve the planetary mass and radius, the PT profile, the surface pressure, the molecular abundances and the cloud parameters. By considering input spectra of different wavelength ranges, resolutions (R), and noise levels (S/N), we aim to determine the requirements to: 1. discriminate Earth- from Venus-like MIR spectra 2. characterize the structure and composition of atmospheres 3. detect potential biomarkers in Earth-twin 4. infer the presence of clouds in atmospheres 5. constrain cloud structure and composition in a Venus-twin We also discuss challenges in the analysis of MIR exoplanet spectra from LIFE via atmospheric retrievals and how differences in the quality of the spectra affect them. Conclusion: With these studies and an additional retrieval study for Earth at different times [6], we find first constraints for the instrument requirements for the LIFE interferometer and identify important limitations and challenges of MIR atmospheric retrieval studies for exoplanets. References: [1] Quanz, S. P., et al. 2022, A&A, 664:A21 [2] Konrad, B. S., et al. 2022, A&A, 664:A23 [3] Mollière, P., et al., 2019, A&A, 627:A67 [4] Dannert, F. A., et al. 2022, A&A, 664:A22 [5] Feroz, F., et al., 2009, MNRAS, 398(4):1601–1614 [6] Alei, E., et al. 2022, A&A, 665:A106 Convection inhibition in the atmosphere of Neptune and Neptune-like planets Jeremy Leconte (LAB/CNRS), Jeremy Leconte, Aymeric Spiga, Sandrine Guerlet, Franck Selsis, Gwenaël Milcareck, Noé Clément, Ehouarn Millour Whether it is inside or outside of the Solar System, the atmospheric structure of Neptune and Neptune like planets remains rather poorly constrained. On the observational side, JWST will soon change by observing our own ice giants, but also temperate sub-neptunes like K2-18b, thanks to their relatively large size compared to terrestrial planets. However, on the theoretical side, models of the atmospheric structure and dynamics of these atmospheres are relatively scarce. In particular, it has been proposed that water (or methane) condensation could shut down convection in planets where it is heavier than the background hydrogen rich atmosphere (like Neptune; Leconte et al. 2017). But the dynamics of this effect has never been studied in 3D and its impact of this on observations (in particular for exoplanets) has never been assessed. I will show results from a 3D cloud-resolving model that we adapted to the study of temperate hydrogen rich atmospheres. This work shows how water condensation naturally shuts down convection in these objects as has been predicted by simple linear theory. Then, we will show how the thermal and compositional structure of these atmospheres is modified. Finally, we will discuss whether convection inhibition yields an observable signature for JWST to detect. Leconte et al. 2017 - https://ui.adsabs.harvard.edu/abs/2017A%26A...598A..98L/abstract New spectral windows into the escaping atmospheres of exoplanets Dion Linssen (University of Amsterdam), Antonija Oklopčić Atmospheric escape is expected to have important consequences for the evolution of planets and has been suggested to create the observed radius valley and hot Neptune desert. To date, escaping exoplanet atmospheres have typically been probed with a handful of spectral lines, such as Lyman alpha, the metastable helium triplet and UV lines of metals. Inferring important characteristics such as the outflow geometry and mass-loss rate from these observations has been difficult due to differing theoretical predictions and model degeneracies. Expanding on the suite of tracers used to probe escaping atmospheres would help to mitigate these challenges. We post-process hydrodynamic outflow models with NLTE photoionization code Cloudy to predict the transit spectrum of typical gas giant planets and we find new spectral lines in the UV and optical that can potentially be used to study their upper atmospheres. By indicating the atmospheric altitude each of these lines probe, we can identify complementary lines which will allow us to better constrain the outflow properties. A neural network approach to accelerate chemical kinetics codes Amy Louca (Leiden Observatory), Julius Hendrix, Yamila Miguel This study is focused on the implementation of neural networks to replace mathematical frameworks in the one-dimensional chemical kinetics code, VULCAN (Tsai et al. 2017; 2021). The underlying time-dependent ordinary differential equations are very time-consuming to compute when using numerical methods. The neural network in this study is designed to replace them. Our data set consists of 13291 hot-Jupiters atmospheres. Using the gravity gradient, temperature-pressure profiles, initial mixing ratios, and stellar flux as free parameters, the neural network is built to predict the mixing ratio outputs. The architecture of the network is composed of individual autoencoders for each input variable to reduce the input dimensionality, which are then used in an LSTM-like neural network to train this sequential data on. Results show that the autoencoders for the mixing ratios, stellar spectra, and pressure gradients are exceedingly successful in encoding and decoding the data. The temperature and gravity gradients are shown to be more difficult to reconstruct using autoencoders. Using the original temperature- and gravity gradients and the encoded data to predict the time-dependent output mixing ratios by training the core network has shown to be successful within errors between different chemical kinetics codes (Venot et al. 2012). In 90% of the cases, the fully trained model is able to predict the evolved mixing ratios of the species in the hot-Jupiter atmosphere simulations with errors in the range [-0.66, 0.65] orders in magnitude. Due to imbalances in the data set, the model is biased to more accurately solve for some examples than others. The fully trained model is 10^3 times faster than the VULCAN simulations while making accurate predictions. YunMa: An Exoplanet Cloud Retrieval Model for Next-Generation Data Sushuang Ma (University College London), Yuichi Ito, Ahmed F. Al-Refaie, Quentin Changeat, Billy Edwards, Giovanna Tinetti The existence of clouds in transit spectra has been a prominent issue in exoplanetary spectroscopy. The formation of clouds can obscure the spectroscopic features from atmospheric chemistry and complicate planetary scenarios. The high-quality transit spectra offered by the next generation of facilities, such as JWST and Ariel, provide a great chance to constrain the exoplanetary cloud formation and its impact on the observation. Corresponding to the observational improvement, we present YunMa, an exoplanetary cloud model optimised for the next-generation data. Integrating YunMa into the TauREx 3 platform enables the parametric cloud microphysics retrieval function, which is a big step in exoplanetary cloud retrieval. Numerical simulations of zonal jets on Uranus and Neptune by the DYNAMICO Planetary Climate Model Gwenael Milcareck (Laboratoire de Météorologie Dynamique, CNRS, Paris, France), Sandrine Guerlet, Aymeric Spiga, Jeremy Leconte, Deborah Bardet, Franck Montmessin Flyby of Uranus and Neptune by Voyager 2 in 1986 and 1989 have shown an intense zonal circulation and an unexpected meteorological activity. Characterized by a prograde jet at mid-latitude in each hemisphere and a retrograde jet centered on the equator, the zonal structure of the wind is similar on these two planets despite a very different seasonal radiative forcing. The retrograde jet is nevertheless more intense on Neptune where it reaches -400 m/s. In parallel with these jets, a meteorological activity in the form of waves, cyclonic and anticyclonic storms like the Great Dark Spot is also present. Understanding atmospheric circulation in gas and ice giant planets (having developed a GCM for Saturn and Jupiter as well), with comparative planetology aspects that could be relevant to the exoplanet community is one of the major current challenges in physics of planetary atmospheres. To reproduce the zonal jets as well as the strong meteorological activity on Uranus and Neptune, 1Â° resolution numerical simulations has been performed with a Global Climate Model (GCM) named DYNAMICO Ice Giants Planetary Climate Model. The GCM used for these studies is composed by a hydrodynamical core which solves shallow-water equations on the rotating sphere based on an icosahedral-hexagonal grid and a radiative-seasonal model tailored for ice giants. The preliminary results obtained from 10 simulated years on Uranus and Neptune highlight a similar zonal wind structure compared to observations and an important eddy activity. Spectral analysis of waves and contribution of eddies to the acceleration or deceleration of the simulated jets will be discussed. Zonal winds in the Venus mesosphere from VIRTIS/VEx temperature sounding Arianna Piccialli (Royal Belgian Institute for Space Aeronomy (BIRA-IASB)), D. Grassi, A. Migliorini, R. Politi, G. Piccioni, P. Drossart Zonal winds in the Venus mesosphere from VIRTIS/VEx temperature sounding A. Piccialli (1), D. Grassi (2), A. Migliorini (2), R. Politi (2), G. Piccioni (2), P. Drossart (3) (1) Royal Belgian Institute for Space Aeronomy, Belgium ([email protected]), (2) INAF - IAPS, Istituto di Astrofisica e Planetologia Spaziali, Via del Fosso del Cavaliere, 100, I-00133 Rome, Italy, (3) Institut d'astrophysique de Paris, CNRS, Sorbonne UniversitÃ© & LESIA, Observatoire de Paris (email: [email protected]) Venus is a natural laboratory to study the atmospheric circulation on a slowly rotating planet. The dynamics of its upper atmosphere (60-120 km) is not only a combination of retrograde zonal wind found in the lower mesosphere and solar-to-antisolar winds that characterize the thermosphere, but in addition strong turbulence and a dramatic variability both on day-to-day as well as longer timescales characterizes this atmospheric layer. Moreover, several wavelike motions with different length scales were detected at these altitudes within and above the clouds and they are supposed to play an important role in the maintenance of the atmospheric circulation on Venus. The basic processes maintaining the super-rotation (an atmospheric circulation located at the clouds level and being 80 times faster than the rotation of the planet itself) and other dynamical features of Venus circulation are still poorly understood [1]. Different techniques have been used to obtain direct observations of wind at various altitudes: tracking of clouds in ultraviolet (UV) and near infrared (NIR) images give information on wind speed at cloud top (~70 km altitude) [2] and within the clouds (~61 km, ~66 km) [3], while ground-based measurements of doppler-shift in CO2 band at 10 Î¼m [4] and in several CO (sub-)millimeter lines [5,6] sound thermospheric and upper mesospheric winds, showing strong variability. In the mesosphere, at altitudes where direct observations of wind are not possible, zonal wind fields can be derived from the vertical temperature structure using the thermal wind equation. Previous studies [7,8,9] showed that on slowly rotating planets, like Venus and Titan, the strong zonal winds at cloud top can be successfully described by an approximation of the Navierâ€“Stokes equation, the cyclostrophic balance in which equatorward component of centrifugal force is balanced by meridional pressure gradient. We will present zonal thermal winds derived by applying the cyclostrophic balance from the Visible and Infrared Thermal Imaging Spectrometer (VIRTIS) temperature retrievals. VIRTIS was one of the experiments on board the European mission Venus Express [10]. It consisted of two channels: VIRTIS-M and VIRTIS-H. For this study, we will analyze the complete VIRTIS dataset acquired between December 2006 and January 2010 [11,12]. References [1] Sanchez-Lavega, A. et al. (2017) Space Science Reviews, Volume 212, Issue 3-4, pp. 1541-1616. [2] Goncalves R. et al. Atmosphere, 12:2., 2021. doi: 10.3390/atmos12010002. [3] Hueso, R. et al. (2012) Icarus, Volume 217, Issue 2, p. 585-598. [4] Sornig, M. et al. (2013) Icarus 225, 828â€“839. [5] Rengel, M. et al. (2008) PSS, 56, 10, 1368-1384. [6] Piccialli, A. et al. A&A, 606, A53 (2017) DOI: 10.1051/0004-6361/201730923 [7] Newman, M. et al. (1984) J. Atmos. Sci., 41, 1901-1913. [8] Piccialli A. et al. (2008) JGR, 113,2, E00B11. [9] Piccialli A. et al. (2012) Icarus, 217, 669â€“681 [10] Drossart, P. et al. (2007) PSS, 55:1653â€“1672 [11] Grassi D. et al. (2008) JGR., 113, 2, E00B09. [12] Migliorini, A. et al. (2012) Icarus 217, 640â€“647. Exoplanets with JWST/NIRSpec: Lessons learned from a year of operations Tim Rawle (ESA), Stephan Birkmann, Catarina Alves de Oliveira The Near-Infrared Spectrograph (NIRSpec) is one of four focal plane instruments onboard the James Webb Space Telescope (JWST), launched on 25 December 2021. After more than a year of stunningly successful operations, we present an overview of initial results from the NIRSpec Bright Object Times Series (BOTS) mode, primarily used for transit/eclipse observations of exoplanets. We will also highlight a few lessons learned from JWST operations, pertinent for future exoplanet missions such as ESA's Ariel. The effect of metallicity on the CH4 and CO quenched abundance in H-dominated atmospheres Vikas Soni (Physical Research Laboratory), Vikas Soni (First author), Kinsuk Acharyya (co-author) Exoplanets show astonishing diversity in their parameter space, including atmospheric metallicity, which significantly affects the atmospheric composition. The effect of metallicity on the thermochemical equilibrium of exoplanet atmospheres has been studied widely. However, the effect on the disequilibrium abundance in the presence of transport (transport abundance) is largely unexplored and has only been studied for some targeted exoplanets. There are many available methods to find the transport abundance. Among these methods, the quenching approximation is the most straightforward way to constrain the transport abundance. In the quenching approximation, the quench level is defined at a pressure level where the chemical and mixing time scales become equal. Above the quench level, the transport abundance is given by the equilibrium abundance at the quench level (quenched abundance). We studied the effect of metallicity on the chemical and vertical mixing timescales for a large parameter space of pressure, temperature, and metallicity (0.1 mbar to 1 kbar, 500-2500 K, 0.1-1000 x solar metallicity). We compute the thermochemical equilibrium abundance for our parameter range and use it to mark the rate-limiting step (RLS) in a reduced chemical network. For this task, we built a network analysis tool to find the RLS and conversion scheme for a given set of molecules. By comparing the calculated mixing time scale and chemical time scale, we find all possible quench level data points in our parameter range and study the effect of metallicity on the location of the quench level. Our equilibrium results are in good agreement with the literature. The CO-CH4 and CO-CO2 equal-abundance curves move to low-temperature and high-temperature, respectively, with increasing metallicity. The abundance of CO and H2O increases linearly, whereas CO2 increases as the square of the metallicity. However, the CH4 abundance increases with metallicity only in the low-temperature and high-pressure regions, where it is a major source of C. The chemical time scale of CO is a weak function of metallicity; however, the chemical time scale of CH4 decreases linearly with increasing metallicity. By comparing the chemical time scale with the mixing time scale, we find that the quenched level of CO moves deep in the atmosphere with increasing metallicity and the CH4 quench level is a complex function of metallicity. For the benchmarking of quenched abundance, we compared the output of an in-house developed full transport chemical kinetics model with the output of the quenching approximation for two test exoplanets. The quenching approximation is accurate within an order of magnitude (which can be further improved by using the mixing length instead of the scale height). We also take three test exoplanets, HR 8799 b, HD 189733b, and Gj 436-b, and find that the quench level data points constrain exoplanets mixing strength and atmospheric metallicity for these exoplanets. Thus, the quench level data points and observed abundance of molecules can be a powerful tool to constrain atmospheric parameters. Atmospheric turbulence and magnetic field amplification in hot Jupiters Clàudia Soriano Guerrero (Institute of Space Sciences) This project discusses the peculiar class of exoplanets called Hot Jupiters (HJs), which are gas giants orbiting very close to their host stars. These planets have inflated radii that cannot be accounted for standard cooling models for planetary evolution. Various possible mechanisms have been proposed, among which is Ohmic dissipation based on the dissipation of currents induced by the magnetic field stretching due to the flow motion. This project focuses on the effect of atmospheric turbulence on magnetic fields and Ohmic dissipation in the upper atmosphere of HJs. Box simulations representing tiny atmospheric columns are used to evaluate where electrical currents are induced by the shear layer and the turbulence and quantify them. We aim to extend previous studies to the ideal magnetohydrodynamic (MHD) regime applicable for high enough conductivities, for very Hot Jupiters. We evaluate the amplifications of the magnetic field and current profile at equilibrium, and study the effects of enforcing turbulent perturbations in addition to the zonal wind in the upper atmosphere. We include realistic profiles for the wind velocity, taking into account more recent results about zonal winds in global circulation models. In conclusion, the simulations performed in this study suggest that the strong electrical currents generated are enough to explain the inflated radii of very Hot Jupiters, if they penetrate inner layers of the planet. Can wave-particle interaction be important for ion heating and escape at Venus? Gabriella Stenberg Wieser (Swedish Institute of Space Physics, Kiruna, SWEDEN), Mats André, Hans Nilsson Wave-particle interaction has been identified as a major ion energization process at Earth. A common type of ion heating is associated with low-frequency broadband electric wave fields. The spectral density of such broadband waves does not exhibit a peak at a certain frequency but the wave power available at the ion gyrofrequency may nevertheless efficiently energize the ions. At Earth this heating mechanism is definitely effective and important. Venus lacks an intrinsic magnetic field and the induced magnetosphere much smaller. The interaction with the solar wind is very different from the terrestrial case and the role of wave-particle interaction has not been much explored. We investigate if ion energization by electric wave power is important also at Venus and compare with the Earth case. High-resolution transmission spectroscopic studies of hot and ultra-hot Jupiters Monika Stangret (INAF - OAPd, Italy) Hot and ultra-hot Jupiters, gas-giant planets with short orbital periods, and hot, extended atmospheres, are the most suitable objects in order to study the chemical composition of the atmospheres using emission and transmission spectroscopy. Their tidally-locked nature leads to big differences between night and day side temperatures, and in consequence differences the atmospheric chemical composition of both terminators. Thanks to a new generation of high-resolution ground-based spectrographs such us HARPS-N, HARPS, CARMENES, and ESPRESSO, we are able to perform those studies. In my poster, I want to present a complex analysis of the chemical composition of a set of hot and ultra-hot Jupiters using high-resolution spectroscopic observations. Using the cross-correlation method and transmission spectroscopy around single lines, we searched for a set of atoms and molecules in the atmosphere. Additionally, by analyzing the Rossiter-McLaughlin effect we measured the obliquity of those systems. Our work determines the temperature in which we differentiate between the hot and ultra-hot Jupiters, and show the importance of complex studies of those object using broad sets of chemical species model. Martian Atmospheric Chemistry of HCl: Implications for the Lifetime of Atmospheric Methane Benjamin Taysum (Deutsches Zentrum für Luft- und Raumfahrt, Institute of Planetary Research), Paul I. Palmer, Mikhail Luginin, Nikolay Ignatiev, Alexander Trokhimovskiy, Alexey Shakun, Alexey Grigoriev, Franck Montmessin, Oleg Korablev, Kevin Olsen We develop a 1-D atmospheric photochemistry model for Mars to interpret hydrogen chloride (HCl) profile measurements collected by the ACS MIR spectrometer aboard the ExoMars Trace Gas Orbiter (TGO) in Mars Year (MY) 34. We include a gas-phase chlorine chemistry scheme and study 1) surface chemistry, 2) hydrolysis, 3) photolysis, and 4) hydration and photolysis of dust grains as possible sources of gas-phase chlorine chemistry. Heterogeneous uptake of chlorine species onto water ice and minerals in Martian dust are loss processes common to all mechanisms. We drive the 1-D model using TGO profile measurements of aerosols and water vapour. We find that mechanism four can reproduce observed HCl profile tendencies during MY34. It reproduces the HCl cut-off at high southern latitudes (< 60°) at ~35 km, and forms layers of HCl between 20-35 km at the tropics. Mechanisms one, two, and three result in significant model biases. % Seasonal variations of Martian HCl are reproduced by mechanism four, yielding low HCl abundances (< 1 ppb) prior to the dust season that rise to 2-6 ppb in southern latitudes during the dust season. We find that the additional Cl atoms released via mechanism four shortens the atmospheric lifetime of methane by a magnitude of 10^2. This suggests the production of Cl via the UV (or other electromagnetic radiation) induced breakdown of hydrated perchlorate in airborne Martian dust, consistent with observed profiles of HCl, helps reconcile observed variations of methane with photochemical models. Venus atmospheric circulation from the cloud features tracking in the VMC/ Venus Express images Dmitrij Titov (Leiden Observatory, Leiden University), D. Titov, I. Khatuntsev, M. Patsaeva, N. Ignatiev Global circulation of the Venus atmosphere is still one of unsolved fundamental problems in the planetary physics. Venus Express collected the longest time series of the planet images in several wavelengths from UV to near-IR that allowed to track winds at different levels within the cloud (50-70 km). Up to a half a million wind vectors were derived from the cloud features tracking. This provided complete characterization of the atmospheric circulation and its variability including changes with altitude, latitude, local solar time as well as influence of the surface topography and long term trends. The talk will present these results, outline potential complementarities with other data sets, and give an outlook for future missions in the coming "Venus Decade". Evolution of Titan's Stratospheric HCN in High Spatial Resolution Lucy Wright (University of Bristol), Nicholas A. Teanby, Patrick G. J. Irwin Saturn's largest moon, Titan, is the only moon in our solar system with a substantial atmosphere. Like Earth, Titan's atmosphere comprises mostly Nitrogen but is also host to many hydrocarbon and nitrile species, produced by photochemistry in the upper atmosphere. These species are good tracers of atmospheric dynamics. From 2004 to 2017, NASA/ESA's Cassini-Huygens spacecraft explored the Saturn system, performing 127 flybys of Titan. On its third flyby, Cassini released the ESA-operated Huygens atmospheric entry probe, which performed measurements on its descent to Titan's surface. Cassini's Composite Infrared Spectrometer (CIRS) observed Titan in the infrared for 13 years, almost half a Titan year. We use nadir observations acquired by the CIRS instrument at low spectral resolution to map trace species in Titan's stratosphere at high spatial resolution. In-situ measurements acquired by the Huygens probe constrain our atmospheric retrievals. We use trace gas distributions to investigate seasonal changes in dynamics near Titan's stratospheric equator. ## Surface geological & geophysical processes A Comparison of Syndynic Bands in Long Period Comets Qasim Afghan (UCL), Geraint H. Jones, Andrew Coates, Oliver Price We have been analysing the dust tails of highly active comets using Finson-Probstein analysis e.g. Afghan et al. (2023). Observations of Comet NEOWISE (C/2020 F3) during its perihelion in July 2020 showed the presence of syndynic bands in the dust tail: bright bands that are accurately bounded by syndynes (lines of constant dust β). NEOWISE's dust tail was segmented into two bright bands, with a darker band in between them. Analysis using a Finson-Probstein model showed a bimodal distribution of dust grain β, where a large proportion of dust grains with β values of around β =1.63±0.02 and β =0.57±0.16 were ejected from the nucleus. The darker band would thus be a comparatively dust sparse region, corresponding to a lack of dust grains with 0.82< β <1.2. Similar syndynic band structures have been observed in other long period comets (LPCs), and the reason for this bimodal distribution is still unknown. This work analyses the syndynic band structures of several LPCs, including C/2020 F3 (NEOWISE), C/2006 P1 (McNaught), C/2011 L4 (PanSTARRS), and C/1995 O1 (Hale-Bopp). Comparisons of dust grain β distributions between the comets show strong agreement: the dust dense and dust sparse regions for these comets all have very similar dust β ranges. Furthermore, this comparison revealed a trimodal β distribution in the dust tails: upon further examination of Comet NEOWISE's dust tail, this third band is faintly visible and thus this comparison has improved on our previous C/2020 F3 study. This commonality between the syndynic bands in these comets suggest that there is some inherent common attribute of these comets that cause this structure. A possible mechanism for this structure, relating to the composition of these comets, is discussed. Afghan, Qasim, Geraint H. Jones, Oliver Price, Andrew Coates. 2023. 'Observations of a dust tail gap in comet C/2014 Q1 (PanSTARRS)'. Icarus 390. doi:10.1016/j.icarus.2022.115286 Using photometry to better understand icy surfaces of our solar system Ines Belgacem (ESA/ESAC), Thomas Cornet, Frédéric Schmidt, Jessica Hogan, François Andrieu, Guillaume Cruz Mermy The icy moon of our solar system are promising candidates in the search for habitability. Using photometry, we want to better understand the history of these fascinating bodies and help identify potential areas of interest for future missions. The study of photometry - reflectance variation with respect to the geometry of observation - can help us better understand the processes at play at the surface. The photometry of a surface is intimately linked to its microtexture (roughness, shape of particles, porosity, ....), and can strongly affect all remote sensing observations if performed in varied geometric conditions. As a result, having a clear understanding of a surface photometry is the first step for any remote sensing applications such as surface mapping or spectroscopy. We have carried out regional studies of Jupiter's icy moons Europa and Ganymede as well as Saturn's moon Enceladus and compared the photometric parameters we obtained with known geological context. With this, we aim to better understand the link between photometry and physical properties of planetary surfaces and identify potential areas of interest for future missions. Diresct deposition of a water ice dependent mantle enabled by improved modelling of the recent Martian climate Joesph Naar (Laboratoire de Météorologie Dynamique, UMR CNRS 8539, Institut Pierre-Simon Laplace, Sorbonne Universités, UPMC Univ Paris 06, 4 place Jussieu, 75005, Paris, France. ), F. Forget, E. Millour, A. Bierjon Geologically recent glacial and periglacial landforms (<100 Myrs) are found on Mars at all latitudes. They are thought to have formed under different climate regimes than the present-day cold and arid Mars. Among these landforms, the water-ice “latitude-dependent mantle” is thought to be only a few hundred thousand years old, therefore as a result of the latest high obliquity excursion up to 35°(in comparison with today’s 25°). With this orbital forcing, the increased insolation on top of the northern polar cap strongly enhances the amount of water in the martian atmosphere. However previous studies aiming at modeling the martian atmosphere at an obliquity of 35° and assuming a permanent reservoir at the north pole like today could not explain how ice could have accumulated outside the polar regions. In these previous studies, the radiative effect of water-ice clouds was not accounted for, which was acceptable in the current martian climate. But previous work using the Mars Planeraty Climate Model (PCM, previously Mars LMD-GCM) demonstrated that their effect becomes preponderant at high obliquity, when the atmospheric humidity is greatly increased. Radiatively active clouds warm the atmosphere and enhance the meridional circulation and transport of water. Following this work, we have improved our representation of water-ice cloud using a temperature-dependent nucleation scheme. In addition, we now take into account the latent heat of sublimation of ground water ice, which is negligible in present-day martian climate. The associated cooling limits summertime sublimation of the northern polar cap but also of the mid-latitude ice deposits. Mid-latitude ice deposits forms in winter at high obliquity through snow precipitation. We study the influence of an increased ice albedo (up to 0.7) accounting for ice freshness on the summer sublimation. Our simulations are performed simply by shifting the obliquity of Mars to 35°, with the northern polar cap as the main atmospheric water reservoir and considering clear sky dust conditions all year long. We find that under the exotic climate at 35° obliquity driven by the radiatively active water-ice clouds, the combination of latent heat of surface water ice and increased albedo allows for a perennial deposition of ice in the mid-latitudes, with yearly accumulation rates consistent with the formation of the latitude dependent mantle. ## Interior structure & processes Terrestrial Exoplanet Internal Structure Constraints Are Not Limited by Host Star Spectroscopic Analyses Alejandro Ross (Johns Hopkins University), Henrique Reggiani, Kevin C. Schlaufman, Mykhaylo Plotnykov, Diana Valencia Exoplanet mass and radius inferences, and therefore internal structure constraints, are based on host star mass and radius inferences. Accurate, precise, homogeneous, and self-consistent exoplanet internal structure constraints therefore demand accurate, precise, homogeneous, and self-consistent host star mass, radius, and elemental abundance inferences. Published terrestrial exoplanet internal structure constraints have often been based on host star mass, radius, and elemental abundance inferences that are not self-consistent. For 20 solar-type stars known to host terrestrial exoplanets, we use all available astrometric and photometric data plus high-resolution optical spectroscopy to infer accurate, precise, homogeneous, and self-consistent photospheric and fundamental stellar parameters as well as elemental abundances. We infer updated planetary masses and radii using these data plus Doppler and transit observables and then use our complete data set to derive the strongest possible constraints on the internal structures of these terrestrial planets. We repeat these same analyses using the high-quality catalogs of photospheric stellar parameters and elemental abundances from SDSS DR17 APOGEE and Brewer et al. (2016, 2018) to assess the impact of differing photospheric stellar parameters and elemental abundance inference approaches on terrestrial exoplanet internal structure modeling. Tidal heating in Io drives non-symmetric volcanic pattern Wouter van der Wal (Delft University of Technology), Teresa Steinke, Marc Rovira-Navarro Jupiter's moon Io is home to widespread volcanism that has been observed by satellite missions and earth-bound telescopes. A compilation of such data shows an offset in volcanic activity of about 30 degrees with respect to the meridian crossing the sub-Jovian point (prime meridian). Although tidal dissipation is the main heat source for Io, tidal dissipation based on symmetric models of Io can not explain the observed offset. However, tidal heating may lead to spatially varying viscosity in Io's sub-surface which feeds back on the tidal dissipation. Here, we investigate whether this feedback can cause the observed offset in volcanic activity. We model tidal dissipation in Io using a finite element model. Temperature, melt fraction and viscosity are calculated assuming that most heating takes place in the asthenosphere and that viscosity is controlled by the melt fraction. The simulation results in a spatial variation in viscosity and hence response time. We calculate a new tidal heating pattern for the viscosity field and iterate until an equilibrium is reached. The final heating pattern has an offset of 15 degrees, which is less than but a significant part of the observed offset. Since our assumptions can be valid for the general case of a rocky moon orbiting close to its central body, our results suggest that exomoons which experience strong tidal dissipation will always exhibit an asymmetric heating pattern. This could lead to strong hotspots and plumes, which improve the chance of the exomoons' detection. Exploring Jupiter's structure using a combination of interior and wind models Maayan Ziv (Department of Earth and Planetary Sciences, Weizmann Institute of Science, Israel), Eli Galanti, Saburo Howard, Tristan Guillot, Yohai Kaspi The interior structure of Jupiter holds information on its formation and evolution processes, with the two research fields highly related to one another. The range of plausible interior structures is constrained by the gravity field measured by the Juno mission to an exquisite precision, the Galileo probe that measured atmospheric abundances and the 1 bar temperature, and the surface winds and their decay profile which have a significant contribution to the gravity field. Most interiors models consistent with Juno's measured gravity moments are agreeing on the presence of a dilute core in Jupiter, but with the cost of discrepancies with Galileo atmospheric observations. Examining the relations between different model parameters is key for finding effective parameters and objectively revealing the parameter combination reproducing the measurements. Here, we use the concentric MacLaurin spheroid method to generate interior models, coupled to an atmospheric model matching the measured abundances and temperatures. Starting from a basic interior solution reproducing Juno's measurements, with a realistic cloud-level wind profile, we explore the relations between different model parameters, identifying solutions search paths, and showing limitations in obtaining solutions fitting to both Juno's and Galileo's observations. ## CuRrent and Future missions The Ariel Science Operations Centre Catarina Alves de Oliveira (ESA) Ariel, the Atmospheric Remote-sensing Infrared Exoplanet Large-survey, was selected as the fourth medium-class mission in ESA's Cosmic Vision programme. It is the first mission dedicated to measuring the chemical composition and thermal structures of hundreds of transiting exoplanets, enabling planetary science far beyond the boundaries of the Solar System. A Science Operations Centre (SOC) located at the European Space Astronomy Centre (ESAC), in Madrid, Spain will be provided by ESA. This contribution summarizes its main responsibilities, including the distribution of data products to the scientific community. The PLATO Mission Heike Rauer (Institute of Planetary Research, DLR and FU Berlin), C. Aerts, KU Leuven, M. Deleuil, LAM, L. Gizon, MPI for Solar System Research, M. Goupil, LESIA/Observatoire de Paris, A. Heras, ESA, M. Mas-Hesse, CSIC/INTA, I. Pagano, INAF, G.P. Piotto, Univ. Padova, D. Pollacco, Univ. Warwick, R. Ragazzoni, INAF, G. Ramsay, Armagh Obs., S. Udry, Univ. Geneva PLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission and designed to detect and characterize extrasolar planets by high-precision, long-term photometric and asteroseismic monitoring of a large number of stars. PLATO will detect small planets around bright stars, including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observation from ground, planets will be characterized for their radius, mass, and age with high accuracy. PLATO will provide us the first large-scale catalogue of well-characterized small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our solar system planets in a broader context. PLATO will study host stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. PLATO is scheduled for a launch date end 2026. Following the successful Critical Milestone Review, ESA has given green light for the implementation of the spacecraft and the payload, which includes the serial production of its 26 cameras. This presentation will give an overview of the PLATO science goals, of its instrument and mission profile status. The M-MATISSE mission: Mars Magnetosphere ATmosphere Ionosphere and Space weather SciencE. An ESA Medium class (M7) candidate. Beatriz Sánchez-Cano (School of Physics and Astronomy, University of Leicester, United Kingdom), François Leblanc, David Andrews, Nicolas Andre, Andrew Coates, Raffaella D'Amicis, Johan De Keyser, Yoshifumi Futaana, Lina Hadid, Pierre Henri, Gunter Laky, Hiromu Nakagawa, Martin PÃ¤tzold, David Pisa, Ferdinand Plaschke, Jim Raines, Hanna Rothkaehl, Štěpán Štverák, Ed Thieman, Daniel Verscharen, Tom Woods, Shoichiro Yokota The "Mars Magnetosphere ATmosphere Ionosphere and Space-weather SciencE (M-MATISSE)" mission is an ESA Medium class (M7) candidate currently in Phase 0 study by ESA. M-MATISSE's main scientific goal is to unravel the complex and dynamic couplings of the Martian magnetosphere, ionosphere and thermosphere (MIT coupling) with relation to the Solar Wind (i.e. space weather) and the lower atmosphere. It will provide the first global characterisation of the dynamics of the Martian system at all altitudes, to understand how the atmosphere dissipates the incoming energy from the solar wind, including radiation, as well as how different surface processes are affected by Space Weather activity. M-MATISSE consists of two orbiters with focused, tailored, high-heritage payloads to observe the plasma environment from the surface to space through coordinated simultaneous observations. It will utilize a unique 3-vantage point observational perspective, with the combination of in-situ measurements by both orbiters and remote observations of the lower atmosphere and ionosphere by radio crosstalk between them. M-MATISSE is the product of a large organized and experienced international consortium. It has the unique capability to track solar perturbations from the Solar Wind down to the surface, being the first mission fully dedicated to understand planetary space weather at Mars. It will revolutionize our understanding and ability to forecast potential global hazard situations at Mars, an essential precursor to any future robotic & human exploration. Mars' ionosphere: The bond between the lower atmosphere and space Beatriz Sanchez-Cano (School of Physics and Astronomy, University of Leicester, United Kingdom), Mark Lester, Olivier Witasse, Herman Opgenoorth, David Andrews, Rob Lillis, Pierre-Louis Blelly, Marco Cartacci, Roberto Orosei, Dikshita Meggi, Katerina Stergiopoulou, Simon Joyce For planets without a global intrinsic magnetic field, the ionosphere is the conducting layer of the atmosphere that is mostly the result of solar EUV photoionization. It is also the layer that connects the neutral atmosphere with space and acts as the main obstacle to the solar wind. The ionosphere's interaction with the solar wind is, therefore, a critical factor for understanding atmospheric evolution of unmagnetised or nearly unmagnetised planets, but also for planetary exploration as it has an impact on current technology deployed on each planet. In this talk, I will present our current knowledge on Mars ionosphere and how it behaves with respect to energy inputs from the solar wind (Space Weather) as well as from the lower atmosphere and how the entire system behaves. In particular, I will focus on recent advances in the understanding of the ionospheric reaction to different Space Weather events during the solar cycle, both from the data analysis and ionospheric modelling perspectives. Some important aspects to consider are the plasma boundaries of the system, the thermosphere-ionosphere coupling, as well as the effect of electron precipitation from large Space Weather events in the lower Martian ionosphere. Finally, I will give my perspective on some of the key outstanding questions that still remain unknown but are part of the next generation of Mars' ionospheric science and exploration, which explains the actual need for multi-spacecraft missions at Mars such as the ESA under evaluation M-MATISSE mission. Ice Giant Missions as Gravitational Wave Detectors Deniz Soyuer (University of Zurich), Lorenz Zwick, Daniel D'Orazio, Prasenjit Saha The past year has seen many papers underlining the significance of a space mission to Uranus and Neptune. Proposed mission plans usually involve a ~10 year cruise time to the ice giants. This cruise time can be utilized to search for low-frequency gravitational waves (GWs) by observing the Doppler shift caused by them in the Earth-spacecraft radio link. We calculate the sensitivity of prospective ice giant missions to GWs in comparison to former planetary missions which searched for GWs. Then, adopting a steady-state black hole binary population, we derive a conservative estimate for the detection rate of extreme mass ratio inspirals (EMRIs), supermassive- (SMBH) and stellar mass binary black hole (sBBH) mergers. For a total of ten 40-day observations during the cruise of a single spacecraft, approximately 0.5 detections of SMBH mergers are likely, if Allan deviation of Cassini-era noise is improved by ~10^2 in the 10^-5 - 10^-3 Hz range. For EMRIs the number of detections lies between O(0.1)-O(100). Furthermore, ice giant missions combined with the Laser Interferometer Space Antenna (LISA) would improve the GW source localisation by an order of magnitude compared to LISA by itself. With a significant improvement in the total Allan deviation, a Doppler tracking experiment might become as capable as LISA at such low frequencies, and help bridge the gap between mHz detectors and Pulsar Timing Arrays. Thus, ice giant missions could play a critical role in expanding the horizon of gravitational wave searches and maybe even be the first to detect the first SMBH merger. Solar energetic particle events detected with housekeeping sensors by Mars Express, Trace Gas Orbiter, Gaia, Rosetta, BepiColombo and Solar Orbiter Olivier Witasse (European Space Agency), Beatriz Sanchez-Cano, Elise W. Knutsen, Dikshita Meggi, Mark Lester, Robert F. Wimmer-Schweingruber, Marco Pinto and the ESA mission teams. While space weather has been a growing field of research and applications over the last 15-20 years, "planetary space weather" is an emerging discipline. In fact, as long as we expand our robotic exploration within the Solar System, monitoring planetary space weather is becoming more necessary than ever, especially to understand the input of energy into a planetary system. Despite this, not every spacecraft is designed for Space Weather science and only a few of them have the necessary particle instrumentation for Space Weather purposes. However, all of them have thousands of housekeeping detectors distributed along the spacecraft. In particular, energetic particles impact detectors and subsystems on a spacecraft and their effects can be identified in selected housekeeping data sets, such as the Error Detection And Correction (EDAC) counters. In this study, we investigate the use of these engineering datasets for scientific purposes by performing the first feasibility study of solar energetic particle detection using EDAC counters from several available ESA Solar System missions, i.e. Mars Express, Trace Gas Orbiter, Gaia, Rosetta, BepiColombo and Solar Orbiter. In order to validate the results, these detections are compared to other observations from scientific instruments on board these missions. Moreover, the potential implications of Space Weather detections based on EDAC sensors at Mars and Comet 67P/Churyumov-Gerasimenko is analyzed. This study has the potential to provide a good observation network for large solar particle event at locations where no dedicated scientific instruments are available.	2023-03-23T11:31:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.520025908946991, "perplexity": 3658.8071358944126}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945144.17/warc/CC-MAIN-20230323100829-20230323130829-00066.warc.gz"}
https://pavpanchekha.com/blog/symmetric-expressions.html	## By Pavel Panchekha ### 10 December 2020 Share under CC-BY-SA. # Detecting Symmetric Expressions As I work on Herbie, my numerical analysis assistant, I'm always thinking about how I could teach it classic numerical analysis tricks. Recently, my student Oliver Flatt and I have been thinking about tricks for symmetric expressions. ## Symmetry for Accuracy Consider the following computation, which is important in statistics: $\log(e^a + e^b)$ The numerical analysis wisdom is that this expression is best evaluated via the expression max(a, b) + log1p(exp(min(a, b) - max(a, b))) There's a lot going on here (law of logarithms, the log1p function, and so on) but I want to focus on min and max. The key is that the original expression, in a and b, has turned into an expression in min(a, b) and max(a, b). Those are the same values as a and b, though which is which depends on the input. And this is similar to another well-known trick for computing the area of a triangle with side lengths A, B, and C: [A, B, C] = sort([A, B, C]) sqrt((C + (B + A)) * (A - (C - B)) * (A + (C - B)) * (C + (B - A))) There's a similar trick for computing the triangle's interior angles, which requires sorting the two side lengths the angle joins. It'd be way cool if Herbie could find these tricks automatically! ## A Proposed Approach Traditionally, Herbie deals with cases like this by adding branches, using an algorithm we call regime inference. But that algorithm basically requires treating each branch as its own special case, and while with two variables there are only two branches, with three variables there are already six, which is more than Herbie can do well. But symmetric expressions don't need to treat each branch as a special case; they are all more or less the same case, with the variables names swapped around. Herbie works based on sampled input points. If we knew that the expression was symmetric in variables A, B, and C, we could just take all the sampled inputs and sort A, B, and C. Then the rest of Herbie would operate on a single case (where the variables come sorted), and at the end we'd take Herbie's results and tack on a sort in front to handle the other cases. Basically nothing in Herbie's internal structure would need to be disturbed! All we need is a way to detect when an expression is symmetric in a set of variables. ## Detecting symmetries This turns out harder than expected. Sometimes, all variables in an expression can be sorted, like in a + b + c. Other times, only a subset can: in a * b + c, it's fine to sort a and b but c must stay itself. Other times, there are two disjoint sets of sortable variables, like in pow(a * d, b + c). But there can also be strange cases, like a^3 b^2 c + b^3 c^2 a + c^3 a^2 b, where you can rotate a, b, and c but you can't sort them. Or what about a * d + b * c, where you can swap a and d, or b and c, and you can also swap the pairs, but you still can't arbitrarily sort all four variables? To abstract a bit, for any expression E[x_1, ..., x_n], some permutations of its variables leave the expression's value unchanged. Those permutations can be composed—they form a group—but in general they are some arbitrary subgroup $$G$$ of the full symmetric group $$S_n$$ on the free variables of E. We want to find the largest product of symmetric subgroups that is contained in $$G$$: $\left( \prod_i S_{n_i} \right) < G < S_n$ First, it's important to note that this largest product is unique. A symmetric group is generated by its pairwise swaps, and if both $$(a, b)$$ and $$(b, c)$$ can be swapped, so can $$(a, c)$$, via the sequence $$(a, b) (b, c) (a, b)$$ familiar to computer scientists as the xor swapping trick. Transitivity suggests a graph, so make a graph where each variable is a node, and an edge between two variables means they can be swapped without affecting the expression's value. Transitivity guarantees that this graph is the union of disjoint cliques, which corresponds to that largest product. So how do we find it? Well, the swap generators suggest a strategy. First, consider each "swapped" form of the expression, with two variables swapped. Test each swapped form for equality to the unswapped form; build a graph of equal ones. In fact, it's not strictly required to test every pair: the connected components of the graph fill in "missing" swaps that you didn't bother testing. And in Herbie, we already incorporate a powerful algorithm, e-graphs, for proving terms equal to one another. In fact, e-graphs can prove several terms equal to one another in parallel. To use e-graphs for this, we create an e-graph with the original expression in it, plus every swapped version. The e-graph is then iterated, which means it uses a bunch of rewrite rules to prove various expressions and subexpressions equal. After it's done, we just need to see which swapped versions ended up equal to the original version, build the graph, compute connected components, and we're done. If we're feeling cheeky, we can even compute connected components using the e-graph structure, though in practice we're talking about 0-20 variables so that isn't really necessary. ## Initial Results I implemented this algorithm in the new symmetry branch in Herbie and it seems to work; I ran it on the Herbie benchmark suite and it found 80 benchmarks with non-trivial symmetries, including one (Linear.V4:\$cdot from linear-1.19.1.3, C) with four separate groups of sortable variables. Oliver and I will be looking into integrating this into Herbie in the near future.	2022-12-04T21:09:59	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5124623775482178, "perplexity": 689.0199539253924}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710980.82/warc/CC-MAIN-20221204204504-20221204234504-00257.warc.gz"}
http://sundials.wikidot.com/stiffness	Stiffness and absolute stability # Absolute stability ## Forward Euler vs. Backward Euler ### The Curtiss-Hirschfelder example The test problem [Curtiss & Hirschfelder, 1952] (1) \begin{align} \dot y = -50 ( y - \cos(t)) \end{align} with different initial conditions $y(0) = y_0$ is a classical example of a stiff system. Indeed, it exhibits two widely different time scales, one corresponding to the slow manifold $y^S(t) = \cos(t)$ and the strongly damped mode $e^{-50t}$, as illustrated by the solution curves (light gray) in the figures below. The absolute stability requirement for the FE method applied to this problem leads to the stepsize restriction $h \le 2/50$. The figure below shows the results of integrating this problem with the FE method and a fixed stepsize $h=2.01/50$. Using a stepsize within the region of absolute stability, leads to a stable method (note that, for accuracy requirements, one may require a smaller stepsize) On the other hand, the BE method is stable even with a stepsize $h=0.5$, as shown in the following figure (a CVODE solution with relative and absolute tolerances of $10^{-4}$ is also shown). ## BDF and Adams-Moulton regions of absolute stability The absolute stability regions for BDF of orders 1 to 6 are shown in the figure below. Note that the stability regions are outside the shaded area for each method. The absolute stability regions for Adams-Moulton methods of orders 1-9 are shown in the figure below. Note that the first two methods — backward Euler (p=1) and trapezoidal (p=2) — are A-stable. page revision: 14, last edited: 17 Apr 2007 18:43 Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-Share Alike 2.5 License.	2017-09-22T04:29:10	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7396201491355896, "perplexity": 657.7945907654005}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818688208.1/warc/CC-MAIN-20170922041015-20170922061015-00022.warc.gz"}
https://par.nsf.gov/biblio/10283648-effects-initial-density-profiles-massive-star-cluster-formation-giant-molecular-clouds	Effects of initial density profiles on massive star cluster formation in giant molecular clouds ABSTRACT We perform a suite of hydrodynamic simulations to investigate how initial density profiles of giant molecular clouds (GMCs) affect their subsequent evolution. We find that the star formation duration and integrated star formation efficiency of the whole clouds are not sensitive to the choice of different profiles but are mainly controlled by the interplay between gravitational collapse and stellar feedback. Despite this similarity, GMCs with different profiles show dramatically different modes of star formation. For shallower profiles, GMCs first fragment into many self-gravitation cores and form subclusters that distributed throughout the entire clouds. These subclusters are later assembled ‘hierarchically’ to central clusters. In contrast, for steeper profiles, a massive cluster is quickly formed at the centre of the cloud and then gradually grows its mass via gas accretion. Consequently, central clusters that emerged from clouds with shallower profiles are less massive and show less rotation than those with the steeper profiles. This is because (1) a significant fraction of mass and angular momentum in shallower profiles is stored in the orbital motion of the subclusters that are not able to merge into the central clusters, and (2) frequent hierarchical mergers in the shallower profiles lead to further losses of more » Authors: ; ; Award ID(s): Publication Date: NSF-PAR ID: 10283648 Journal Name: Monthly Notices of the Royal Astronomical Society Volume: 502 Issue: 4 Page Range or eLocation-ID: 6157 to 6169 ISSN: 0035-8711 The properties of young star clusters formed within a galaxy are thought to vary in different interstellar medium conditions, but the details of this mapping from galactic to cluster scales are poorly understood due to the large dynamic range involved in galaxy and star cluster formation. We introduce a new method for modelling cluster formation in galaxy simulations: mapping giant molecular clouds (GMCs) formed self-consistently in a FIRE-2 magnetohydrodynamic galaxy simulation on to a cluster population according to a GMC-scale cluster formation model calibrated to higher resolution simulations, obtaining detailed properties of the galaxy’s star clusters in mass, metallicity, space, and time. We find $\sim 10{{\ \rm per\ cent}}$ of all stars formed in the galaxy originate in gravitationally bound clusters overall, and this fraction increases in regions with elevated Σgas and ΣSFR, because such regions host denser GMCs with higher star formation efficiency. These quantities vary systematically over the history of the galaxy, driving variations in cluster formation. The mass function of bound clusters varies – no single Schechter-like or power-law distribution applies at all times. In the most extreme episodes, clusters as massive as 7 × 106 M⊙ form in massive, dense clouds with high star formation efficiency. Themore »	2023-02-09T08:24:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3839319944381714, "perplexity": 2195.329357477687}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764501555.34/warc/CC-MAIN-20230209081052-20230209111052-00830.warc.gz"}
https://www.abs.gov.au/research/economy/price-indexes-and-inflation/guide-consumer-price-index-17th-series/introduction-17th-series-australian-consumer-price-index	# Introduction of the 17th Series Australian Consumer Price Index Describes the changes that will be made to the CPI and SLCIs as a result of the introduction of the 17th series expenditure patterns Released 6/11/2017 ## Preface The purpose of this information paper is to describe the changes that will be made to the Consumer Price Index (CPI) and Selected Living Cost Indexes (SLCIs) as a result of the introduction of the 17th series expenditure patterns. The first publications based on the 17th series will be in respect of the December quarter 2017, which are due to be released on 31 January 2018 (CPI) and 7 February 2018 (SLCIs). Australia has produced indexes of retail price inflation going back as far as 1901. Prior to the introduction of the CPI in 1960, there were five series of retail price indexes compiled by the (then) Commonwealth Bureau of Census and Statistics. Since 1960, the Australian Bureau of Statistics (ABS) has maintained a program of periodic reviews of the CPI to ensure that it continues to meet community needs. The main objective of these reviews is to update the household expenditure information used to set the item weights in the CPI, but they also provide an opportunity to reassess the scope and coverage of the index. The SLCIs, incorporating the Pensioner and Beneficiary Living Cost Index (PBLCI) and the Analytical Living Cost Indexes (ALCIs) have also been reviewed as part of the 17th series. These indexes are produced as a by-product of the CPI, with weights also derived from the Household Expenditure Survey (HES). The 17th series review is a minor review of the CPI and SLCIs, consisting of an update of the upper level (expenditure class) weights in line with the latest HES, and a simple examination of structures and methodologies. This information paper provides an overview of the changes to the CPI and SLCIs that will be introduced with the 17th series from the December quarter 2017. It describes the household expenditure data used to calculate the weights and the ways in which some of the data have been adjusted to align with CPI and SLCI requirements. The paper also presents the updated weighting patterns and some background on the major shifts in weights between the 16th and 17th series. There are no changes to the classification structure or publications in respect of the 17th series. The ABS will release an updated A Guide to the Consumer Price Index: 17th Series (cat. no. 6440.0) in conjunction with the release of the 17th series CPI on 31 January 2018. The Consumer Price Index: Concepts, Sources and Methods (cat. no. 6461.0) will also be updated to reflect the changes made during the 17th series review. The updated version is expected to be released in February 2018. Readers requiring further information should contact: Consumer Price Index Section Australian Bureau of Statistics Locked Bag 10 BELCONNEN ACT 2616 Telephone: 02 6252 6654 Email:[email protected] David W. Kalisch Australian Statistician ## Background 1.1 The ABS first compiled the CPI in 1960 with a time series extending back to the September quarter 1948. Prior to introducing the CPI, the ABS and its predecessor agency, the Commonwealth Bureau of Census and Statistics, produced a number of discrete retail price indexes, each constructed with fixed quantity weights and spanning different lengths of time from 1901 to 1960 – see Chapter 3: Historical Background of Consumer Price Index: Concepts, Sources and Methods (cat. no. 6461.0) for more detail. The introduction of the CPI heralded a different approach to constructing price indexes. Rather than compiling a set of discrete fixed–weighted indexes, the objective became to produce a series of short–term fixed–weighted indexes that were to be regularly linked together to provide a single continuous measure of price change. This strategy was adopted to ensure that, at any point in time, the weighting patterns and item coverage of the CPI were relevant to user requirements and reflected contemporary economic conditions. As a result, the ABS has maintained a program of periodic reviews of the CPI to ensure that it continues to meet community needs. 1.2 The ABS also publishes the Analytical Living Cost Indexes (ALCIs) and the Pensioner and Beneficiary Living Cost Index (PBLCI), collectively known as the Selected Living Cost Indexes (SLCIs, cat. no. 6467.0). The ALCIs have been compiled and published since June 2000 and were developed in recognition of the widespread interest in the extent to which the impact of price change varies across different groups of households in the Australian population. The PBLCI was introduced in the June quarter 2009 and is a measure of the effect of changes in prices experienced by Age pensioner and Other government transfer recipient households. These indexes are also evaluated as part of the periodic review program. 1.3 The most important objective of these reviews is to update the CPI and SLCI weighting patterns, which represent the average expenditure of Australian households on goods and services. When analysing a new set of weights compared with the previous set, it is important to note that the weights are relative to each other rather than being absolute. As a result, the weight of a product could fall, for example, even though the expenditure per household on the product has increased over time. This occurs when the increase is less than the average increase for all products. Products in the CPI and SLCIs include both goods and services purchased by households. 1.4 The ABS classifies these reviews as either 'major' or 'minor' depending on the issues being considered during a particular review. In general, a minor review is restricted mainly to updating the weighting patterns. As well as updating the weights, a major review involves examining the structure and purpose of the CPI and SLCIs, their underlying classification and commodity coverage. The 17th series review is a minor review. 1.5 This information paper details the new weighting patterns, as well as discussing the key enhancements in the 17th series and providing an overview of data sources and methodologies used in deriving the weights. The paper also provides an updated estimate of the amount of upper level substitution bias in the Australian CPI. There will be no changes to the classification structure or publications in respect of the 17th series. 1.6 Associated with this information paper are two data cubes available on the ABS website: Consumer Price Index: 17th Series Weighting Pattern (cat. no. 6473.0), which contains the 17th series CPI weights, points contributions and average weekly expenditures; and Selected Living Cost Indexes: 17th Series Weighting Pattern (cat. no. 6474.0), which contains the 17th series weights and average weekly expenditures for the four household types: Employee, Age pensioner, Other government transfer recipient, and Self–funded retiree. It also contains the 17th series weights and average weekly expenditures for the Pensioner and Beneficiary Living Cost Index, which combines the Age pensioner and Other government transfer recipient households. 1.7 The 17th series CPI and SLCI weights will be implemented in the December quarter 2017, due to be released on 31 January 2018 and 7 February 2018 respectively. ## Enhancements implemented in the 17th series CPI and SLCIs ### Summary 2.1 The 17th series CPI and SLCIs include a number of enhancements which will be incorporated from the December quarter 2017. These enhancements will improve the quality of the indexes and better position the ABS for the annual re–weighting of the CPI using National Accounts Household Final Consumption Expenditure (HFCE) data from December quarter 2018. The 17th series CPI will be linked to previous CPI series, providing a continuous measure of price change since 1948. The All groups CPI (headline measure) will not be revised. The enhancements are: • updated CPI and SLCI expenditure class (EC) weights derived from the 2015-16 Household Expenditure Survey (HES) and other data sources; • updated geographical coverage to the Australian Statistical Geography Standard (ASGS) 2011; • changes to data sources and methodologies in deriving weights for the following ECs in the CPI: New dwelling purchase by owner–occupiers, Insurance, and Other financial services; • updated expenditure estimates used to derive the weights for the Self–funded retirees sub–group in the SLCIs; and • changes to the method used to estimate the upper level substitution bias in the Australian CPI. 2.2 A summary of the main changes is provided below. More detailed information can be found in later chapters of this information paper. 2.3 From 2018, the CPI will be re–weighted annually in December quarters. Further information on the forthcoming annual re–weighting can be found in Chapter 6: Upcoming work. 2.4 Additionally, as noted in Information Paper: An Implementation Plan to Annually Re–weight the Australian CPI (cat. no. 6401.0.60.005), the ABS has documented a method to calculate EC contributions to percentage change with annually re–weighted indexes. Empirical analysis of this approach can be found in Appendix 3. 2.5 The 16th series CPI review resulted in a number of outcomes which required further investigation. These are detailed in Outcome of the 16th Series Australian Consumer Price Index Review (cat. no. 6469.0). Appendix 4 provides an update on these outcomes. ### Updated geographical coverage to the Australian Statistical Geography Standard (ASGS) 2011 2.6 The geographical coverage of the CPI and SLCIs is predominantly based on the capital city average household expenditure data obtained from the HES. The 16th series was derived from the 2009-10 HES capital city Statistical Divisions, which were collected based on the Australian Standard Geographical Classification (ASGC). 2.7 In line with the 2015-16 HES, the geographical coverage of the CPI and SLCIs has been updated to the Australian Statistical Geography Standard (ASGS) 2011 for the 17th series, with the capital cities defined by Greater Capital City Statistical Areas (GCCSAs). For more information, refer to Australian Statistical Geography Standard (ASGS): Volume 1 – Main Structure and Greater Capital City Statistical Areas, July 2011 (cat. no. 1270.0.55.001). 2.8 The change from Statistical Divisions to GCCSAs has resulted in an expansion of the capital city boundaries for Melbourne, Brisbane, Adelaide and Perth. This is also the case for Canberra, however the actual difference in population is minimal. The definitions of Sydney and Darwin have remained largely unchanged. The impact of these boundary changes on price collection is being addressed through the CPI’s regular sample maintenance and review program. ### New dwelling purchase by owner-occupiers 2.9 In the CPI, New dwelling purchase by owner–occupiers refers to the expenditure on net additions of household sector dwellings as a measure of owner–occupier housing costs, and includes new homes (excluding land) and major improvements. Specifically, expenditure on New dwelling purchase by owner–occupiers comprises of four components: owner–occupied housing, first home owners' grants, alterations and additions, and installed appliances. 2.10 Previously, estimates of net additions to the owner–occupier dwelling stock were derived from Census data on the number of owner–occupier households, moved forward by household projections from Household and Family Projections, Australia (cat. no. 3236.0). For the 17th series, National Accounts estimates of the stock of owner–occupied dwellings have been used. These estimates are benchmarked to the Census. 2.11 The data sources for expenditure on the alterations and additions and installed appliances components have also changed in the 17th series. These estimates were previously obtained from the HES. For the 17th series, National Accounts estimates have been used in deriving the weights. The data source for alterations and additions is the National Accounts alterations and additions component of Private gross fixed capital formation (GFCF), while expenditure on installed appliances is sourced from HFCE data. ### Insurance 2.12 The weights for Insurance in the CPI should reflect the service provided by insurers to the household sector in aggregate. This is represented by the difference between the premiums paid and the claims received, otherwise known as the insurance service charge (ISC). This differs from the expenditure reported in the HES, which are the gross premiums paid by households. 2.13 In previous series reviews, adjustments were made to the HES data for CPI weighting purposes, using data obtained from the Australian Prudential Regulation Authority (APRA) and insurance companies. 2.14 For the 17th series, the weight for Insurance in the CPI has been derived using National Accounts estimates of the insurance service charge, which align conceptually with the CPI. This will also be the data source used when the CPI is annually re–weighted. ### Other financial services 2.15 Other financial services include real estate agent services, legal and conveyancing services, stockbroking services and taxes on property transfers (i.e. stamp duty). 2.16 In past series reviews, expenditure on real estate agent services was derived from property transaction data and unpublished ABS survey data on real estate agents’ fees. From the 17th series, the real estate fees component of the National Accounts Private GFCF ownership transfer costs series has been used. 2.17 The data sources for the remaining components of Other financial services have remained unchanged from the 16th series. ### Expenditure estimates used to derive the rights for the self-funded retirees sub-group in the SLCIs 2.18 The SLCIs are produced as a by-product of the CPI, with weights also derived from the HES. As a result, use of HES expenditures at the capital city level is preferred for the SLCIs, as it aligns the weighting and price collection scope of the two sets of indexes. 2.19 For the 16th series, the expenditure weights for the SLCIs were calculated using 2009-10 HES weighted average of eight capital cities expenditures for all population sub–groups except Self–funded retirees. The weights for Self–funded retiree households were derived using national expenditures, due to high relative standard errors (RSEs) in the capital city estimates. 2.20 For the 17th series, the weighted average of eight capital cities expenditure estimates have been used for all population sub–groups. An analysis of the 2015-16 HES results has shown that expenditure weights at the capital city level are sufficiently reliable for all household types. ### Estimating the upper level substitution bias in the Australian CPI 2.21 In order to provide an estimate of the potential item (upper level) substitution bias in the fixed–weight Australian CPI, the ABS constructs a retrospective superlative index during series reviews. This analysis can only currently be conducted retrospectively when the HES data is available. 2.22 Superlative indexes allow for product substitution as they make use of weights for both the earlier and later periods under consideration, whereas the Laspeyres index uses only base period weights. 2.23 Under the previous approach of estimating substitution bias, a quarterly superlative index was derived using the published, price updated weights. For the 17th series, the ABS has improved the estimation of the superlative index to better reflect true inflation. This index is now derived on a financial year basis, using the original weights from the HES and financial year estimates of price change. This new approach is preferred as it ensures consistency with the original period of the weights. 2.24 Updated estimates of substitution bias for the 1998-99 to 2015-16 period are available from Chapter 5: Estimating the upper level substitution bias in the Australian CPI. ## Description of the 17th series weighting pattern: sources and methods 3.1 A comprehensive description of the CPI methodology is outlined in Consumer Price Index: Concepts, Sources and Methods (cat. no. 6461.0). This will be updated to reflect the changes in the 17th series CPI and is scheduled for release in February 2018. 3.2 The 17th series CPI, consistent with the 13th, 14th, 15th and 16th series, has been designed as a general measure of price inflation for the household sector. The CPI measures changes in the price of a fixed quantity of goods and services acquired by consumers in metropolitan private households. 3.3 The SLCIs measure the impact of changes in prices on the out–of–pocket expenses incurred by households to gain access to a fixed quantity of consumer goods and services. They have been compiled and published since June 2000 and are prepared for four types of Australian households: • Employee households (i.e. those households whose principal source of income is from wages and salaries); • Age pensioner households (i.e. those households whose principal source of income is the age pension or veterans affairs pension); • Other government transfer recipient households (i.e. those households whose principal source of income is a government pension or benefit other than the age pension or veterans affairs pension); and • Self–funded retiree households (i.e. those households whose principal source of income is superannuation or property income and where the HES defined reference person is 'retired' (not in the labour force and over 55 years of age)). 3.4 The PBLCI was added to the suite of living cost indexes in the June quarter 2009 and combines the Age pensioner and Other government transfer recipient households. Unlike the CPI, the SLCIs are compiled on an outlays basis. 3.5 There are three areas of expenditure in which the CPI and the SLCIs differ. These are: • Purchase of dwellings • Under the acquisitions approach used in the CPI, the net purchase of housing, the increase in volume of housing due to renovations and extensions, plus other costs (e.g. maintenance costs and council rates) are all included for owner–occupied households. Of note, land is excluded from the calculation of housing in the Australian CPI as it is considered an investment rather than consumption. This approach aligns with international statistical standards and the primary purpose of the CPI as a macro–economic indicator. Changes in rental are measured for that part of the population that resides in rented dwellings. The CPI excludes interest paid on mortgages. • Under the outlays approach used in the SLCIs, the changes in the amount of interest paid on mortgages (measured as part of Insurance and financial services) and other costs (e.g. maintenance costs and council rates) are included for owner–occupied housing. In addition, changes in rental are measured for that part of the reference population that resides in rented dwellings. • Insurance (other than health insurance) • Under the acquisitions approach, the weight for insurance in the CPI relates to the net value of the service provided by the insurance company to the household sector as a whole. In simple terms, this is the amount of premiums paid by households, less the amounts reimbursed by way of claims. • Under the outlays approach used for the SLCIs, the weight relates to the gross value of insurance premiums paid by households. • Financial services • The CPI includes services relating to the acquisition, holding and disposal of financial and real assets. This includes deposit and loan facilities provided by financial institutions and costs associated with the acquisition and disposal of real estate, such as stamp duty and real estate commission fees. • The SLCIs include mortgage interest and consumer credit charges, but exclude all other financial services (i.e. deposit and loan facilities (direct charges), and other financial services). 3.6 In determining the composition of the CPI and SLCI baskets (and item weights), the objective is to reflect the contemporary experiences of households. The starting point for compiling the weights is the results of the ABS 2015-16 HES. The HES obtained information on the spending habits of Australian households throughout the 2015-16 financial year. ### 2015-16 HES data 3.7 The 2015-16 HES collected information from a sample of 10,046 households over the period July 2015 to June 2016. Data was collected using a diary of personal expenditures in which usual residents aged 15 years and over record their expenditure over a two week period. A household level computer assisted interview questionnaire also collected information on household characteristics, expenditures common to all household members (e.g. utility bills) and irregular or infrequent expenditures. The recall period for the irregular or infrequent expenditures varied: 3 months including furniture and house repairs; last payment including general rates, electricity and health services; and the last 12 months including motor vehicle purchase, motor vehicle repair and maintenance, education, overseas holiday travel and house alterations and additions. See Household Expenditure Survey, Australia: Summary of Results, 2015-16 (cat. no. 6530.0) for more information on the HES. 3.8 The 2015-16 HES was collected under the Australian Statistical Geography Standard (ASGS) introduced in 2011. This is a change from the Australian Standard Geographical Classification (ASGC) used for the 2009-10 HES. The ASGS provides a common framework of statistical geography used by the ABS to enable the publication of statistics that are comparable. 3.9 The detailed HES expenditure items are classified according to the ABS Household Expenditure Classification (HEC). A correspondence exists between the CPI and HEC. Most HEC codes have a direct correspondence to one CPI expenditure class. Where a one–to–one correspondence could not be established due to the broad nature of a HEC code or insufficient information being provided by households, splits were determined either on a prorate basis, using industry data or subjectively across appropriate expenditure classes. In most cases where splits were required, the expenditures involved were relatively small. The CPI to HEC correspondence will be published as a data cube in Consumer Price Index: Correspondence with 2015-16 Household Expenditure Classification, Australia (cat. no. 6446.0.55.001) with the implementation of the 17th series CPI on 31 January 2018. 3.10 The CPI to HEC correspondence was applied to the HES data to derive household average weekly expenditure for 2015-16 at the expenditure class level. The average weekly expenditure was used to analyse both the 2015-16 expenditure and the changes since the 2009-10 HES. 3.11 Although the HES provides a comprehensive coverage of household expenditure, various adjustments are made to the HES average weekly expenditures for use in the CPI and SLCIs. In most cases the adjustments to expenditure were made without compensating adjustments to other expenditure in the CPI and SLCI baskets. The implication is that changes in such expenditure were assumed to have come from, or gone into savings. 3.12 For the 17th series, National Accounts data has been used to derive expenditure for some of the CPI ECs, representing a change from the data sources used previously. These changes result in consistency with the data sources to be used under annual re–weighting of the CPI from December quarter 2018, and were brought forward to better position the CPI for this shift. These changes have been earlier communicated by the ABS in Information Paper: Increasing the Frequency of CPI Expenditure Class Weight Updates (cat. no. 6401.0.60.002). ### Under–reporting of alcohol and tobacco expenditures in the HES 3.13 Historically, HES expenditure on alcohol and tobacco is under–reported when compared to information from other sources. As a result, HES estimates are adjusted for under–reporting based on factors derived at the national level using National Accounts HFCE data. These factors are applied to the HES expenditure estimates for each capital city. The 2015-16 HES estimated expenditure for alcohol at a little under half, and tobacco at a little over one third of the respective National Accounts estimates. 3.14 As households do not always separately identify alcohol and meal expenditures when reporting expenditure on restaurant meals in the HES, a small adjustment is made using the proportion of reported meal expenditure that is alcohol, estimated from an analysis of HES unit records. Meal expenditure is reduced by the proportion of reported meal expenditure that is alcohol, with the difference then included in expenditure on alcohol. This adjustment does not impact overall household expenditure. ### Audio, visual and computing equipment 3.15 The 2015-16 HES data provided the latest information on household expenditure on Audio, visual and computing equipment which was then price updated to the September quarter 2017. However, for Audio, visual and computing equipment this approach may lead to underestimation of the weight in the CPI and SLCIs due to the relatively high volume growth in the quality (size and features) of these high technology goods compared to other products. Therefore, a volume increase of around 12% has been calculated from the National Accounts HFCE components between 2015-16 and September quarter 2017. 3.16 As noted in paragraph 3.7, some expenditures are collected in the HES as recalled items rather than diary entries. To the extent that prices for these items change between the time the household purchased them and their inclusion in the HES, expenditures will not accurately reflect the underlying quantities acquired during the HES reference year. 3.17 To address this, adjustments are made for items where the recall period is the last twelve months, such as education and overseas holiday travel. No adjustments are made for items where the recall period is the last three months, since these adjustments would be small. Additionally, no adjustment is made for items where the recall period is the last payment, as these typically have a short billing cycle (often quarterly), or options to pay periodically (e.g. local government rates). 3.18 For information on how recall adjustments are calculated, refer to paragraphs 6.18 and 6.19 of Consumer Price Index: Concepts, Sources and Methods, 2016 (cat. no. 6461.0). ### Salary sacrifice 3.19 Salary sacrifice is an arrangement between an employee and employer whereby part of the employee's pre–tax cash salary is traded for non–cash benefits. Conceptually, these arrangements should be captured in both gross wages and salaries, and household expenditure. 3.20 The items that have been adjusted for salary sacrifice include motor vehicles. To ensure the expenditure on motor vehicles includes all motor vehicles purchases (i.e. including via salary sacrifice), adjustments are made to the relevant HES items. For that reason, salary sacrifice amounts reported against motor vehicles are allocated to motor vehicle purchases, registration, insurance, motor vehicle repair and servicing, and automotive fuel. 3.21 The HES data was compared across capital cities and over time to validate the 17th series expenditures at the expenditure class level. The HES expenditure in 2009-10 was revalued to 2015-16 dollars to derive the volume changes between the two HES reference years and compared to the 2015-16 HES. 3.22 A number of unit record adjustments were made, in particular to the smaller capital cities where HES sample sizes are smaller and, in general, the standard errors are larger. The outlier adjustment method used was winsorisation, which involves replacing an unrepresentative expenditure by the next largest estimate. Where unit record outliers could not be identified, differences were further investigated. A small number of volume changes could not be validated, resulting in adjustments using either alternative volume data or based on market intelligence. ### New dwelling purchase by owner-occupiers 3.23 New dwelling purchase by owner–occupiers in the CPI includes the net additions of household sector dwellings as a measure of owner–occupier housing costs. This includes new homes (excluding land) and major improvements. Sales of houses that take place between households (generally established dwellings) are excluded so that the weights relate only to net additions to the housing stock arising from household purchases from other sectors (i.e. from businesses such as builders and developers). Expenditure on New dwelling purchase by owner–occupiers comprises of four components: owner–occupied housing, first home owners’ grants, alterations and additions, and installed appliances. 3.24 To derive the owner–occupied housing component, expenditure is estimated by multiplying the average value of private dwelling completions for the reference period by the change in the owner-occupied housing stock. 3.25 The average value of private dwelling completions for 2015-16 is obtained from Building Activity, Australia (cat. no. 8752.0). 3.26 The change in the owner–occupied dwelling stock is sourced from National Accounts HFCE estimates. This differs to the 16th series where the change was derived using 2006 Census of Population and Housing capital city counts of owner–occupied households, moved forward using household projections from Household and Family Projections, Australia (cat. no. 3236.0). 3.27 Consistent with standard practice relating to the inclusion of subsidies in the CPI, subsidies paid to first home buyers are treated as negative expenditure and subtracted from the new dwelling purchase by owner–occupiers house acquisition expenditure. 3.28 Expenditure on alterations and additions is derived from the alterations and additions component of Private GFCF from the National Accounts. Expenditure on installed appliances is sourced from HFCE data. Both items are added to the estimate for house acquisition to provide the total expenditure on New dwelling purchase by owner–occupiers. This differs from the 16th series, where both items were derived from the HES. ### Motor vehicles 3.29 The weight for Motor vehicles in the CPI and SLCIs is derived from National Accounts HFCE data. This weight reflects purchases of new cars, transfer of used cars to the household sector (from business or government) and the service fee from the transfer of second hand cars. ### Tertiary education 3.30 Expenditure on higher education in the HES includes Higher Education Loan Program (HELP) payments made by households upfront, plus any HELP repayments made through the taxation system during the reference period. This measure aligns with the outlays approach used for the SLCIs, however is not consistent with the concept of an acquisitions–based CPI, where expenditures should reflect the cost to households of the education service acquired during the reference period. The CPI scope includes the actual payments made during the period (upfront payments), plus fees for education services acquired during the period, but deferred to be paid at a later date. 3.31 To align the household expenditure on tertiary education fees in the CPI, HELP expenditures are calculated using data from the Department of Education and Training on total upfront and deferred fees, and the number of students paying HELP loans. ### Insurance 3.32 The Insurance EC covers comprehensive insurance for dwellings (including contents), motor vehicles and compulsory third party (CTP) insurance. For the purpose of measuring household price inflation, the weight for insurance in the CPI should reflect the cost of the service provided by insurers (gross premiums less claims), rather than the value of gross premiums paid. The latter is reported in the HES. 3.33 Expenditure on contents, motor vehicle and CTP insurance are derived from National Accounts HFCE data. The insurance for dwellings component is excluded from HFCE as it is considered intermediate consumption in the National Accounts. Expenditure on insurance for dwellings is instead sourced from National Accounts estimates of intermediate consumption of the Ownership of dwellings industry. These National Accounts estimates align with the conceptual basis of Insurance in the CPI. 3.34 This differs from the 16th series where HES gross premiums were adjusted onto a net basis using information collected by the Australian Prudential Regulation Authority (APRA) and from insurance companies. 3.35 Expenditures funded by claims are added back to the appropriate items. The data source has been changed to be consistent with National Accounts data. This differs to the 16th series, where claims–to–premiums ratios were calculated using APRA and insurance company data, and then applied to the HES gross premiums. 3.36 It should be noted that HES estimates of insurance are used in deriving the expenditure weights in the SLCIs. As the SLCIs are measured on an outlays basis, the weight of Insurance reflects the gross value of premiums paid by households. ### Financial services 3.37 Expenditure on financial services in the CPI cannot be sourced from the HES as it is either not directly observable or the HES did not capture the transactions in sufficient volumes or detail. The Financial services sub–group includes two expenditure classes: Deposit and loan facilities (direct charges) and Other financial services. ### Deposit and loan facilities (direct charges) 3.38 Expenditure on Deposit and loan facilities (direct charges) is determined through the use of administrative data sets (obtained from financial institutions and government reporting agencies) of financial institution fees and charges for Australian households. ### Other financial services 3.39 Other financial services include real estate agent services, legal and conveyancing services, stockbroking services and taxes on property transfers (stamp duty). 3.40 The real estate fees component of the National Accounts Private GFCF ownership transfer costs series is used to derive expenditure on real estate agent services. This represents a change from the 16th series, where expenditure was derived from property transaction data over the 2009-10 period and unpublished ABS survey data on real estate agents’ fees. 3.41 Expenditure on legal and conveyancing services is also derived from the Private GFCF ownership transfer costs series from National Accounts. 3.42 National Accounts HFCE data is used to derive an estimate of household expenditure on stockbroking services. 3.43 Expenditure on taxes on property transfers is compiled using data supplied by the State and Territory Revenue Offices. ### Revaluing expenditure to the link period 3.44 The expenditure weights derived from the HES are based on expenditures (i.e. price x quantity) in 2015-16 (the weight reference period). These new expenditure patterns will not be introduced into the CPI and SLCIs until the December quarter 2017 (with September quarter 2017 as the link period). Prior to implementation, in line with current CPI and international practice, the expenditures have been revalued to the September quarter 2017 to preserve the underlying quantities, but take into account the price changes that have occurred between the weight reference and link periods. 3.45 The calculation of the revalued estimates involves taking the 2015-16 expenditures and multiplying them by revaluation factors. These factors are derived as the ratio of the component’s September quarter 2017 price index to the average of its quarterly price indexes for 2015-16. ## 17th series expenditure weights 4.1 The CPI and SLCI weights reflect the relative expenditures of the CPI population group and SLCI sub–groups. The weights reflect average expenditure of households and not the expenditure of an 'average household'. The household average weekly expenditure (AWE) and corresponding 17th series CPI weights for the CPI groups are shown in Table 4.1. ### Table 4.1 - 17th series CPI, average weekly expenditure and weights, September quarter 2017, weighted average of eight capital cities CPI groupAverage weekly expenditure (2015-16 quantities, September quarter 2017 prices) (a) CPI weight $% All groups CPI1,594.18100.0 Food and non–alcoholic beverages256.5516.09 Alcohol and tobacco113.027.09 Clothing and footwear56.563.55 Housing361.4922.68 Furnishings, household equipment and services149.629.39 Health86.575.43 Transport164.5110.32 Communication42.702.68 Recreation and culture202.6212.71 Education68.054.27 Insurance and financial services92.505.80 a. Derived from 2015-16 ABS Household Expenditure Survey and other sources. Note: Any discrepancies between totals and sums of components in this table are due to rounding. 4.2 The 17th series CPI weights and household average weekly expenditure by group, sub–group and expenditure class as at September quarter 2017 are shown in Appendix 1 and in the data cube Consumer Price Index: 17th Series Weighting Pattern (cat. no. 6473.0). For the SLCIs, this information is available from Selected Living Cost Indexes: 17th Series Weighting Pattern (cat. no. 6474.0). 4.3 Total household expenditure in the CPI basket increased by 16.3% from$1,371.30 per week in 2009-10 (at June quarter 2011 prices) to $1,594.18 in 2015-16 (at September quarter 2017 prices). The All groups CPI increased 14.3% over the same period, while wages growth was 19.3% (Wage Price Index, cat. no. 6345.0). Table 4.2 summarises the changes in expenditure by group. ### Table 4.2 - Average weekly expenditure between The 16th And 17th series CPI CPI group16th series average weekly expenditure (2009-10 quantities, June quarter 2011 prices) (a) 17th series average weekly expenditure (2015-16 quantities, September quarter 2017 prices) (b) Percentage change$$% All groups CPI1,371.301,594.1816.3 Food and non–alcoholic beverages230.87256.5511.1 Alcohol and tobacco96.87113.0216.7 Clothing and footwear54.5856.563.6 Housing305.75361.4918.2 Furnishings, household equipment and services124.79149.6219.9 Health72.5686.5719.3 Transport158.39164.513.9 Communication41.8142.702.1 Recreation and culture172.30202.6217.6 Education43.6768.0555.8 Insurance and financial services69.7192.5032.7 a. Derived from 2009-10 ABS Household Expenditure Survey and other sources. b. Derived from 2015-16 ABS Household Expenditure Survey and other sources. Note: Any discrepancies between totals and sums of components in this table are due to rounding. ### Changes in weighting patterns 4.4 A detailed comparison of the 16th and 17th series CPI weights is presented in Appendix 2. Before analysing the changes to the weighting patterns over time, a number of points should be noted. ### Quantities underlying the weights are fixed 4.5 Although the weights are expressed in terms of expenditure shares, it is not the expenditure shares (where expenditure is given by the product of quantity and price) that are held constant (or fixed) from period to period. What are held constant are the quantities of products underpinning these expenditures. Weights are presented in expenditure terms because it is not possible to present quantity weights in a comparable way. The relative expenditure shares of items will change over time in response to changes in relative prices. The weights in the 17th series CPI and SLCIs generally relate to expenditures in 2015-16. These have been revalued using price movements to September quarter 2017 (the 'link' quarter) prices, maintaining fixed '2015-16 quantities'. For more information see Chapter 4: Price Index Theory in Consumer Price Index: Concepts, Sources and Methods (cat. no. 6461.0). ### Weights are relative 4.6 The weight of an expenditure class depends on how expenditure on that class compares to total expenditure (i.e. expenditure shares). If the increase in expenditure on a particular expenditure class in the reference period is greater than the increase in total expenditure between two series, the weight of that expenditure class will increase. For example, between the 16th and 17th series, the expenditure share on 'Restaurant meals' in the CPI increased from 2.81% to 3.32%, driven by an increase in average weekly expenditure of 37.3%. Conversely, if the increase in expenditure on a particular expenditure class in the reference period is less than the increase in total expenditure between two series, the weight of that expenditure class will decrease. For example, in the 17th series the expenditure on 'Waters, soft drinks and juices' increased by less than the increase in overall expenditures. As a result, the weight fell from 0.87% in the 16th series to 0.75% in the 17th series. ### Changes in weights between the 16th and 17th series 4.7 The changes in CPI and SLCI weights between the 16th and 17th series can be broken down into price and volume effects. The volume change captures both quality and quantity changes between the reference years 2009-10 and 2015-16. The volume changes were calculated by removing the price change (corresponding price index measure) between the two periods. The corresponding CPI and SLCI price movements were used as the measures of price change. 4.8 For the CPI population, households continue to spend the most on Housing, followed by Food and non–alcoholic beverages and Recreation and culture. Although Food and non–alcoholic beverages remains one of the most heavily weighted CPI groups, it fell as a proportion of household spending between the 16th and 17th series. Communication and Clothing and footwear represent the smallest portions of household expenditure. 4.9 The changes in CPI weights and average weekly expenditures for a selected number of groups and ECs are discussed in more detail below. All analysis refers to the weighted average of the eight capital cities. ### Food and non–alcoholic beverages group 4.10 Despite average weekly expenditure rising by$25.68, the weight of the Food and non–alcoholic beverages group decreased 0.75 percentage points (pp) to 16.09%. This reflects the strong competition that has occurred on food items over recent years, which has kept prices and expenditure growth relatively low. Compared to the 16th series, weights fell across most food products. 4.11 The weight for Fruit fell from 1.60% to 1.07%. Average weekly expenditure decreased 22.1% from $21.97 to$17.11. The 16th series weight for Fruit was impacted by adverse weather conditions, which affected supply and pushed up prices. These conditions have not been as prevalent or as long–lived during the 17th series, resulting in the weight for Fruit returning to more normal levels. 4.12 Partially offsetting the falls was Restaurant meals, which recorded the strongest increase in weight within the group (+0.51pp). Average weekly expenditure increased from $38.55 to$52.94. This is supported by strong price and volume growth, as consumer preferences shift from goods towards experiences. ### Housing group 4.13 Average weekly expenditure on Housing increased by 18.2% between the 16th and 17th series, from $305.75 to$361.49. Rents and Electricity were the major contributors to the increase in average weekly expenditure. 4.14 A moderate increase in the weight of Housing was recorded (+0.38pp), with a greater proportion of expenditure on Rents and Utilities partially offset by a fall for New dwelling purchase by owner–occupiers (Graph 4.1). 4.15 The weight of Utilities, comprising Water and sewerage, Electricity, and Gas and other household fuels, increased 0.45pp to 4.06%. Average weekly expenditure rose 30.8%, from $49.45 to$64.66. This increase was predominantly price driven, with prices rising 45.6% between 2009-10 and 2015-16. Higher wholesale and network costs have contributed to the rise. ### Detailed information: In the CPI, owner–occupied housing is represented by purchases of new dwellings (net additions to the housing stock) and the increase in the volume of housing due to renovations and extensions. This can be a challenging concept to understand. One way to think about it is the following. The CPI measures price inflation for the household sector. Therefore it is necessary to consider the purchases of dwellings between the household sector and other sectors of the economy, rather than within the sector. From this perspective, it is only purchases of newly built dwellings and those dwellings that have been acquired by households from outside the sector (e.g. private purchases of houses previously owned by the government) that are relevant. Purchases of established dwellings generally occur between households and are excluded. Additionally, the CPI is interested in measuring the prices of consumption goods and services. Land is considered an investment purchase, as it does not deteriorate over time, and is therefore out of scope. This leaves the CPI to only measure the price of new dwelling structures. New dwelling purchase by owner–occupiers is the major component of Housing costs and household spending overall for the CPI population. However, its weight fell between the 16th and 17th series, from 8.67% to 7.78%, with average weekly expenditure increasing by only $5.21. Although there has been an overall increase in the rate of additions to the owner–occupier dwelling stock since 2009-10, driven by strong building activity over recent years, there has also been a compositional shift, led by strong price growth in detached houses, towards cheaper apartment living. The proportion of apartment construction approvals has risen from 18.2% to 34.7% of total new dwelling approvals between 2009-10 and 2015-16 (Building Approvals, Australia (cat. no. 8731.0)) . The increase in apartment construction has delivered dwellings that are less expensive than low density housing, due to increased supply and lower construction costs brought on by cheaper inputs. Coupled with price growth for other residential construction rising at a much slower pace compared to house construction between 2009-10 and 2015-16 (7.4% vs. 17.2%, Producer Price Indexes), this has resulted in a decrease in the weight of New dwelling purchase by owner–occupiers in the CPI. Conversely, Rents, the second most significant component of the CPI and Housing group increased in weight between the 16th and 17th series, from 6.71% to 7.22%. Average weekly expenditure rose 25.1%, from$92.01 to $115.12. It should be noted that this value represents an average expenditure across the entire CPI population, and not just households that rent. The increase in the weight for Rents was due to rises in both prices and volumes. Strong growth in house prices over the last 5 years has led to an increase in the proportion of renters in Australia’s capital cities, pushing up expenditure on rents. 2016 Census data shows that 30.2% of occupied private dwellings are rented, up from 28.8% in 2011. The strong demand for rental properties has also impacted prices, with price growth of 20.2% between 2009-10 and 2015-16. ### Table – Weights for housing group, 16th and 17th series comparison, CPI Component 17th series weight (a) % 16th series weight (a) % Change in weight from 16th series pp Housing group22.6822.30+0.38 New dwelling purchase by owner–occupiers7.788.67-0.89 Rents7.226.71+0.51 a. Expenditure as a proportion of total household spending. ### Furnishings, household equipment and services group 4.16 Average weekly expenditure on Furnishings, household equipment and services increased by 19.9% to$149.62. This resulted in the weight of the group increasing from 9.10% to 9.39%. 4.17 Child care was the predominant contributor to the rise, increasing as a proportion of household expenditure from 0.69% to 1.35%. This was partially offset by falls in weights for a number of the goods components, including Furniture (-0.24pp), Household textiles (-0.12pp) and Major household appliances (-0.09pp), driven by subdued price growth as a result of retail competition and imports. ### Detailed information: Child care in the CPI and SLCIs encompasses services provided at community, private and family–based child care establishments. Both full–time and part–time care are included. Expenditure is measured on an out–of–pocket basis, i.e. gross fees payable, less any subsidies households receive on child care services. The expenditure share of Child care in the CPI has risen from 0.69% to 1.35% between the 16th and 17th series. Average weekly expenditure increased by 127.1%, from $9.47 to$21.51. While this figure might appear low, it should be noted that it represents the average weekly expenditure (on a net basis) of all households in the CPI population, not just those who use child care services. This rise in the expenditure and weight of Child care is driven by increased demand, which has also resulted in significant upward pressure on prices. Contributing to increased demand has been rising workforce participation, particularly for women. Over the last 20 years, the participation rate of women in the workforce has increased from 53.8% in January 1997 to 59.1% in January 2017 (Labour Force, Australia, cat. no. 6202.0). Between 2009-10 and 2015-16, the increase has been around 0.8 of a percentage point. The rise in workforce participation has contributed to a strong increase in the number of children in approved care, as well as increased hours for those in care (Early Childhood and Child Care in Summary, Department of Education and Training). Approved care refers to care provided by Long Day Care, Family Day Care and In-Home Care, Outside School Hours and Occasional Care services. In particular, the number of children in approved care increased 43.5% between September quarter 2009 and June quarter 2016. While pushing up costs for families, this is also resulting in increased costs for child care centres which are being passed on to parents in the form of higher fees. Also contributing to price growth has been changes in industry standards, including higher qualification requirements for teachers in early childhood care (implemented on 1 January 2014) and increased educator–to–child ratios (implemented on 1 January 2016). Overall, prices for child care have risen 60.0% between 2009-10 and 2015-16, the largest rise of all ECs apart from Tobacco. The rise in expenditure, driven by higher gross fees and volumes, has more than offset increases in government financial assistance for child care between the 16th and 17th series, resulting in a significant increase in the weight of Child care in the CPI. In terms of the SLCIs, Employee households are the most likely to use child care services, and therefore were the most heavily impacted by these conditions. The expenditure share of Child care rose 0.90pp for Employee households, to 1.72% of total expenditure. ### Table - Weight of child care, 16th and 17th series comparison, CPI and by household type Household type 17th series weight (a) % 16th series weight (a) % Change in weight from 16th series pp CPI1.350.69+0.66 PBLCI (b)0.570.26+0.31 Employee households1.720.82+0.90 Age pensioner households--- Other government transfer recipient households1.050.44+0.61 Self–funded retiree households--- a. Expenditure on child care as a proportion of total expenditure for each household type. b. PBLCI is an aggregation of Age Pensioner and Other government transfer recipient households. ### Health group 4.18 Although the Health group recorded a moderate increase in weight from the 16th series (5.29% to 5.43%), there has been a slight shift in expenditure share away from Pharmaceutical products, which decreased from 1.17% to 1.03%, predominantly due to subdued price growth. 4.19 In contrast, the weight for Medical and hospital services rose from 3.42% to 3.73%, and is the predominant driver of Health costs increasing as a proportion of overall household spending. Average weekly expenditure increased by 27.0%, from $46.85 to$59.49. The strong rise in private health insurance premiums over this period was the major contributor to the increase. Between 2010 and 2016, premiums increased 5.71% per year on average at the industry weighted level (Department of Health). ### Detailed information: Pharmaceutical products are a fundamental component of the health system and are used by a large number of households to prevent, alleviate and cure illness. With an ageing population, there is a greater reliance on these medicines. As a result, changes in prices will have a relatively large effect on household out–of–pocket expenses, that is, the final price the household pays after subsidies. Price growth of pharmaceutical products has been fairly subdued compared to other health costs such as Private Health Insurance, which has seen significant price increases since 2009-10. Weak price growth for pharmaceuticals reflects additional medicines being added on to the Pharmaceutical Benefits Scheme (PBS) schedule, as well as government initiatives such as Simplified Price Disclosure. In 2015-16 alone, there were 370 new and amended PBS listings (Department of Health 2015-16 Annual Report). This included high cost medicines for the treatment of breast cancer, melanoma and hepatitis C. The Simplified Price Disclosure program builds on the changes to price disclosure policy made in 2012 under Expanded and Accelerated Price Disclosure (EAPD), and allows PBS prices to be adjusted to market prices more quickly than the previous approach. This measure came into effect in 2014. A more recent initiative allowing pharmacists to offer a discount of up to $1.00 on scripts where a co–payment is made (from 1 January 2016) has also contributed to the fall in weight between the 16th and 17th series. Combined with increased retail competition in the industry, these government initiatives are helping to subdue the rate of price growth and reduce households’ out–of–pocket costs. The following table presents the proportion of household expenditure on pharmaceutical products by household type and for the CPI. Age pensioners spend the greatest proportion of their expenditure on pharmaceutical products, more than double the proportion spent by CPI households, but also showed the largest fall in weight between the 16th and 17th series, as they benefit most from these government programs. ### Table - Weight of pharmaceutical products, 16th and 17th series comparison, CPI and by household type Household type 17th series weight (a) % 16th series weight (a) % Change in weight from 16th series pp CPI1.031.17-0.14 PBLCI (b)1.922.06-0.14 Employee households0.951.06-0.11 Age pensioner households2.493.06-0.57 Other government transfer recipient households1.441.39+0.05 Self–funded retiree households2.002.08-0.08 a. Expenditure on pharmaceutical products as a proportion of total expenditure for each household type. b. PBLCI is an aggregation of Age Pensioner and Other government transfer recipient households. ### Transport group 4.20 Transport costs fell as a proportion of total household expenditure, recording the largest fall of all the groups in the CPI (-1.23pp). Average weekly expenditure on Transport rose by only 3.9%, from$158.39 to $164.51. 4.21 The main driver was Automotive fuel, which recorded a fall in weight of 0.77pp to 2.78%. Average weekly expenditure decreased 8.8% from$48.67 to $44.39. This was predominantly a result of falls in the world oil price. 4.22 Motor vehicles also recorded a fall in weight, with average weekly expenditure remaining relatively unchanged between the 16th and 17th series. Vehicles have become cheaper over the period, driven by increased competition between brands for sales, manufacturing changes which have enabled cars to be built more cheaply, and a higher proportion of imported cars being sold. ### Education group 4.23 The Education group recorded the largest increase in weight in the 17th series CPI, up 1.09pp to 4.27%, although it still remains a small component of household spending. Secondary education recorded the largest increase, up 0.44pp to 1.70%. This was followed by Preschool and primary education, up 0.40pp to 0.92%, and Tertiary education, up 0.25pp to 1.65%. ### Q: What factors are behind the Education group recording the largest increase in weight between the 16th and 17th series CPI? ### A: Prices and enrolment numbers have increased across all levels of education between 16th and 17th series. ### Detailed information: The cost of education at any level can be driven by several factors such as; changes in student numbers, government regulatory policies on education or funding, or standards (e.g. increased teacher–to–student ratios, services or syllabus). For CPI purposes, the Education group comprises all expenditure on primary, secondary and tertiary education, and preschool services. Both private and public institutions are included. Education is a necessity and compulsory at certain levels, so it is very difficult for households to avoid any price changes. Despite the availability of schools and universities, households may not substitute in response to price changes. This is because parents might have a particular preference in the type or location of their child’s education, or because prices change similarly across the various institutions available to them. Any growth in student enrolment puts additional pressure on schools, resulting in increased costs which are generally passed on. The number of student enrolments increased between 2009-10 and 2015-16. As of May 2016, nearly 20% of the population were enrolled in some form of study, with the proportion of people studying increasing across most of the demographics in the past 10 years (Education and Work, Australia, cat. no. 6227.0). At the primary and secondary education levels, the number of enrolments increased 9.0% between 2009 and 2016 (Schools, Australia, cat. no. 4221.0). Additionally, between 2009 and 2016, there has been a slight shift in preference towards non–government schools, which are typically more expensive. The number of students enrolled in non–government schools (catholic and independent) increased 10.4%, compared to an 8.2% rise for government schools. This trend has started to reverse in the last two years. The increased enrolments have contributed to higher fees for students. Prices rose across all the ECs between 2009-10 and 2015-16: Preschool and primary education (+37.7%), Secondary education (+41.6%) and Tertiary education (+33.9%). ### Table - Weights for education group, 16th and 17th series comparison, CPI Component 17th series weight (a) % 16th series weight (a) % Change in weight from 16th series pp Education group4.273.18+1.09 Preschool and primary education EC0.920.52+0.40 Secondary education EC1.701.26+0.44 Tertiary education EC1.651.40+0.25 a. Expenditure as a proportion of total household spending ### Expenditure weights for the SLCIs 4.24 The SLCIs are produced as a by-product of the CPI, with the main conceptual difference being that the SLCIs are constructed on an outlays basis, while the CPI is constructed on an acquisitions basis. The SLCIs are designed to measure the change in out–of–pocket living expenses of four Australian household types: Employee, Age pensioner, Other government transfer recipient, and Self–funded retirees. The PBLCI combines the Age pensioner and Other government transfer recipient household types. See paragraphs 3.3 to 3.5 for SLCI concepts and conceptual differences. 4.25 At the 8 caps level, average weekly expenditure grew for all population sub–groups between the 16th and 17th series (Graph 4.2). The increase ranged from$71.42 for PBLCI households, to 204.75 for Employee households. 4.26 Housing and Food and non–alcoholic beverages remain the significant components of household expenditure for most population sub–groups. All sub–groups recorded an increase in weight for Housing, driven by Rents and Utilities. Other government transfer recipients recorded the most significant rise, due to having a greater proportion of renters. 4.27 The weight of Health also increased across all population sub–groups, with Self–funded retirees and Age pensioners showing the largest movements, increasing from 8.53% to 10.31% and 8.85% to 10.22% respectively. These rises were driven by Medical and hospital services, following significant increases in private health insurance premiums over the period. 4.28 Conversely, Clothing and footwear has fallen as a proportion of expenditure across all population sub–groups. This is driven predominantly by price falls in garments as a result of increased competition from online and international entrants to the Australian retail market. 4.29 Changes in the weights for Insurance and financial services varied across the sub–groups, driven by the different proportions of owner–occupier and renter households. Employee and Other government transfer recipient households recorded falls in weight driven by lower interest charges, with the cash rate reaching record lows during 2015-16. Exposure to mortgages is lower for the remaining household types, and combined with increases in gross premiums for insurance, resulted in increases in their weights for Insurance and financial services. ### Q: Why do price changes in Utilities affect Age pensioner and Other government transfer recipient households relatively more than other households? ### A: Because Age pensioner and Other government recipient households spend the greatest proportion of their household budget on utilities. ### Detailed information: When the prices of products change, what’s important to consumers is: by how much did the price change; the proportion of the household budget spent on these products; and whether substitute products are available so consumers can avoid some of these price changes. Household Utilities are essential features of Australian dwellings. Utilities, for the purposes of the Australian CPI and SLCIs, relate to: Water and sewerage, Electricity, and Gas and other household fuels. Utilities are consumed by households during most home based activities, whether it’s boiling the kettle for a cup of tea, taking a shower or watching TV. The amount of water, electricity and gas consumed by households and their prices can significantly impact household budgets. In part this is because it’s very difficult for consumers to avoid price changes for utilities. That is, substitutes aren’t readily available. The proportion of the household budget spent on utilities is also important when prices change. The following table presents the proportion of household expenditure on utilities by household type and for the CPI. Age pensioner and Other government transfer recipient households (and subsequently Pensioner and beneficiary households) spend the greatest proportion of their household budget on utilities; significantly more than the proportion spent by Employee households. So when the price of utilities change, it is Age pensioner and Other government transfer recipient households that are most affected. ### Table - Weights of utilities, 16th and 17th series comparison, CPI and by household type Household type 17th series weight (a) % 16th series weight (a) % Change in weight from 16th series pp CPI4.063.61+0.45 PBLCI (b)6.285.48+0.80 Employee households3.943.28+0.66 Age pensioner households6.836.09+0.74 Other government transfer recipient households5.825.06+0.76 Self–funded retiree households5.094.03+1.06 a. Expenditure on utilities as a proportion of total expenditure for each household type b. PBLCI is an aggregation of Age Pensioner and Other government transfer recipient households ## Estimating the upper level substitution bias in the Australian CPI 5.1 Consumers’ purchasing patterns react to price change over time, where goods and services with high inflation are typically substituted with low inflation alternatives. Like most CPIs, the Australian CPI uses a fixed–base Laspeyres–type formula (also known as the Lowe index formula), which measures the change in the cost of purchasing the same basket of goods and services in the current period, as was purchased in a specified base period. This overstates the price change of the basket as it is not able to take account of the substitution consumers make in response to relative price change and changes in preferences, resulting in substitution bias. 5.2 With each release of the new CPI weights, the ABS constructs a retrospective superlative–type index which more closely reflects true inflation. This enables an estimate of the upper level substitution bias in the Australian CPI to be derived. This superlative index takes the weights from both the earlier and later periods into consideration, thereby accounting for substitution across goods and services (in this case expenditure classes). 5.3 In the past, the ABS has used the following methodology to derive an estimate of the substitution bias: • Construct Laspeyres–type (Lowe), Paasche–type and superlative Fisher–type indexes at the All groups CPI level, using the published CPI weights. These weights have been price updated from the period of the HES survey (1998-99, 2003-04 and 2009-10) to the link period, which is the quarter prior to the implementation of the weights (June quarter 2000, June quarter 2005 and June quarter 2011). • For the Paasche–type index, which requires current period weights, a linear model is applied between re–weighting periods to obtain quarterly weights. • An estimate of the upper level substitution bias is then obtained as the difference between the Fisher–type index (the geometric mean of the Laspeyres and Paasche) and the Laspeyres–type index, which represents the CPI. 5.4 As part of the 17th series review, the ABS conducted an investigation into the methodology used to estimate substitution bias. This has resulted in changes to the previous methodology, enabling more accurate estimates to be calculated. 5.5 The methodology applied in the 17th series is as follows: • Calculate financial year Laspeyres and Paasche–type indexes, instead of quarterly, using the original HES weights for each series of the CPI and financial year estimates of price change. Under this approach, the Laspeyres index is a true Laspeyres, and not a Lowe index as was previously the case. • For the Paasche index, the weights for each financial year in between re–weighting periods are interpolated using a linear model. • The geometric mean of the Laspeyres and Paasche approximates the Fisher. • The Fisher is compared to the Laspeyres index to estimate the level of substitution bias, consistent with international practice. 5.6 This approach results in a more accurate estimate of true inflation, due to the original financial year weights being used, and the period of the indexes and weights now aligning. 5.7 Using this methodology, the ABS has produced an upper level substitution bias estimate for the 1998-99 to 2015-16 period. The results reveal that the amount of bias in the Australian CPI is on average 0.22 of a percentage point per year between 1998-99 and 2015-16, due to the inability to take account of the upper level item substitution effect. This is lower than previously estimated (+0.24 of a percentage point between June 2000 and June 2011), predominantly due to the low inflationary environment over recent years. 5.8 The results also show that the average annual substitution bias increases at a faster rate the longer the period between re–weights. Table 5.1 illustrates that the average annual bias is 0.11 one year after a re–weight, increasing to 0.20 in the sixth year. Table 5.1 Average annual item substitution bias (a) Time since re-weightBias (Laspeyres - Fisher) 1 year0.11 2 years0.17 3 years0.17 4 years0.18 5 years0.21 6 years (b)0.20 1. This takes the average of the annual substitution bias for the 1998-99 to 2003-04, 2003-04 to 2009-10 and 2009-10 to 2015-16 periods. 2. The six year average annual substitution bias is only based on the 2003-04 to 2009-10 and 2009-10 to 2015-16 periods. 5.9 With the move to annual re–weighting, the ABS will continue to review the methodology for producing estimates of substitution bias. While the weights will be updated more frequently in future, there are other challenges such as differing data sources that need to be addressed. The ABS will conduct these investigations and provide an update of intentions in due course. ## Upcoming work 6.1 The weights detailed in this information paper will be implemented into the CPI and SLCIs in the December quarter 2017 publications, due to be released on 31 January 2018 and 7 February 2018 respectively. 6.2 Coinciding with the update of the weights will be the introduction of new CPI index methods (known as multilateral methods) for 28 ECs. These methods enable a census of products to be used from transactions datasets and the weighting of prices at the product level, enhancing the quality of the CPI. For further information on this change, see Information Paper: An Implementation Plan to Maximise the Use of Transactions Data in the CPI (cat. no. 6401.0.60.004). 6.3 From 2018, the Australian CPI will be re–weighted annually in December quarters. The primary data source for updating the weights in inter–HES years will be HFCE data from the National Accounts. The approach and plan to annually re–weight the CPI was detailed in the following information papers: 6.4 Due to household income characteristics not being available from the HFCE data, it had been proposed to continue to re–weight the SLCIs six–yearly using HES data. The ABS is continuing to investigate methods to annually re–weight the SLCIs, which was raised by key stakeholders in consultations as further research to consider. Further information on the re–weighting of the SLCIs will be published in 2018. 6.5 In relation to the Deposit and loan facilities (indirect charges) index, also known as Financial Intermediation Services Indirectly Measured (FISIM), the ABS will continue to engage internationally to resolve the methodological challenges associated with its measurement. Although it had been intended to reintroduce FISIM into the headline CPI in time for the 17th series, this has not been possible due to the lack of an internationally accepted methodology for its measurement. The ABS will continue to produce the analytical series ‘All groups CPI including Deposit and loan facilities (indirect charges)’. Once the methodology and data are sufficiently robust to produce high quality estimates, the ABS will consider reintroducing FISIM into the headline CPI. ## Appendix 1 - 17th series CPI, average weekly expenditure and weights ### Show all Average weekly expenditure for theWeighted average of eight capital citiesin September quarter 2017 Percentage contributionto the All groups CPI inSeptember quarter 2017% FOOD AND NON–ALCOHOLIC BEVERAGES 256.55 16.09 Group Sub-group Expenditure class Bread 8.56 0.54 Cakes and biscuits 10.42 0.65 Breakfast cereals 2.06 0.13 Other cereal products 2.63 0.17 Beef and veal 7.52 0.47 Pork 4.91 0.31 Lamb and goat 3.50 0.22 Poultry 6.82 0.43 Other meats 5.88 0.37 Fish and other seafood 6.23 0.39 Milk 5.78 0.36 Cheese 4.70 0.29 Ice cream and other dairy products 5.34 0.34 Fruit 17.11 1.07 Vegetables 20.43 1.28 Eggs 1.96 0.12 Jams, honey and spreads 2.13 0.13 Food additives and condiments 4.68 0.29 Oils and fats 2.68 0.17 Snacks and confectionery 14.95 0.94 Other food products n.e.c. 8.84 0.55 Coffee, tea and cocoa 3.71 0.23 Waters, soft drinks and juices 12.01 0.75 Restaurant meals 52.94 3.32 Take away and fast foods 40.76 2.56 Spirits 13.46 0.84 Wine 28.35 1.78 Beer 29.69 1.86 Tobacco 41.51 2.60 Garments for men 9.64 0.60 Garments for women 20.23 1.27 Garments for infants and children 5.51 0.35 Footwear for men 2.26 0.14 Footwear for women 5.08 0.32 Footwear for infants and children 1.20 0.08 Accessories 10.76 0.68 Cleaning, repair and hire of clothing and footwear 1.88 0.12 Rents 115.12 7.22 New dwelling purchase by owner–occupiers 124.07 7.78 Maintenance and repair of the dwelling 34.25 2.15 Property rates and charges 23.39 1.47 Water and sewerage 16.28 1.02 Electricity 34.57 2.17 Gas and other household fuels 13.81 0.87 Furniture 22.19 1.39 Carpets and other floor coverings 4.86 0.31 Household textiles 7.87 0.49 Major household appliances 6.58 0.41 Small electric household appliances 5.28 0.33 Glassware, tableware and household utensils 6.84 0.43 Tools and equipment for house and garden 6.10 0.38 Cleaning and maintenance products 4.13 0.26 Personal care products 17.01 1.07 Other non–durable household products 21.04 1.32 Child care 21.51 1.35 Hairdressing and personal grooming services 14.80 0.93 Other household services 11.40 0.72 Pharmaceutical products 16.49 1.03 Therapeutic appliances and equipment 2.33 0.15 Medical and hospital services 59.49 3.73 Dental services 8.25 0.52 Motor vehicles 44.38 2.78 Spare parts and accessories for motor vehicles 11.65 0.73 Automotive fuel 44.39 2.78 Maintenance and repair of motor vehicles 30.83 1.93 Other services in respect of motor vehicles 21.53 1.35 Urban transport fares 11.73 0.74 Postal services 1.33 0.08 Telecommunication equipment and services 41.37 2.59 Audio, visual and computing equipment 19.44 1.22 Audio, visual and computing media and services 11.13 0.70 Books 3.92 0.25 Newspapers, magazines and stationery 7.69 0.48 Domestic holiday travel and accommodation 42.67 2.68 International holiday travel and accommodation 50.24 3.15 Equipment for sports, camping and open–air recreation 9.37 0.59 Games, toys and hobbies 12.84 0.81 Pets and related products 7.09 0.44 Veterinary and other services for pets 5.90 0.37 Sports participation 15.60 0.98 Other recreational, sporting and cultural services 16.73 1.05 Preschool and primary education 14.72 0.92 Secondary education 27.09 1.70 Tertiary education 26.25 1.65 Insurance 18.89 1.19 Deposit and loan facilities (direct charges) 9.56 0.60 Other financial services 64.04 4.02 a. Any discrepancies between totals and sums of components in this Appendix are due to rounding ## Appendix 2 - comparison of the 16th and 17th series CPI weighting patterns ### Show all 16th series17th series GroupPercentage contribution to the All groups CPI in June quarter 2011 % Percentage contribution to the All groups CPI in September quarter 2017 % Sub–group Expenditure class FOOD AND NON–ALCOHOLIC BEVERAGES16.84 16.09 Bread and cereal products 1.71 1.49 Cakes and biscuits 0.74 0.65 Breakfast cereals 0.18 0.13 Other cereal products 0.21 0.17 Meat and seafoods 2.29 2.19 Beef and veal 0.39 0.47 Pork 0.36 0.31 Lamb and goat 0.26 0.22 Poultry 0.49 0.43 Other meats 0.38 0.37 Fish and other seafood 0.41 0.39 Dairy and related products 1.15 0.99 Milk 0.42 0.36 Cheese 0.34 0.29 Ice cream and other dairy products 0.39 0.34 Fruit and vegetables 2.95 2.35 Fruit 1.60 1.07 Vegetables 1.34 1.28 Food products n.e.c. 2.17 2.21 Eggs 0.11 0.12 Jams, honey and spreads 0.14 0.13 Food additives and condiments 0.30 0.29 Oils and fats 0.17 0.17 Snacks and confectionery 0.97 0.94 Other food products n.e.c. 0.47 0.55 Non–alcoholic beverages 1.14 0.99 Coffee, tea and cocoa 0.27 0.23 Waters, soft drinks and juices 0.87 0.75 Meals out and take away foods 5.43 5.88 Restaurant meals 2.81 3.32 Take away and fast foods 2.62 2.56 ALCOHOL AND TOBACCO7.06 7.09 Alcoholic beverages 4.75 4.49 Spirits 0.91 0.84 Wine 1.64 1.78 Beer 2.20 1.86 Tobacco 2.32 2.60 Tobacco 2.32 2.60 CLOTHING AND FOOTWEAR3.98 3.55 Garments 2.52 2.22 Garments for men 0.74 0.60 Garments for women 1.47 1.27 Garments for infants and children 0.31 0.35 Footwear 0.61 0.54 Footwear for men 0.14 0.14 Footwear for women 0.34 0.32 Footwear for infants and children 0.13 0.08 Accessories and clothing services 0.86 0.79 Accessories 0.74 0.68 Cleaning, repair and hire of clothing and footwear 0.12 0.12 HOUSING22.30 22.68 Rents 6.71 7.22 Rents 6.71 7.22 New dwelling purchase by owner–occupiers 8.67 7.78 New dwelling purchase by owner–occupiers 8.67 7.78 Other housing 3.31 3.62 Maintenance and repair of the dwelling 2.05 2.15 Property rates and charges 1.26 1.47 Utilities 3.61 4.06 Water and sewerage 0.90 1.02 Electricity 1.99 2.17 Gas and other household fuels 0.72 0.87 FURNISHINGS, HOUSEHOLD EQUIPMENT AND SERVICES9.10 9.39 Furniture and furnishings 1.91 1.70 Furniture 1.63 1.39 Carpets and other floor coverings 0.28 0.31 Household textiles 0.61 0.49 Household textiles 0.61 0.49 Household appliances, utensils and tools 1.43 1.56 Major household appliances 0.50 0.41 Small electric household appliances 0.24 0.33 Glassware, tableware and household utensils 0.43 0.43 Tools and equipment for house and garden 0.26 0.38 Non–durable household products 2.86 2.65 Cleaning and maintenance products 0.29 0.26 Personal care products 1.11 1.07 Other non–durable household products 1.46 1.32 Domestic and household services 2.29 2.99 Child care 0.69 1.35 Hairdressing and personal grooming services 0.90 0.93 Other household services 0.69 0.72 HEALTH5.29 5.43 Medical products, appliances and equipment 1.32 1.18 Pharmaceutical products 1.17 1.03 Therapeutic appliances and equipment 0.14 0.15 Medical, dental and hospital services 3.97 4.25 Medical and hospital services 3.42 3.73 Dental services 0.56 0.52 TRANSPORT11.55 10.32 Private motoring 10.81 9.58 Motor vehicles 3.25 2.78 Spare parts and accessories for motor vehicles 0.99 0.73 Automotive fuel 3.55 2.78 Maintenance and repair of motor vehicles 1.67 1.93 Other services in respect of motor vehicles 1.35 1.35 Urban transport fares 0.74 0.74 Urban transport fares 0.74 0.74 COMMUNICATION3.05 2.68 Communication 3.05 2.68 Postal services 0.12 0.08 Telecommunication equipment and services 2.93 2.59 RECREATION AND CULTURE12.56 12.71 Audio, visual and computing equipment and services 2.53 1.92 Audio, visual and computing equipment 1.56 1.22 Audio, visual and computing media and services 0.98 0.70 Newspapers, books and stationery 1.08 0.73 Books 0.40 0.25 Newspapers, magazines and stationery 0.68 0.48 Holiday travel and accommodation 4.76 5.83 Domestic holiday travel and accommodation 2.47 2.68 International holiday travel and accommodation 2.29 3.15 Other recreation, sport and culture 4.20 4.24 Equipment for sports, camping and open–air recreation 0.61 0.59 Games, toys and hobbies 0.78 0.81 Pets and related products 0.38 0.44 Veterinary and other services for pets 0.40 0.37 Sports participation 0.94 0.98 Other recreational, sporting and cultural services 1.09 1.05 EDUCATION3.18 4.27 Education 3.18 4.27 Preschool and primary education 0.52 0.92 Secondary education 1.26 1.70 Tertiary education 1.40 1.65 INSURANCE AND FINANCIAL SERVICES5.08 5.80 Insurance 1.40 1.19 Insurance 1.40 1.19 Financial services 3.68 4.62 Deposit and loan facilities (direct charges) 0.76 0.60 Other financial services 2.92 4.02 ALL GROUPS100.00100.00100.00100.00100.00100.00 a. Any discrepancies between totals and sums of components in this Appendix are due to rounding ## Appendix 3 - calculating EC contributions to change with an annually re-weighted CPI ### Show all 1 The availability of annual HFCE data from the National Accounts provides the ABS with an opportunity to update CPI EC level weights more frequently. However, the annual re–weight of the Australian CPI will pose a challenge when calculating contributions to the annual percentage change in the All groups CPI. This is because the contribution will depend not only on changes in prices, but also changes in the weights. 2 To address this, the ABS investigated an approach to estimate the contributions of individual ECs to the annual percentage change of the All groups CPI under annual re–weighting. This methodology was published in Information Paper: An Implementation Plan to Annually Re–weight the Australian CPI (cat. no. 6401.0.60.005). 3 In the current CPI where the weights are fixed for a number of years, deriving the contribution of ECs to the annual rate of inflation does not pose a problem, since the annual rate of inflation is based on a single set of weights. The annual rate of inflation for any given period is derived as the percentage change between the index number in that period, and the index number from the corresponding quarter of the previous year. For example, the annual rate of inflation in March quarter 2019 is the percentage change between the March quarter 2019 and March quarter 2018 index numbers. 4 The proposed approach, stated below, derives an approximate expression for the annual rate of inflation that distinguishes between the contribution due to the percentage price changes of the ECs and changes in the weights of the ECs. For a single EC n, in March quarter 2019, the contribution can be written as: $$Cont_{na}^{2019Q1} \approx w_{n}^{2018 Q 1} \times \left(\frac{P_{n}^{2019 Q 1}}{P_{n}^{2018 Q 1}}-1\right)+ \frac{P_{n}^{2019 Q 1} / {P_{n}^{2018 Q 3}}} {\widehat{P}^{2019 Q 1}/{\widehat{P}^{2018 Q 3}}}\left(w_{n}^{2018 Q 3}-\widehat{w}_{n}^{2018 Q 3}\right)$$ where: $$w_{n}^{2018 Q 1}$$ = weight of EC n to All groups CPI in March quarter 2018 $$P_{n}^{2019 Q 1}$$ = price index of EC n in March quarter 2019 $$P_{n}^{2018 Q 1}$$ = price index of EC n in March quarter 2018 $$P_{n}^{2018 Q 3}$$ = price index of EC n in September quarter 2018 $$\widehat{P}^{2019 Q 1}$$ = price index of the All groups CPI in March quarter 2019 using the weights of the previous short–term series $$\widehat{P}^{2018 Q 3}$$ = price index of the All groups CPI in September quarter 2018 using the weights of the previous short–term series $$w_{n}^{2018 Q 3}$$ = weight of EC n to the All groups CPI in September quarter 2018 $$\widehat{w}_{n}^{2018 Q 3}$$ = weight of EC n to the All groups CPI in September quarter 2018 under the previous short–term series Detailed information on the decomposition is available from the Appendix of Information Paper: An Implementation Plan to Annually Re–weight the Australian CPI (cat. no. 6401.0.60.005). 5 The ABS has conducted an empirical analysis to assess the proposed methodology, using price indexes compiled from annually updated weights. The t-1 indexes from the Information Paper: Increasing the Frequency of CPI Expenditure Class Weight Updates (cat. no. 6401.0.60.002) formed the basis of this empirical test. As noted in this paper, these indexes span the period September quarter 2005 to September quarter 2015 and exclude the Deposit and loan facilities (direct charges) EC. 6 This proposed method was applied by decomposing the equation into the two components. The first component of the equation measures the contribution of an EC due to its annual percentage change. Summed across all ECs, this component is expected to be slightly higher than the annual inflation rate based on the chained index, as annually updating the weights most likely lowers measured inflation. The empirical results from the analysis support this relationship. 7 The second component measures the contribution of each EC to the annual inflation rate due to the change in its expenditure share, where the expenditure shares are made 'comparable' by price updating them to the link quarter. Summed across all ECs, this component is generally expected to be small and negative. The empirical results from the analysis support this relationship. 8 Lastly, summing the two components across all ECs approximates the annual rate of inflation in the All groups CPI exactly to 2 decimal points over the entire analysis period, demonstrating that the decomposition works well. ## Appendix 4 - update to 16th CPI review outcomes ### Show all This appendix provides an update on progress with the outcomes from the 16th series CPI review, detailed in Outcome of the 16th Series Australian Consumer Price Index Review (cat. no. 6469.0). Outcome Status 1.1 The principal purpose of the CPI is household inflation measurement and the acquisitions approach will remain the conceptual basis for compiling the CPI. Consistent with maintaining this conceptual basis, owner–occupied housing (OOH) will continue to be measured as the change in the price of gross fixed capital formation (GFCF of houses, net of land. A weighting pattern representative of all private households in the eight capital cities will continue to be used. Household inflation measurement continues to be principal purpose of the CPI. Consistent with this purpose, the acquisitions approach remains the conceptual basis for compiling the CPI. 1.2 The current quarterly publication of the outlays based Analytical Living Cost Indexes (ALCIs) and the Pensioner and Beneficiary Living Cost Index (PBLCI) will be maintained, and the current research to determine the need for improved coverage of outlets and products in the PBLCI will be completed. Where there is a clearly demonstrated need, and additional resources are provided, other complementary quarterly price indexes on an outlays basis will be produced for particular population subgroups on a case–by–case basis. The ALCIs and PBLCI publications were combined into a single product Selected Living Cost Indexes, Australia (cat. no. 6467.0) from the September quarter 2012 release. Since the 16th series, additional outlets and products have been added to the PBLCI to enhance the coverage and the representativeness of price movements. This is an ongoing process for the ABS and is addressed through a rolling sample and index review program. No user requirements for additional indexes compiled on an outlays basis have been identified. 1.3 There was significant demand for a monthly CPI. The ABS is persuaded there would be a significant benefit from more timely and responsive economic management if a CPI of equivalent quality to the current quarterly index were available monthly. Additional funding will be required to meet the costs involved in compiling a monthly index. In the absence of additional funding, the ABS has investigated alternative data sources and methods to facilitate the production of a monthly CPI. These include multilateral methods and data collection techniques such as webscraping. Additionally, as part of the CPI's rolling review program, prices which are currently collected and compiled on a non–monthly basis are being assessed to determine if monthly collection is suitable. For further information on which ECs are currently collected monthly, see Attachment 2: Price Collection Schedule of Enhancing the Australian CPI: A roadmap (cat. no. 6401.0.60.001). 1.4 a) The indirectly measured component of the Deposit and loan facilities index (i.e. financial intermediation services indirectly measured (FISIM)) will be removed from the headline CPI from the commencement of the 16th series in September quarter 2011. Complete 1.4 b) The Deposit and loan facilities index will comprise direct fees and charges only and will be renamed 'Deposit and loan facilities - direct fees' from the commencement of the 16th series in September quarter 2011. Complete 1.4 c) A new analytical series, comprising the All groups CPI inclusive of FISIM, will be published on a quarterly basis from the commencement of the 16th series in September quarter 2011. Complete 1.4 d) The methodology for measuring the price of FISIM will be refined for the analytical series, informed by international developments in this area. An information paper covering the developments in the measurement of FISIM and other financial services will also be released. The ABS has engaged internationally in attempts to resolve the measurement challenges associated with FISIM. However, many of the challenges identified as part of the 16th series remain, and at present there is no internationally endorsed methodology for the measurement of FISIM. As a result, the ABS will not reintroduce FISIM into the headline CPI for the 17th series. The ABS will continue to produce the analytical series 'All groups CPI including Deposit and loan facilities (indirect charges)', and work with our international partners in the resolution of measurement challenges. 1.4 e) The ABS will continue to work with data providers (financial institutions) to obtain the high quality, detailed data necessary to measure FISIM robustly. Data quality for the FISIM measure has improved since the 16th series review. The ABS maintains strong relationships with the financial institutions providing data for FISIM and continually works with these providers to ensure a clear understanding of the data. 1.4 f) A Deposit and loan facilities index comprising direct fees and FISIM will be re–introduced into the headline CPI when the ABS is satisfied that the methodology and data are sufficiently robust to produce high quality estimates. The ABS plans to reintroduce FISIM measurement within the CPI in time for the 17th series CPI. See response to 1.4 d) 1.5 The ABS will investigate methodologies for other significant financial services that are currently not covered in the CPI (e.g. superannuation charges) and introduce them into the CPI when the ABS is satisfied that the methodology and data are sufficiently robust to produce high quality estimates. Superannuation and other significant financial services are continuing to be investigated as part of the ABS's rolling review program, which ensures estimates are fit–for–purpose and representative. It is noted that financial services are particularly difficult to measure due to data availability and methodological challenges. 1.6 Subject to availability of the additional funding required, the frequency of CPI weight updates will be increased from six–yearly to four–yearly, via a more frequent Household Expenditure Survey (HES). In the absence of additional funding, the ABS has reprioritised and investigated the use of alternative data sources to enhance the quality of the CPI and enable more frequent re–weighting. From 2018, the CPI will be annually re–weighted using National Accounts HFCE data in inter–HES years. 1.7 To ensure a robust measure of the CPI, strategies to minimise possible sources of bias in the CPI will be continued (e.g. the use of scanner data will be explored). The ABS commenced a research program in 2015 aimed at enhancing the Australian CPI. As a result of this program, the ABS is moving to annual re–weighting of the CPI and implementing multilateral methods for 28 ECs from the December quarter 2017. Both of these changes will enhance the representativity and quality of the CPI. 1.8 The ABS will provide more information on the quality adjustment processes used in the CPI to better inform the public on circumstances where quality adjustments take place. The ABS updated the Consumer Price Index: Concepts, Sources and Methods (cat. no. 6461.0) in 2016 to include additional information on the quality adjustment process. This publication will be updated annually to incorporate changes in data sources, processes and methods. 1.9 The ABS sees potential with the use of scanner data in the CPI, both to improve reliability and reduce data collection costs, and will continue to explore the use of scanner data for CPI and related purposes, leveraging international experience with the use of such data. The ABS has invested considerable resources in investigating the use of scanner data. Scanner data is currently used to price products that represent approximately 25% of the weight of the CPI. Furthermore, the ABS will be introducing multilateral methods for 28 ECs of the CPI from December quarter 2017. This will result in a census of products being used from the scanner data and the weighting of prices at the product level, enhancing the quality of the CPI. 1.10 The CPI and all related series will be presented on a reference base of 2009-10 = 100.0, commencing with the September quarter 2012 CPI. Complete 1.11 The Australian CPI will continue to use the ABS Consumer Price Index Commodity Classification (CPICC). The ABS will take action internationally to influence a revision of the Classification of Individual Consumption According to Purpose (COICOP) to address shortcomings which prevent its use as the primary product classification in the CPI. The ABS continues to engage and influence the international review of COICOP which is currently ongoing. Once this review is finalised, the ABS will investigate potential changes to the CPICC to align more closely with COICOP. 1.12 A correspondence between CPICC and the Input–Output Product Classification (IOPC) will be compiled and published for the 16th series CPI. Complete 1.13 The ABS will continue to produce analytical measures of underlying inflation. The current seasonal adjustment methods will be replaced by standard ABS seasonal adjustment methods. The ABS will produce seasonally adjusted estimates of the CPI, and of significant seasonal components (using standard ABS seasonal adjustment methodologies), from the commencement of the 16th series in September quarter 2011. The production of seasonally adjusted individual capital city indexes will be subject to appropriate funding. The unadjusted CPI will continue to be the official headline measure. Complete. No user requirements for seasonally adjusted indexes at the capital city level have been identified. 1.14 The ABS will publish an All groups excluding food and energy index as part of the analytical series, from the September quarter 2011. Complete 1.15 The ABS will update the tradable and non–tradable series classifications, from the September quarter 2011. Complete. The tradable and non–tradable series classifications were updated in the September quarter 2011, and again in the December quarter 2016. 1.16 The ABS will discontinue the Average Retail Prices (ARP) publication from the September quarter 2011; the June quarter 2011 release will be the final issue. Complete 1.17 The ABS will engage in discussions with potential users of low level CPI data to discuss how their needs might best be met on a case–by–case basis. The ABS will not develop a confidentialised unit record file (CURF) of collected prices. The ABS continues to engage with users as to how their lower level data requirements are best met. 1.18 The ABS will explore cost effective options to expand CPI coverage beyond capital cities. However, this must be considered in the context of competing priorities within the ABS work program. The data requirements to expand CPI coverage beyond the capital cities are being addressed through transactions data and webscraping. 1.19 The ABS will undertake the development and publication of annual spatial price indexes (SPIs) for capital cities, subject to appropriate funding and consideration of competing priorities within the ABS work program. Since the 16th series, the ABS has investigated the need to develop and publish spatial price indexes. No user requirements for these indexes have been identified at present. 1.20 The ABS will investigate annual SPIs with an expanded scope to include rest of state components, subject to appropriate funding and consideration of competing priorities within the ABS work program. As above ## References ### Show all Australian Bureau of Statistics (ABS) 2010, Information Paper: Outcome of the 16th Series Australian Consumer Price Index Review, cat. no. 6469.0, ABS, Canberra. ABS 2015, Information Paper: Enhancing the Australian CPI: A road map, cat. no. 6401.0.60.001, ABS, Canberra. ABS 2016, Australian System of National Accounts, 2015-16, cat. no. 5204.0, ABS, Canberra. ABS 2016, Australian System of National Accounts: Concepts, Sources and Methods, cat. no. 5216.0, ABS, Canberra. ABS 2016, Census of Population and Housing: Census Dictionary, 2016, cat. no. 2901.0, ABS, Canberra. ABS 2016, Education and Work, Australia, May 2016, cat. no. 6227.0, ABS, Canberra. ABS 2016, Information Paper: Increasing the Frequency of CPI Expenditure Class Weight Updates, cat. no. 6401.0.60.002, ABS, Canberra. ABS 2017, Building Approvals, Australia, Aug 2017, cat. no. 8731.0, ABS, Canberra. ABS 2017, Consumer Price Index, Australia, Sep 2017, cat. no. 6401.0, ABS, Canberra. ABS 2017, Consumer Price Index: Concepts, Sources and Methods, 2016, cat. no. 6461.0, ABS, Canberra. ABS 2017, Household Expenditure Survey, Australia: Summary of Results, 2015-16, cat. no. 6530.0, ABS, Canberra. ABS 2017, Information Paper: An Implementation Plan to Annually Re-weight the Australian CPI, cat. no. 6401.0.60.005, ABS, Canberra. ABS 2017, Information Paper: An Implementation Plan to Maximise the Use of Transactions data in the CPI, cat. no. 6401.0.60.004, ABS, Canberra. ABS 2017, Labour Force, Australia, Aug 2017, cat. no. 6202.0, ABS, Canberra. ABS 2017, Producer Price Indexes, Australia, Sep 2017, cat. no. 6427.0, ABS, Canberra. ABS 2017, Residential Property Price Indexes: Eight Capital Cities, Jun 2017, cat. no. 6416.0, ABS, Canberra. ABS 2017, Schools, Australia, 2016, cat. no. 4221.0, ABS, Canberra. ABS 2017, Selected Living Cost Indexes, Australia, Sep 2017, cat. no. 6467.0, ABS, Canberra. ABS 2017, Wage Price Index, Australia, Jun 2017, cat. no. 6345.0, ABS, Canberra. Department of Education and Training 2011, Child Care Update - June Quarter 2010, Department of Education and Training, Canberra. Department of Education and Training 2017, Early Childhood and Child Care in Summary June Quarter 2016, Department of Education and Training, Canberra. Available at: https://www.education.gov.au/early-childhood-and-child-care-summary-reports. Department of Health 2016, Department of Health Annual Report, 2015-16, Department of Health, Canberra. Available at: https://www.health.gov.au/resources/publications/department-of-health-annual-report-2015-16. Department of Health 2017, Average premium increases by insurer by year, Department of Health, Canberra. Available at: https://www1.health.gov.au/internet/main/publishing.nsf/Content/privatehealth-average-premium-round. Department of Health 2017, Pharmaceutical Benefits Scheme (PBS), Department of Health, Canberra. Available at: http://www.pbs.gov.au/pbs/home. ## Abbreviations ### Show all ABS Australian Bureau of Statistics ALCI Analytical Living Cost Index APRA Australian Prudential Regulation Authority ASGC Australian Standard Geographical Classification ASGS Australian Statistical Geography Standard AWE Average Weekly Expenditure COICOP Classification of Individual Consumption According to Purpose CPI Consumer Price Index CPICC Consumer Price Index Commodity Classification CTP Compulsory Third Party EC Expenditure Class FISIM Financial Intermediation Services Indirectly Measured GCCSA Greater Capital City Statistical Area GFCF Gross Fixed Capital Formation HEC Household Expenditure Classification HELP Higher Education Loan Program HES Household Expenditure Survey HFCE Household Final Consumption Expenditure ISC Insurance Service Charge n.e.c. not elsewhere classified NSO National Statistical Office PBLCI Pensioner and Beneficiary Living Cost Index PP Percentage Point SLCI Selected Living Cost Index ### Previous catalogue number This release previously used catalogue number 6470.0.55.001.	2021-05-07T01:43:17	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.34357503056526184, "perplexity": 4299.967596873011}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988774.18/warc/CC-MAIN-20210506235514-20210507025514-00177.warc.gz"}
https://www.usgs.gov/center-news/volcano-watch-supersized-eruptions-are-all-rage	# Volcano Watch - Supersized eruptions are all the rage! Release Date: Last week, several HVO scientists were accompanied to Puu Oo by a film crew producing a NOVA program for PBS. The producer was interested in the research we're doing on an active volcano, but the main focus of the program is an eruption that happened long ago and far away-about 74,000 years ago on the island of Sumatra. Mike thought he was moving to a tropical paradise, but here he is back in the snow, preparing to measure tilt at the summit of Mauna Loa. (Public domain.) The eruption of Toba Volcano was the largest eruption in the last two million years, and, according to some theories, almost wiped out our human ancestors. The scale of the Toba eruption is difficult to comprehend. Pyroclastic flows (hot flows of ash and pumice) covered an area of at least 20,000 square kilometers (7,700 sq mi), with deposits as thick as 600 m (2,000 ft) near the vents. Ash fall was widespread over much of southeast Asia. An ash layer approximately 15 cm (6 in) thick was deposited over the entire Indian subcontinent. Our appreciation of the magnitude of this eruption continues to grow as Toba ash is recognized farther and farther from the source. The volume of the Toba eruption is estimated at 2,800 cubic kilometers (670 cu mi). To give some comparison with more recent eruptions, the 1980 eruption of Mount St. Helens produced less than 1 cubic kilometer (0.25 cu mi). Vesuvius (A.D. 79) erupted about 5 cubic kilometers (1.2 cu mi), and Krakatoa in Indonesia (1883) about 12 cubic kilometers (3 cu mi). Closer to home, the volume of Kīlauea's ongoing eruption is about 2.6 cubic kilometers (0.6 cu mi), erupted over the last 22 years. The most widespread hazard from such an eruption is its effect on global climate. Large, explosive eruptions eject huge amounts of volcanic ash and gas that reach the stratosphere. Sulfur dioxide gas reacts with atmospheric moisture to form tiny droplets of sulfuric acid. The droplets and ash particles both absorb heat and reflect solar radiation, cooling the lower atmosphere. While ash tends to settle out of the stratosphere within months, the aerosol of sulfuric acid can remain in the stratosphere for 2-3 years before dissipating. We have no direct knowledge of the length or severity of global cooling caused by the Toba eruption. Some scientists, however, have speculated that a severe "volcanic winter" triggered by the eruption, combined with the effects of ash fallout, may have brought about the near extinction of early humans in the path of the Toba fallout. You can still see the remains of this eruption on Sumatra, where beautiful Lake Toba fills the caldera formed when the magma chamber emptied. The area has been rattled by several major earthquakes in the last century, but there have been no eruptions at Toba in historical time. In light of recent events, it may seem that Sumatra is particularly prone to natural disasters. In fact, so-called "super eruptions" have occurred in many parts of the earth, including several in the western United States. The largest known explosive eruption in the world originated from the La Garita caldera in the San Juan Mountains of Colorado approximately 28 million years ago. The ash-flow deposit from this eruption, known as the Fish Canyon Tuff (tuff is consolidated ash), has an estimated volume of 5,000 cubic kilometers (1,200 cu mi). At Yellowstone (the subject of this column and a television special a few weeks ago), the largest eruption produced a volume of ash only slightly less than that of Toba about 2 million years ago. As noted in our earlier column, the odds of such an event occurring in our lifetime are vanishingly small, but that needn't lessen our desire to learn more about these amazing eruptions. ### Volcano Activity Update Eruptive activity at Puu Oo continues. Glow is visible from several vents within the crater on clear nights. The PKK lava tube continues to produce intermittent surface flows from above the top of Pulama pali to the ocean. Surface flows are active on the coastal plain inland of East Laeapuki and Kamoamoa, within 30 m (100 ft) of the sea cliff. Lava has been entering the ocean at East Laeapuki since April 25. This is the closest activity to the end of Chain of Craters Road, in Hawaii Volcanoes National Park, and is located about 4.7 km (3 miles) from the ranger shed. Expect a 2-hour walk each way and bring lots of water. Stay well back from the sea cliff, regardless of whether there is an active ocean entry or not. Heed the National Park warning signs. During the week ending April 28, 2 offshore earthquakes were felt on Hawaii Island. A magnitude-4.2 quake occurred 52 km (32 miles) southeast of Naalehu (beyond Loihi) at a depth of 9 km (6 miles) at 3:01 a.m. on Saturday, April 23; this earthquake was felt at various places on the island. A magnitude-3.4 quake occurred 65 km (40 miles) northwest of Kailua at a depth of 13 km (8 miles) at 8:13 a.m. on Tuesday, April 26; it was felt at Kailua and Waimea. Mauna Loa is not erupting. During the week ending April 20, 6 earthquakes were recorded beneath the summit area. Four were deep and long-period in nature. Inflation has slowed beneath the summit over the last few weeks.	2020-01-20T08:25:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3081377148628235, "perplexity": 5251.016762161496}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250598217.23/warc/CC-MAIN-20200120081337-20200120105337-00162.warc.gz"}
https://www.ansto.gov.au/news/global-development-small-modular-reactors	# Global development in small modular reactors A key aspect of ANSTO’s legislated mandate is to inform Australians on the facts and significant developments relating to nuclear science and technology, including emerging small modular reactor (SMR) designs. Small modular reactors, or SMRs, refers to a class of modern reactors that are essentially “small”, and each unit can be manufactured in a factory. Typical designs have power levels between 10 and 300 MWe. They are “modular” in the sense that each unit can be assembled next to another and scaled up or down to meet the local electricity needs. SMRs have advantages in safety, design, waste and fuel management, and environmental footprint, among other features. In this regard, there were many significant developments in North America, the United Kingdom, and elsewhere in the world relating to SMR technologies in the latter half of 2020. Some of these developments have been highlighted below. ## United States The most significant development was the announcement by the United States Department of Energy (DOE) that the US Government would partially fund the development of two next-generation small modular reactor demonstration models through the provision of US$160 million under the country’s new Advanced Reactor Demonstration Program. As reported on the energy.gov website, the DOE is awarding TerraPower LLC and X-energy US$80 million each initially to build two advanced nuclear reactors in cost-shared partnerships with industry, with the expectation that the reactors will be operational within seven years. TerraPower will use the funds to develop the Natrium™ reactor, a sodium cooled fast reactor, in partnership with GE Hitachi. X-energy will deliver a commercial four-unit nuclear power plant based on its Xe-100 reactor design, which encompasses a high-temperature gas-cooled reactor and an advanced fuel fabrication facility. According to the DOE, both projects incorporate a range of design features that not only will enhance safety, but also will make them affordable to construct and operate—paving the way for the US to deploy highly competitive advanced reactors domestically and globally. The full cost of the project is expected to be over US\$3 billion. The DOE is also planning to build the Versatile Test Reactor, a sodium fast reactor design, to provide the high-energy and high-flux neutrons necessary for the development of materials for use in advanced power reactors. The project to build the test reactor by 2026 is being led by the Idaho National Laboratory in partnership with five other national laboratories. In addition, in early November 2020, NuScale Power announced that its SMR design had been ‘uprated’ to 77 MWe; an increase of 25% from the earlier forecast power output of 60 MWe, which the company says will lead to significant cost savings. NuScale also announced options for smaller four-module and six-module plant sizes, in addition to its flagship 12-module plant. Beyond its power generation application, NuScale also released the results of a new evaluation that indicates that a single NuScale Power Module (NPM) could economically produce almost 50 tonnes of hydrogen fuel per day. The study, originally conducted by the Idaho National Laboratory, says that the improved power output of the NPM allows it to produce 20 percent more hydrogen from water than had been previously reported. Canada has recently released a Small Modular Reactor Action Plan that builds on its 2018 Small Modular Reactor Roadmap. The Plan, which involves more than 100 partners, outlines the development, demonstration, and deployment of SMRs for multiple applications at home and abroad. Canadian Nuclear Laboratories (CNL), ANSTO’s counterpart institution, has identified SMRs as one of eight strategic initiatives it is pursuing as part of its long-term strategy, with the goal of siting an SMR by 2026. At present, four proponents are engaged in the four-stage invitation process, which was launched in 2018, to evaluate the construction and operation of a demonstration SMR at a CNL site. U-Battery Canada Ltd has a design for a 4MWe high-temperature gas reactor. StarCore Nuclear is overseeing a proposed 14 MWe high-temperature gas reactor, and Terrestrial Energy is developing a 190 MWe integral molten salt reactor. These three projects have completed the first stage of the process. Ultra Safe Nuclear Corporation (USNC) and Ontario Power Generation (OPG) intend to build, own, and operate a proposed Micro Modular Reactor (MMR). The MMR is a 15 MW thermal, 5 MW electrical high-temperature gas reactor. This project is in the third stage of CNL's process to site a demonstration SMR at it Chalk River site and is currently undergoing an environmental assessment. Separately, in October 2020, OPG announced plans to pave the way for the deployment of SMRs by advancing engineering and design work with three developers of grid-scale SMRs: GE Hitachi (GEH), Terrestrial Energy, and X-energy. At the same time, GEH has entered into MoUs with five Canadian companies to set up a supply chain for its SMR design. ## The United Kingdom On the other side of the Atlantic, the UK is continuing an investment of about £460 million, which commenced in 2016 and will go through to this year (2021), to develop next generation advanced nuclear reactor technologies. About £7 million of funding is for regulators to build the capability and capacity needed to assess and license small and novel reactor designs. Up to £44 million has been allocated to the Advanced Modular Reactor (AMR) Feasibility and Development (F&D) project, a two-stage advanced modular reactor program administered by Innovate UK. In November 2020, the UK Government announced an investment of £215 million into SMRs to accelerate a Rolls Royce concept design. Read more A co-invested low cost nuclear ( LCN) program aims to see the commercial deployment of a fleet of SMRs by the 2030s. Rolls Royce is heading a consortium of UK nuclear companies to deploy 440 MWe light water reactor-based SMRs. The design, a patented modular concept for a reactor, is in the early stages. The company signed a Memorandum of Understanding with US utility Exelon Generation to pursue the potential for Exelon to operate its SMRs in the UK and internationally. ## South Korea South Korea has made progress on its 100 MWt System Integrated Modular Advanced Reactor (SMART), which is being developed by the Korean Atomic Energy Research Institute, another ANSTO counterpart institution and collaborator. Smart Power successfully submitted an SMR Licensing Advisory Report in July 2020. ## Australia And back home, in September 2020, the Australian Government listed SMRs as a 'watching brief' item in its First Australian Technology Investment Statement. The Statement refers to prospective technologies with transformative potential, perhaps where developments are currently driven primarily overseas. International developments in SMRs will be closely monitored and supporting infrastructure and other needs assessed. Read more Explore some of our reports on developments relating to small modular reactors and next-generation reactor designs. A look at global developments in nuclear reactor technologies ## A way forward for nuclear technology in Australia with public approval Parliamentary report Not without your approval: a way forward for nuclear technology in Australia ## Molten salt reactor technologies ANSTO's contribution to the development of molten salt reactor technologies ## Tags Nuclear Fuel Cycle Innovation	2022-12-05T23:54:20	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3685736656188965, "perplexity": 5391.676539592176}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711064.71/warc/CC-MAIN-20221205232822-20221206022822-00561.warc.gz"}
http://wikimechanics.org/banner-pair-production	Banner: Pair Production Verb Definition Pair Production $\Delta n^{\sf{q}} \left( \sf{P}_{\it{i}} \right) = 0 \ \ \forall \sf{q}$ 6-18 page revision: 9, last edited: 26 Aug 2018 18:14 Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License	2020-04-03T00:33:16	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.39103153347969055, "perplexity": 11383.288382560162}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370509103.51/warc/CC-MAIN-20200402235814-20200403025814-00070.warc.gz"}
https://www.anl.gov/article/diamond-proves-useful-material-for-growing-graphene	# Argonne National Laboratory Press Release \| Argonne National Laboratory # Diamond proves useful material for growing graphene Graphene is the stuff of the future. For years, researchers and technologists have been predicting the utility of the one-atom-thick sheets of pure carbon in everything from advanced touch screens and semiconductors to long-lasting batteries and next-generation solar cells. But graphene’s unique intrinsic properties – supreme electrical and thermal conductivities and remarkable electron mobility, to name just a few – can only be fully realized if it is grown free from defects that disrupt the honeycomb pattern of the bound carbon atoms. A team led by Materials Scientist Anirudha Sumant with the U.S. Department of Energy’s (DOE) Argonne National Laboratory’s Center for Nanoscale Materials (CNM) and Materials Science Division, along with collaborators at the University of California-Riverside, has developed a method to grow graphene that contains relatively few impurities and costs less to make, in a shorter time and at lower temperatures compared to the processes widely used to make graphene today. Theoretical work led by Argonne nanoscientist Subramanian Sankaranarayanan at the CNM helped researchers understand the molecular-level processes underlying the graphene growth. I’d been dealing with all these different techniques of growing graphene, and you never see such a uniform, smooth surface.” The new technology taps ultrananocrystalline diamond (UNCD), a synthetic type of diamond that Argonne researchers have pioneered through years of research. UNCD serves as a physical substrate, or surface on which the graphene grows, and the source for the carbon atoms that make up a rapidly produced graphene sheet. When I first looked at the [scanning electron micrograph] and saw this nice uniform, very complete layer, it was amazing,” said Diana Berman, the first author of the study and former postdoctoral research associate who worked with Sumant and is now an Assistant Professor at the University of North Texas. I’d been dealing with all these different techniques of growing graphene, and you never see such a uniform, smooth surface.” Current graphene fabrication protocols introduce impurities during the etching process itself, which involves adding acid and extra polymers, and when they are transferred to a different substrate for use in electronics. The impurities introduced during this etching and the transferring step negatively affect the electronic properties of the graphene,” Sumant said. So you do not get the intrinsic properties of the graphene when you actually do this transfer.” The team found that the single-layer, single-domain graphene can be grown over micron-size holes laterally, making them completely free-standing (that is, detached from the underlying substrate). This makes it possible to exploit the intrinsic properties of graphene by fabricating devices directly over free-standing graphene. The new process is also much more cost-effective than conventional methods based on using silicon carbide as a substrate. Sumant says that the 3- to 4-inch silicon carbide wafers used in these types of growth methods cost about $1,200, while UNCD films on silicon wafers cost less than$500 to make. The diamond method also takes less than a minute to grow a sheet of graphene, where the conventional method takes on the order of hours. The high quality of graphene was confirmed by the UC Riverside co-authors Zhong Yan and Alexander Balandin by fabricating top-gate field-effect transistors from this material and measuring its electron mobility and charge carrier concentration. It is well known that certain metals, such as nickel and iron, dissolve diamond at elevated temperatures, and the same process has been used for many years to polish diamond,” said Sumant. He and his team used this property to employ nickel in converting the top layer of diamond into amorphous carbon, but it was not clear how these freed carbon atoms converted instantly into high-quality graphene. After Sumant’s and Berman’s initial breakthrough of growing graphene directly on UNCD, Sankaranarayanan and his postdocs Badri Narayanan and Sanket Deshmukh, computational material scientists at the CNM used resources at the Argonne Leadership Computing Facility (ALCF) to help the team better understand the mechanism of the growth process underlying this interesting phenomenon using reactive molecular dynamic simulations. Computer simulations developed by Narayanan, Deshmukh and Sankaranarayanan showed that certain crystallographic orientation of nickel-111 highly favor nucleation, and subsequent rapid growth of graphene; this was then confirmed experimentally. These large-scale simulations also showed how graphene forms. The nickel atoms diffuse into the diamond and destroy its crystalline order, while carbon atoms from this amorphous solid move to the nickel surface and rapidly form honeycomb-like structures, resulting in mostly defect-free graphene. The nickel then percolated through the fine crystalline grains of the UNCD, sinking out of the way and removing the need for acid to dissolve away excess metal atoms from the top surface. It is like meeting a good Samaritan at an unknown place who helps you, does his job and leaves quietly without a trace,” said Sumant. The proven predictive power of our simulations places us in a position of advantage to enable rapid discovery of new catalytic alloys that mediate growth of high-quality graphene on dielectrics and move away on their own when the growth is completed,” added Narayanan. In addition to the utility in making minimally defective, application-ready graphene for things like low-frequency vibration sensors, radio frequency transistors and better electrodes for water purification, Berman and Sumant say that the Argonne team has already secured three patents arising from their new graphene growth method. The researchers have already struck a collaboration with Swedish Institute of Space Physics involving the European Space Agency for their Jupiter Icy Moons Explorer (JUICE) program to develop graphene-coated probes that may help exploratory vehicles sense the properties of plasma surrounding the moons of Jupiter. Closer to home, the team has also crafted diamond and graphene needles for researchers at North Carolina University to use in biosensing applications. The Argonne researchers are now fine-tuning the process – tweaking the temperature used to catalyze the reaction and adjusting the thickness of the diamond substrate and the composition of the metal film that facilitates the graphene growth – to both optimize the reaction and to better study the physics at the graphene-diamond interface. We’re trying to tune this more carefully to have a better understanding of which conditions lead to what quality of graphene we’re seeing,” Berman said. Other Argonne authors involved in the study were Alexander Zinovev and Daniel Rosenmann. The paper, Metal-induced rapid transformation of diamond into single and multilayer graphene on wafer scale,” is published in Nature Communications. The study used resources of the CNM and the ALCF as well as the National Energy Research Scientific Computing Center at Lawrence Berkeley National Laboratory, all DOE Office of Science User Facilities. Additional support was provided by the U.S. Department of Energy’s Office of Science. Argonne National Laboratory seeks solutions to pressing national problems in science and technology. The nation’s first national laboratory, Argonne conducts leading-edge basic and applied scientific research in virtually every scientific discipline. Argonne researchers work closely with researchers from hundreds of companies, universities, and federal, state and municipal agencies to help them solve their specific problems, advance America’s scientific leadership and prepare the nation for a better future. With employees from more than 60 nations, Argonne is managed by UChicago Argonne, LLC for the U.S. Department of Energy’s Office of Science. The U.S. Department of Energy’s Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information, visit the Office of Science website.	2020-09-28T07:43:54	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3425537645816803, "perplexity": 2822.210474199498}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401598891.71/warc/CC-MAIN-20200928073028-20200928103028-00044.warc.gz"}
https://par.nsf.gov/biblio/10370862	Department of Biological Sciences University of Alabama Tuscaloosa Alabama USA"/> Department of Biological Sciences University of Alabama Tuscaloosa Alabama USA"/> Department of Biological Sciences University of Alabama Tuscaloosa Alabama USA"/> Department of Biological Sciences University of Alabama Tuscaloosa Alabama USA"/> Department of Biological Sciences University of Alabama Tuscaloosa Alabama USA"/> Identifying potential drivers of distribution patterns of invasive Corbicula fluminea relative to native freshwater mussels (Unionidae) across spatial scales Authors: ; ; ; ; Award ID(s): Publication Date: NSF-PAR ID: 10370862 Journal Name: Ecology and Evolution Volume: 12 Issue: 3 ISSN: 2045-7758 Publisher: Wiley Blackwell (John Wiley & Sons) 1. We report on spectroscopic measurements on the$4f76s28S7/2∘<#comment/>→<#comment/>4f7(8S∘<#comment/>)6s6p(1P∘<#comment/>)8P9/2$transition in neutral europium-151 and europium-153 at 459.4 nm. The center of gravity frequencies for the 151 and 153 isotopes, reported for the first time in this paper, to our knowledge, were found to be 652,389,757.16(34) MHz and 652,386,593.2(5) MHz, respectively. The hyperfine coefficients for the$6s6p(1P∘<#comment/>)8P9/2$state were found to be$A(151)=−<#comment/>228.84(2)MHz$,$B(151)=226.9(5)MHz$and$A(153)=−<#comment/>101.87(6)MHz$,$B(153)=575.4(1.5)MHz$, which all agree with previously published results except for A(153), which shows a small discrepancy. The isotope shift is found to be 3163.8(6) MHz, which also has a discrepancy with previously published results.	2023-03-22T15:50:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 6, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24744148552417755, "perplexity": 7859.702129037564}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943845.78/warc/CC-MAIN-20230322145537-20230322175537-00116.warc.gz"}
https://finalfantasy.fandom.com/wiki/Paeon	## FANDOM 37,128 Pages Relm: I couldn't miss the chance to practice my drawing! Regenerates HP for all allies while singing Final Fantasy Brave Exvius description Paeon (癒しの歌 or いやしのうた, Iyashi no Uta?, lit. Song of Healing), also known as Paean, Healing Harmony, and Healing Song, is a recurring ability in the series. ## Appearances Edit ### Final Fantasy III Edit Paeon is an ability of the Sing command, accessible by the Bard while equipped with the Dream Harp. It restores HP to the party equal to the following: $HP Recovery = Recipient's Max HP x (10 + JobLv / 11)%$ ### Final Fantasy IV: The After Years Edit Healing Harmony is an ability usable by Edward via the Bardsong command at a 1/5 chance. It casts Cure on one ally or the entire party. ### Final Fantasy Dimensions II Edit This section about an ability in Final Fantasy Dimensions II is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it. ### Theatrhythm Final Fantasy Edit Paeon comes in three levels of power, and restores HP to the party over the duration of a stage, the amount of HP restored depending on the level of the Paeon. Paeon is learned by Princess Sarah, Aerith, Garnet, Yuna, and Cosmos. The five learn all three levels of Paeon. #### Theatrhythm Final Fantasy Curtain Call Edit Paeon (Lv1) is a reactive ability that has costs 10 CP to equip. It is active for the entire length of the stage. It slowly but constantly refills the HP gauge and has low strength. it is learned by Rosa (level 15), Celes (level 30), Eiko (level 15), Yuna (level 10), Prishe (level 25), Lilisette (level 10), and Cosmos (default). Paeon (Lv2) is a reactive ability that costs 22 CP to equip. It is active for the entire length of the stage. It slowly but constantly refills the HP gauge and has medium strength. It is learned by Rosa (level 55), Celes (level 70), Eiko (level 45), Yuna (level 50), Prishe (level 60), Lilisette (level 50), and Cosmos (level 30). Paeon (Lv3) is a reactive ability that costs 30 CP to equip. It is active for the entire length of the stage. It slowly but constantly refills the HP gauge and has full strength. It is learned by Eiko (level 85), Yuna (level 85), and Cosmos (level 70). #### Theatrhythm Final Fantasy All-Star Carnival Edit This section about an ability in Theatrhythm Final Fantasy All-Star Carnival is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it. ### Final Fantasy Record Keeper Edit This section about an ability in Final Fantasy Record Keeper is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it. ### Final Fantasy Explorers Edit This section about an ability in Final Fantasy Explorers is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it. ### Final Fantasy Brave Exvius Edit This section about an ability in Final Fantasy Brave Exvius is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it. ## Gallery Edit This gallery is incomplete and requires images added. You can help the Final Fantasy Wiki by uploading images. ## Etymology Edit A paean is a song or lyric poem expressing triumph or thanksgiving. Community content is available under CC-BY-SA unless otherwise noted.	2020-01-24T23:51:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23448212444782257, "perplexity": 13693.403052301896}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250626449.79/warc/CC-MAIN-20200124221147-20200125010147-00451.warc.gz"}
https://nepis.epa.gov/Exe/ZyPURL.cgi?Dockey=900S0Z00.txt	United States Environmental Protection Agency Solid Waste And Emergency Response (OS-420) WF EPA510-R-93-001 January 1993 Hyperventilate Users Manual (v1.01 and v2.0) A Software Guidance System Created For Vapor Extraction Applications Vapor Treatment Unit Pump lllllll Ground Surface Wcll Contaminated Soil IBM EPA 510 R 93 001 c.2 Printed on Recycled Paper ------- ------- Hyperventilate Users Manual A Software Guidance System Created for Vapor Extraction Applications A Practical Approach to tht Design, Operation, and Monitoring of In-Situ Soil Venting Systems Eoooomld Crur<4 >r Pnl C. Jokuo», Pk.D. SbcO Development WtJthoDo v Rexuch C«nr About Thfc StMfc Go to Ftrsl C«rd Fteld TtStl V System Desica '(-—— —— J liVewtacPMsftk? T •^ Si laveitfcttioa V ^ •• Yipor f f TVettment Uatt_ ••• by Paul C. Johnson, Ph.D. Shell Development Westhollow Research Center Environmental R&D P. O. Box 1380 Houston, TX 77251 Apple® Macintosh™ HyperCard™ compatible version 1.01 For sale by the U.S. Government Printing Office Superintendent of Document, Mail Stop: SSOP, Washington, DC 20402-9328 ------- ------- - H^rVentilate Users Manual Addendwn- Addendum for Microsoft Windows/Spinnaker PLUS Version 2.0 Summary Hyperventilate - the software guidance system created for vapor extraction applications is now available for IBM-compatible computers. In general, this new version (vi.O) appears and functions like the original Apple Macintosh HyperCard version. Due to differences in the computer platform and operating environment, however, there are some minor modifications. This addendum to the original users manual identifies those modifications. Hyperventilate v2.0is a product of collaboration between Shell Oil Company and U.S. EPA, and is still under evaluation. Should you encounter problems that you think are "bugs", please write to the author identifying the problem. Modifications • software platform The original Hyperventilate program was developed and operated under the Apple Macintosh HyperCard software environment, and initially there were no plans to develop an IBM-compatible version. Due to popular demand; however, the author relented and used the least painful method of adaption to the new platform. This was accomplished through the use of Spinnaker PLUS, a HyperCard-like program that can utilize pre-v2.0 HyperCard stacks and functions on both Macintosh and IBM-compatible platforms. The Microsoft Windows/Spinnaker PLUS version requires the user to have both Microsoft Windows and a "run-time" version of Spinnaker PLUS (Windows 3.0 version). Infor- mation on Spinnaker PLUS can be obtained from: Spinnaker Software 201 Broadway Cambridge, MA 02139 (617)494-1200 • stack names As listed on p4, of the original users manual, Hyperventilate for the Apple Macintosh consists of eight files. The Spinnaker PLUS version contains only seven files. The names are: HyperCard Version Name Soil Venting Stack Soil Venting Help Stack System Design Air Permeability Test Aquifer Characterization Compound list Update HypeVent f77.rl Spinnaker PLUS Versdon Name SVS. sta SVHS.sta SD.sta APT.sta AQ.sta CLU.sta HYPEVENT.exe none ------- installation all files must be copied into the PLUS directory on your hard disk. starting Hyperventilate v2.0b To startHyperVentilate v2.0b, open the Windows 'Tile Manager", navigate to within the PLUS directory, then open (double-click on) the tile SVS.sta. printing cards You may experience difficulties with some of the "Print" buttons in the program. Read your PLUS manual to overcome these difficulties. appearance of cards Generally, the cards appear as they are printed in the manual. Due to platform differences, however, some text will appear different This problem is unavoidable with Windows- based systems, as different users will have their computers configured with different screen fonts. tab keys Some cards utilize spreadsheets. In die HyperCard version the "tab" key is used to navigate through these tables. In the PLUS version the"tab"keyisnot active and you must use the "arrow" keys. speed Due to platform differences, the PLUS version does not operate as smoothly, or quickly, as the HyperCard version. The user will notice that with time the execution speed of the program will slow; therefore, it is recommended that you periodically exit from Windows and restart the system. On some machines, when Hyperventilate accesses the external compiled code HYPEVENTEXE after clicking on the "Generate Predictions" button on card 16 of the SVS.sta stack, there will be a long pause (as long as a few minutes) as PLUS Windows, andHYPER\T^^'£XEfightove^availablemeInory. Typicallycard 17 will eventually be displayed with a shaded rectangle along a portion of its lower base while this battle is occurring. Be patient and wait for the screen to blank out and display die message "HANG ON..." indicating that HYPEVENT.EXE is running. If you have limited memory (<4MG), or too many applications open, this message will not be displayed, and you will be returned to card 17 as if the program had run. The user needs to be aware that this may occur. ------- - Hyperventilate Adndum- Software Installation Procedure A discussion on how to load both Spinnaker PLUS and Hyperventilate * Loading Spinnaker PLUS * Creating the Spinnaker PLUS Icon and Opening Spinnaker PLUS • Loading Hyperventilate • Installing Spinnaker PLUS "Run-Time" Version with Hyperventilate These directions presume that the user has a working knowledge of Microsoft Windows. The operation of Spinnaker PLUS, and therefore the IBM-compatible version of Hyperventilate requires Microsoft Windows Version 3.0 or higher. If you arc using a version of Hyperventilate with a "run time" version of SpinnakerPLUS, skip to the "Loading Hyperventilate" instructions. Loading Spinnaker PLUS The Spinnaker PLUS package contains three 3.5-inch and three 5.25-inch diskettes from which to install the program. Use these steps to install the program: 1 . Enter Windows. 2. Double-click on the "Main" window icon (if this window is not already open). 3. Double-click on the "File Manager" icon; this will display the "Directory Tree" window. 4. Insert Disk 1 into the appropriate drive (A or B). 5. In the upper left corner of the "Directory Tree" window you will see symbols representing the drives on your system. Click on the drive (A or B) where you just inserted Disk 1. 6. A listing of the files on Disk 1 will appear, double click on the file "plssetup.exe". 7. Awindowcalled"SpinnakerPLUS Setup" will appear. Change the path of theinstallation from"C:NPLUS" to "C:\WINDOWS\PLUS" (Note: "C"is a standard drive specification; you should use the letter that designates where Windows is installed on your system). Click on "Continue." The program will start copying files from Disk 1 . Follow the rest of the instructions and prompts on the screen. 8. When the installation has been completed, exit the 'Tile Manager" and exit Windows. .. .l7?JtfJi?A-i r.ffflfACfl f, .w. • . ------- ~ Hyperventilate Users Manual Addendum- Creating the Spinnaker PLUS Icon and Opening Spinnaker PLUS 1. Re-enter Windows. (Note: exiting and re-entering Windows is a step recommended by the manufacturer of Spinnaker PLUS). 2. Close all windows so that the "Program Manager" window is the only one displayed on your screen. 3. At the bottom of the window, there will be program icons displayed for "Main," "Accessories," and others. Is there a program icon named "Windows Applications?" If yes, double-click on it and go to Step 4. If no, continue with Steps 3a-c to create one. 3a. dick on "File" and drag down to "New." A window called "New Program Object" will appear. 3b. Check to make sure "Program Group" is selected; click on "OK." A window called "Program Group Properties" will appear. 3c. The cursor will be located at the description field. Type in the words "Windows Applications" and click on "OK." An empty window will appear called "Windows Applications." 4. Withthiswindowopen,clickon"File"anddragdownto"New." Awindowcalled"New Program Object" will appear. 5. Check to make sure "Program Item" is selected; click on "OK." A window called "Program Item Properties" will appear. 6. Click on "Browse." A window called "Browse" will appear. 7. Under "Directories," double-click on "plus." 8. Under "File Name," double-click on the "plus.exe" file. This will bring you back to the "Program Item Properties" window. 9. Click on "Change Icon," click on the icon for "Plus," and click on "OK." 10. You will now be back at the "Program Item Properties" window. Click on "OK." 11. You will now be back to the "Windows Applications" window displaying your "Plus" icon. 12. Double-click on the "Plus" icon to run Spinnaker PLUS. Addendum 4 ------- Loading Hyperventilate The Hyperventilate package contains one 3.5-inch diskette from which to install the program. Theprogramcan be installed fromeitherthe DOS promptorfrom within Windows. The folio wing procedures are used for both types of installations (Note: For these installation procedures, the 3.5-inch drive from which you will be installing the program is assumed to be the B drive). DOS Installation 1. Insert the Hyperventilate disk into the appropriate drive. 2. From the C:N> prompt in DOS, type "COPY B:\. C:\WINDOWSPLUS". Windows Installation 1. Follows Steps 1 -5 of the "Loading Spinnaker Plus." 2. Click on the B:\folder icon so that it is highlighted and/or a dotted line appears around it 3. Ch"ckon"File"anddragdowntothe"Copy" command. The"Copy"windowwillappear. 4. The curser will be located at the "To" path. Type in "C:\WINDOWS\PLUS"; click on "OK." 5. When the installation is complete, exit from the "File Manager." Opening Hyperventilate 1. Enter Windows. 2. Double-click on the "Windows Applications" icon (if this window is not already open). 3. Double-click on the "Plus" icon. 4. Close the "Home" window. 5. Click on "File" and drag down to "Open." The window "Open Stack" will appear. 6. Either double-click on the "SVS.STA" file or click on "SVS.STA" and then click on "Open." The user is now in Hyperventilate. ------- - Hyperventilate Users Mamuil Addenditm- Ihstalling Spinnaker PLUS "Run-Time" Version with Hyperventilate 1. Create a subdirectory on the hard disk for Hyperventilate and Spinnaker PLUS "Run Time." For example, from the C:\> prompt, type "MD WINDOWSNPLUS". 2. Copy all die files from both the Spinnaker PLUS "Run Time" diskette and the Hyperventilate diskette to the subdirectory. For example, from the C:\> prompt, type "COPY B:. C:\WINDOWS\PLUS". 3. Follow directions in "Creating the Spinnaker PLUS Icon and Opening Spinnaker PLUS" with die following exception: substitute "plusrtexe" for "plus.exe" in Step 8. 4. Follow directions for "Opening Hyperventilate" to run die program. .Addendum.^.. ------- - Hyperventilate Users Manual • Disclaimer The Hyperventilate software package was completed under a Federal Technology Transfer Act Cooperative Research and Development Agreement between EPA and Shell CHI Company, signed in 1990. EPA is facilitating the distribution of Hyperventilate because the Agency has found the software and manual to be helpful tools, especially in teaching users about in situ soil venting and in guiding them through a structured thought process to evaluate the applicability of soil venting at a particular site. EPA's Office of Underground Storage Tanks advocates the use of innovative cleanup technologies, and in situ soil venting isrecognized as an effective remediation alternative for many underground storage tank sites. Hyperventilate is based on the document titled, "A Practical Approach to die Design, Operation, and Monitoring of Soil Venting Systems" by P. C Johnson, C. C. Stanley, M. W. Kemblowski, J. D. Colthart, and D. L. Byers, published 1990 by Shell Oil Company. The program asks a series of questions and forms a "decision tree" in an attempt to identify the limitations of in situ soil venting for soils contaminated with gasoline, solvents or other relatively volatile compounds. EPA and Shell Oil Company make no warranties, either express or implied, regarding the Hyperventilate computer software package, its merchantability, or its fitness for any particular purpose. EPA and Shell Oil Company do not warrant that this software will be error free or operate without interruption. EPA and Shell Oil Company do encourage testing of this product. EPAwillnotprovideinstatlationservicesortechnicalsupportinconnectionwiththeHyperVen^ computer software package. Neither will EPA provide testing, updating or debugging services in connection with the enclosed computer software package. The Hyperventilate computer software package and this manual are not copyrighted. ------- - Hyperventilate Users Manual - Disclaimer Shell Oil Co. makes no warranties, either express or implied, regarding the enclosed computer software package, its merchantability, or its fitness for any particular purpose. Shell Oil Co. does not warrant that this software will be error free or operate without interruption. The exclusion of implied warranties is not permitted by some states. The above exclusion may not apply to you. This warranty provides you with specific legal rights. There may be other rights that you may have which vary from state to state. Apple is a registered trademark of Apple Computer, Inc. Macintosh and HyperCard are trademarks of Apple Computer, Inc. f77.rl is a product of Absoft Corp Comments/Suggestions? Comments and/or suggestions about the usefulness of this program can be mailed to: Paul C. Johnson Shell Development Westhollow Research Center P.O. Box 1380 Room EC-649 Houston, TX 77251-1380 Please do not call the author and/or Shell with questions about the use or interpretation of results from this program. ------- -Hyperventilate Users Manual - Foreword Hyperventilate is a software guidance system for vapor extraction (soil venting) applications. Initial development of this program occured under the Apple Macintosh HyperCard environment, due to its programming simplicity, ability to incorporate text and graphics, and interfacing with other Macintosh programs (such as FORTRAN codes, etc.). The objective was to create a user-friendly software package that could be both educational for the novice environmental professional, and functional for more experienced users. HyperVentilate will not completely design your vapor extraction system, tell you exactly how many days it should be operated, or predict the future. It will guide you through a structured thought process to: (a) identify and characterize required site-specific data, (b) decide if soil venting is appropriate at your site, (c) evaluate air permeability test results, (d) calculate the minimum number of vapor extraction wells, and (e) quantify how results at your site might differ from the ideal case. HyperVentilate is based on the article "A Practical Approach to the Design, Operation, and Monitoring of Soil Venting Systems" by P. C. Johnson, C. C. Stanley, M. W. Kemblowski, J. D. Colthart, and D. L. Byers [Ground Water Monitoring Review, Spring 1990, p. 159 -178], The software performs all necessary calculations and contains "help cards" that define the equations used, perform unit conversions, and provide supplementary information on related topics. In addition, a 62-compound user-updatable library (to a maximum of 400 compounds) is also included. HyperVentilate version 1.01 for the Apple Macintosh requires an Apple Macintosh (Plus, SE, SE/30, II, HX, or portable) computer equipped with at least 1 MB RAM (2 MB preferred) and the Apple HyperCard Software Program (v.2.0 or greater) This manual is not intended to be a primer on soil venting (although the software is) and it is assumed that the user is familiar with the use of an Apple Macintosh personal computer. ------- ------- - Hyperventilate Users Manual - Table of Contents Title Page I II in IV v v.i V.2 V.3 V.3.1 V.3.2 V.3.3 V.3.4 VI Appendices A B C D E F G Disclaimer Foreword Introduction Definition of Some Terms Appearing in this Manual Software/Hardware Requirements Loading Hyperventilate Software Using Hyperventilate - Starting Hyper Ventilate - General Features of Cards - Sample Problem Exercise - Navigating Through Hyperventilate - Is Venting Appropriate? - Field Permeability Test -System Design References i ii 2 4 4 4 5 5 7 8 8 12 22 26 35 36 Soil Venting Stack Cards Soil Venting Help Stack Cards Air Permeability Test Cards Aquifer Characterization Cards System Design Cards Compound List Update Cards A Practical Approach to the Design, Operation, and Monitoring of In Situ Soil Venting Systems ------- -Hyperventilate Users Manual - I. Introduction In situ vapor extraction, or soil venting is recognized as an attractive remediation alternative for "permeable" soils contaminated with "volatile" compounds. As Figure 1 illustrates, vapors are removed from extraction wells, thereby creating a vacuum and vapor flow through the subsurface. Until the residual contamination is depleted, contaminants will volatilize and be swept by the vapor flow to extraction wells. While its use has been demonstrated at service stations, Superfund sites, and manufacturing locations (see Hutzler et al. [1988] for case study reviews), vapor extraction systems are currently designed more by intuition than logic. In fact, many systems are installed at sites where the technology is not appropriate. "A Practical Approach to the Design, Operation, and Monitoring of In Situ Soil Venting Systems" [Johnson et al. 1990a - see Appendix G] is a first attempt at creating a logical thought process for soil venting applications. The article, which is based on earlier results of Thornton and Wootan [1982], Marley and Hoag [1984], Johnson et al. [1990], and discussions with several of these authors, describes a series of calculations for determining: (a) if soil venting is appropriate at a given site, (b) limitations of soil venting, and (c) system design parameters, such as minimum number of extraction wells and potential operating conditions. Hyperventilate is a software guidance system based on the Johnson et al. [1990a] article. The software performs all necessary calculations and contains "help cards" that define the equations used, perform unit conversions, and provide supplementary information on related topics. In addition, a 62-compound updatable chemical library (to a maximum of 400 compounds) is included. Initial development of this program occured under the Apple Macintosh HyperCard environment, due to its programming simplicity, ability to incorporate text and graphics, and interfacing with other Macintosh programs (such as FORTRAN codes, etc.). The objective was to create a user-friendly software package that could be both educational for the novice environmental professional, and a functional tool for more experienced users. The OASIS [1990] system created at Rice University for groundwater contamination problems is another excellent example of the use of HyperCard as a technology transfer tool. This document is a users manual for Hyper Ventilate. It contains sections describing the installation and operation of the software. During the development of Hyperventilate, the goal was to create a guidance system that could be used with little or no instruction. Experienced Apple Macintosh users, therefore, can load and explore the capabilities of this program after glancing at the "Loading Hyperventilate Software" section. Those users that are less comfortable about exploring software without a manual are encouraged to read through it once, and work through the sample problem. It is intentionally brief, and a beginner should be able to navigate through the system in less than a couple hours. It is assumed that the user has some previous Macintosh experience. If not, consult a Macintosh users manual for a quick tutorial. ------- -Hyperventilate Users Manual - Pressure Gauge Vapor Flow Air Bleed Line I Vacuum f Pump Flow Meter Vapor Well Vapor Treatment Unit Flow Meter Contaminated Soil Vapor Flow Groundwater Table flume Figure 1. Schematic of a typical vapor extraction operation. ------- - Hyperventilate UsersManual- II. Definition of Some Terms Appearing in this Manual button - an object on a "card" that causes some action to be performed when "clicked" on card - an individual screen that you view on your monitor click - refers to the pressing and releasing of the button on your mouse drag - refers to holding down the mouse button while moving the mouse field - a text entry location on a "card" HyperCard - a programming environment created by Apple Computer, Inc. mouse - the device used to move the cursor within your monitor select - refers to "dragging" the cursor across a "field" stack - a group, or file, of "cards" III. Software/Hardware Requirements Apple Macintosh Hyper Ventilate version 1.01 requires an Apple Macintosh (or equivalent) computer equipped with at least 1 MB RAM (2 MB preferable), a hard disk, and the Apple HyperCard Software Program (v 2.0). Check to make sure that your system software is compatible with your version of HyperCard. IV. Loading Hyperventilate Software Hyperventilate is supplied on an 800 kB double-sided, double density 3.5" diskette. Follow the instructions listed below to insure proper operation of the software. 1) Insert the Hyperventilate disk into your computer's floppy drive. The Hyperventilate disk should contain the files: - "Soil Venting Stack" -"Soil Venting Help Stack" - "System Design" - "Air Permeability Test" - "Aquifer Characterization" - "Compound List Update" - "HypeVent" - "f77.rl" 2) Copy these files onto your hard disk. They must be copied into the folder that contains the "HyperCard" program, or else the software will not operate properly. 3) Eject the Hyperventilate disk ------- - Hyperventilate Users Manual • V. Using Hyperventilate The authors of Hyperventilate intend it to be an application that requires little pre- training for the user. It is mouse-driven and instructions are included on each card, so please take the time to read them when you first use Hyperventilate. This section of the users manual is divided into three subsections. Start-up instructions are given in the first, basic features of the cards are described in the second, and a sample exercise is presented in the third. For reference, copies of all cards, as well as more details on each are given in Appendices A through F. V.I. Starting Hyperventilate 1) Those users with color monitors should use the "Control Panel" (pull down the "tf" menu and select "Control Panel", then click on the "Monitors" icon) to set their monitors to black and white, and two shades of grey. 2) To avoid unnecessary "card-flipping", set the "Text Arrows" option in your "Home" stack "User Preferences" card to on. You can get to this card from within any HyperCard application by selecting "Home" under the "Go" menu. This will take you to the first card in the "Home" stack. At this point click on the left- pointing arrow and the "User Preferences" card will appear on your screen. Then click on the square to the left of "Text Arrows" until an "X" appears in the square. 3) Hyperventilate is started by double-clicking on the "Soil Venting Stack" file icon from the Finder (or Desktop), or by choosing "Open" under the "File" menu (Note that using a more advanced version of HyperCard than the one under which this system was developed (v 2.0) may require you to first "convert" each of the seven HyperCard stacks contained in Hyperventilate). 4) Your monitor should display the card shown in Figure 2. Note that there are a number of buttons on this card; there are two at the lower left comer, and then each file folder tab is also a button (some cards may contain less obvious "hidden" buttons; try clicking on the authors name on the title card for example). Clicking on any of these will take you to another card. For example, clicking on the "About This Stack" button will take you to the card shown in Figure 3, which gives a brief description about the use of buttons and fields. Read this card well. 5) Explore for a few minutes. Try to see where various buttons will take you, try entering numbers in fields, or play with calculations. Again, just remember to read instructions given on the cards. ------- - Hyperventilate Users Manual - Buttons XI A Practical Approach to the Design, Operation, and Monitoring of In-Situ Soil Venting Systems wsioa 1.01 «19«1 AH Rifttt fiwtmi Economics t HyjuCwi Buck Cnttti >y: PavlC. Johnson, Ph-D. Amy J. Strttntm Shell Development WwthoDo v R«j«»reh Center About This Stack Go to First Card 4 SyMMnMontorinc ^ Field Tests System Design 4 Sit Investigation -f About Soil Venting Is Venting Feasible? Vapor FlDV \ Buttons Figure 2. First Card of the "Soil Venting Stack" stack. Help: Stack Information Buttons Buttons have been placed in each card. Clicking on any button vill perform an action, such as: Go Home 10 rust card in Venting Stack Goe next cam Oo t> Help card text field (Calculate) Perform »C«Jculatkm When curious, dick on Symbols, or Fields Fields may contain information, or they may be a place for you to input numbers. Scrolling Field: dick on tiro vs to move xt up or do va Bond Data Field: When you see MI I-beam conor tppeu in a boxed field, click the mouse in The box «> set Hie cursor. Then you m»y enter dtte.. A bunon vlll ten usu»Dy be pushed to perform en ection or cekuktion. Click on the wrovs , or move the box up or dovn vlthihe mouse. In this n. TOU can Try this example: Enter Number in Box I 11 inches (Click for calculation) 2.54 centimeters Figure 3. Card HI of the "Soil Venting Help Stack" stack. ------- -Hyperventilate UsersMamal- V.2. General Features of Cards Figures 4 and 5 are examples of cards from the "Soil Venting Stack" stack and "System Design" stack. There are a few general features of these cards that users should understand: a) Each card (with the exception of the first card of the "Soil Venting Stack" stack) has been numbered for easy reference with the printouts given in Appendices A through F. In the "Soil Venting Stack" these numbers appear in the bottom center of each card (i.e. number "3" in Figure 4). In other stacks these numbers appear at either the top or bottom corners of the card (i.e. "SD1" in Figure 5). b) Airow buttons are included at the bottom of some cards. Clicking on right-pointing arrow will advance you to the next card in the stack; clicking on the left-pointing arrow will take you in the opposite direction. c) The identifying card numbers in the "Soil Venting Stack" stack are also fields into which text can be typed. You can skip to other parts of the "Soil Venting Stack" stack by selecting this field, typing in the card number of your destination (within the "Soil Venting Stack"), and then hitting the "return" key. d) Many cards have a house button in the lower left corner. Clicking on this button will take you to the first card of the "Soil Venting Stack" stack, which is the card displayed at start-up (see Figure 2). ^^^^^^^^m^^^^^^^^^^^^^^^^^^mt^^^^^^^^^^^^m^mmm^^^^^^^^^^^^^f^^^m In-Situ Soil Venting System Design Process Ton ran click on «ny block in ftis dicnm get more information about (hut pwticukr >p. Or jou era begin »t the start of die pieces by ctjckine °n either the "LetX or Spill Discovered" box, or fee urov M the bonom of (his card. (Let* or Spffl Discovered} "Clean- Sits Figure 4. Card 3 of the "Soil Venting Stack" stack. V ------- •Hyperventilate Users Manual - Number of Venting Wells... The procedure forestimatinc fee required number of extraction vclb is similar to the process used previously to determine if venting Is appropriate at a given site. As illustrated at the right, vt vill estimate single vertical veil flovrates, calculate the minimum vapor flov required, determine fee anal extent of influence, and then factor in any site-specific limitations. This information tten determines the necessuy number of extraction veDs. Jost proceed «foDo v the steps dictated on [ tie foDovinj cards—> Flovrate Eattmatlon Maximum Removal Rate Volume Requirement Slw- Specific Limiwions Area of Influence Requirement Figure 5. Card SD1 of the "System Design" stack. V.3. Sample Problem Exercise In the following a sample problem is executed in excruciating detail. Those not wishing to work along with the example are encouraged to utilize Appendices A through F as references for more details on the less obvious functions of some cards. This "Sample Problem Exercise" is divided into to four subsections that address: navigating through Hyperventilate (§V.3.1), screening sites to see if soil venting is an appropriate technology (§V.3.2), interpreting air permeability test data (§V.3.3), and guidance for designing soil venting systems (§V.3.4). V.3.1 Navigating Through Hyperventilate Step 1: Location: The "Desktop" or Finder. Action: Start-up HyperVentilate by double-clicking on the "Soil Venting Stack" icon, or click once on this icon and then choose "Open" from the "File" menu. Result: HyperVentilate will start-up and display the title card (Figure 2). Step 2: Location: Tit'e Card of the "Soil Venting Stack" stack. Action: Click on the "About This Stack" button. Result: You are now at card HI of the "Soil Venting Help Stack" stack (Figure 3). ------- Step 3: Location: Card HI of the "Soil Venting Help Stack" stack. Action: Play with the buttons and scrolling field. Practice entering a number in the field in front of "inches". Place the cursor in the box. It will change from a hand to an "I-bar" as it enters the field. Hold down the mouse button and drag the I-bar across the entry, which will become hilited. Now type in another number, or hit the delete key. Practice until you feel comfortable selecting text and entering numbers. Then click on the "Click for Calculation" button. When you are done practicing, click on the "Return" button. Result: Return to the title card of the "Soil Venting Stack" (Figure 2). Step 4: Location: Tide Card of the "Soil Venting Stack" stack. Action: Click on the "Economics" file folder tab. Result: You are now at card 27 of the "Soil Venting Stack" stack. Take a quick glance at this card, which is displayed in Figure 6. Step 5: Location: Card 27 of the "Soil Venting Stack" stack. Action: Click on the "House" button in the lower left corner. Result: You are back at the title card (Figure 2). Step 6: Location: Title card of the "Soil Venting Stack" stack. Action: Click on the "Go to First Card" button. Result: You are now at card 1 of the "Soil Venting Stack" stack (Figure 7). Economics... For typical service station sites, clean-up costs can range from $100K-$250K for the venting operation alone, depending on the complexity of the site, clean- up time, permitting requirements, and the type of vapor treatment system used. The tvo major costs are generally associated vith the vapor treatment unit and "Click* on any item belov (8t hold button dovn) to see costs associated vith that item. ft Figure 6. Card 27 of the "Soil Venting Stack" stack. ------- -Hyperventilate Users Manual - This HyperCard Stack vas created to help guide environmental scientists through the thought process necessary to decide if and hov soil venting night be applied to remediate a given site. The organization and logic of this stack follovs the paper: A Practical Approach to the Design, Operation, and Monitoring of In-Situ Soil Venting Systems Uy: P. C. Jobason, C. C. Stuley, M, W. Kemllovskl, J. D. ColHuit, & D. L. Byes* published in Ground Water Monitoring Reviev, Spring 1990, p. 159-178 If M tikis toiat yom to aot feel comforatla witk ttt* vst of Qt» tanois, click oic« on '?• for note iifo on the neckamics of tkis slack... Figure 7. Card 1 of the "Soil Venting Stack" stack. Step 7: Location: Card 1 of the "Soil Venting Stack" stack. Action: Click on the right-pointing arrow. Result: You are now at Card 2 of the "Soil Venting Stack" stack (Figure 8). Step 8: Location: Card 2 of the "Soil Venting Stack" stack. Action: Read the text, and click on the "down" and "up" arrows on the displayed text field under "About Soil Venting..." to make the field scroll. Then click on the left-pointing arrow at the card bottom. Result: You are now back at card 1 of the "Soil Venting Stack" (Figure 7). Step 9: Location: Card 1 of the "Soil Venting Stack" stack. Action: Click on the right pointing arrow. Result: You are again at card 2 of the "Soil Venting Stack" stack (Figure 8). By now you should feel comfortable using the left- and right- pointing arrows to travel through the stack. Step 10: Location: Card 2 of the "Soil Venting Stack" stack. Action: Click on the "?" button in the lower right corner of the card. This button indicates that there is a "Help" card containing additional information. Result: You are now at card H2 of the "Soil Venting Help Stack" stack (Figure 9). Scroll through the list of references, then click on the "Return" button to return to card 2 of the "Soil Venting Stack" stack. At this point you should feel comfortable navigating around in Hyperventilate. 10 ------- r About Soil Veatiag... Soil Venting (a.k.a. "in-situ soil venting", "vacuum extraction", & "in-situ vapor extraction") is rapidly becoming one of the most practiced soil remediation processes for permeable soils contaminated vith relatively volatile hydrocarbons. The underlying phenomena that influence the success of any soil venting operation are easily understood. By applying a vacuum Vepor Treatment Unit Vacuum B lover Figure 8. Card 2 of the "Soil Venting Stack" stack. Help: About Soil Venting More information about sofl venting cut be found in the foDo Vine articles: M. C. Mtrky and O. I. Hoeg, Induced Soil Venting for (be RecoveryfRes>r»tion of Gasoline Hydrocarbons in tbe Vados Zone, NWWA/API Conference on Petroleum Hydrocarbons and Organic Chemicals in Orotindvewr, Houston, TX, 1984. P. C. Johnson, M. W Kembfcvstt, and J. D. Colftart, Practical Screening Models for Sofl Venting Applications, NWWA/API Conference on Petroleum Hydrocarbons and Organic Chemicals in Groundvurr, Houston, TX, 1988. N. J. HuttJer, B. E. Mtnphy, tad J. S. Oierte, S» of Technology Reviev: Sofl Vapor Extraction Sysfcms, U.S.H.P.A, CR-814319-OM, 1988. D. J. Wilson, A. N. Claike, and J. H. Claike, Sofl Clean-tip byin-Jttu Aeration.!. Mathematical Modelling, Sep. Science Tech., 23:991-1037,1988. H2 Return [Print References] Figure 9. Card H2 of the "Soil Venting Help Stack" stack. 11 ------- - Hyperventilate Users Manual - V.3.2 Sample Problem Exercise • Is Venting Appropriate? In fV.3.2. you will work through an example problem to illustrate how one might decide if venting is appropriate at any given site. For the purpose of this example we will use the example site information given in Figure 10. North South 10' 20 _ § j 30, 50 — 60—I • M» « • H • .m * * •1 • ^^p> • -0.3 1 •0.2- - j "0.02 -0.0 .0.0 I OT - I -0.0 • 1.7 1 -24 i ,73 l L9.5 ' k V Tank Sandy V Backfill Clay V ------- -Hyperventilate Users Manual - Using your newly developed navigational skills and the right pointing arrow located at the bottom of each card, slowly step your way through the stack until you reach card 7 of the "Soil Venting Stack" stack (Figure 11). Take your time to read the text and "Help" cards associated with each card along the way. Step 1: Location: Card 7 of the "Soil Venting Stack" stack. Action: Read this card. It explains the process that you will use to decide if venting is appropriate. Then advance to card 8 of the "Soil Venting Stack" stack. Result: You are now at card 8 of the "Soil Venting Help Stack" stack (Figure 12). Step 2: Location: Card 8 of the "Soil Venting Help Stack" stack. Action: Read the instructions on this card. Take the time to read the information on the two "Help" cards: "Info about Calculation" and "About Soils (& Unit Conversions)". Now we will evaluate the efficacy of applying in situ soil venting to the lower soil zone (45 - 50 ft below ground surface) in Figure 10, which is composed of fine to medium sands. It also is the zone of highest hydrocarbon residual levels (>20000 mg/kg TPH in some areas). IB Venting Appropriate? Read This i FlOVIMB Estimation At this point ve vill proceed through a simple thought process to decide if soil venting is a feasible alternative. As mentioned earlier, the three main factors that govern the success of a venting operation are: - vapor flovrate - vapor concentrations - subsurface stratigraphy (or the location of contaminants relative to the vapor flovpath) Maximum Vapor Concentration Maximum Removal Ratt Figure 11. Card 7 of the "Soil Venting Stack" stack. ------- - Hyperventilate Users Manual- Flowrate Estimation: O Medium Sand ® Fine Sand OSiltySand O Clayey Silts O Input Your Ovn Permeability Range Permeability Range (darcy) 1) Choott Sou Type, or Optional- Enter your 2) Enter W«n Rid to (in) 3) Enter Rtdtw of Influent (fO , Intern! Thickness1 4) Optional - Enter your ova v»U vacuum (406* - max) 5) Click button t> eilcuk* Predicted Plovnte Ranees I 1 I toT 10 I Veil Radius Radius of Influence in ft Interval Thickness* I 66 Ift [ —>Calculate Flovrate Ranges— ] tUcloui of >cnu«i iattrvil, or Predicted Flovrate Ranges WeU Vacuum P. (torijO) Fk)Vi»te (SCFM) .1.0. 20 Q.33 1.30 Figure 12. Card 8 of the "Soil Venting Slack" stack. Step 3: Location: Card 8 of the "Soil Venting Stack" stack. Action: Choose the "Fine Sand" soil type, and enter: well radius = 2 in radius of influence = 40 ft interval thickness = 6.6 ft user input vacuum = 200 in H2O into the appropriate fields, then click on the "-^-Calculate Flowrate Ranges<-" button. Result: The flowrate ranges are calculated and displayed. Your screen should now look like Figure 12. The calculated values are estimates of the flowrate to a single vertical well (and are only valid estimates when your conditions are consistent with the assumptions built into the calculation - see Johnson et al. [1990a, b] for more details). Step 4: Location: Card 8 of the "Soil Venting Stack" stack. Action: Click on the right pointing arrow to advance to card 9. Read the information on this card, then advance to card 10 Result: You are now at card 10 of the "Soil Venting Stack" stack (see Figure 13). Step 5: Location: Card 10 of the "Soil Venting Stack" stack. Action: Assume that the soil temperature at our sample site is 18° C. Enter this value in the appropriate field, then hit the "return" key. This action clears all values from the other fields. ------- -HyperventilateUsers[Manual - Vapor Concentration Estimation - Calculation T) Type in Temperature (C) (hit ) Click to Enter Composition of Contaminant T) or Choose one of the Default Distributions T) Click to Viev Distributions, (optional) T) Click to Perform Calculations 18 O Enter Distribution O "Fresh" Gasoline ® "Weathered" Gasoline C Viev Distributions") ® Perform Calculations Sum of Mass Fractions Results: Calc. Vapor Pressure Calc. Vapor Concentration •iiftYHovDo I M««su» » Distribution?] Figure 13. Card 10 of the "Soil Venting Stack" stack. Help: Compound List \| Viev Only Mode \| Compound Name Mass Fraction Molecular Weight (c) Vapor 1 2 3 4 5 6 7 8 9 10 propane isobutane o-butane trans-2-butene cis-2-butene 3-methyl-l-butene isopentane 1-pentene 2-methyl-l-butene 2-melhyl- 1, 3-butadiene 0.00 0.00 0 0 0 0 0.0069 0.0005 0.0008 0.0000 44.1 58.1 58.1 56.1 56.1 70.1 72.2 70.1 70.1 68.1 8. 04673 K> 2.75865 n 1.97431 if 1.84196 Ii! 1.67019 II 0.88399 11 0.73146 11 0.64989 m 0.62093 if 0.60914 K> I 0.99628 Sum of Mass Fwctons (ihoxild b« .1) Hov Do I Mewuie a Dlstribution?^« Rttum te Vapor Cone. Estimation Card Figure 14. Card H16 of the "Soil Venting Help Stack" stack. 15 ------- -Hyperventilate Users Manual - At this site the residual hydrocarbon is a "weathered" gasoline, so choose this selection from the three composition options listed. The "Fresh" and "Weathered" gasoline selections correspond to pre- programmed compositions that are useful for estimation purposes. If you knew the composition of your residual, then you could enter it by selecting the "Enter Distribution" option. Click on the "View Distributions" button to take a look at the compound library and the pre-specified composition of "weathered" gasoline. Result: You are now at card HI6 of the "Soil Venting Help Stack" stack (see Figure 14). Step 6: Location: Card H16 of the "Soil Venting Help Stack" stack. Action: View the library and pre-specified composition. If you are interested, explore some of the help cards. Then click on the "Return to Vapor Cone. Estimation Card" button to return to card 10 of the "Soil Venting Stack" stack. Result: You are now at card 10 of the "Soil Venting Stack" stack (Figure 13). Step 7: Location: Card 10 of the "Soil Venting Stack" stack. Action: Click on the "Perform Calculations" button. Result: Hyperventilate calculates the maximum possible vapor concentration corresponding to the specified composition and temperature. The results are displayed in Card 10 of the "Soil Venting Stack" stack, which should now look like Figure 13. Step 8: Location: Card 10 of the "Soil Venting Stack" stack. Action: Using the right-pointing arrow button, advance to card 11 of the "Soil Venting Stack" stack. Take the time to read the text, then click on the "Calculate Estimates" button Result: You are at card 12 of the "Soil Venting Stack" stack. The calculated flowrates and maximum possible removal rates are displayed along with an updated list of the input parameters that you have entered. Your screen should look like Figure 15, if you have chosen the "Ib/d" units. Step 9: Location: Card 12 of the "Soil Venting Stack" stack. Action: Click on the right-pointing arrow button. You are now at card 13 of the "Soil Venting Stack" stack. Read the text, then enter: estimated spill mass = 4000 kg desired remediation time = 180 d Now click on the "~>Press to Get Rates<~" button ------- -Hyperventilate Users Manual - Maximum Remo val Rate Estimate* select your unit preference beta v OUcg/m Ho: These are "maximum removal rates", and should only be used as screening estimates to determine if venting is even feasible at a given site. Continue on to the next card to assess if These rales an acceptable... Temperature (C) Soil Type Sofl Permeability Range (darcy) Well Radius (in) Radius of Influence (ft) Contaminant Type Permeable Zone Thickness (ft) Pv - Well Plovrate Estimates Max. Removal Rate Estimates Vacuum [SCFM] [»'J (inHjO) (single veil) (single veil) ™.5.._. ...IQ .. 20 40 120 200 .... 0,66 .... } 30_ 2.54 ....JLZ..L.... ... 6,83 1007 to to to to to to to ....112... 6.5$, 13...Q2._ 25.38 68.27™ 100.66 6 . .....12 25 52 ._.....&0_ 178_ 364 to to to to to to to ....._.6.2 __12L_ 2.5J 517 7.o,9_ 1778 3636 Figure 15. Card 12 of the "Soil Venting Stack" stack. I Soil Veatiog Appropriate? Enter At this point, you compare the maximum possible removal rate vith your desired removal rate. If the maximum removal rate does not exceed your desired removal rate, then soil venting is not likely to meet your needs, and you should consider another treatment technology, or make your needs more realistic. In the next cards, ve vill refine the removal rate estimates, in ®kg Estimated Spill Massl 4000] Q ib (2J Enter Desired i—Tgj Remediation Time ' vAx ^ ->Press to get Rates<- J Single Vertical Well Results days Desired Removal Rate: Gauge Vacuum (in H20): Min Flovrate @ 200 in H2O Max Ftovrate @ 200 inH2O Max. Est Removal Rate: (lover estimate) • per veil j^ (upper estimate) - per veil [~ 200 ID. 07 100.66 (inHZOJ [SCFM] [SCFM) 164.892 IfcMJ Figure 16. Card 13 of the "Soil Venting Stack" stack. 17 ------- - HyperVentUate Users Manual - Result: Your screen should now look like Figure 16. Note that your desired removal rate (=22 kg/d) is less than the estimated maximum removal rates for a single vertical well (=165 to 1650 kg/d). At this point in the screening exercise, therefore, soil venting still appears to be a viable option. Step 10: Location: Card 13 of the "Soil Venting Stack" stack. Action: Click on the right-pointing arrow button to advance to card 14 of the "Soil Venting Stack" stack. Read the text, then advance to card 15 of the "Soil Venting Stack" by clicking on the right-pointing arrow button. Again, take the time to read the text, then advance to card 16 of the "Soil Venting Stack" stack. The focus of these cards is the prediction of vapor concentrations and removal rates as they change with time due to composition changes. It is important to try to understand the concepts introduced in these cards. Result: You are at card 16 of the "Soil Venting Stack" stack (see Figure 17). Step 11: Location: Card 16 of the "Soil Venting Stack" stack. Action: This card is used to finalize your input data prior to calculating vapor concentration and residual soil contamination composition changes with time. Read the instructions in the order that they are numbered. Note that the summary table in the upper right corner of the card contains all the parameter values that you have input thus far. The instructions describe how to change these values, but at this point we will retain the displayed values. Because it is difficult to present the behavior of each compound in a mixture composed of an arbitrary number of compounds, the output is simplified by reporting the behavior in terms of "boiling point" ranges. This simply represents a summation of all compounds whose boiling points fall between pre-specified values. Presented in this fashion, the model results can be interpreted much more quickly. Click on the "tell me more about BP ranges..." button, read the help card, then return to card 16 of the "Soil Venting Stack" stack. Click on the "-->Set Default BP Ranges<~" button. Your screen should now look like Figure 17. Click on the "Generate Predictions" button Result: The message "Sit Back and Relax..." will appear on your screen, followed by a screen on which the following appears: "Copyright © Absoft Corp 1988 Copyright © Shell Oil Co 1990 HANG ON -— YOU WILL BE RETURNED TO HYPERCARD... # OF COMPOUNDS IN LIBRARY • 62" Then card 17 of the "Soil Venting Stack" stack will appear. ------- - Hyperventilate Users Manual - Model Predict/oat To the rightist summary of the data you havt input Ifyouvishto change a»y of the tafo, then click on the parameter name, and redo the calculations on the cud you vill be taken to. Press the blinking 'Return' button to come back The model returns output that tllovs you lo deterniine iwidual unounts of compounds falling vithin 5 boOinc point IUICM. Type in your OVA nnces, or choose the default values. lllHI Son Type Sofl PenwibflHy Rant e (daicy) Well Radius (in) Radius of InOoence (ft) Comuoinut Type Penneable Zone Thickness (ft) [ —> get Default BP Ranges <— .!.. Boilinsf Point Ranee -=5DL ..11.1...... Jo, 144 tp ?0 £.. ...IQ.......UOJ.JIU..C £. c H4 250 Generate Predictions til me more about BP runes. Figure 17. Card 16 of the "Soil Venting Stack" stack. —> Import Oata<— ^ S«nmttd Vapor 0.20S3H03 FIRST PRESS TOE IMPORT n ATA R T TTIt iM I These an the results for the contaminant type that you have QtfM(O) L-airt f-residual .00 .24 .57 .98 1.49 2.11 2.87 381 Vapor Cone. [» Initial] 100.000 75.062 58.631 48.078 39.390 31.941 25.916 21 ISO Residual Level [98 Initial] 100.000 95.000 90.022 65.034 60.034 75.035 70.035 65037 £ Mia Yalnn* ID Benum ImlflAl t>»M«uil 1 ijii Temperature (C): ry Contaminant Type: BP«1 Residual [96 total] .690 .123 .000 .000 .000 .000 .000 .000 BP2 Residual [96 total] 11.650 9.263 6.755 4.512 2.632 1.222 .385 068 BP3 Residual [96 total] 24.010 23.982 23.474 22.403 20.771 18.503 15.556 12.053 128 48 \|L~^ l- If 0.10 \| MJM!,,!! 18 \| Weatheiei Gasolla* BP4 Residual [96 total] 22.140 23.000 23.820 24.577 25.246 25.766 26.031 25.919 BPttS Residual [96 total] 41.510 43.632 45.950 48.509 51.350 54.509 58.028 61.959^ ^> 'B ?£ m m IHUl h«j Figure 18. Card 17 of the "Soil Venting Stack" stack. V ------- - Hyperventilate Users Manual - Step 12: Location: Card 17 of the "Soil Venting Stack" stack. Action: Read the instructions, then click on the "~>Import Data<~" button. Result: Your screen should look like Figure 18. The table in the lower part of the card lists model predictions: vapor concentration and residual soil concentration (expressed as a percentage of their initial values), as well as the composition of the residual (expressed as a percentage of the total for each boiling point range) as a function of the amount of air drawn through the contaminated soil. Note that as the volume of air drawn through the soil increases, the vapor concentration and residual soil levels decrease, and the composition of the residual becomes richer in the less volatile compounds (BP Range #5). In the upper right comer of the card are displayed the saturated, or initial, vapor concentration and the minimum amount of air that must be drawn through the soil per gram of initial contaminant to achieve at least a 90% reduction in the initial residual level. This value is used in future calculations as a design parameter. Step 13: Location: Card 17 of the "Soil Venting Stack" stack. Action: Click on the right-pointing arrow to advance to card 18 of the "Soil Venting Stack" stack. Result: You are at card 18 of the "Soil Venting Stack" stack, which should resemble Figure 19. Read the text. A summary of your input parameters appears on the right side of this card. At the bottom appears two calculated values representing the range of the minimum number of wells required to achieve a 90% reduction in the initial residual level in the desired remediation time. These values correspond to idealized conditions, however, they can be used to gauge the efficacy of soil venting at your site. For example, in this case the minimum number of wells ranges between 0.7 - 7, which is not an unreasonable number for a site the size of a service station. If the range had been 100 - 1000, then it might be wise to consider other remediation options. It is important to recognize that model predictions are intended to serve as guidelines, and are limited in their ability to describe behavior that might be observed at any given site. One should use all the information available, in addition to idealized model predictions to make rational decisions about the applicability of soil venting. ------- - Hyperventilate Users Manual - Step 14: Location: Card 18 of the "Soil Venting Stack" stack. Action: Click on the right-pointing arrow button to advance to can! 19. Result: You are now at card 19 of the "Soil Venting Stack" stack. This card lists several phenomena that can cause one to achieve less than ideal removal rates. Take the time to explore each of these options, then return to card 19 of the "Soil Venting Stack" stack. I^^^^^^^^M^MW^^^^^H^^^BM^^^^^^^^HMWiV^^^^^^B^^MP^^^^H^^^^M^^^^^^B Is Venting Appropriate? This is a complete summary of the data and results. Based upon these numbers, a "minimum number of veils" has been calculated, vhich should give you some indication of hov appropriate venting is for your application. Note that this is the number of veils if circumstances are ideal. Temperature [C]: ConttainBAtTyp: ^_ Soil Type: [^ Well Radius [in]: Eat. Radius of Influence [ft]: Penmetble Zone Thickness [ft]: Flown per Well (120" Vtc) [SCFMJ ZTovn* per Well (120" Vtc) [SCFM] Min. VoL of Air [Uf-iesidukl]: Estimated SpflJ Mtsj: Desired RemediatJon Time [dtyi]: 18 Wmtk«ra< GuolfB* 6.6 6.83 68.27 128.48 4000 180 OB Tour Inpwt Parameters Figure 19. Card 18 of the "Soil Venting Stack" stack. 21 ------- - Hyperventilate Users Manual - Field Tests Figure 20. Card 20 of the "Soil Venting Stack" stack. V.3.3 Sample Problem Exercise - Field Permeability Test. Note: It is recommended that you always plot and visually inspect your data prior to attempting to fit it to any theory. In this example, we use Hyperventilate to analyze air permeability test data from the site pictured in Figure 10. We will focus on results from the lower fine to medium sand zone (45 - 50 ft below ground surface). Advance to card 20 (Figure 20) of the "Soil Venting Stack" stack to begin. Step 1: Location: Card 20 of the "Soil Venting Stack" stack. Action: Using the right-pointing arrow, advance to card 21 of the "Soil Venting Stack" stack. Read the text, then click on the "Air Permeability Test" button. Result: You are at card API of the "Air Permeability Test" stack. Step 2: Location: Card API of the "Air Permeability Test" stack Action: Read the instructions, then click on the "Show Me Set-up" button. Take a look at the figure, then click the "Return" button to return to card API of the "Air Permeability Test" stack. Now click on the "Test Instructions" button. Result: You are at card AP3 of the "Air Permeability Test" stack. Step 3: Location: Card AP3 of the "Air Permeability Test" stack. ------- -Hyperventilate[Users Manual - Action: Step 4: Step 5: Result: Location: Action: Result: Location: Action: Result: Read the text, look at the sample data (click on the "show me sample data" button) then enter the following values for this example: soil layer thickness estimated radius of influence air permeability test flowrate = 6.6 ft = 50 ft = 15CFM Click on the "-->Calculate<--" button to estimate how long the air permeability test should be conducted. Your results should match those displayed below in Figure 21. Card APS of the "Air Permeability Test" stack. Click on the "Return" button to return to card API of the "Air Permeability Test" stack. Then click on the "Data Analysis" button. You are now at card APS of the "Air Permeability Test" stack. Card APS of the "Air Permeability Test" stack. Read the text, then step through cards AP6 and AP7, until you reach card APS of the "Air Permeability Test" stack. You are now at card APS of the "Air Permeability Test" stack. Air Permeability Test - Instructions 1) Identify soil zones to be treated 2) Install vapor extraction vell(s) in this zone(s). Existing monitoring veils may be used, vhen the screen interval extends only into the zone to be treated Note the extraction veil radius and borehole size. Insure that the veil is not "connected" to other soil zones through the borehole (use cement/grout i™, to seal annular borehole region). [ shov me sample data FOR Volwne EstiiMtioa: Enter 1) Soil Layer Thickness {ft]: 2) Estimated Radius of Influence [ft]: 3} Air Perm. Tesi Flovrue {CFM J: 6.6 50 15 ( -> Calculate < Pore Volume: Time to Extract a Pore Volume: APS Figure 21. Card APS of the "Air Permeability Test" stack. 23 ------- -Hyperventilate Users Manual - Step 6: Location: Action: Card AP8 of the "Air Permeability Test" stack. Read the text, click the "clear" buttons to clear any entries from columns, then enter the following data: r = 53 ft r = 32.4 ft Time Gauge Vacuum [mini fin H?O1 9 0.1 11 0.2 15 0.2 23 0.4 30 0.7 40 1.3 100 2.8 flowrate screened interval thickness Time fmin] 4 7 9 12 16 24 30 39 52 77 99 110 121 141 = 15 = 6.6 Gauge Vacuum [in H?O1 1.2 3.0 4.3 5.5 6.9 9.9 11 13 16 20 21 23 24.5 25.5 SCFM ft Step 7: While entering the data it is convenient to place the curser in the time column, type in the time value, then use the "tab" key to advance to the vacuum reading column. Enter the corresponding vacuum value, then hit the "tab key again. As you see, this advances the curser to the time column again. Now click the "~>Calculate<~" button. Result: Your results should match those displayed in Figure 22. Soil permeability values have been calculated by fitting the field data to the theoretical model described in cards APS - AP7 of the "Air Permeability Test" stack. Location: Card APS of the "Air Permeability Test" stack. Action: Review the results, then click on the "Explanation & Statistics" button. This advances you to card AP9 of the "Air Permeability Test" stack, which lists correlation coefficients for the data fitting process. These values give an indication of how well the model describes the behavior observed in the field. Values approaching unity indicate a good fit. Your results should match those given in Figure 23. 24 ------- -Hyperventilate Users Manual - Air Permeability Tett - Data Analysis (cont.) Eater radial 2) distances of monitoring poino Enter measured —< 2) times and gauge vacuums ^3) Enter (optional): a)ftovra* L 15 1(SCFM) b) screened interval thickness 6.6 I (ft) 53 (min) (inH20) r= j 32.4 \|(0) (nun) (in H20) 9 11 15 23 30 40 100 O.I 0.2 0.2 0.4 0.7 1.3 2.8 o " , 4 7 9 12 16 24 30 39 52 7V 1.2 3 4.3 5.5 6.9 9.9 11 13 16 20 -6 J & is .. <> Figure 22. Card APS of the "Air Permeability Test" stack. Air Permeability Test - Data Analysis (cont.) On the previous Card (AP8), the da» you input vere fit to the Approximate expression given on Card AP6. It vs analyzed using both methods described on card AP7, if you input values for the extraction veB ftovrate (Q) and the stratum thickness (in). Belov each column of data, the tvo calculated permeability values aic denoted by: darcy(A) - refers to calculation method 1 (see Card AP7) - refers to calculation method 2 (see Card AP7) During the regression analyses, the data expressed w pairsof points (ln(t),P') are fit to a tine The "correlation coefficient", r, is a measure of hov veil the date conform to the theoretical curve. As i-->l, the data points all fall on the theoretical curve. At the right are given the correlation coefficient values for the three data sets For more info on the meaning of r, consult any introductory Statistics book. Correlation Coef. (r) data set tl \|0.941158 \| data set t2 I 0.98602 data set 13 I NoDat Figure 23. Card AP9 of the "Air Permeability Test" stack. V ------- - Hyperventilate Users Manual - System Design Slulr/* T««ffl» riUf fa* O«>------- -Hyperventilate Users Manual - System Design... At the right is a list of the components of a venting system design. Click on each to conduct the indicated phase of the design process Remember: It is not our intention ID provide a generic recipe for vacuum extraction system design; instead v» suggest the lollo vine •» » structured thought process. As you shall see, even in a structured thought process, intuition tnd experience play importat roles. Then la no substitute for a food fundamental understanding of vapor flov processes, transport phenomena, tad groundvater flov! O Number of Extraction Wells OWell Location O Veil Construction O Surf ace Seals O Groundvater Pumping System O Vapor Treatment 33* Figure 25. Card 24 of the "Soil Venting Stack" stack. Number of Venting Wellt . . . The procedure for estimating the required number of extraction veils to stanfltr tt the venting a appropriate at a given st. As fllustt»fcd at ft right, v» vill eitlmaie single vertical veil flovrates, calculate the minimum vapor flov required, determine ine anal enent of influence, and then factor in any site-specific limitations. This information then determines the necessary number of extraction veils. Jut proceed to folio v the steps dictated on the foDoving cards — > FJovrate Estimation Maximum Removal Rate Minimum Volume Requirement Site- Specific Limitations Ana of Influence Reauinment N\_ Hunter (i . °' A-^ Sxtnctlom sy Wells Figure 26. Card SD1 of the "System Design" stack. V ------- -Hyperventilate Users Manual - Step 3: Location: Card 24 of the "Soil Venting Stack" stack. Action: Select "Number of Extraction Wells" from the list of options. Result: Card SD1 of the "System Design" stack should be displayed, as pictured in Figure 26. Step 4: Location: Card SD1 of the "System Design" stack. Action: Read the text, then use the right-pointing arrow to advance to card SD2. Result: Card SD2 of the "System Design" stack should be displayed. Step 5: Location: Card SD2 of the "System Design" stack. Action: Read the instructions on the card, enter the following values into the table, then click on the "Update" button: Parameter subsurface interval (ft BGS) description of contaminant radial extent of contamination (ft) interval thickness (ft) average contaminant concentration Medium Sand 10-30 gasoline 20 20 100 Soil Zone Clavev Silt 30-43 gasoline 20 13 1000 Fine Sand 43-50 gasoline 20 7 10000 Result: Card SD2 should now resemble Figure 27. Step 6: Location: Card SD2 of the "System Design" stack. Action: Use the right-pointing arrow to advance to card SD3 of the "System Design" stack. Result: Card SD3 of the "System Design" stack should be displayed. Step 7: Location: Card SD3 of the "System Design" stack. Action: Read the text. Note that "clicking" on many of the table headings will take you to "help" cards. Take a few minutes to explore the use of these, then enter the following information: Parameter permeability (darcy) design vacuum (in H2O) WeU Construction: Radius of Influence (ft) Extraction Well Radius (in) Extraction Well Screen Thickness (ft) Medium 10-100 40 40 2 10 Soil Zone Sand Clayey Silt 0.01 -0.1 40 40 2 5 Fine Sand 1- 10 40 40 2 5 ------- - Hyperventilate Users Manual - Design Input Parameters. . . (soilstiaticraphy fc containinant characteristics) Please enter the required information for etch distinct soil layer, click on (he "Upde* " button, and then proceed to the neit cud (i.e. cUck on rijht irrov at bottom). f the »b kev can be used to me ve betveen cells) Select the totrt mas tinit* that you prefer C Clear All Entries J OPb] Description of SoU Unit J. JLltaL 4 DepthBOS* 30 «L A ... _»,. _»., 3SL .... to SB- Description of Contamination Contaminant Distribution ntiu [A] JO. 20 [ftl JO. —JUKU- 1000 CeJe. To«l Mess DC] J2IL2. 0.0 •Maw Grauf Bwfut Figure 27. Card SD2 of the "System Design" stack. Design Input Parameters... Please envr the nguixed infoimation for eech distinct soil layer, and then proceed to the next card. No: - click on an; (able headinc to tet more info - use tab key to move betveen cells O MtUva, Su* On&i'oi O Billy Bui Extraction Wefl Construction • Ewtr or ckMf• (nm Ust «t to) rjgil Figure 28. Card SD3 of the "System Design" stack. V ------- - Hyperventilate Users Manual - The "Critical Volume of Air" is calculated by the same procedure used previously in §V.3.2 (steps 10 -13). To initiate this calculation, "click" on the "Critical Volume of Air*" heading. Result: Card SD5 of the "System Design" stack appears on your screen (Figure 29). Step 8: Location: Card SD5 of the "System Design" stack. Action: Read the text carefully. The focus of this card is the prediction of vapor concentrations and removal rates as they change with time due to composition changes. It is important to try to understand the concepts introduced in this card. For more information, read the reference article contained in the appendix. Click on the "Do a Calculation" button to advance to card SD6 of the "System Design" stack (Figure 30). Result: Card SD6 of the "System Design" stack appears on your screen. Step 9: Location: Card SD6 of the "System Design" stack. Action: This card is used to finalize your input data prior to calculating vapor concentration and residual soil contamination composition changes with time. Read the instructions in the order that they are numbered, then enter "18" for the temperature and select "weathered gasoline" from the three composition options. Because it is difficult to present the behavior of each compound in a mixture composed of an arbitrary number of compounds, the output is simplified by reporting the behavior in terms of "boiling point" ranges. This simply represents a summation of all compounds whose boiling points fall between pre-specified values. Presented in this fashion, the model results can be interpreted much more quickly. Click on the "tell me more about BP ranges..." button, read the help card, then return to card SD6 of the "System Design" stack. Click on the "~>Set Default BP Rangeso-" button. Your screen should now look like Figure 30. Click on the "Generate Predictions" button Result: The message "Sit Back and Relax..." will appear on your screen, followed by a screen on which the following appears: "Copyright © Absoft Corp 1988 Copyright © Shell Oil Co 1990 HANG ON YOU WILL BE RETURNED TO HYPERCARD... # OF COMPOUNDS IN LIBRARY = 62" Then card SD7 of the "System Design" stack will appear as shown in Figure 31. ------- -HyperventilateUsersManual- Critical Volume Calculation... typically observed In venting operations. The results an plotted in this vay t> emphasize that Ac degree of remediation that can be achieved by venting depends mainly on the volume of vapor extracted divided by the initial mail of residual hydrocarbon. For the example pictured at the right, approximately 100 liters of air must be vitbdravn from the subsurface In order to remove about 90O of a single gram QC/QC(UO) 1 % Removed 100 Return to Design Weathered Gasoline T-20C 10% moisture content C(t=0)« 222 mgrt Figure 29. Card SD5 of the "System Design" stack. Critical Volume Predictions... Simply enter the temperature at the right, and then specify the composition of your contaminant. If you are unsure about this, elicit on the "About Composition..." button located at the low right The model returns output that alia vs you to determine residual amount! of compounds falling; vithin 5 boiling point ranges. Type in your ovn ranges, or choose the default values. tell me more about BP ranges. Contaminant Composition (choose one) J~ 1 L_ ;> Enter Distribution D "Fresh" Gasoline i) "Weathered" Gasoline ( Viev Distributions J ( ~> get Default BP Ranges <— ) .M!i.ngP.oint.Bange....»3.. M!.i.Gg.P.oint.RaBge..4. Boilinp Point Ranfe ------- - Hyperventilate Users Manual - Step 10: Location: Action: Result: Step 1 1 : Location: Action: Result: Step 12: Step 13: Step 14: Location: Action: Result: Location: Action: Result: Location: Action: Result: Card SD7 of the "System Design" stack. Read the instructions, then click on the "-->Import Data<~" button. Your screen should look like Figure 3 1 . The table in the lower part of the card lists model predictions: vapor concentration and residual soil concentration (expressed as a percentage of their initial values), as well as the composition of the residual (expressed as a percentage of the total for each boiling point range) as a function of the amount of air drawn through the contaminated soil. Note that as the volume of air drawn through the soil increases, the vapor concentration and residual soil levels decrease, and the composition of the residual becomes richer in the less volatile compounds (BP Range #5). In the upper right corner of the card are displayed the saturated, or initial, vapor concentration and the minimum amount of air that must be drawn through the soil per gram of initial contaminant to achieve at least a 90% reduction in the initial residual level. This value is used in future calculations as a design parameter. Card SD7 of the "System Design" stack. Click on the "Return to System Design" button A dialog box will appear asking: "Transfer Critical Volume Value?". Click on the "Yes" button. You will now be prompted by another dialog box asking: "What soil unit # is this value for?". Enter "1" into the appropriate place then click on the "OK" button. You will now be transferred back to card SD3 of the "System Design" stack. Note that the value "128.48" has been entered into the "Critical Volume of Air11 column for the medium sand soil unit. Card SD3 of the "System Design" stack. Enter "128" into the "Critical Volume of Air" column for the clayey silt and fine sand soil units. For this example problem enter "100" for the efficiency in all three soil units Card SD3 should now resemble Figure 28. Card SD3 of the "System Design" stack. Click on the right-pointing arrow at the bottom of the page to advance to Card SD4 of the "System Design" stack. Card SD4 of the "System Design" stack should appear on your screen. Card SD4 of the "System Design" stack. Assume that you wish to remediate this site in 180 days. Enter "180" in the "Time for Clean-up" column for each soil unit. Click on the "Update" button. Hyperventilate calculates a range of flowrates to a single vertical well, then uses this value and other input parameters to determine the minimum number of wells required based on two approaches. ------- 'Hyperventilate Users Manual - To read about these, click on the "Number of Wells" column heading. Your card SD4 should resemble Figure 32. // is importani to recognize that model predictions are intended to serve as guidelines, and are limited in their ability to describe behavior that might be observed at any given site. One should use all the information available, in addition to idealized model predictions to make rational decisions about the applicability of soil venting. You can read about the effect of venting at this site in the article: "Soil Venting at a California Site: Field Data Reconciled with Theory", by P. C. Johnson, C. C. Stanley, D. L. Byers, D. A. Benson, and M. A. Acton, in Hydrocarbon Contaminated Soils and Groundwater: Analysis, Fate, Environmental Health Effects, and Remediation Volume 1,P.T. Kostecki and E. J. Calabrese, editors, Lewis Publishers, p.253 - 281, 1991. 33 ------- - Hyperventilate Users Manual - —> Import Data <--J Saturated Taper n 0' rm»/r i In'L1 FIRST PRESS THE IMPORT DATA BUTTON! These are the results for the contaminant type that you have L-ato g-iesidual .00 .24 .57 .98 1.49 2.11 2.87 3.81 Vapor Cone. I» Initial] 100.000 75.062 58.631 48.078 39.390 31.941 25.916 ^1.150 Residual Lewi [* Initial] 100.000 95.000 90.022 85.034 80.034 75.035 70.035 65.037 £ Min Volwott to 1 ^ >90» of Initial IJji Temperatui$ Contamlnai BPI1 Residual [96 total) .690 .123 .000 .000 .000 .000 .000 .000 BP2 Residual [96 total] 11.650 9.263 6.755 4.512 2.632 1.222 .385 .068 EtolDDV Resliwl e(O: « Type: BPI3 Residual [SB total] 24.010 23.982 23.474 22.403 20.771 18.503 15.556 12.053 128.48 \| JrJShlSi 18 \| Wettheiet Gasoline BP»4 Residual [96 total] 22.140 23.000 23.820 24.577 25.248 25.766 26.031 25.919 BPtS Residual 41.510 O 43.632 ~ 45.950 fl 48.509 I! 51.350 \| 54.509 56.028 \|\| 61.959 O Return to System Design Figure 31. Card SD7 of the "System Design" stack. Design Input Parameter.. Pleasa enter (1) the desired time period for remediation, (2) the design gauge vacuum, and then (3) click the "update" button. No: - click on any table heading to get more info - we tab key to move berveen cells Minimum Number of Wells Description of Soil Unit Tune for Clean-up Mays\| Design Vacuum ------- - Hyperventilate Users Manual - References Hutzler, N. J,, Murphy, B. E., and Gierke, J. S., State of Technology Review: Soil Vapor Extraction Systems, U.S.E.P.A, EPA/600/2-89/024, June 1989. Johnson, P. C, Kemblowski, M. W., and Colthart, J. D., Practical Screening Models for Soil Venting Applications, NWWA/API Conference on Petroleum Hydrocarbons and Organic Chemicals in Groundwater, Houston, TX, 1988. Johnson, P. C., Stanley, C. C., Kemblowski, M., W., Byers, D. L., and Colthart, J. D., A Practical Approach to the Design, Operation, and Monitoring of In Situ Soil Venting Systems, to appear in Ground Water Monitoring Review, Spring 1990. Marley, M. C., and Hoag, G. E., Induced Soil Venting for the Recovery/Restoration of Gasoline Hydrocarbons in the Vadose Zone, NWWA/API Conference on Petroleum Hydrocarbons and Organic Chemicals in Groundwater, Houston, TX, 1984. Marley, M. C., Baehr, A. L., and Huh, M. F., Evaluation of Air-Permeability in the Unsaturated Zone using Pneumatic Pump Tests: 1. Theoretical Considerations, in review, 1990. Thornton, J. S. and Wootan, W. L., Venting for the Removal of Hydrocarbon Vapors from Gasoline Contaminated Soil, J. Environ. Sci. Health, A17(l), 31-44, 1982. Newell, C. J., Haasbeek, J. F., and Bedient, P. B., OASIS: A Graphical Decision Support System for Ground-Water Contaminant Modeling, Ground Water, 28 (2), 224 - 234, March - April 1990. ------- ------- - Hyperventilate Users Manual - Appendix A: "Soil Venting Stack" stack cards. ------- 'Soil Venting Stack" Cards A1 p I A Practical A t»tb Uooitoruc of lB-Sita Soil V« m»IJI •mi AaH0uai DdoaCMia •1C. JU A»TJ. i tf n.o. M«l1M>«tak ff OttoOMClf* I«Tn •T Tbi» HypaOrt Stact v» u «d to halp guuto mnu unmulit icantott through tt» ttttvte frocM Mcavjary to doada if ant bov (oil wntug migM 1» appliad IP ra foUowitbapana i »gT»i «» Tl» orgunboo and lope ef UMJ rack ckto •i UoKtoruc of I»-Sit» Soil Votuf C. C. >h»by, M. W. Lnumtt. J. D. Cdtel. * D. L. ) nd Wnv UaBitoni«Rnwv, Spring 1990, p. 159-178 Soti Vtnhag (».»«. 'u wring, •^icuantanetwo, Ic in-ntu Tipef mutUmi") n npdl; taconiag «o> rf Ot mod f« pnmiil Kib taflunot Iha weeaa) ef anf toil ivtiag ofMnboci •• MBly uudaritoid. By^^7ii«iiKui ID tl» follow* canto v» vflt wun U* • latk or 9ill l» tan ilaeomd, No» wt vill Off Ormifb » l»gdl to ( art dupUp da flovdvt tte if tto uferttBthn«btpncm. Clickint viUu B7 [IDCMI box viD Mfei f»u to tW «q»ct «f ttt ttougU Soil Venting System Design Process Invwtifilioa • nil im»Higaii)u n conducud to BOOB Of Mil VBd * ............ * ........... ' ...... Tte mttct on pntrtial human and rawMan. and it conductad in a nlatnalrihoitpriodor, on* •qlon Ite (Mtaiit7 of «D traM Otnammtioo («, q«d, fnittiBf pnttan ta wtrtfatad. m ttao 0» fin! Soil Vwung it mod liWy to bt HBOMBM vtaB foilt «• mtdjmA t QlD-SituBtortinJalioo O^ftiMififrtii^rttiliKmi OSolw* ExtndiaaSoil Voting M ite pou* «• vill prooMd Urougb a 0104. proc«i to (tacidt if Mil At telonltM I ------- 'Soil Venting Stack* Cards A2 O top* Y«* O»o Pwmdility Rang* Til inrtilitj lti»t« I I Itol Ifl I Vdl Radn I 2 I in Ratal of laftam I 40 lit I 6.6 in rate oecw* vbmmr Om npon ronowl by anting w ' or in tqvilitniaa vilh (be IntheraacardyouviUutuBMa of JOW O tfai uMnctMtt in tte i^frv krfl oocnr of th0 uul cvd. Vapor CMMHUMMM 1 Typ« in Tonponhn (C) (tit ) Calculation 20 J Click to EiMr Contortion of Coolan»nM O Enter Diitnbuaon ! or O 'FrBh' Gasoline Cboon one of tht Drfwlt DirtnbUiOM ® • Wnttond" Gawlme T) Click to Vwv DiUhbuboB, (optiond) T) Click to Parfonn CalniMxM C VJOT Dutnbuuopi 3 O P«fonn CalcublKW Remov! Rte Estintmtes Tht nmowi rate occm vl Ua Kport ronowd by wntmg or in equilibnun nth U» Th> 'RonMil Rate' if amply OB prodict of )!• flovnto tim« te npor caocartntooo. R«to Vipor z V»por ConcntratioB Flovrat* ean mf 5 10 20 •4 60 120 2on 0.33 0.66 1.30 ?-5L J.71 6. S3 1007 to to to to In to to 3.32 6.S9 >3.tt? 2S.3S 37.09 6127 10066 6 12 25 52 SO 17S 3M 121 2SI 517 799 1778 3636 At Ihu potnt, you coopv* the with you- diond ran»il rate. If OB do« not (End yo«r dwnd iwoml rate, ttm soil wring » ootltMy to OBM TOtr andi, Dndi UMJIV rwlifttc. Imhaanitanb. T»villr«ru» CD Enter Ownd Remediation Tins O «««t • UftRW»<— Sugte Venial taHZO): pan 9200 _UJ IOt.66 MM) \|hK20; \|1CFH\| [: «^->-»-«» rjfrr Ml MM) W) oriy• • Ibiteaf, ad ^\|M te raRmd if ^cfting is TypioUy doing toil untinft tbtz (vbntetottl por fiovrate • W of not1 [QC(tXQC(UQ)],«bilttni ..-j\|'--_ TJlllI ,—I. — UUffUBUUM "UUI II tott votinte of i .1 .01 .001 .0001 ------- •Soil Venting Stack' Cards A3 Is Veatiaf Appropriate IK Wa (120- Y«J [tCPM] NotolW MM.TciA(m-wil.lt of wtUf if Clidt on (to tah» to OB rij* to System Design System Desifa... ------- "Soil Venting Stack* Cards A4 System Dcsira... Economics... System SJbat Down •Click' OB 107 item telov (t hold button don) to M cocte vitk that item. TrgKiotl clMD-up Ineti HOOK - J250K for tta wting on •idnbmdootbBiftumM pomtiil iapKt flat «7 randtal m»y bm on «r clMo-up tiini, ptrmiaing Kd tfci typt of O £>lncti«B V«U V ^or C O EHr«tioa V«U Vtpor Compontto* too to ralKMi to nftr Tte tvo mjor COM •• Titb Uv OSoil Borin* EMa Acknowledgements. ------- ------- r 'Hyperventilate Users Manual - Appendix B: "Soil Venting Help Stack" stack cards. ------- •Soil Venting Help Slack' Cards B1 Help: Stack Information Buttons Biraom have been placed in each curd. Clicking on any button will perform in action. tuA ac When curiaiu, click an Symbol, Picmet or Tea. Fields Field! my contain information, or they my be i place for yon to input nimben. Scrolling Fi«M: Help: About Soil Venting Un» afonpuo. Awl (oil wumi OB te rood t> » followiit Orp V Onmtwua. tfaUM, TX. I Or\|>Ke N.I.Itaotot. B.E. Mun».l»U S OMB. SUB orTuhDotoiy SCVBW: Soil Vapor Eincioe I SyiMHl. UJB^jk, CRJU319-01-1. 1«M. \| D.I. Wilaoa. A. N. OKto. «d J. H.d«». Soil r>M->p by ffltu Acnao^ I ISM, Help: In-Situ Soil Venting System Design Process Help: Preliminary Site Investigation Thi if the deciiion prooeM iha one nuut follow to: I) decide if toil vetoing it tpplioble it a given cite & Z) design in effective toil venting iyttem ll ii tn tbridged vention of Rfure 2 in M Practical Approach to tte Duif. Opmtiat, A Mont/WMf ofln-Siut Soil V,HIM, Syntmt". by P. C. Johnon. C. C Stanley. M. W. Kcmbtowiki, 1. D. Colthvt, Kid D. L Bycn. Mow infonniiion about rile invcmimoon and rcmedution can be found in the following nuclei: API Publication 1C28 "A Guide to the Aseunxnt and Remediation of Underground Petroleum American Petroleum Innitulc, 1230 L Street Nonhwen, Waihington DC, 20005 Help: Thermal Desorption Pntm Dtteriptiea in i thermal dexirptii proccaa, aoik conuuninaicd with voUnlc/iemi-voUUJe orfanic ire heated, and the volatilized contaminUM are nripped with air, •team, or combuation producu (burner flue (ate) at relatively nodeat tonptnmn comparad wiih incinentica (200-500'C > 1000-1200'CX Ihedcaortaed organic oonuunuumu are Help: Incineration FnctH Dticriflio* Incinenuon, or the thermal douwcuon of waoea, it a complete dcatruction technology that can be uaed to treat aoila contaminated with a wide range of hazardous organic •ea. Contaminated aoila. tludgea, or liquid waitca are added to a high-Umpenturc combuition (rotary kiln, fixed hearth, multiple heanh. nuidixed bed, liquid Pncfti Dtterifdam Compoatrat a an above-ground soil mmatonent lechniqiie in which amended toil, containing organic waittt, it placed in large pile* and aerated. The tendon enhances microbial dejradation by providing oxygen to Hie toil/wane. Wife time, the deoompofed wane i§ reduced in weight and volume, and Ite proceaa produce, a ttabifoed. enriched. humu»-like maurial. Pratfii Dncripllau "Landfmrming" icfen to the practice of tprcading organic over an are* of land, then relying on natural microbial action to degrade the wine. It in widely accepted and con-effective practice for Ihe treatment of petroleum hydrocarbon, chlorinated compound!, and peadcidea. Inthu procew aoil-uMciated roieroorganiBn§ (bacteria and ------- •Soil Venting Help Stack Cards B2 Help: In-Situ Biostimulation Help: Solidification / Stabilization Dttcrtfttfm Pnattt DttcrifUf* Treatment of groundwter Hid toil comanunaiion below the water able ("utiiriied zone") by in-«ini bioctimulaiian involve, flic addition of nutrienn and/or O2 (uwally ai H2O2 or liquid O2) 10 m aquifer in order to enhance the degradation of the hydrocarboni by indigenoua uil microbe. The nutriena mi oxygenate added above (mind to Stabilisation and \| ir Em] UK Taa eqaMioa totow • ia> Help: Unit Conversion (k and K) I > am nlae tf kydnuMe andxb>riiy m fenaMUiir n be cnvuvd DCaoOKaaaalcaiai O cmk O ftM • on1 O darcy Compwud Nimt uobuiane n-buune truw-2-bulene cia-2-bulene 3-methyl-1-buune 1-pcniene 2-meihyl-l.buUnc 2-methyl- IJ-buladiene Man MaUcalar Prm.r< Fr.di.. Wri.lt (.) 0.00 0.00 0 0 0 0 0.0069 0.0005 0.0001 1.0000 .1 5..1 58.1 56.1 56.1 70.1 72.2 70.1 70.1 68.1 0.94 0.7S 0.7 047 04S ------- 'Soil Venting Help Stack" Cards B3 Summary Card: Site Characterization Compound List Default Data Acomplete tile tttrumemmuat determine tie following: Svburracc Characterbliei CaataminM Dcltaeatloa • enmiofri Help: Data for Fortran Program Help: How Do I Measure a Distribution? Ml* Vcr » Compound Na MdtoilirCQ W«H. 01 («-) (AOD) SohiMlitr Du. 9T» CodT 20-C cu-2-bbBB» 3-oxrtyl-l ITt-l t^JBW-1. 44.1 St.l 51.1 56.1 56.1 70.1 72.2 70.1 70.1 «l.l »J i.n 2.11 1.J7 1.7J 0.96 0.71 0.7 07 OJ55 62 »9 61 430 430 130 4« 141 113 62 73 537 946 20 204 701 l«3 710 52) 323 0.00 OJM> 0 0 0 0 O.OOW 0.0009 O.OOM o.oo«o Help: Calculate a Distribution Help: About Calculation In dm eniimtion of equilibrium (•Hinted) vipor conocmnlioni. we mume ttut the conuminim coocenmtiom in fral enough (>200 m\|At TTH) flat it U dilthbuled between vipor, locfeed. ditiolved-in-ioil- moimre, A fiee-phuct. In thii cue, the oqutlion u the right •pjttia Oook for -JUouH'i UW * Ae Idoil Gw LJW-in my IpUiiMxiynuiuoi tcxioook fof RferenoEt). We do correct for • nal v^gr nManm Help: 6a) Dilution Effects [Bypassing] Help: 6b) Liquid Layers SM< View Viw Tbefnure ibove depicuihe cue where ume npan "liypMi taum of conmiintion. nd flmdbre the npon removed from the unction well npretem t mixture of the vcpon obninod from both contmintted md elan vipor nowpMhi. One am roughly judge the tmounl of byp«nn» by the weU placement, fcncning, md conuunirmu diflhbutioa Genenlly, otnerved la Figure fib, rapor flowi pnllel to, but not through, the tone of iorutr^trieugn^icmtiniwtnniterreiiiunceiiviDorphuc diffuriaa. ThU would be the cue for • Uyer of liquid hydrocarbon rening on top of m irrfxnnemble Brali or the witer table. ThU problem wu studied by lohntan «t «109M. NWWVAP1 Pcmtoim Hydroorbont Conference) for ------- "Soil Venting Help Stack" Cards H25 B4 Help: 6c) Low Permeability Lenses Help: 6c) Low Permeability Lenses - Equations i HI In the situation depicted above, vipor flow I put, rather than through the contaminated toil zone, nich as might be the cue for • contaminated clay lent surrounded by sandy aoili. In this case vapor diffusion through the clay to the flowing vapor limit* the removal rale (the removal rale actually become* Lars Da • Calculation c l=j/d\| Undine of •oricd-oW UK \m\ o • pmu [•) cudndnl MM) i* a) \|BS/kfj UDC Id] Derivations for that equations arc given in Johnson, « al - "A Practical Approach u the Design, Operation and Monitoring of In Situ Soil Venting System** • 1990. These Equations are valid for single-component Help: Default Boiling Point Ranges Help: Boundary Layer Equations The Fonnn program HYPEVENT will report residual levels of compounds filling between user specified boiling point ranges. The default values have been chosen so that residual levels of compounds with boiling points between the following compounds are grouped together: Propane • Isopemane (-50 to 28 C) bopenunc - Benzene (21 to 80 C) Benzene - Toluene (80 - 111 C) Toluene- Xylenes(111 - 144C) Xylenes - Methylnapihalene (144-250 C) The equation above estimates the removal rale from a layer of liquid product by a •ingle well, baaed on a Boundary Layer Theory approach to the problem. It it not directly applicable to mixtures, because it aaaaaaaaaaaaaaavaal left Do • Calculation 1» - P,)] R«t * fHinmnrt rnacvd rue T\| * efficMicy lelim* ti p* * «Toc«* BDil verpor (haTuHoa eocffiocBt toa^/kj jt s vucoHCy at ui j» IJ, i ]0-4 f/bB-« ^ « ami penneibilicy BO vtipor flow \|c»2j Rj > ndtu* tf nnuEBDB of ycBhnf weU [em) 1^. => voui&f iMdl ndta* [cm\| PAM > kbMttt.* atobamt pcwtoc - 1 X)l« x 106 t/an-a P, "itadufcpreMP B,-cr the nearest minute should be sufficient- Samplc devices are Rolen watches, hour glasses, sun dials, and timers. ------- •Soil Venting Help Stack' Cards 85 Vapor Flow Rates... Pressure/Vacuum Readings. Vipor flow rates from each extraction well «nd into any injection wellt should be monitored. Sample meuurint devices include pilot tubet, oriface plates and rotameters. It ii important to hive calibrated these device at the field operating prcaauroi and temperatures n Pla» Pressuref/Vacuums ihoukl be manured at each extraction and injection well. In addition, subsurface pressure distributions (measured with loae tone inullaiioni) are uaeful for deia mining the zone of influence and vapor flow patha. Typical preuure/vacuum measuring devieea include manometer! and differential prcaaurc (augea. Vapor Concentrations & Composition... Temperature... The vapor concentration and coR^Maition liutii each extraction well ahould be analyzed pehodicatly. This data ia multiplied by the extraction well flowrate u> calculate the removal rate (i.e. Ib/day). and cumulative amount of cotvaTunant removed. By itself, vapor concentration dan doe» not give a complete picture of the system* performance. Dcucam The aoil and ambi 4, 4, nt lemptratiirea can have a significant effect on the performance of aoil venting system. The aoil temperature affectt the contaminant vapor concentration!, while the ambient temperature controli whether or not condensation. or even freezing will be aigiuficani. Por future reference, therefore, it ii aseJul to record the ambient and aoil temperatures. Water Table Soil Gas Concentration & Composition... Whenever the contaminated lone lie» near the groundwater table (within 3 to 5 ft), it ia important to monitor the water table level tt> ensure that contaminated soil! remain fnpiTifd to vapor flow. Measuring the water table level during venting ia not a trivial talk becaiue the monitoring well muat remain scaled. Uncapping the well releaaea the vacuum and any effect that it hat on the water table level. WuehaBWan Theac ahould be measured periodically at different radial distance from the vapor extraction weUXi). Data from aoil gaa sampling ii valuable for three reasons: (1) by comparing extraction well concemrauona with aoil gas ooneentrationa, it is possible to catimaie the fraction of vapor that ia flowing through the contaminated ic (i.e. the 'efficiency'' of Cumulative Amount Removed. Extraction Well Vapor Concentration. CUMULATIVE AMOUNT REMOVED it determined by integrating the measured removal rates (flowrate x \| concentration) wWt time. While this value indicates how much contaminant ha* been removed, it • \| usually not very useful tar determining when to lake confirmation borings unless the original spill mass ia known very accurately, la most cases that CW6) Tua>(daya) EXTRACTION WELL VAPOR CONCENTRATION the vapor concemraiiona are good indication! of how effectively the venting rynem is working, but in vapor extraction well concentrations are not strong evidence that aoil concentration! may also be due to other phenomena such aa water table level increases, mass transfer resistance (mart) ------- •Soil Venting Help Stack" Cards B6 Extraction Weil Vapor Composition... Soil Gas Data... EXTRACTION WELL VAPOR COMPOSITION when combined with vipof concentration* Out dm fivei more in»i\|htinu>theeffeaivGneMofihc •yaem. If the local vtpor change in campotition. it» probably due to increaaed raw transfer micanrr (wafer able ipwellinj. drying-out of low penncability lonta, etc.), and ii net SOU. GAS DATA Ihif du ii the mo meful becniie it yiddi infonmlion about the midual oompocilioa nd enatt of Soil Gu Monilorlng IniUlUtlan KctulU Vq am (•« Vipof ooncsimtMM mi notf in ftnenJ, be luod ID dcurmine the rartkul lord, euept in the limit of \| v«9 lowrakkwl kwli (when propooiocul to »oil rc«------- ------- -Hyperventilate Users Manual- Appendix C: "Air Permeability Test" stack cards. ------- •Air Permeability Stack' Cards C1 Air Permeability Tests... The purpoee of in air permeability lot if to obtain lite-cpecific data thai will be Calculate <- ] Air Permeability Test - Sample Data Pictured at the rifht are the MU vacumu nMawBDBnti from an air penneability inanity TV cpecific opentini in A Practical Approach u> te DenfA Operation, and Momtoriai of In Situ Soil Vomt\| Synem", by P. C Air PermeaMlity Test Data Analyrfs The expecttd decnaie in labeurface preacure (incrmae in \|au\|e vacuum) P if predicted by: <«»MfMi«iltl*0\|«>naB«a> Air Permeability Test - Data Analysis (cont.) For (r C\|iH k P** t) < 0.1, the \|overniii\| equation cm be approximated by the exfroaiaa: TUf Equation praScif that a plot of P* -vt- ln(t) ihould be a Mrai\|ht line wiQi slope A and y-imeraept B equal to: Air Permeability Test - Data Analysis (cont.) The permeability, k. can dm be calculated by on* of two mothodc ft-. The fim if applicable when both Qtflowraic) and n> (well acre ^•^ known accurately. The caJcnlamd tlope A U uaed: © The Kcond appmeh if uaed whenever Q or m am not known wiA confidence. Jn thif caw, both the tlopc, A. and Wercept, B, m uaed: Air Permeability Test - Data Analysis (cont.) ------- •Air Permeability Stack" Cards C2 Mr Permeability Test - Data Analysis (cont.) 1» ^ JUIIIM. rmi Cfilt). te Hit 1 in i M«. II nil •hail njij >irt •>mli i i lii m tin muiimm inpnajw i«m i« mil nrt. if mil ni\|iiil » ijim fw TW KncCMAIT) ------- ------- - Hyperventilate Users Manual - Appendix D: "Aquifer Characterization" stack cards. ------- •Aquifer Characterization" Stack Cards D1 Aquifer Characterization: To achieve efficient ««««. the to expand ID air flow, ttaerafon, in moat caaea where the reaidual toil conlaminatian liet clow to, or below, the Mined nil lilili). ii milll ••Mill In Aquifer Characterization: Shu mo* vantiai fjMam are tamltod •bow "phreaUc aquifere" (iquitei with MrfWii), ID* two prinvy njuif• pmmno* needed for oetign K • HyilTBIIllIT OOBOuOUVIly S • •fltoiv* porouty {or fpedrw yield) Itofim tedion of ihe fundvncnul Aquifer Characterization: Th«« penmeun (K and S) cen be eclkMUd uinf Iht nnlu of e modwd (rouadwaier pump ten with i comua punrii« nu. The mutu tra UMD oampend igiiact nandord type eurvei* for ^wafic aquifer titmiiam (i.e. leaky, unconfined aquifers, stt). pump MM, md data analyst. " bunon below far more alfeiraatioa on ftuf Ml, bill taata. Aquifer Characterization - References ). Bev. -Hyonulici of OnoadwaW. McGnw-Hilt. 1979. ISBN CMTT-OW170-9. p.4«3.490. R. A. fnei and I. A. Cherry. "Groundw.ier-, Premiee-Hall. 1979. ISBN 0-13-MS312-. p. «9 - Ml ------- - Hyperventilate Users Manual - Appendix E: "System Design" stack cards. ------- 'System Design Stack Cards E1 Number of Venting Well* ml oBMm tar ««* ttaa ml try, dkk cm die TptaB* tana, mt tat pnncd •> te Mil end (it. dick » n\|M H fvllB^ C Cl«ir All EHrin J prom mat pcvioojty ID iaamam t vaumj at ^^tafoat it • ftWB «•. A> lUmmanl ic <• li^tt, »• oil ingle MTBMI »«U downrt, rolfnlut V.DOJ flew mpn* fee ml UMU of isflaoBO. fetor 11 ray iK-ipcafictuxu Design Input (DfediucdBmcpcralfor ten 0) dick ibe "upd*' Maumim Nmber of Welli Volume Predictions.., Critical Volume Calculation... O Enur Oinribuiian Q -Frah" Gasoline ® "Wottwrcd' Gisolme If »« « mom ikav itaw. die • fe 'About bana tocttd u Ibe law ri\|bL -> Stt DcfuH BP R»\|« nwml mm. wMb to 100 200 Q«An(t»0) (1/j) Generate Crtdlctlon« Removal Efficiency... Tta nibivfiB • difficult to ) S.UrmUJ Vapor Mi* V.l.m. to Kcmo« >** «T Uilicl Rt.id««l I Ttcv me 4« MttlBfor Ac me atamet m "A Pnoial Appraxt» die DB^K. OJWMOB, ud Moniwmj of Ii Sim Soil Low Permobiliiy Laim Ground W»tcr Upoclling R«mm to Symm IX»igi ------- •System Design* Slack Cards E2 Help: Well Parameters Help: Minimum Number of Wells No. tar rf Wen." * akvbM >> to n» •WtU Rjdin.-. kpunliiilkiterasiMaflkt i>lisafSl»iltajarasiMaflkMU I -— -* >— --\| H-\| —--•:- , mpierirf •• p. •niii. • <» «oii fen-Mi. —I liaaniltflh* ~\| T tap— —. J 1 Tta •roica'aa •«». »>•» fle gage \|IIM«M» im Tte Contaminant Composition Vkw Compoand Num Wtiakt (t) 1 2 3 4 S 6 7 S 9 10 propane isobutane n-butane tnns-2-butene cj*2"butcne 3 -methyl- 1-buiene mpoicuic l-pentene 2-methyl- 1 -buteoe 2-methyl- 1 >buudieoe 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00000 44.1 51.1 SS.1 56.1 56.1 70.1 72.2 70.1 70.1 61. 1 8.5 O 2.93 111 \| 1.97 li 1.79 1 0.96 0.7S 1 0.7 t 0.67 ! 0.65 O • lomof Mi«fWoa> How Do I Measure a Distribution? Determining the exact composition of complex mixtures (such as gasoline) requires specialized analytical techniques. For the purpose of estimating the response to venting, however, an approximaie composition can be used with very food results. To determine an approximate distribution, one must analyze the mixture by gas chromaiofraphic analyses. Prior u> the analyses, choose about 6-10 marker compounds whose properties are well known. Calculate a Distribution taftlKlOCnMrV K4m4lpMB»»iM> • Bill fc.TAfao.ih.oist. Tsca. Click CMcaUat. OjOO OM 0.00 1111 t>M OM OM OM OM 0.00 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 Well Location To be able to fuccestflilry locale extraction wells, pauivc well, and nir&oc seal one must have * good understanding of vapor flow behavior. Wells location* should be chosen to maximize vapor flow through the contaminated zone, while mintmizint vapor flow through other tone. If one mil is sufficient, il should almost always be placed in the geometric center of the Return to Design Well Construction Surface Seals Welk should be screened only through the zone of contamination, unless the permeability to vapor flow is so low that removal rate would be greater if flow were induced in an adjacent soil layer. Removal rate estimates for various mass-transfer limited scenario* are discussed elsewhere in this stack. Based on predictive equations, the flowrace is nprrtal to mmtssf by 15* when the exttmction well PVCPtpe Surface seals, such s* polymer-based linen and asphalt, concrete, or clay caps, are sometime* used to control the vapor flow pains. Figure 12 Ulusttmies the effect thai a surface seal will have on vapor flow panerns. For shallow treatment zones (<5 m) the surface seal will have a significsni effect on the vapor flow paths, and seals can be added or removed u achieve me desired vapor flowpath. For tl'OpCB'MllHIlfalX ------- -System Design' Stack Cards E3 Bp««l»( (»»->) of tta Cranadwaur Ubto wiU ootw S^apor Treatment Systems CttraXly UMK I four nun pnwem mifcbte ------- Hyperventilate Users Manual- Appendix F: "Compound List Update" stack cards. ------- "Compound List Update* Stack Cards F1 Compound List Update Thit card it provided at • utility to let you add, or deklc compound! from Die Compound Lid Data BMC Ihit th* program utet. You may not deloe or change the propeniea of the bate 62 compound, tince ihete are needed for the two deftuh fatoline cue calculation (i.e. the "Frah" and "Weathered" gatolinet). If you wish to change any of ihc properbe of the added chemical!. Tint delete them, then reinsert them into the Compound lift Du* Bate. Follow the direction below: T} Qaafc OK of Ac foOowil«: ®ia»rl clumul QttltU ekciniul [T) Iqw «e pnacwi u K nabi r» or \em) CWmieal ___ M«lt»iar Wciiht (j/mot.) Viper Preunre }2C [•in-1 Boiliaa Pool «>1 aim 1C] Expound NOODOB Not A«n\|icdl ------- - Hyperventilate Users Manual - Appendix G: Reprint of: "A Practical Approach to the Design, Operation, and Monitoring of In Situ Soil Venting Systems" ------- Reprinted from the Spring 1990 Issue of Ground Water Monitoring Review A Practical Approach to the Design, Operation, and Monitoring of In Situ Soil-Venting Systems by P.C Johnson, C.C. Stanley, M.W. Kemblowski, D.L. Byers, andJ.D. Colthan Abstract When operated properly, in situ soil venting or vapor extraction can be one of the most cost-effective remediation processes for soils contaminated with gasoline, solvents, or other relatively,volatile compounds. The components of soil-venting systems are typically off-the-shelf items, and the installation of wells and trenches can be done by reputable environmental firms. However, the design, operation, and monitoring of soil-venting systems are not trivia!. In fact, choosing whether or not venting should be applied at a given site is a difficult decision in itself. If one decides to utilize venting, design criteria involving the number of wells, well spacing, well location, well construc- tion, and vapor treatment systems must be addressed. A series of questions must be addressed to decide if venting is appropriate at a given site and to design cost-effective in situ soil-venting systems. This series of steps and questions forms a "decision tree" process. The development of this approach is an attempt to identify the limitations of in situ soil venting, and subjects or behavior that are currently difficult to quantify and for which future study is needed. Introduction When operated properly, in situ soil venting or vapor extraction can be a cost-effective remediation process for soils contaminated with gasoline, solvents, or other relatively volatile compounds. A "basic" system, such as the one shown in Figure 1, couples vapor extraction (recovery) wells with blowers or vacuum pumps to remove vapors from the vadose zone and thereby reduce residual levels of soil contaminants. More complex sys- tems incorporate trenches, air injection wells, passive wells, and surface seals. Above-ground treatment sys- tems condense, adsorb, or incinerate vapors; in some cases vapors are simply emitted to the atmosphere through diffuser stacks. In situ soil venting is an espe- cially attractive treatment option because the soil is treated in place, sophisticated equipment is not required, and the cost is typically lower than other options. The basic phenomena governing the performance of soil-venting systems are easily understood. By applying a vacuum and removing vapors from extraction wells, vapor flow through the unsaturated soil zone is induced. Contaminants volatilize from the soil matrix and are swept by the carrier gas flow (primarily air) to the extrac- tion wells or trenches. Many complex processes occur on the microscale, however, the three main factors that control the performance of a venting operation are the chemical composition of the contaminant, vapor flow rates through the unsaturated zone, and the flow path of carrier vapors relative to the location of the contamin- ants. The components of soil-venting systems are typically off-the-shelf items, and the installation of wells and trenches can be done by reputable environmental firms. However, the design, operation, and monitoring of soil- venting systems is not trivial. In fact, choosing whether or not venting should be applied at a given site is a difficult question in itself. If one decides to utilize vent- ing, design criteria involving the number of wells, well spacing, well location, well construction, and vapor treatment systems must be addressed. It is the current state-of-the-art that such questions are answered more by experience than by rigorous logic. This is evidenced by published soil venting "success stories" (see Hutzler et al. 1988 for a good review), which rarely include insight into the design process. In this paper, a series of questions are presented that must be addressed to: • Decide if venting is appropriate at a given site. • Design cost-effective in situ soil-venting systems. This series of steps and questions forms a "decision tree" process. The development of this approach is an attempt to identify the limitations of in situ soil venting, and subjects or behavior that are currently difficult to quantify and for which future study is needed. The "Practical Approach" Figure 2 presents a flow chart of the process dis- cussed in this paper. Each step of the flow chart will be discussed in detail, and where appropriate, examples are given. The Site Characterization Whenever a soil contamination problem is detected or suspected, a site investigation is conducted to charac- ------- terize and delineate the zone of soil and ground water contamination. In general, the site characterization is conducted in two stages. The emergency response and abatement phase assesses the immediate impact on potential human and environmental receptors, and is conducted in a relatively short period of time (days). A detailed site characterization then follows. Its purpose, like the emergency response and abatement phase, is to determine potential migration pathways and assess the environmental impact associated with present condi- tions and future migration of the contaminants. Often the sequence of steps following initial response and abatement is as follows: • Background review: Involves assembling historical records, plot plans, engineering drawings (showing utility lines), and interviewing site personnel. This information is used to help identify the contaminant, probable source of release, zone of contamination, and potentially impacted areas (neighbors, drinking water supplies, etc.). * Preliminary site screening: Preliminary screening tools such as soil-gas surveys and cone penetrometers are used to roughly define the zone of contamination and the site geology. Knowledge of site geology is essential to determine probable migration of conta- minants through the unsaturated zone. • Detailed she characterization: Soil borings are drilled and monitoring wells are installed. • Contaminant characterization: Soil and ground water samples are analyzed to determine contaminant con- centrations and compositions. Costs associated with site investigations can be rela- tively high depending on the complexity of the site and size of the spill or leak. For large spills and complex site geological/hydrogeological conditions, site investi- gation costs may begin to approach remediation costs. In addition, the choice and design of a remediation system is based on the data obtained during the site investigation. For these reasons it is important to ensure that specific information is collected, and to validate the quality of the data. If it is presumed that in situ soil venting will be a candidate for treatment, then the following information needs to be obtained during the preliminary site investi- gation: • Subsurface characteristics — site geology: This includes the determination of soil stratigraphy (va- dose and saturated zone) and characteristics of dis- tinct soil layers (i.e., soil type, permeability estimates). While they are not essential, the moisture content, total organic carbon, and permeability of each distinct soil layer also provides useful information that can be used to choose and design a remediation system. • Subsurface characteristics — site hydrogeology: Depth to ground water, and the ground water gradi- ent must be known, as well as estimates of the aquifer hydraulic conductivity. • Contaminant delineation: The distribution of con- taminants in the saturated and vadose zones needs to be assessed. This includes the extent of the free- phase hydrocarbon, residual hydrocarbon, and solu- Vapor Treatment Unit • Vapor Extraction Well Vapor Flow Contaminated Soil Vapor Flow Free-Liquid Hydrocarbon Groundwater Table Sotubk Plume Figtm 1. "Basic" in situ soil-venting system. Process Output Syaetn Shut-On FffHre 2. In stta soil-venting system design process. ------- ble hydrocarbon. Soil samples should be analyzed to determine which contaminants are present at what levels (contaminant composition). Specific analytical methods should be used to identify target compounds (i.e., benzene, toluene, or xylenes) and total hydrocar- bons present. For soil analyses these methods are: EPA 8240, 8020, 8010 - volatile organic chemicals (VOCs) EPA 8270 - semivolatile organic chemicals EPA 418.1 - total petroleum hydrocarbons (TPH). The corresponding methods for water samples are: EPA 8240, 8020, 8010 - volatile organic chemicals (VOCs) EPA 8270 • semivolatile organic chemicals EPA 418.1 - total petroleum hydrocarbons (TPH). With the current high cost of chemical analyses it is important to intelligently select which analyses should be performed and which samples should be sent to a certified laboratory. Local regulations usu- ally require that a minimum number of soil borings be performed, and target compounds must be ana- lyzed based on the suspected composition of the con- tamination. Costs can be minimized and more data obtained by utilizing field screening tools, such as hand-held vapor meters or portable field gas chroma- tographs (GCs). These instruments can be used to measure both residual soil contamination levels and headspace vapors above contaminated soils. At a minimum, soil samples corresponding to lithology changes or obvious changes in residual levels (based on visual observations or odor) should be analyzed. For complex contamination mixtures, such as gas- oline, diesel fuel, and solvent mixtures, it is not prac- tical or necessary to identify and quantify each com- pound present. In such cases it is recommended that a "boiling point" distribution be measured for a representative sample of the residual contamination. Boiling point distribution curves, such as shown in Figure 3 for "fresh" and "weathered" gasoline samples, can be constructed from GC analyses of the residual soil contamination (or free product) and knowledge of the GC elution behavior of a known series of compounds (such as straight-chain alkanes). Compounds generally elute from a GC packed column in the order of increas- ing boiling point, so a boiling point distribution curve is constructed by grouping all unknowns that elute between two known peaks (i.e., between n-hexane and n-heptane). Then they are assigned an average boiling point, molecular weight, and vapor pressure. Use of these data will be explained later. The cone penetrometer, which is essentially an instrumented steel rod that is driven into the soil, is becoming a popular tool for preliminary site screening investigations. By measuring the shear and normal forces on the leading end of the rod, soil structure can be defined and permeability or hydraulic conduc- tivity can be estimated. Some cone penetrometers are also constructed to allow the collection of vapor or ground water samples. This tool has several advan- 1.0 Cumulative Weight og< Fraction 0.6 0.4 0.2 0.0 T(°C) b Figure 3. Boiling point distribution curves for samples of •fresh" and "weathered" gasolines. tages over conventional soil boring techniques (as a preliminary site characterization tool): (1) the subsur- face soil structure can be defined better; (2) no soil cuttings are generated; and (3) more analyses can be performed per day. • Temperature (both above and below ground surface) Contaminant vapor concentrations are dependent on temperature, and therefore, removal rates are strongly influenced by subsurface temperatures. Above-ground temperatures will influence the selec- tion of materials and construction of the above- ground vapor treatment system. Results from the preliminary site investigation should be summarized in contour plots, fence diagrams, and tables in preparation for deciding whether venting is appropriate, and for the final design of the system. Deciding if Venting Is Appropriate As previously stated, the three main factors govern- ing the behavior of any in situ soil-venting operation are the vapor flow rate, contaminant vapor concentra- tions, and the vapor flow path relative to the contamin- ant location. In an article by Johnson et al. (1988), simple mathematical equations were presented to help quantify each of these factors. Following it is illustrated how to use these "screening models"and the information col- lected during the preliminary site investigation to help determine if in situ soil venting is appropriate at a given site. In making this decision the following questions will be answered: 1. What contaminant vapor concentrations are likely to be obtained? 2. Under ideal vapor flow conditions (he., 100 -1000 scfm vapor flow rates), is this concentration great enough to yield acceptable removal rates? 3. What range of vapor flow rates can realistically be achieved? 4. Will the contaminant concentrations and realistic vapor flow rates produce acceptable removal rates? 5. What residual, if any, will be left in the soil? What ------- vapor composition and concentration changes will occur with time? How do these values relate to the regulatory requirements? 6. Are there likely to be any negative effects of soil venting? Negative answers to questions 2 or 4 will rule out in situ soil venting as a practical treatment method. What Contaminant Vapor Concentrations Are Likely to Be Obtained? Question 1 can be answered based on the results of soil-vapor surveys, analyses of headspace vapors above contaminated soil samples, or equilibrium vapor models (Johnson et al. 1988). In some cases just knowing which compounds are present is sufficient to estimate if venting is feasible. In the absence of soil-vapor survey data, contaminant vapor concentrations can be estimated. The maximum vapor concentration of any compound (mixture) in extracted vapors is its equilibrium or "satur- ated" vapor concentration, which is easily calculated from knowledge of the compound's (mixture's) molecu- lar weight, vapor pressure at the soil temperature, resid- ual soil contaminant composition, and the ideal gas law: (1) where: Ces, = estimate of contaminant vapor concentration [mg/L] Xj = mole fraction of component i in liquid-phase residual (Xj = 1 for single compound) Pi" = pure component vapor pressure at tempera- ture T [atm] MW,J = molecular weight of component i [mg/mole] R = gas constant = 0.0821 l-atm/tnole-0K T - absolute temperature of residual [°K]. Table 1 presents data for some chemicals and mix- TABLE 1 Selected Compounds and Their Chemical Properties (Johnson et al. 1988) Compound n-pentane n-hexane trichloroethane benzene cyclohexane trichloroethylene n-heptane toluene tetrachloroethylene n-octane chlorobenzene p-xylene ethylbenzene m-xylene o-xylene styrene n-nonane n-propylbenzene 1,2,4 trimethylbenzene n-decane DBCP n-undecane n-dodecane napthalene tetraethyllead gasoline1 weathered gasoline2 Mw ------- tures accidentally released to the environment. There are more sophisticated equations for predicting vapor concentrations in soil systems based on equilibrium par- titioning arguments, but these require more detailed information (organic carbon content, soil moisture) than is normally available. If a site is chosen for remediation, the residual total hydrocarbons in soil typically exceed 500 mg/kg. In this residual concentration range most of the hydrocarbons will be present as a separate or "free" phase, the contaminant vapor concentrations become independent of residual concentration (but still depend on composition), and Equation 1 is applicable (Johnson et ai. 1988). In any case, it should be noted that these are estimates only for vapor concentrations at the start of venting, which is when the removal rates are generally greatest. Contaminant concentrations in the extracted vapors will decline with time due to changes in composi- tion, residual levels, or increased diffusionat resistances. These topics will be discussed in more detail. Under Ideal Vapor Flow Conditions ~. ) - conctnmoon in medune-equviknl pom (wl/vol.) unio •" Ffeu 4. !• sft» rat) i nte tad vtpor concentration. complete the cleanup within eight months, then Raccepu- We = 6.3 kg/d. Based on Figure 4, therefore, Cen would have to average >1.5 mg/L (2400 ppmou) for Q=2800 l/min (100 cfm) if venting is to be an acceptable option. Generally, removal rates <1 kg/d will be unacceptable for most releases, so soils contaminated with compounds (mixtures) having saturated vapor concentrations less than 0.3 mg/L (450 ppmCH4) will not be good candidates for venting, unless vapor flow rates exceed 100 scfm. Judging from the compounds listed in Table 1 , this corre- sponds to compounds with boiling points (Tb)>150 C, or pure component vapor pressures <0.0001 atm evalu- ated at the subsurface temperature. listica lly What Range of Vapor How Rates Can Re Be Achieved? Question 3 requires that realistic vapor flow 'rates for the site-specific conditions be estimated. Equation 5, which predicts the flow rate per unit thickness of well screen Q/H [cm3 /s], can be used for this purpose: k [l-(PA,m/Pw)2] (5) where: k « u, = Pw = pA------- This equation is derived from the simplistic steady- s :ate radial flow solution for compressible flow (Johnson ct al. 1988), but should provide reasonable estimates for vapor flow rates. If k can be measured or estimated, then the only unknown parameter is the empirical "ra- dius of influence" Rt. Values ranging from 9m (30 ft) to 30m (100 ft) are reported in the literature (Hutzler et al. 1988) for a variety of soil conditions, but fortun- ately Equation 5 is not sensitive to large changes in Rj. for estimation purposes, therefore, a value of Rt=12m (40 ft) can be used without a significant loss of accuracy. Typical vacuum well pressures range from 0.95 - 0.90 atm (20 - 40 in H2O vacuum). Figure 5 presents pre- dicted flow rates per unit well screen thickness Q/H, expressed in "standard" volumetric units Q/H (= Q/ H(Pw/PAtm) for a 5.1cm radius (4-in diameter) extrac- tion well, and a wide range of soil permeabilities and applied vacuums. Here H denotes the thickness of the screened interval, which is often chosen to be equal to the thickness of the zone of soil contamination (this minimizes removing and treating any excess "clean" air). For other conditions the Q/H values in Figure 5 can be multiplied by the following factors: Rw a 5.1cm (2 in) R, = 7.6m (25 ft) - multiply Q/H by 1.09 Rw = 5.1cm (2 in) R, = 23m (75 ft) - multiply Q/H by 0.90 Rw 7.6cm (3 in) R, - 12m (40 ft) - multiply Q/H by 1.08 Rw = 10cm (4 in) R, = 12m (40 ft) - multiply Q/H by 1.15 Rw = 10cm (4 in) R, = 7.6m (25 ft) - multiply Q/H by 1.27 As indicated by the preceding multipliers given, changing the radius of influence from 12m (40 ft) to 23 m (75 ft) only decreases the predicted flow rate by 10 percent. The largest uncertainty in flow rate calcula- i ions will be due to the air permeability value k, which can vary by one to three orders of magnitude across a site and can realistically only be estimated from boring log data within an order of magnitude. It is prudent, therefore, to choose a range of k values during this phase of the decision process. For example, if boring logs indicate fine sandy soils are present, then flow rates should be calculated for k values in the range of 0.1ntaminant vapors. For this "best" case the estimated removal rate is given by Equation 2: noo (m vm-min) Vapor Flowme (scfm/ft) .0001 - o.ot i 0.001! .i i 10 too ton Soil Permeabilty (dajcy) vacuum uprated a equivalent water column heiihu Figure 5. Predicted steady-state flow rates (per unit well screen thickness) for a range of soil permeabilities and applied vapor flow / SMfeVKW b) liquid e c) Figure 6. Scenarios for removal rate estimates. R«, = Ccsl 0 (2) Changes in- Cest are still being neglected with time due to composition changes. Other less optimal condi- tions are often encountered in practice and it is useful to be able to quantify how much lower the removal rate will be from the value predicted by Equation 2. We will consider the three cases illustrated in Figures 6a, b, and c. ------- In Figure 6a a fraction of the vapor flows through uncontaminated soil. The fraction can be roughly esti- mated by assessing the location of the well relative to the contaminant distribution. In Figure 6a for example, it appears that roughly 25 percent of the vapor flows through uncontaminated soil. The maximum removal rate for this case is then: R^Ml-'WQCes, (6) In Figure 6b, vapor flows parallel to, but not through, the zone of contamination, and the significant mass transfer resistance is vapor phase diffusion. This would be the case for a layer of liquid hydrocarbon resting on top of an impermeable strata or the water table. This problem was studied by Johnson et al (1988) for the Case of a single component. The solution is: Cesl JM (eDu/k)"2 (ln(RI/Rw)/(PAlm - PJ]"2 where: T) = efficiency relative to maximum removal rate D = effective soil-vapor diffusion coeffici- ent [cnvVs] p. = viscosity of air = 1.8 x 10 g/cm-s k = soil permeability to vapor flow [cmz] H = thickness of screened interval [cm] R{ = radius of influence of venting well [cm] Rw - venting well radius [cm] PAIID = absolute ambient pressure = 1.016 x 10* g/cm-sj Pw = absolute pressure at the venting well (g/cm-s2] R! < r < R2 = defines region in which contamina- tion is present. Note that the efficiency T\ is inversely proportional to the screened interval thickness H because a larger interval will, in this geometry, pull in unsaturated air that has passed above the liquid-phase contamination. D is calculated by the Millington-Quirk (Millington and Quirk 1961) expression, which utilizes the molecular diffusion coefficient in air D°, the vapor-filled soil poros- ity eA, and the total soil porosity €?: D = D° where eA and eA are related by: (8) (9) Here pb and 6M are the soil bulk density [g/cma] and soil moisture content [g-H2O/g-soil]. As an example, consider removing a layer of contam- ination bounded by sandy soil (k=l darcy). A 5.1cm (4 in) radius vapor extraction well is being operated at Pw=0.90 atm (0.91 x 10* g/cm-s1), and the contamination extends from the region Rt = Rw = 5.1cm to R2 = 9m (30 ft). The well is screened over a 3m (10 ft) interval. Assuming that: Pb = 1.6 g/cm5 6M = 0.10 D" » 0.087 cm'/s eT = 0.30 RI = 12 m then the venting efficiency relative to the maximum removal rate (Equation 2), calculated from Equations 7 through 9 is: •n = 0.09 = 9%. Figure 6c depicts the situation in which vapor flows primarily past, rather than through the contaminated soil zone, such as might be the case for a contaminated clay lens surrounded by sandy soils. In this case vapor- phase diffusion through the clay to the flowing vapor limits the removal rate. The maximum removal rate in this case occurs when the vapor flow is fast enough to maintain a low vapor concentration at the permeable/ impermeable soil interface. At any time t a contaminant- free or "dried out" zone of tow permeability will exist with a thickness 5. An estimate of the removal rate R«, from a contaminated zone extending from R] to R2 is: = IE (10) where D is the effective porous media vapor diffusion coefficient (as calculated previously from Equations 8 and 9) and Ces, is the estimated equilibrium vapor con- centration (Equation 1). With time 8(t) will grow larger. In the case of a single component system the dry zone thickness can be calculated from the mass balance: (H) where C, is the residual level of contamination in the low permeability zone [g-contamination/g-soil], and all other variables have been defined. The solution to Equations 10 and 11 yields the following equation that predicts the change in removal rate with time: (12) As an example, consider the case where benzene (Q, = 3.19 x 10* g/cm3 @20 C) is being removed from a zone extending from RI = 5.1cm to R2 = 9m. The initial residual level is 10,000 ppm (0.01 g-benzene/g-soil), pt = 1.6 g/cms, D° = 0.087 cmVs, and eT = eA = 0.30. Figure 7 presents the predicted removal rates and "dry" zone thickness 8(t) as a function of time. Note that it would take approximately one year to clean a layer 1.5m (5 ft) thick, for a compound as volatile as benzene. Equa- tion 12 predicts high initial removal rates; in practice, however, the removal rate will be limited initially by the vapor-phase diffusion behavior described previously for Figure 6b. Mixture removal rates for the situations depicted in Figures 6b and 6c are difficult to estimate because ------- changes in composition and liquid-phase diffusion affect the behavior. Currently there are no simple analytical solutions for these situations, but it can be postulated that they should be less than the rates predicted previ- ously for pure components. The use of equilibrium-based models to predict required removal rates will be discussed under the next question. What Residual, If Any, Will Be Left in the Soil? What Vapor Composition and Concentration Changes Will Occur With Time? How Do These Values Relate to the Regulatory Requirements? As contaminants are removed during venting, the residual soil contamination level decreases and mixture compositions become richer in the less volatile com- pounds. Both of these processes result in decreased vapor concentrations, and hence, decreased removal rat ;s with time. At low residual soil contamination levels (<500 ppm) Equation 1 becomes less valid as sorption and dissolution phenomena begin to affect the soil resid- ual - vapor equilibrium. In the limit of low residual contamination levels, contaminant equilibrium vapor concentrations are expected to become proportional to the residual soil contaminant concentrations. As venting continues and residual soil levels decrease, therefore, it becomes more difficult to remove the residual contami- nation. It is important to realize that, even with soil venting, there are practical limitations on the final soil contamination levels that can be achieved. Knowledge of these limits is necessary to realistically set cleanup criteria and design effective venting systems. The maximum efficiency of a venting operation is limited by the equilibrium partitioning of contaminants between the soil matrix and vapor phases. The maxi- mum removal rate is achieved when the vapor being rerioved from an extraction well is in equilibrium with the contaminated soil Models for predicting this maxi- mum removal rate have been presented by Marley and Hcag (1984) and Johnson et al. (1988). The former con- sidered only compositions in a residual free-phase, while the latter also considered the effects of sorption and dissolution processes. A complete discussion of the development of these models is not appropriate here, bu: we will discuss the use of the predictions. The change in composition, vapor concentration, removal rate, and residual soil contamination level with time are functions of the initial residual composition, vapor extraction well flow rate, and initial soil contami- nation level. It is not necessary to generate predictions foi every combination of variables, however, because with appropriate scaling all results will form a single curve for a given initial mixture composition. Figure 8a presents the results computed with the model presented by Johnson et al. (1988) for the "weathered" gasoline mixture whose composition is given by Table 2. The important variable that determines residual soil levels, vapor concentrations, and removal rates is the ratio Qt/ M(t=0), which represents the volume of air drawn through the contaminated zone per unit mass of conta- 1000 (kg/d) 100. 10 i benzene (20 C) R, »S.l cm R2»900cm 200 "Dry" Zone Thickness 6 (cm) 100 0 100 200 300 400 500 Time (d) Figure 7. Estimated maximum removal rates for a venting operation Untiled by diffusion. a) % removed .0001 100 200 Qi/m(t=0) (I/g) b) QC/QC(t=0) .01 .001 .0001 Weathered Gasoline T-20°C 10% moisture content dinted front 4.ph>K » C0=0) = 270 mgfl Approximate Composition 100 80 % removed "60 •40 20 300 0 100 200 Qt/m(l=0) (1/g) Figure 8. Maximum predicted removal rates for a weathered gasoline: (a) full composition (b) approximate composition. minant. In Figure 8, the scaled removal rate (or equiva- lently the vapor concentration) decreases with time as the mixture becomes richer in the less volatile com- pounds. While a detailed compositional analysis was availa- ble for this gasoline sample, an approximate composi- tion based on a boiling point distribution curve predicts similar results. Figure 8b presents the results for the approximate mixture composition also given in Table 2. Model predictions, such as those shown in Figure 8 for the gasoline sample defined by Table 2, can be used to estimate removal rates (if the vapor flow rale is speci- fied), or alternatively the predictions can be used to estimate vapor flow rate requirements (if the desired removal rate is specified). For example, if we wanted to reduce the initial contamination level by 90 percent. ------- TABLE 2 Composition Compound Name propane isobutane ii-butane trans-2-butene cis-2-butene 3-methyi-l-butene isopentane 1-pentene 2-methyl-l-butene 2-methyl-t,3-buladiene iwpentane trans-2-pentene 2-methyl-2-butene 2-methyl- 1 ,2-butadiene 3,3-dimethyI-l -buiene cyclopentane 3-methyl-l-pentene 2,3-dimethylbutane 2-methylpentane 3-methylpentane n-hexane methylcyclopentane 2.2-dimethylpentane benzene cyclohexane 2.3-dimethylpentane 3-methylhexane 3-ethylpentane n-heptane 2,2,4- 1 rime thy 1 pe n t a ne methylcyclohexane 2,2-dimethylhexane toluene 2,3,4- trimethylpentane 3-me thy (heptane 2-methylheptane n-octane 2,4,4-trimethylhexane 2,2-dimethylheptane e thy (benzene p-xylene m-xytene 3,3,4-trimeihylhexane o-xy!ene 2,2,4- trimethylheptane n-noname 3,3,5-trimethylheptane n-propylbenzene 2,3,4-trimelhylheptane 1,3,5-trimethylbenzene 1 ,2-4-(rimeihylbenzene n-decane methylpropylbenzene di methy le thy (benzene n-undecane 1 ,2,4,5-tetramethylbenzene 1 ,23,4-tetramethylbenzene 1 ,2,4-trimethyl-5-ethylbenzene n-dodecane napthalene n-hexylbenzene meihylnapthalene Total (Mass Fractions) off Fresh and Weathered Gasolines Mw (8> 44.1 58.1 58.1 56.1 56.1 70.1 72.2 70.1 70.1 68.1 72.2 70.1 70.1 68.1 84.2 70.1 84.2 86.2 86.2 86.2 86.2 84.2 100.2 78.1 84.2 100.2 100.2 100.2 100.2 114.2 98.2 114.2 92.1 114.2 114.2 114.2 114.2 128.3 128.3 106.2 106.2 106.2 128.3 106.2 142.3 128.3 142.3 120.2 142.3 120.2 120.2 142.3 134.2 134.2 156.3 134.2 134.2 148.2 170.3 128.2 162.3 142.2 Fresh Gasoline 0.0001 0.0122 0.0629 0.0007 0.0000 0.0006 0.1049 0.0000 0.0000 0.0000 0.0586 0.0000 0.0044 0.0000 0.0049 0.0000 0.0000 0.0730 0.0273 0.0000 0.0283 0.0083 0.0076 0.0076 0.0000 0.0390 0.0000 0.0000 0.0063 0.0121 0.0000 0.0055 0.0550 0.0121 0.0000 0.0155 0.0013 0.0087 0.0000 0.0000 0.0957 0.0000 0.0281 0.0000 0.0105 0.0000 0.0000 0.0841 0.0000 0.0411 0.0213 0.0000 0.0351 0.0307 0.0000 0.0133 0.0129 0.0405 0.0230 0.0045 0.0000 0.0023 1.0000 Weathered Gasoline 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0069 0.0005 0.0008 0.0000 0.0095 0.0017 0.0021 0.0010 0.0000 0.0046 0.0000 0.0044 0.0207 0.0186 0.0207 0.0234 0.0064 0.0021 0.0137 0.0000 0.0355 0.0000 0.0447 0.0503 0.0393 0.0207 0.0359 0.0000 0.0343 0.0324 0.3000 0.0034 0.0226 0.0130 0.0151 0.0376 0.0056 0.0274 0.0012 0.0382 0.0000 0.0117 0.0000 0.0493 0.0707 0.0140 0.0170 0.0289 0.0075 0.0056 0.0704 0.0651 0.0000 0.0076 0.0147 0.0134 1.0000 Approximate Composition 0 0 0 0 0 0 0.0177 0 0 0 0 0 0 0 0 0.0738 0 0 0 0 0 0 0 0 0.1761 0 0 0 0 0 0 0 0.1926 0 0 0 0 0 0 0 0 0.1641 0 0 0 0 0 0.1455 0 0 0 0 0 0.0534 0 0 0.1411 0 0 0 0.0357 0 1.00000 ------- then Figure 8 predicts that ~ 100 1-air/g-gasoline will be required. This is the minimum amount of vapor required, because it is based on an equilibrium-based mode]. The necessary minimum average vapor flow rate is then equal to the spill mass times the minimum required vapor flow/mass gasoline divided by the desired duration of venting. Use of this approach is illustrated in the service station site example provided at the end of this paper. Figure 8 also illustrates that there is a practical limit to the amount of residual contaminant that can be removed by venting alone. For example, it will take a minimum of 1001-vapor/g-gasoline to remove 90 percent of the weathered gasoline defined in Table 2, while it will take about 200 1-air/g-gasoline to remove the remaining 10 percent. In the case of gasoline, by the time 90 percent of the initial residual has been removed, the residual consists of relatively insoluble and non- volatile compounds. It is important to recognize this limitation of venting, and when setting realistic cleanup target levels, they should be based on the potential envi- ronmental impact of the residual rather than any specific total residual hydrocarbon levels. Because mandated cleanup levels are generally independent of the remedia- tion method, this also indicates that soil venting will often be one of many processes used during a given site remediation. It is not difficult to envision that in the future soil venting may be followed or coupled with enhanced biodegradation to achieve lower cleanup levels. It is appropriate to mention at this point that the mathematical models presented in this paper are being used as "tools" to help plan and design venting system. As with any models, they are mathematical descriptions of processes that at best approximate real phenomena, and care should be taken not to misapply or misinterpret the results. Are There Likely to Be Any Negative Effects of Soil Venting? It is possible that venting will induce the migration of off-site contaminant vapors toward the extraction wells. This may occur at a service station, which is often in close proximity to other service stations. If this occurs, one could spend a lot of time and money to unknowingly clean up someone else's problem. The solution is to establish a "vapor barrier" at the perimeter of the con- taminated zone. This can be accomplished by allowing vapor flow into any perimeter ground water monitoring wells (which often have screened intervals extending above the saturated zone), which then act as passive air supply wells. In other cases it may be necessary to install passive air injection wells, or trenches, as illustrated in Figure 9a. As pointed out by Johnson et al. (1988), the applica- tion of a vacuum to extraction wells can also cause a water table rise. In many cases contaminated soils lie just above the water table and they become water satur- ated, as illustrated in Figure 9b. The maximum rise occurs at, or below the vapor extraction well, where the water table rise will be equal to the vacuum at that point Off-Silt Passive Air Injection Well or Perimeter Gnxmdwtier Moniiorirtf Well b) Wiier Table Upwellinj Caused by Vicinal) Figure 9. (i) Use of passive vapor wells to prevent migration of off-rite contaminant vapors, (b) Water table rise caused by the applied vacuum. expressed as an equivalent water column height (i.e., in ft H2O). The recommended solution to this problem is to install a dewatering system, with ground water pump- ing wells located as close to vapor extraction wells as possible. The dewatering system must be designed to ensure that contaminated soils remain exposed to vapor flow. Other considerations not directly related to vent- ing system design, such as soluble plume migration con- trol and free-liquid product yield, will also be factors in the design of the ground water pumping system. Design Information If venting is still a remediation option after answer- ing the questions above, then more accurate information must be collected. Specifically, the soil permeability to vapor flow, vapor concentrations, and aquifer charac- teristics need to be determined. These are obtained by two field experiments: air permeability and ground water pumping tests, described briefly next. Air Permeability Tests Figure 10 depicts the setup of an air permeability test. The object of this experiment is to remove vapors at a constant rate from an extraction well, while monitor- ing with time the transient subsurface pressure distribu- tion at fixed points. Effluent vapor concentrations are also monitored. It is important that the test be conducted properly to obtain accurate design information. The extraction well should be screened through the soil zone that will be vented during the actual operation. In many cases existing ground water monitoring wells are suffici- ent, if their screened sections extend above the water table. Subsurface pressure monitoring probes can be ------- Preuurc V«po» Rownwtcr Pressure Swiping Probes Fipre 10. Air-pernMtMltty lest system. driven soil-vapor sampling probes (for <20 ft deep con- tamination problems) or more permanent installations. Flow rate and transient pressure distribution data are used to estimate the soil permeability to vapor flow. The expected change in the subsurface pressure distribu- tion with time P'(r,t) is predicted (Johnson et al.) by: (13) For (r2 eji/4kPAUnt)<0.1 Equation 13 can be approxi- mated by: P' = Here P' 4jon(k/u) -0.5772 - In Alm (14) = "gauge" pressure measured at distance r and time t = stratum thickness = radial distance from vapor extraction well = soil permeability to air flow = viscosity of air = 1.8 x 10^ g/cm-s = air-filled soil void fraction = time = volumetric vapor flow rate from extraction well = ambient atmospheric pressure = 1.0 atm = 1.013 x 10» g/cm-s2. Equation 14 predicts a plot of p'-vs- In(t) should be a straight line with slope A and y-intercept B equal to: m r k ix e t Q A = B = 4m(k/u) Q 4nm(k/iO -0.5772 - In Aim (15) The permeability to vapor flow can then be calculated from the data by one of two methods. The first is applica- ble when Q and m are known. The calculated slope A is used: 4Aiun The second approach must be used whenever Q or m is not known. In this case the values A and B are both used: + 0.5772) (17) Equation 13 can also be used to choose the locations of subsurface pressure monitoring points before con- ducting the air permeability test, given an estimation of k and the flow rate to be used. Vapor samples should be taken at the beginning and end of the air permeability test, which should be con- ducted for a long enough time to extract at least one "pore volume" VP of vapor from the contaminated soil zone. This ensures that all vapors existing in the forma- tion prior to venting are removed. The vapor concentra- tion at the start of the test is representative of the equi- librium vapor concentration, while the concentration measured after one pore volume has been extracted gives an indication of realistic removal rates and the mixing or diffusional limitations discussed in association with Figure 6. The time rp for one pore volume to be removed is: TP = Vp/Q = €A irR2 H/Q (18) where R, H, eA, and Q are the radius of the zone of contamination, vertical thickness of the zone of contami- nation, air-filled void fraction, and volumetric vapor flow rate from the extraction well. For example, consider the case where R=12 m, H=3 m, eA=0.35, and Q=0.57 mj /min (20 ft3 /mm). Then Tp=475 m V0.57 m} /min=833 min=14 h. Ground Water Pumping Tests To achieve efficient venting, the hydrocarbon-con- taminated soil has to be exposed to air flow, which in turn requires that the water table be lowered to counter- act the water upwelling effect caused by the decreased vapor pressure in the vicinity of a venting well (Johnson et al. 1988) and to possibly expose contaminated soil below the water table. Thus the ground water pumping system has to have a sufficient pumping rate and be operated for a long enough time period to obtain the required drawdowns. Because most venting systems are installed above phreatic aquifers, two aquifer parame- ters are needed for the design: average transmissivity T and storage coefficient S. These parameters can be esti- mated using the results of the standard transient ground water pumping test with a constant pumping rate (Bear 1979). Using the estimated values, the required pumping rate may be calculated as follows: Q = 4irT S(r,t)/W(u) (19) where: W(u) is the well function (Bear 1979) of u = Sr2/ ------- 4Tt, and s(r,t) is the required drawdown at distance r and pumping time equal to t. System Design In this section the questions that must be answered in order to design an in situ soil-venting system will be discussed. It is not the authors' intention to provide a generic "recipe" for soil-venting system design; instead, a structured thought process to guide in choosing the number of extraction wells, well spacing, well construc- tion, etc. is suggested. Even in a structured thought process, intuition, and experience play important roles. There is no substitute for a good fundamental under- standing of vapor flow processes, transport phenomena, and ground water flow. Choosing the Number of Vapor Extraction Wells Three methods for choosing the number of vapor extraction weils are outlined in the following text. The greatest number of wells from these three methods is then the value that should be used. The objective is to satisfy removal rate requirements and achieve vapor removal from the entire zone of contamination. For the first estimate residual contaminant composi- tion and vapor concentration changes with time are neg- lected. The acceptable removal rate Raccepiabie is calcu- lated from Equation 4, while the estimated removal rate from a single well Res, is estimated from a choice of Equations 2,6,7, or 12 depending on whether the speci- fic site conditions are most like Figure 6a, 6b, or 6c. The number of wells Nwens required to achieve the acceptable removal rate is: - Raeceptable/Resl (20) Equations 2,6, and 7 require vapor flow estimates, which can be calculated from Equation 5 using the measured soil permeability and chosen extraction well vacuum Pw. At this point one must determine what blowers and vacuum pumps are available because the characteristics of these units will limit the range of feasible (PW,Q) values. For example, a blower that can pump 100 scfm at 2 in. H2O vacuum may only be able to pump 10 scfm at 100 in. H2O vacuum. The second method, which accounts for composition changes with time, utilizes model predictions, such as those illustrated in Figure 8. Recall that equilibrium- based models are used to calculate the minimum vapor flow to achieve a given degree of remediation. For exam- ple, if we wish to obtain a 90 percent reduction in resid- ual gasoline levels, Figure 8 indicates that ~ 1001-vapor/ g-gasoline must pass through the contaminated soil zone. If our spill mass is 1500kg (=500 gal), then a mini- mum of 1.5 x 10" 1-vapor must pass through the conta- minated soil zone. If the target cleanup period is six months, this corresponds to a minimum average vapor flow rate of 0.57 m3 /min (=20 cfm). The minimum num- ber of extraction wells is then equal to the required minimum average flow rate/flow rate-per-well. The third method for determining the number of wells ensures that vapors and residual soil contamina- tion are removed from the entire zone of contamination Nmin- This is simply equal to the ratio of the area of contamination Acon,.™,,^,,,,, to the area of influence of a single venting well irR]2: Acontl (21) This requires an estimate of RI, which defines the zone in which vapor flow is induced. In general, RI depends on soil properties of the vented zone, properties of sur- rounding soil layers, the depth at which the well is screened, and the presence of any impermeable bound- aries (water table, clay layers, surface seal, building basement, etc.). At this point it is useful to have some understanding of vapor flow patterns because, except for certain ideal cases (Wilson et al. 1988), one cannot accurately predict vapor flow paths without numerically solving vapor-flow equations. An estimate for RI can be obtained by fitting radial pressure distribution data from the air permeability test to the steady-state radial pressure distribution equation (Johnson et al. 1988): P(r). P. [! + ------- a) welh I) b) viporflcw . line injection well c) Figure 11. Venting well configurations. in a "stagnant" region in the middle of the wells where air flow would be small in comparison to the flow induced outside the triplate pattern boundaries. This problem can be alleviated by the use of "passive wells" or "forced injection" wells as illustrated in Figure lib (it can also be minimized by changing the vapor flow rates from each welt with time). A passive well is simply a well that is open to the atmosphere; in many cases ground water monitoring welts are suitable. If a passive or forced injection well is to have any positive effect, it must be located within the extraction well's zone of influence. Forced injection wells are simply vapor wells into which air is pumped rather than removed. One must be careful in choosing the locations of forced injec- tion wells so that contaminant vapors are captured by the extraction wells, rather than forced off-site. To date there have not been any detailed reports of venting operations designed to study the advantages/disadvan- tages of using forced injection wells. Figure lie presents another possible extraction/injection well combination. As illustrated in Figure 9, passive wells can also be used as vapor barriers to prevent on-site migration of off- site contamination problems. For shallow contamination problems (<4m below ground surface) vapor extraction trenches combined with surface seals may be more effective than vertical wells. Trenches are usually limited to shallow soil zones because the difficulty of installation increases with depth. Surface seals, such as polymer-based liners and asphalt, concrete, or clay caps, are sometimes used to control the vapor-flow paths. Figure 12 illustrates the effect that a surface seal will have on vapor-flow pat- "opra" mil tuifice b> impermeable K»l Fignie 12. Effect of surface seal on vapor flow path. cement cip S) Figure 13. (a) Extraction well construction, and (b) air-tight groMd water level meawuiag system. terns. For shallow treatment zones (------- increase by 15 percent when the extraction well diameter is increased from 10cm (4 in) to 20cm (8 in). This implies that well diameters should be as large as is practically possible. A typical well as shown in Figure 13a is constructed from slotted pipe (usually PVC). The slot size and num- ber of slots per inch should be chosen to maximize the open area of the pipe. A filter packing, such as sand or gravel, is placed in the annulus between the borehole and pipe. Vapor extraction wells are similar to ground water monitoring wells in construction but there is no need to filter vapors before they enter the well. The filter packing, therefore, should be as coarse as possible. Any dust carried by the vapor flow can be removed by an above-ground filter. Bentonite pellets and a cement grout are placed above the filter packing. It is important that these be properly installed to prevent a vapor flow "short-circuiting." Any ground water monitoring wells installed near the extraction wells must also be installed with good seals. Vapor Treatment Currently, there a-four main treatment processes available: • Vapor combustion units: Vapors are incinerated and destruction efficiencies are typically >95 percent. A supplemental fuel, such as propane, is added before combustion unless extraction well vapor concentra- tions are on the order of a few percent by volume. This process becomes less economical as vapor con- centrations decrease below — 10,000 ppmv. * Catalytic oxidation unhs: Vapor streams are heated and then passed over a catalyst bed. Destruction effi- ciencies are typically >95 percent. These units are used for vapor concentrations <8000 ppmv. More con- centrated vapors can cause catalyst bed temperature excursions and meltdown. • Carbon beds: Carbon can be used to treat almost any vapor streams, but is only economical for very low emission rates (<100 g/d) • Diffuser stacks: These do not treat vapors, but are the most economical solution for areas in which they are permitted. They must be carefully designed to minimize health risks and maximize safety. Ground Water Pumping System In cases where contaminated soils lie just above or below the water table, ground water pumping systems will be required to ensure that contaminated soils remain exposed. In designing a ground water pumping system it is important to be aware that upwelling (draw- up) of the ground water table will occur when a vacuum is applied at the extraction well (see Figure 9b). Because the upwelling will be greatest at the extraction wells, ground water pumping wells should be located within or as close to the extraction wells as possible. Their surface seals must be airtight to prevent unwanted short- circuiting of airflow down the ground water wells. System Integration System components (pumps, wells, vapor treating units, etc.) should be combined to allow maximum flexi- bility of operation. The review by Hutzler et al. (1988) provides descriptions of many reported systems. Specific requirements are: • Separate valves, flow meters, and pressure gauges for each extraction and injection well. • Air filter to remove particulates from vapors upstream of the pump and flow meter. • Knock-out pot to remove any liquid from vapor stream upstream of the pump and flow meter. Monitoring The performance of a soil-venting system must be monitored in order to ensure efficient operation, and to help determine when to shut off the system. At a minimum the following should be measured: • Date and time of measurement. • Vapor flow rates from extraction wells and into injec- tion welts: These can be measured by a variety of flow meters including pilot tubes, orifice plates and rotameters. It is important to have calibrated these devices at the field operating pressures and tempera- tures. • Pressure readings at each extraction and injection well can be measured with manometers or magnahelic gauges. • Vapor concentrations and compositions from extrac- tion wells: total hydrocarbon concentration can be measured by an on-line total hydrocarbon analyzer calibrated to a specific hydrocarbon. This information is combined with vapor flow rate data to calculate removal rates and the cumulative amount of contam- inant removed. In addition, for mixtures the vapor composition should be periodically checked. It is impossible to assess if vapor concentration decreases with time are due to compositional changes or some other phenomena (mass transfer resistance, water table upwelling, pore blockage, etc.) without this information. Vapor samples can be collected in evacu- ated gas sampling cylinders, stored, and later ana- lyzed. • Temperature: ambient and soil. • Water table level (for contaminated soils located near the water table): It is important to monitor the water table level to ensure that contaminated soils remain exposed to vapor flow. Measuring the water table level during venting is not a trivial task because the monitoring well must remain sealed. Uncapping the well releases the vacuum and any effect that it has on the water table level. Figure 13b illustrates a moni- toring well cap (constructed by Applied Geosciences Inc., Tustin, California) that allows one to simulta- neously measure the water table level and vacuum in a monitoring well. It is constructed from a commer- cially available monitoring well cap and utilizes an electronic water level sensor. Other valuable, but optional measurements are: • Soil-gas vapor concentrations and compositions: These should be measured periodically at different radial distances from the extraction well. Figure 14 ------- 1/8" OD Teflon Tubinf Ground Surface Box ConMiimif Vipor Sunpliiii Pom AThomooaupia Jang Figure 14. Vadose zone monitoring well installation. shows the construction of a permanent monitoring installation that can be used for vapor sampling and subsurface temperature measurements. Another alternative for shallow contamination zones is the use of soil-gas survey probes. Data from soil-gas probes are valuable for two reasons: (1) by comparing extrac- tion well concentrations with soil-gas concentrations it is possible to estimate the fraction of vapor that is flowing through the contaminated zone 4>=Cex,r«,jon weii/Cjoi, g». and (2) it is possible to determine if the zone of contamination is shrinking toward the extrac- tion well, as it should with time. Three measuring points are probably sufficient if one is located near the extraction well, one is placed near the original edge of the zone of contamination, and the third is placed somewhere in between. These monitoring installations can also be useful for monitoring subsurface vapors after venting has ceased. Determining When to Turn Off the System Target soil cleanup levels are often set on a site-by- site basis, and are based on the estimated potential impact that any residual may have on air quality, ground water quality, or other health standards. They may also be related to safety considerations (explosive limits). Generally, confirmation soil borings, and sometimes soil-vapor surveys are required before closure is granted. Because these analyses can be expensive and often disrupt the normal business of a site, it would be valuable to be able to determine when confirmation borings should be taken. If the monitoring is done as suggested previously, then the following criteria can be used: • Cumulative amount removed: Determined by inte- grating the measured removal rates (flow rate x con- centration) with time. While this value indicates how much contaminant has been removed, it is usually not very useful for determining when to take confir- mation borings unless the original spill mass is known accurately. In most cases that information is not avail- able and cannot be calculated accurately from soil- boring data. * Extraction well vapor concentrations: The vapor con- centrations are good indications of how effectively the venting system is working, but decreases in vapor extraction well concentrations are not strong evidence that soil concentrations have decreased. Decreases may also be due to other phenomena such as water table level increases, increased mass transfer resist- ance due to drying, or leaks in the extraction system. • Extraction well vapor composition: When combined with vapor concentrations these data offer more insight into the effectiveness of the system. If the total vapor concentration decreases without a change in composition, it is probably due to one of the phe- nomena mentioned previously, and is not an indica- tion that the residual contamination has been signific- antly reduced. If a decrease in vapor concentration is accompanied by a shift in composition toward less volatile compounds, on the other hand, it is most likely due to a change in the residual contaminant concentration. For residual gasoline cleanup, for example, one might operate a venting system until benzene, toluene, and xylenes were not detected in the vapors. The remaining residual would then be composed of larger molecules, and it can be argued that these do not pose a health threat through volatili- zation or leaching pathways. • Soil-gas contaminant concentration and composition: These data are the most useful because it yields infor- mation about the residual composition and extent of contamination. Vapor concentrations cannot, in gen- eral, be used to determine the residual level, except in the limit of low residual levels (note that Equation 1 is independent of residual concentration). It is important to consider the effect of continued soil-venting system operation on soil-gas sampling results. Results taken during operation, or immediately after shutdown, can be used to assess the spatial extent of contamination and composition of the vapors. After the system is shut down, vapors will begin to migrate away from the source and equilibrate on a larger scale. True soil- vapor concentrations can be, measured once equilib- rium concentrations are attained in the sampling zone; at least two sampling times will be required to determine that equilibration has occurred. Due to the diffusion of vapors, samples taken after shutdown are not good indicators of the spatial extent of the conta- minated zone. Other Factors Increased Biodegradation It is often postulated that because the air supply to the vadose zone is increased, the natural aerobic micro- biological activity is increased during venting. While the argument is plausible and some laboratory data are available (Salanitro et al. 1989), conclusive evidence supporting this theory has yet to be presented. This is due in part to the difficulty in making such a mea- surement. A mass balance approach is not likely to be useful because the initial spill mass is generally not known with sufficient accuracy. An indirect method would be to measure CO2 levels in the extraction well ------- vapors, but this in itself does not rule out the possibility that O2 is converted to CO2 before the vapors pass through the contaminated soil zone. The best approach is to measure the CVCOa concentrations in the vapors at the edge of the contaminated zone, and in the vapor extraction wells. If the CO2/O2 concentration ratio increases as the vapors pass through the contaminated soil, one can surmise that a transformation is occurring, although other possible mechanisms (inorganic reac- tions) must be considered. An increase in aerobic mic- robial populations would be additional supporting evid- ence. In Situ Heating/Venting The main property of a compound that determines whether or not it can be removed by venting is its vapor pressure, which increases with increasing temperature. Compounds that are considered non-volatile, therefore, can be removed by venting if the contaminated soil is heated to the proper temperature. In situ heating/vent- ing systems utilizing radio-frequency heating and con- duction heating are currently under study (Dev et al. 1988). An alternative is to reinject heated vapors from catalytic oxidation t>r combustion units into the con- taminated soil zone. Air Sparging Due to seasonal ground water level fluctuations, con- taminants sometimes become trapped below the water table. In some cases ground water pumping can lower the water table enough to expose this zone, but in other cases this is not practical. One possible solution is to install air sparging wells and then inject air below the water table. Vapor extraction wells would then capture the vapors that bubbled up through the ground water. To date, success of this approach has yet to be demon- strated. This could have a negative effect if foaming, formation plugging, or downward migration of the resid- ual occurred. Application of the Design Approach to a Service Station Remediation In the following, the use of the approach discussed previously and outlined in Figure 2, is demonstrated for a service station remediation. Preliminary Site Investigation Prior to sampling it was estimated that 2000 gallons of gasoline had leaked from a product line at this operat- ing service station site. Several soil borings were drilled and the soil samples were analyzed for total petroleum hydrocarbons (TPH) and other specific compounds (benzene, toluene, xylenes) by a heated-headspace method utilizing a field GC-FID. Figure 15 summarizes some of the results for one transect at this site. The following relevant information was collected: • Based on boring logs there are four distinct soil layers between 0 - 18m (0-60 ft) below ground surface (BGS). Figure 15 indicates the soil type and location of each of these layers. * Depth to ground water was 15m, with fine to medium sand soils. JO- J. 1 i-- 1 w- Vapor ? — * » =« \ WWiM SMHliH mo_ \ J «" •"r v. r , (Kkllll \ \ Fine to CtmStM Silly CUjr * Otyey Silt Medium Swd • 03 / Ml .« ' WT7 •151 J»7 Dill 1.1 ' MaiifoM a.X' °w?Si2r* t A . D j .u , 214 . •1 ant • • 0)1 •0.1' •M . 1-J 1J »f HB-17 SuUcOmnd wwrlttk KB 7HB-5 HB25 IV.pt. HB3 HB-21 ««»«yWdll Rtcovnj Wdl] Figure 15. Initial tout hydrocartwn distribution (mg/kg-soil] and location of lower zone vent well. • The largest concentrations of hydrocarbons were detected in the sandy and silty clay layers adjacent to the water table. Some residual was detected below the water table. Based on the data presented in Figure 15 it is estimated that - 4000kg of hydrocarbons are present in the lower two soil zones. • Initially there was some free-liquid gasoline floating on the water table: this was subsequently removed by pumping. A sample of this product was analyzed and its approximate composition («20 percent of the compounds could not be identified) is listed in Table 2 as the "weathered gasoline." The corre- sponding boiling point distribution curve for this mix- ture has been presented in Figure 3. • Vadose zone monitoring installations similar to the one pictured in Figure 14 were installed during the preliminary site investigation. Deciding if Venting b Appropriate For the remainder of the analysis the contaminated soils located just above the water table will be the focus. • What contaminant vapor concentrations are likely to be obtained? Based on the composition given in Table 2, and using Equation 1, the predicted saturated TPH vapor concen- tration for this gasoline is: Ceit = 220 mg/L Using the "approximate" composition listed in Table 2 yields a value of 270 mg/L. The measured soil-vapor concentration obtained from the vadose zone monitoring well was 240 mg/L. Due to composition changes with time, this will be the maximum concentration obtained during venting. • Under ideal flow conditions is this concentration great enough to yield acceptable removal rates? ------- Equation 4 was used to calculate R(K!eept.bie- Assum- ing M\$pm = 4000kg and T = 180 d, then: R.ccept.We = 22 kg/d Using Equation 2, Ceit = 240 mg/L, and Q = 28001/ min (100 cfm): Re« = 970 kg/d which is greater than R»cccpl.bie- • What range of vapor flow rates can realistically be achieved? Based on boring logs, the contaminated zone just above the water table is composed of fine to medium sands, which have an estimated permeability 1< k < 10 darcy. Using Figure 5, or Equation 5, the predicted flow rates for an extraction well vacuum Pw = 0.90 atm are: 0.04 < Q < 0.4 m3/m-min Rw = 5.1cm, RI = 12m 0.43 < Q < 43 ftVft-min Rw = 2.0 in, R, = 40 ft. The thickness of this zone and probable screen thick- ness of an extraction well is about 2m (6.6 ft). The total flow rate per well through this zone is estimated to be 0.08l«.m) 0 HB-14D(t=9.8cn) + HB-IO (r7.6m) n1^ a -^ D -f^o0 f .v° dP H f + + a ° ^s0 ° T O t x * 1 10 o £° A k A A 100 1000 Time (min) FIfwe 16. Air permeability test results: (a) vapor extraction lest; (b) air injection test [In HjO] denote vacuums expressed a* equivalent water column heights. determine the permeability to vapor flow. The k values ranged from 2 to 280 darcys, with the median being ~8 darcys. System Design • Number of vapor extraction wells: Based on the 8 darcys permeability, and assuming a 15cm diameter (6 in) venting well, a 2m screened section, Pw = 0-90 atm (41 in H2O vacuum) and R\|=12m, then Equation 5 predicts: Q = 0.7 mVmin = 25 cfm Based on the preceding discussion, a minimum aver- age flow rate of 1.5 mj/min is needed to reduce the residual to 1000 ppm in six months. The number of wells required is then 1.5/0.7 = 2, assuming that 100 percent of the vapor flows through contaminated soils. It is not likely that this will occur, and a more conservative esti- mate of 50 percent vapor flowing through contaminated soils would require that twice as many wells (four) be installed. A single vapor extraction well (HB-25) was installed in this soil layer with the knowledge that more wells were likely to be required. Its location and screened interval are shown in Figure 15. Other wells were installed in the day layer and upper sandy zone, but in this paper only results from treatment of the lower contaminated ------- isone will be discussed. A ground water pumping well was installed to maintain a 2m drawdown below the static water level. Its location is also shown in Figure IS. {System Monitoring Three vadose monitoring wells similar in construc- tion to the one pictured in Figure 14 were installed so that the soil temperature, soil-gas concentrations, and subsurface pressure distribution could be monitored at three depths. One sampling port is located in the zone idjacent to the aquifer. The vapor flow rate from HB- 25 and vapor concentrations were measured frequently, ind the vapor composition was determined by GC-F1D analysis. In addition, the water level in the ground water monitoring wells was measured with the system pictured n Figure 13b. The results from the first four months of operation are discussed in following text In Figure 17a the extraction well vacuum and corre- sponding vapor flow rate are presented. The vacuum was maintained at 0.95 aim (20 in H2O vacuum), and :he flow rate was initially 12 scfm. It gradually decreased :o about 6 scfm over 80 d. For comparison, Equation 5 predicts that Q=12 cfm for k=8 darcys. Increasing the applied vacuum to 0.70 atm (120 in H2O vacuum) had little effect on the flow rate. This could be explained by increased water table upwelling, which would act to decrease the vertical cross section available for vapor How. The scatter in the flow rate measurements is prob- ably due to inconsistent operation of the ground water pumping operation, which frequently failed to perform properly. Figure 17b presents the change in vapor concentra- tion with time. Fifteen specific compounds were identi- fied during the GC-FID vapor analyses; in this figure i he total concentration of known and unknown com- ]x>unds detected between five boiling point ranges are presented: methane - isopentane (<28 C) isopentane - benzene (28 - 80 C) benzene - toluene (80 - 111 C) toluene - xylenes (111 -144 C) >xylenes (>144 C). There was a shift in composition toward less volatile compounds in the first 20 days, but after that period the composition remained relatively constant. Note that Ihere is still a significant fraction of volatile compounds present. Within the first two days the vapor concentra- tion decreased by 50 percent, which corresponds to the time period for the removal of the first pore volume of air. Comparing the subsequent vapor concentrations with the concentrations measured in the vadose zone monitoring wells indicates that only (80 mg/L)/(240 mg/ L)* 100=33% of the vapors are flowing through contamin- ated soil. Figure 18a presents calculated removal rates (flow rate x concentration) and cumulative amount (1 gal = :i kg) removed during the first four months. The decrease in removal rate with time is due to a combina- tion of decreases in flow rate and hydrocarbon vapor concentrations. After the first four months approxi- mately one-fourth of the estimated residual has been HB-25 100 Vacuum (in HO) M 120 100 80 to 40 0. 4 1? — •-- HMK \' "''",.' i * • *, /'' V i' ^ '15 10 •5 Ftowraie (SCFM) 20 40 60 10 100 120 Time (d) E vMaynu ttpmwt u equivalent wuer eohnui height b) 0 20 40 60 80 100 120 Time (d) Figure 17. Soil-venting retails: () vacuum/flow rate data, (b) concentration/composition data. a) Removal « Rale (kg/d) so 400 200 too Cumulative Recovered (gal) 20 40 60 0 100 120 Time (d) b) ftH.O 2 0.3- 0.0 I 10 Time (min) (ft HO) denote vtcuums expressed is equivalent water column heights Figure 18. Soil-venting results: (a) removal rate/cumulative recovered, (b) water table rise. removed from this lower zone. On day 80 the vacuum was increased from 20 -120 in H2O vacuum and the subsequent increase in subsur- ------- face vacuum and water table upweiling as monitored. Figure 18b presents the results. Note that the water table rise paralleled the vacuum increase, although the water table did not rise the same amount that the vacuum did. Figure 19 compares the reduced measured TPH vapor concentration C(t)/C(t=0) with model predic- tions. C(t=0) was taken to be the vapor concentration after one pore volume of air had passed through the contaminated zone (=80 mg/L), m(t=0) is equal to the estimated spill mass (=4000 kg), and V(t) is the total volume of air that has passed through the contaminated zone. This quantity is obtained by integrating the total vapor flow rate with time, then multiplying it by the fraction of vapors passing through the contaminated zone (=0.33). As discussed, the quantity 4> was esti- mated by comparing soil-gas concentrations from the vadose zone monitoring installations with vapor concen- trations in the extraction well vapors. There is good quantitative agreement between the measured and pre- dicted values. Based on the data presented in Figures 15 through 19 and the model predictions in Figure 8, it appears that more extraction wells (• 10 more) are needed to reme- diate the site within a reasonable amount of time (< 2 years). Conclusions A structured, technically based approach has been presented for the design, construction, and operation of venting systems. While an attempt has been made to explain the process in detail for those not familiar with venting operations or the underlying governing phe- nomena, the most effective and efficient systems can only be designed and operated by personnel with a good understanding of the fundamental processes involved. The service station spill example presented supports the validity and usefulness of this approach. There are still many technical issues that need to be resolved in the future. The usefulness of forced or pas- sive vapor injection wells is often debated, as well as other means of controlling vapor flow paths (impermea- ble surface covers, for example). A well-documented demonstration of the effectiveness of soil venting for the removal of contaminants from low-permeability soils is also needed. It is clear from the simplistic model- ing results presented in this paper that venting will be less effective in such situations. Without a comparison with other viable treatment alternatives, however, it is difficult to determine if soil venting would still be the preferred option in such cases. Other topics for future study include: enhanced aerobic biodegradation by soil venting, the possibility of decreasing residual contami- nant levels in water-saturated zones by air sparging/ vapor extraction, and optimal operation schemes for multiple vapor extraction well systems. References Bear, J.1979. Hydraulics of Groundwater, McGraw-Hill. Dev, H., G.C. Sresty, I.E. Bridges, and D. Downey, 1.0 0.8 C(t)/C(t=0) 0.6 CftVC(l=«) predicted C(lVC(l=0) measured weathered gasoline m(t=0)-4000kg 0.4 0.2 0123456789 10 V(t)/m(t=0) (1/g) Figure 19. Comparison of model predictions and measured response. 1988. Field test of the radio frequency in situ soil decontamination process. In Superfund '88: Proceed- ings of the 9th National Conference, HMCRI, Novem- ber 1988. Hutzler, N. J., B.E. Murphy, and J.S. Gierke. 1988. State of Technology Review: Soil Vapor Extraction Sys- tems, U.S EPA, CR-814319-01-1. Johnson, P.C., M.W. Kemblowski, and J.D. Colthart. 1988. Practical screening models for soil venting applications. In Proceedings of NWWA/AP1 Confer- ence on Petroleum Hydrocarbons and Organic Chem- icals in Ground Water, Houston, Texas. Marley, M.C., and G.E. Hoag. 1984 Induced soil venting for the recovery/restoration of gasoline hydrocarbons in the vadose zone. In Proceedings of NWWA/API Conference on Petroleum Hydrocarbons and Organic Chemicals in Ground Water, Houston, Texas. Millington, R.J. and J.M. Quirk. 1961. Permeability of Porous Solids, Trans. Faraday Soc., 57:1200-1207. Salanitro, J. P., M.M. Western, and M.W. Kemblowski. 1989. Biodegradation of aromatic hydrocarbons in unsaturated soil microcosms. Poster paper presented at the Fourth National Conference on Petroleum Contaminated Soils, University of Massachusetts, Amherst, September 25-28. Wilson, D. J., A.N. Clarke, and J.H. Clarke. 1988. Soil Clean-up by in situ aeration. I. Mathematical Modell- ing, Sep. Science Tech., voj. 23 pp. 991-1037. Biographical Sketches Paul C. Johnson, Ph.D., joined Shell Development Co.'s (Westhollotv Research Center, Room EC-649, P.O. Box 1380, Houston, TX 77251- 1380) Environmental Science Department in 1987 after earning his B.S. in chemical engineering from the Uni- versity of California, Davis, and his Ph. D. in chemical engineering from Princeton University. His current areas of research include the development and evalua- tion of soil treatment processes, modeling and measur- ing transport phenomena in porous media, and the development of transport models for predicting emis- sions and exposures used in environmental risk ------- assessments. Curtis C. Stanley received Ms degree in geology with an engineering minor from North Carolina State Uni- versity in 1979, He is currently a senior hydrogeologist for Shell Oil Co, (Westhollow Research Center, 2236 Two Shell Plaza, Houston, TX 77082) and is responsi- ble for hydrogeologic response at-Shell's retail facilities. Stanley is a Certified Professional Geological Scientist and also a Certified Ground Water Professional with the NWWA's Association of Ground Water Scientists ami Engineers. He is also a member of API's Ground Water Technology Taskforce and is an EPA Peer Reviewer. Marian W. Kemblowski, Ph.D., is a senior research engineer in the Environmental Science Department at Shtil Development Co. (Westhollow Research Center, Houston, TX 77082) where he has worked since 1985. He obtained his M.S. degree in civil engineering from tht Technical University of Warsaw, Poland, in 1973 andhisPh.D. in ground water hydrology from the Insti- tute for Land Reclamation in Warsaw, Poland, in 1978. In 1980 -1981 he was a visiting hydrologist in the New Mtxico School of Mining and Technology. From 1981 to 1985 he worked as an assistant scientist at the Uni- versity of Kansas. His principal research interests are in t'he areas of numerical analysis, transport in porous media, and ground water monitoring systems. Dallas L. Byers is a technical associate in the Envi- ronmental Science Department at Shell Development. After receiving his B.S. degree in zoology from the Uni- versity of Nevada, Las Vegas, he was employed by the Texas Water Quality Board as a quality control chemist for 3'/2 years. In 1977 he joined Shell (Westhollow Research Center, Houston, TX 77082) where he cur- rently is providing technical assistance and support for research in the fate of chemicals in soil and gorund water. James D. Colthart, Ph.D,, has been in a variety of R&D and technical planning positions since joining Shell (Westhollow Research Center, Houston, TX 77082) in 1966. He has a B.E. from Yale University and a Ph.D. from Rice University, both in chemical engineering. Currently he is the research manager of Shell Development Co. Air, Waste, and Groundwater Group. ------- ------- SOFTWARE held by Library Database Coordinator, piease inquire at Circulation Desk ------- -------	2022-01-24T05:57:28	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4892565906047821, "perplexity": 8619.683561678856}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304515.74/warc/CC-MAIN-20220124054039-20220124084039-00499.warc.gz"}
https://large-numbers.fandom.com/wiki/Ballium%27s_number	## FANDOM 1,081 Pages Ballium's number is a number coined in a parody YouTube video by Meerkats Anonymous, in which a fictional physicist Samuel Ballium claims it to be "the largest number."[1][2]According to the video, Ballium's number is exactly $(794{,}843{,}294{,}078{,}147{,}843{,}293.7 + 1/30) \cdot e^{\pi^{e^\pi}}$ In the video, a spoof on newscasts about scientific findings, Ballium explains how he accidentally added "Hamlet" to an equation he was working on and stumbled upon this number. The video also goes on to say that the "Microsoft calculator struggles to produce an output, even when set to scientific mode." The number is in fact smaller than a googolplex. This can be shown easily enough, by rounding $$e$$ and $$\pi$$ up to the next nearest integer and replacing the first component with $$10^{21}$$: $\text{Ballium's number} < 10^{21} \cdot 3^{4^{3^4}} = 10^{21} \cdot 3^{4^{81}} = 10^{21} \cdot 3^{2^{162}} = 10^{21} \cdot 3^{10^{162 \log_{10} 2}} < 10^{21} \cdot 3^{10^{162 \cdot 0.4}} =$ $10^{21} \cdot 3^{10^{64.8}} < 10^{21} \cdot 10^{10^{64.8}} = 10^{21 + 10^{64.8}} < 10^{10^{64.8} + 10^{64.8}} < 10^{10^{65.8}} < 10^{10^{66}}$ This is less than $$10^{10^{100}}$$, so Ballium's number is smaller than googolplex. In fact, $$10^{10^{66}}$$ is a very generous upper bound. The actual value is closer to $$10^{10^{11}}$$. It can be shown that: $10^{10^{11}} < \text{Ballium's number} < 10^{10^{12}}$ Ballium's number contains roughly 138 billion digits before the decimal point, storage of which is possible on today's computers. However, the process of computing those digits exactly may be impractically long. The exact number of digits before the decimal point is 138,732,019,350. Ballium's number is a typical example of common attempts to name a very large number. Its form seems to be largely inspired by Skewes' number, but it fails to be very large, mainly because the topmost exponent of the second component is too small. Ballium's number is also an example of ultrafinitism. ## Notes and referencesEdit Community content is available under CC-BY-SA unless otherwise noted.	2020-01-28T03:31:27	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7425916194915771, "perplexity": 770.6248335579896}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251773463.72/warc/CC-MAIN-20200128030221-20200128060221-00373.warc.gz"}
https://www.ctcms.nist.gov/potentials/iprPy/notebook/stacking_fault_static.html	# stacking_fault_static calculation style Lucas M. Hale, [email protected], Materials Science and Engineering Division, NIST. ## Introduction The stacking_fault_static calculation style evaluates the energy of a single generalized stacking fault shift along a specified crystallographic plane. ### Version notes • 2019-07-30: Description updated and small changes due to iprPy version. • 2020-05-22: Version 0.10 update - potentials now loaded from database. • 2020-09-22: Calculation updated to use atomman.defect.StackingFault class. Setup and parameter definition streamlined. ### Disclaimers • NIST disclaimers • The system’s dimension perpendicular to the fault plane should be large to minimize the interaction of the free surface and the stacking fault. ## Method and Theory First, an initial system is generated. This is accomplished using atomman.defect.StackingFault, which 1. Starts with a unit cell system. 2. Generates a transformed system by rotating the unit cell such that the new system’s box vectors correspond to crystallographic directions, and filled in with atoms to remain a perfect bulk cell when the three boundaries are periodic. 3. All atoms are shifted by a fractional amount of the box vectors if needed. 4. A supercell system is constructed by combining multiple replicas of the transformed system. 5. The system is then cut by making one of the box boundaries non-periodic. A limitation placed on the calculation is that the normal to the cut plane must correspond to one of the three Cartesian ($$x$$, $$y$$, or $$z$$) axes. If true, then of the system’s three box vectors ($$\vec{a}$$, $$\vec{b}$$, and $$\vec{c}$$), two will be parallel to the plane, and the third will not. The non-parallel box vector is called the cutboxvector, and for LAMMPS compatible systems, the following conditions can be used to check the system’s compatibility: • cutboxvector = ‘c’: all systems allowed. • cutboxvector = ‘b’: the system’s yz tilt must be zero. • cutboxvector = ‘a’: the system’s xy and xz tilts must be zero. A LAMMPS simulation performs an energy/force minimization on the system where the atoms are confined to only relax along the Cartesian direction normal to the cut plane. A mathematical fault plane parallel to the cut plane is defined in the middle of the system. A generalized stacking fault system can then be created by shifting all atoms on one side of the fault plane by a vector, $$\vec{s}$$. The shifted system is then relaxed using the same confined energy/force minimization used on the non-shifted system. The generalized stacking fault energy, $$\gamma$$, can then be computed by comparing the total energy of the system, $$E_{total}$$, before and after $$\vec{s}$$ is applied $\gamma(\vec{s}) = \frac{E_{total}(\vec{s}) - E_{total}(\vec{0})}{A},$ where $$A$$ is the area of the fault plane, which can be computed using the two box vectors, $$\vec{a_1}$$ and $$\vec{a_2}$$, that are not the cutboxvector. $A = \left\| \vec{a_1} \times \vec{a_2} \right\|,$ Additionally, the relaxation normal to the glide plane is characterized using the center of mass of the atoms above and below the cut plane. Notably, the component of the center of mass normal to the glide/cut plane is calculated for the two halves of the the system, and the difference is computed $\delta = \left<x\right>^{+} - \left<x\right>^{-}.$ The relaxation normal is then taken as the change in the center of mass difference after the shift is applied. $\Delta\delta = \delta(\vec{s}) - \delta(\vec{0}).$ ## Demonstration ### 1. Library imports Import libraries needed by the calculation. The external libraries used are: [1]: # Standard library imports from pathlib import Path import os import shutil import datetime # http://www.numpy.org/ import numpy as np # https://github.com/usnistgov/atomman import atomman as am import atomman.lammps as lmp import atomman.unitconvert as uc # https://github.com/usnistgov/iprPy import iprPy print('Notebook last executed on', datetime.date.today(), 'using iprPy version', iprPy.__version__) Notebook last executed on 2020-09-22 using iprPy version 0.10.2 #### 1.2. Default calculation setup [2]: # Specify calculation style calc_style = 'stacking_fault_static' # If workingdir is already set, then do nothing (already in correct folder) try: workingdir = workingdir # Change to workingdir if not already there except: workingdir = Path('calculationfiles', calc_style) if not workingdir.is_dir(): workingdir.mkdir(parents=True) os.chdir(workingdir) # Initialize connection to library ### 2. Assign values for the calculation’s run parameters #### 2.1 Specify system-specific paths • lammps_command is the LAMMPS command to use. • mpi_command MPI command for running LAMMPS in parallel. A value of None will run simulations serially. [3]: lammps_command = 'lmp_serial' mpi_command = None • potential_name gives the name of the potential_LAMMPS reference record in the iprPy library to use for the calculation. • potential is an atomman.lammps.Potential object (required). [4]: potential_name = '1999--Mishin-Y--Ni--LAMMPS--ipr1' # Retrieve potential and parameter file(s) potential = library.get_lammps_potential(id=potential_name, getfiles=True) #### 2.3. Load initial unit cell system • ucell is an atomman.System representing a fundamental unit cell of the system (required). Here, this is loaded from the database for the prototype. [5]: # Create ucell by loading prototype record ucell = am.load('crystal', potential=potential, family='A1--Cu--fcc', database=library) print(ucell) avect = [ 3.520, 0.000, 0.000] bvect = [ 0.000, 3.520, 0.000] cvect = [ 0.000, 0.000, 3.520] origin = [ 0.000, 0.000, 0.000] natoms = 4 natypes = 1 symbols = ('Ni',) pbc = [ True True True] per-atom properties = ['atype', 'pos'] id atype pos[0] pos[1] pos[2] 0 1 0.000 0.000 0.000 1 1 0.000 1.760 1.760 2 1 1.760 0.000 1.760 3 1 1.760 1.760 0.000 #### 2.4. Specify the defect parameters • hkl gives the Miller (hkl) or Miller-Bravais (hkil) plane to create the free surface on. • cutboxvector specifies which of the three box vectors (‘a’, ‘b’, or ‘c’) is to be made non-periodic to create the free surface. • shiftindex can be used for complex crystals to specify different termination planes. • a1vect_uvw, a2vect_uvw specify two non-parallel Miller crystal vectors within the fault plane corresponding to full planar shifts from one perfect crystal configuration to another. • a1, a2 are the fractional shifts along a1vect_uvw, a2vect_uvw to apply to the system. [6]: hkl = [1, 1, 1] cutboxvector = 'c' shiftindex = 0 a1vect_uvw = [ 0.0,-0.5, 0.5] a2vect_uvw = [ 0.5,-0.5, 0.0] a1 = 0.5 a2 = 0.0 #### 2.5. Modify system • sizemults list of three integers specifying how many times the ucell vectors of $$a$$, $$b$$ and $$c$$ are replicated in creating system. • minwidth specifies a minimum width that the system should be along the cutboxvector direction. The given sizemult in that direction will be increased if needed to ensure that the system is at least this wide. [7]: sizemults = [5, 5, 10] minwidth = uc.set_in_units(0.0, 'angstrom') #### 2.6. Specify calculation-specific run parameters • energytolerance is the energy tolerance to use during the minimizations. This is unitless. • forcetolerance is the force tolerance to use during the minimizations. This is in energy/length units. • maxiterations is the maximum number of minimization iterations to use. • maxevaluations is the maximum number of minimization evaluations to use. • maxatommotion is the largest distance that an atom is allowed to move during a minimization iteration. This is in length units. [8]: energytolerance = 1e-8 forcetolerance = uc.set_in_units(0.0, 'eV/angstrom') maxiterations = 10000 maxevaluations = 100000 maxatommotion = uc.set_in_units(0.01, 'angstrom') ### 3. Define calculation function(s) and generate template LAMMPS script(s) #### 3.1 sfmin.template [9]: with open('sfmin.template', 'w') as f: f.write("""#LAMMPS input script that performs an energy minimization #for a system with a stacking fault box tilt large <atomman_system_pair_info> <fix_cut_setforce> thermo_style custom step lx ly lz pxx pyy pzz pe thermo_modify format float %.13e compute peatom all pe/atom min_modify dmax <dmax> dump dumpit all custom <maxeval> <sim_directory>.dump id type x y z c_peatom dump_modify dumpit format <dump_modify_format> minimize <etol> <ftol> <maxiter> <maxeval>""") #### 3.2 stackingfaultrelax() [10]: def stackingfaultrelax(lammps_command, system, potential, mpi_command=None, sim_directory=None, cutboxvector='c', etol=0.0, ftol=0.0, maxiter=10000, maxeval=100000, dmax=uc.set_in_units(0.01, 'angstrom'), lammps_date=None): """ Perform a stacking fault relaxation simulation for a single faultshift. Parameters ---------- lammps_command :str Command for running LAMMPS. system : atomman.System The system containing a stacking fault. potential : atomman.lammps.Potential The LAMMPS implemented potential to use. mpi_command : str, optional The MPI command for running LAMMPS in parallel. If not given, LAMMPS will run serially. sim_directory : str, optional The path to the directory to perform the simulation in. If not given, will use the current working directory. cutboxvector : str, optional Indicates which of the three system box vectors, 'a', 'b', or 'c', has the non-periodic boundary (default is 'c'). Fault plane normal is defined by the cross of the other two box vectors. etol : float, optional The energy tolerance for the structure minimization. This value is unitless. (Default is 0.0). ftol : float, optional The force tolerance for the structure minimization. This value is in units of force. (Default is 0.0). maxiter : int, optional The maximum number of minimization iterations to use (default is 10000). maxeval : int, optional The maximum number of minimization evaluations to use (default is 100000). dmax : float, optional The maximum distance in length units that any atom is allowed to relax in any direction during a single minimization iteration (default is 0.01 Angstroms). lammps_date : datetime.date or None, optional The date version of the LAMMPS executable. If None, will be identified from the lammps_command (default is None). Returns ------- dict Dictionary of results consisting of keys: - 'logfile'* (str) - The filename of the LAMMPS log file. - 'dumpfile' (str) - The filename of the LAMMPS dump file of the relaxed system. - 'system' (atomman.System) - The relaxed system. - 'E_total' (float) - The total potential energy of the relaxed system. Raises ------ ValueError For invalid cutboxvectors. """ # Build filedict if function was called from iprPy try: assert __name__ == pkg_name filedict = calc.filedict except: filedict = {} # Give correct LAMMPS fix setforce command if cutboxvector == 'a': fix_cut_setforce = 'fix cut all setforce NULL 0 0' elif cutboxvector == 'b': fix_cut_setforce = 'fix cut all setforce 0 NULL 0' elif cutboxvector == 'c': fix_cut_setforce = 'fix cut all setforce 0 0 NULL' else: raise ValueError('Invalid cutboxvector') if sim_directory is not None: # Create sim_directory if it doesn't exist sim_directory = Path(sim_directory) if not sim_directory.is_dir(): sim_directory.mkdir() sim_directory = sim_directory.as_posix()+'/' else: # Set sim_directory if is None sim_directory = '' # Get lammps units lammps_units = lmp.style.unit(potential.units) #Get lammps version date if lammps_date is None: lammps_date = lmp.checkversion(lammps_command)['date'] # Define lammps variables lammps_variables = {} system_info = system.dump('atom_data', f=Path(sim_directory, 'system.dat').as_posix(), potential=potential, return_pair_info=True) lammps_variables['atomman_system_pair_info'] = system_info lammps_variables['fix_cut_setforce'] = fix_cut_setforce lammps_variables['sim_directory'] = sim_directory lammps_variables['etol'] = etol lammps_variables['ftol'] = uc.get_in_units(ftol, lammps_units['force']) lammps_variables['maxiter'] = maxiter lammps_variables['maxeval'] = maxeval lammps_variables['dmax'] = uc.get_in_units(dmax, lammps_units['length']) # Set dump_modify format based on dump_modify_version if lammps_date < datetime.date(2016, 8, 3): lammps_variables['dump_modify_format'] = '"%i %i %.13e %.13e %.13e %.13e"' else: lammps_variables['dump_modify_format'] = 'float %.13e' # Write lammps input script template_file = 'sfmin.template' lammps_script = Path(sim_directory, 'sfmin.in') with open(lammps_script, 'w') as f: f.write(iprPy.tools.filltemplate(template, lammps_variables, '<', '>')) # Run LAMMPS output = lmp.run(lammps_command, lammps_script.as_posix(), mpi_command, logfile=Path(sim_directory, 'log.lammps').as_posix()) # Extract output values thermo = output.simulations[-1]['thermo'] logfile = Path(sim_directory, 'log.lammps').as_posix() dumpfile = Path(sim_directory, f'{thermo.Step.values[-1]}.dump').as_posix() E_total = uc.set_in_units(thermo.PotEng.values[-1], lammps_units['energy']) # Return results results_dict = {} results_dict['logfile'] = logfile results_dict['dumpfile'] = dumpfile results_dict['system'] = system results_dict['E_total'] = E_total return results_dict #### 3.3 stackingfault() [11]: def stackingfault(lammps_command, ucell, potential, hkl, mpi_command=None, sizemults=None, minwidth=None, even=False, a1vect_uvw=None, a2vect_uvw=None, conventional_setting='p', cutboxvector='c', faultpos_rel=None, faultpos_cart=None, a1=0.0, a2=0.0, atomshift=None, shiftindex=None, etol=0.0, ftol=0.0, maxiter=10000, maxeval=100000, dmax=uc.set_in_units(0.01, 'angstrom')): """ Computes the generalized stacking fault value for a single faultshift. Parameters ---------- lammps_command :str Command for running LAMMPS. ucell : atomman.System The crystal unit cell to use as the basis of the stacking fault configurations. potential : atomman.lammps.Potential The LAMMPS implemented potential to use. hkl : array-like object The Miller(-Bravais) crystal fault plane relative to ucell. mpi_command : str, optional The MPI command for running LAMMPS in parallel. If not given, LAMMPS will run serially. sizemults : list or tuple, optional The three System.supersize multipliers [a_mult, b_mult, c_mult] to use on the rotated cell to build the final system. Note that the cutboxvector sizemult must be an integer and not a tuple. Default value is [1, 1, 1]. minwidth : float, optional If given, the sizemult along the cutboxvector will be selected such that the width of the resulting final system in that direction will be at least this value. If both sizemults and minwidth are given, then the larger of the two in the cutboxvector direction will be used. even : bool, optional A True value means that the sizemult for cutboxvector will be made an even number by adding 1 if it is odd. Default value is False. a1vect_uvw : array-like object, optional The crystal vector to use for one of the two shifting vectors. If not given, will be set to the shortest in-plane lattice vector. a2vect_uvw : array-like object, optional The crystal vector to use for one of the two shifting vectors. If not given, will be set to the shortest in-plane lattice vector not parallel to a1vect_uvw. conventional_setting : str, optional Allows for rotations of a primitive unit cell to be determined from (hkl) indices specified relative to a conventional unit cell. Allowed settings: 'p' for primitive (no conversion), 'f' for face-centered, 'i' for body-centered, and 'a', 'b', or 'c' for side-centered. Default behavior is to perform no conversion, i.e. take (hkl) relative to the given ucell. cutboxvector : str, optional Indicates which of the three system box vectors, 'a', 'b', or 'c', to cut with a non-periodic boundary (default is 'c'). faultpos_rel : float, optional The position to place the slip plane within the system given as a relative coordinate along the out-of-plane direction. faultpos_rel and faultpos_cart cannot both be given. Default value is 0.5 if faultpos_cart is also not given. faultpos_cart : float, optional The position to place the slip plane within the system given as a Cartesian coordinate along the out-of-plane direction. faultpos_rel and faultpos_cart cannot both be given. a1 : float, optional The fractional coordinate to evaluate along a1vect_uvw. Default value is 0.0. a2 : float, optional The fractional coordinate to evaluate along a2vect_uvw. Default value is 0.0. atomshift : array-like object, optional A Cartesian vector shift to apply to all atoms. Can be used to shift atoms perpendicular to the fault plane to allow different termination planes to be cut. Cannot be given with shiftindex. shiftindex : int, optional Allows for selection of different termination planes based on the preferred shift values determined by the underlying fault generation. Cannot be given with atomshift. If neither atomshift nor shiftindex given, then shiftindex will be set to 0. etol : float, optional The energy tolerance for the structure minimization. This value is unitless. (Default is 0.0). ftol : float, optional The force tolerance for the structure minimization. This value is in units of force. (Default is 0.0). maxiter : int, optional The maximum number of minimization iterations to use (default is 10000). maxeval : int, optional The maximum number of minimization evaluations to use (default is 100000). dmax : float, optional The maximum distance in length units that any atom is allowed to relax in any direction during a single minimization iteration (default is 0.01 Angstroms). Returns ------- dict Dictionary of results consisting of keys: - 'E_gsf' (float) - The stacking fault formation energy. - 'E_total_0' (float) - The total potential energy of the system before applying the faultshift. - 'E_total_sf' (float) - The total potential energy of the system after applying the faultshift. - 'delta_disp' (float) - The change in the center of mass difference between before and after applying the faultshift. - 'disp_0' (float) - The center of mass difference between atoms above and below the fault plane in the cutboxvector direction for the system before applying the faultshift. - 'disp_sf' (float) - The center of mass difference between atoms above and below the fault plane in the cutboxvector direction for the system after applying the faultshift. - 'A_fault' (float) - The area of the fault surface. - 'dumpfile_0' (str) - The name of the LAMMMPS dump file associated with the relaxed system before applying the faultshift. - 'dumpfile_sf' (str) - The name of the LAMMMPS dump file associated with the relaxed system after applying the faultshift. """ # Construct stacking fault configuration generator gsf_gen = am.defect.StackingFault(hkl, ucell, cutboxvector=cutboxvector, a1vect_uvw=a1vect_uvw, a2vect_uvw=a2vect_uvw, conventional_setting=conventional_setting) # Check shift parameters if shiftindex is not None: assert atomshift is None, 'shiftindex and atomshift cannot both be given' atomshift = gsf_gen.shifts[shiftindex] elif atomshift is None: atomshift = gsf_gen.shifts[0] # Generate the free surface (zero-shift) configuration sfsystem = gsf_gen.surface(shift=atomshift, minwidth=minwidth, sizemults=sizemults, even=even, faultpos_rel=faultpos_rel) abovefault = gsf_gen.abovefault cutindex = gsf_gen.cutindex A_fault = gsf_gen.surfacearea # Identify lammps_date version lammps_date = lmp.checkversion(lammps_command)['date'] # Evaluate the zero shift configuration zeroshift = stackingfaultrelax(lammps_command, sfsystem, potential, mpi_command=mpi_command, cutboxvector=cutboxvector, etol=etol, ftol=ftol, maxiter=maxiter, maxeval=maxeval, dmax=dmax, lammps_date=lammps_date) # Extract terms E_total_0 = zeroshift['E_total'] pos_0 = zeroshift['system'].atoms.pos shutil.move('log.lammps', 'zeroshift-log.lammps') shutil.move(zeroshift['dumpfile'], 'zeroshift.dump') # Evaluate the system after shifting along the fault plane sfsystem = gsf_gen.fault(a1=a1, a2=a2) shifted = stackingfaultrelax(lammps_command, sfsystem, potential, mpi_command=mpi_command, cutboxvector=cutboxvector, etol=etol, ftol=ftol, maxiter=maxiter, maxeval=maxeval, dmax=dmax, lammps_date=lammps_date) # Extract terms E_total_sf = shifted['E_total'] pos_sf = shifted['system'].atoms.pos shutil.move('log.lammps', 'shifted-log.lammps') shutil.move(shifted['dumpfile'], 'shifted.dump') # Compute the stacking fault energy E_gsf = (E_total_sf - E_total_0) / A_fault # Compute the change in displacement normal to fault plane disp_0 = (pos_0[abovefault, cutindex].mean() - pos_0[~abovefault, cutindex].mean()) disp_sf = (pos_sf[abovefault, cutindex].mean() - pos_sf[~abovefault, cutindex].mean()) delta_disp = disp_sf - disp_0 # Return processed results results = {} results['E_gsf'] = E_gsf results['E_total_0'] = E_total_0 results['E_total_sf'] = E_total_sf results['delta_disp'] = delta_disp results['disp_0'] = disp_0 results['disp_sf'] = disp_sf results['A_fault'] = A_fault results['dumpfile_0'] = 'zeroshift.dump' results['dumpfile_sf'] = 'shifted.dump' return results ### 4. Run calculation function(s) [12]: results_dict = stackingfault(lammps_command, ucell, potential, hkl, mpi_command = mpi_command, sizemults = sizemults, minwidth = minwidth, a1vect_uvw = a1vect_uvw, a2vect_uvw = a2vect_uvw, cutboxvector = cutboxvector, shiftindex = shiftindex, a1 = a1, a2 = a2, etol = energytolerance, ftol = forcetolerance, maxiter = maxiterations, maxeval = maxevaluations, dmax = maxatommotion) [13]: results_dict.keys() [13]: dict_keys(['E_gsf', 'E_total_0', 'E_total_sf', 'delta_disp', 'disp_0', 'disp_sf', 'A_fault', 'dumpfile_0', 'dumpfile_sf']) ### 5. Report results #### 5.1 Define units for outputting values • length_unit is the unit of area to display delta displacemets in. • area_unit is the unit of area to display fault area in. • energyperarea_unit is the energy per area to report the surface energy in. [14]: length_unit = 'nm' area_unit = 'nm^2' energyperarea_unit = 'mJ/m^2' #### 5.2 Print $$A_{fault}$$, $$E_{gsf}$$, and $$\Delta\delta$$ [15]: print('Values for fractional shift = (%f, %f)' % (a1, a2)) print('A_fault = ', uc.get_in_units(results_dict['A_fault'], area_unit), area_unit) print('E_gsf = ', uc.get_in_units(results_dict['E_gsf'], energyperarea_unit), energyperarea_unit) print('delta_disp = ', uc.get_in_units(results_dict['delta_disp'], length_unit), length_unit) Values for fractional shift = (0.500000, 0.000000) A_fault = 5.365198866947918 nm^2 E_gsf = 924.3579463239225 mJ/m^2 delta_disp = 0.015655877018008368 nm	2021-12-09T01:27:44	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3819437026977539, "perplexity": 14849.292603911232}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363641.20/warc/CC-MAIN-20211209000407-20211209030407-00510.warc.gz"}
https://gea.esac.esa.int/archive/documentation/GDR3/Data_analysis/chap_cu3qso/sec_cu3qso_char/ssec_cu3qso_common.html	# 12.3.8 Sources in common between the two extragalactic tables It should be noted that certain sources are present in both integrated extragalactic tables. A total of 174 146 sources fall in that category. Figure 12.21 shows their source density distribution on the sky. Figure 12.22 shows, for each table, the $G$ magnitude distribution of these sources, indicating the contribution of each module. The distribution of their classes for the DSC (Combmod class label), Vari-Classification and OA classifiers respectively is as follows: • DSC (174 146 sources in total from this module in the common sample): 156 970 as ‘galaxy’, 12 933 as ‘quasar’. The rest is spread over the remaining classes. • Vari-Classification (27 058 sources in total from this module in the common sample): 20 845 as ‘AGN’, 4688 as ‘GALAXY’, 766 as Eclipsing Binary, 363 as RR Lyrae. The rest is spread over the remaining classes. • OA (105 463 sources in total from this module in the common sample): 46 773 as ‘QSO’, 48 097 as ‘GALAXY’. The rest is spread over the remaining classes. As can be seen, the majority of the sources in common in the two tables are labelled as ’galaxy’ according to DSC. Finally, almost half (28 688) of all sources reported as having a detected host galaxy are present in the sample of sources common to the two tables. This is 92% of all sources from the Surface brightness module being present in this common sample. All in all we suggest that the extragalactic sources in common between the two tables are mostly galaxies, even if a large fraction probably has an active nucleus. Stellar contaminants are also expected, especially in the regions with clear over-density in the sky distribution.	2023-03-29T05:57:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 2, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5921974778175354, "perplexity": 1928.1445287011084}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948951.4/warc/CC-MAIN-20230329054547-20230329084547-00673.warc.gz"}
https://www.federalreserve.gov/econres/notes/feds-notes/common-and-idiosyncratic-inflation-20200305.htm	March 05, 2020 ### Common and idiosyncratic inflation1 Matteo Luciani One of the major challenges that the Federal Reserve faces in achieving its goal of maintaining price stability is to avoid responding to sector- or industry-specific relative price changes or—even worse—to measurement error. Rather, the Federal Reserve should respond only to macroeconomic shocks, that is, to those shocks that affect all prices and thus change the general price level of goods and services. Thus, determining how much of a current change in prices is driven by macroeconomic factors, as opposed to idiosyncratic developments or measurement error, is a crucial task for the Federal Reserve. In this note, we disentangle changes in prices due to economy-wide (common) shocks from changes in prices due to idiosyncratic shocks. To do so, we use a new statistical methodology that is entirely data-driven, i.e., it does not make any "structural" economic assumptions or ad hoc judgments about what factors are affecting prices. Indeed, although some idiosyncratic shocks are related to identifiable events (such as changes in Medicare reimbursement rates or one-off changes in the index for wireless telephone services) not all such shocks can be reliably traced to specific developments. Therefore, a statistical model capable of effecting this sort of decomposition is necessary. The main product of our methodology is a decomposition of the PCE price index excluding food and energy (henceforth "core" PCE). We choose to decompose core PCE prices instead of total PCE prices for a couple reasons. First, although the objective of the Federal Reserve is specified in terms of the inflation rate of the overall PCE price index, food and energy prices can be extremely volatile and therefore "core inflation usually provides a better indicator than total inflation of where total inflation is headed in the medium term" (Yellen, 2015, p. 10). Second, food and energy prices are often driven by idiosyncratic factors that are beyond the influence of monetary policy (Blinder, 1997). Methodology Our methodology involves two steps. In the first step, by estimating a dynamic factor model on a dataset of disaggregated PCE prices, we decompose the inflation rate of each item into two components. The first component—the common component—is meant to reflect price changes that are attributable to economy-wide (i.e., common) factors, such as the amount of slack in the economy or movements in the prices of non-labor inputs to production, such as commodity prices, as well as prices of imported goods and services. By contrast, the second component—the idiosyncratic component—is meant to capture relative price movements that reflect sector specific developments, such as the massive decline in prices for wireless telephone services in March 2017, or it can also reflect measurement error, such as sampling error.2 In the second step, after the common components for each individual series have been computed, we aggregate them together to construct the common component of core PCE price inflation by using the series' weights in the overall core PCE price index. This yields an estimate of the portion of core PCE price inflation that can be attributed to common (macroeconomic) factors, which we call "common core inflation." Empirical analysis We estimate the dynamic factor model on a dataset of 146 disaggregated monthly PCE prices from January 1995 to June 2019.3 The dataset that we use represents a particular disaggregation of PCE prices in which each disaggregated (or sub) price index is constructed from a distinct data source. Most PCE prices are measured using a corresponding sub-index from the CPI, a few of them are measured using PPIs, and a number of others are imputed. As a result, some disaggregated PCE prices are based on the same CPI (or PPI) series, which means that there are PCE sub-price indexes that are identical (or nearly so).4 To avoid having sub-indexes that are highly correlated by construction, we combine all sub-indexes whose source data is the same.5 We begin by looking at how our model characterizes PCE prices in terms of common and idiosyncratic dynamics. To this end, Table 1 reports the standard deviation of monthly core PCE price inflation (common core inflation) at different frequencies. As we can see, common core inflation accounts for 8.5% of the total variation in core PCE price inflation. However, common core inflation is much less variable at high frequencies, which means that it accounts for more than 18% of the mid- to low-frequency fluctuations (i.e. those with period longer than one year) in core PCE price inflation, and very little of the ultra-high frequency fluctuations with period shorter than six months. ##### Table 1: Standard deviation of core PCE price inflation and common core inflation Overall $\tau \ge 60$ $12 \le \tau \lt 60$ $6 \le \tau \lt 12$ $\tau \lt 6$ 0.612 0.055 0.090 0.094 0.391 0.053 0.01 0.022 0.008 0.012 8.61 18.65 24.56 8.52 3.18 This table reports the variance of monthly core PCE price inflation, $\sigma_{\pi^c}^2$, and of common core inflation, $\sigma_{\chi^c}^2$, at different frequencies. The second column reports the overall variance. The third column reports the variance of fluctuations with period $\tau$ longer than 60 months, a.k.a. longer than five years, explained by the common component. The fourth column reports the variance of fluctuations with period between one and five years. The fifth column reports the variance of fluctuations with period between six months and one year. Finally, the sixth column reports the variance of fluctuations with period shorter than six months. Figure 1 shows the common and idiosyncratic decomposition of monthly core PCE price inflation. In each plot, the red line is common core inflation, that is, the portion of the one-month percent change in the core PCE price index that is attributable to common shocks, while the blue line gives the idiosyncratic component. By construction, these two components sum to overall core PCE inflation, which is shown in the plots as a black line. Finally, the panel on the left covers the period from 2010 to 2019, while the right panel zooms in on the experience of the last two calendar years with 2019 shaded in light blue. ##### Figure 1: Common and Idiosyncratic Decomposition Core PCE Prices – Monthly Percent Page By looking at the left plot of Figure 1, we can see that the idiosyncratic component held down core PCE price inflation for most of 2010. Indeed, in 2010 several well-known idiosyncratic negative shocks lowered core inflation, such as the collapse of the index for luggage in January, the very low reading for Medicare hospital services prices in October, and an exceptionally long series of negative readings in the index for apparel. Similarly, idiosyncratic factors held down core inflation in both 2014 and 2015, two years in which medical prices were low in part due to the implementation of the Affordable Care Act. Another episode worth noting is March 2017, when core PCE price inflation was heavily affected by the collapse in the price index for wireless telephone services. Finally, in several years the contribution of the idiosyncratic component is positive at the beginning of the year (in January in particular), while it is negative in the second half of the year, thus showing that the residual seasonality in core PCE prices documented by Peneva (2014) is an idiosyncratic phenomenon.6 Moving to the right panel, we can see that in 2018 idiosyncratic inflation was slightly positive in 9 out of 12 months and strongly negative in August, when prices were held down by, among other factors, the lowest-ever reading for the percent change in the CPI for dental services. As a result, the total contribution of idiosyncratic inflation was nearly zero over 2018 as a whole. Finally, in January, February, and March 2019, idiosyncratic shocks (mainly to non-market-based prices) held down core PCE price inflation by a cumulative 27 basis points, while in April, May and June 2019, they boosted core inflation by a cumulative 20 basis points. ##### Figure 2. Common and Idiosyncratic Decomposition Core PCE Prices – Year-on-Year Inflation Figure 2 shows the common and idiosyncratic decomposition of the 12-month percent change in the core PCE price index. Here, the red line denotes year-on-year common core inflation, i.e., the common component's contribution to the overall 12-month percent change of the core PCE price index (which is given by the black line). Put differently, the red line tells us what core inflation would have been had there been no idiosyncratic price shocks over the past 12 months. As we can see from Figure 2, core PCE price inflation and common core inflation moved largely in sync in 2008 and 2009, when the economy was affected by a large macroeconomic shock, and macroeconomic variation likely dominated idiosyncratic variation in the data. After that, idiosyncratic variation has been more important, and core PCE prices have fluctuated around a fairly stable rate of common core inflation. In particular, our model classifies the 2010 downturn in core PCE price inflation as entirely idiosyncratic, and it also suggests that the 2015 and 2017 downturns in core PCE price inflation were due to idiosyncratic dynamics. As a result, since 2010, while year-on-year core PCE prices inflation fluctuated within a range of 1.2 percentage points, common core inflation fluctuated within a much narrower range of 0.4 percentage point. Hence, these results suggest that most of the swings in core PCE price inflation during the current expansion were mostly idiosyncratic in nature. Finally, Table 2 shows estimates of a Phillips curve model à la Yellen (2015) from which we can compare the response of core PCE price inflation and common core inflation to changes in economic slack. As we can see, in the shorter term, core common core inflation respond less, but the estimated relationship is strongly statistically significant; in the longer term, however, the response of common core inflation is a bit higher. Moreover, common core inflation responds to economic slack, while the idiosyncratic component does not. That said, even after filtering out idiosyncratic factors, the estimated Phillips curve is extremely flat post-1995. ##### Table 2. Price inflation Phillips Curve: 1995:Q4—2019:Q2 Variable $\pi_t^c$ $\chi_t^c$ $\xi_t^c$ Economic slack: coefficient -0.051 -0.031 -0.009 (-0.03) (-0.008) (0.029) Economic slack: long-run multiplier -0.067 -0.075 -0.01 $\tau\ ^2$ 0.28 0.659 0.131 Notes: The second column reports estimates for core PCE price inflation, $\pi_t^c$. The third column reports estimates for common core inflation, $\chi_t^c$. The fourth columns reports estimates for the idiosyncratic component of core PCE price inflation, $\xi_t^c$. Standard error in parenthesis. For detail on the estimated Phillips curves see the working paper version of this note. Conclusions In this note, we disentangle changes in prices due to economy-wide (common) shocks from changes in prices due to idiosyncratic shocks. To do so, we introduce a new statistical model that is entirely data-driven, i.e., it does not make any "structural" economic assumptions or ad hoc judgments about what factors are affecting prices. We estimate the model on a dataset of 146 disaggregated PCE prices from January 1995 to June 2019. Our model classifies as idiosyncratic many well-known episodes, such as the March 2017 collapse in the index of wireless telephone services, and it suggests that most of the fluctuations in core PCE prices since 2010 have been idiosyncratic in nature. Finally, our estimate of the Phillips curve suggest that the flattening of the Phillips curve is not about noise or non-macroeconomic factors. References Blinder, A. S. (1997). Measuring short-run inflation for central bankers - commentary. Review, pages 157–160. Federal Reserve Bank of St. Louis. Peneva, E. (2014). Residual seasonality in core consumer price inflation. FEDS Notes 2014-10-14, Board of Governors of the Federal Reserve System. Yellen, J. L. (2015). Inflation dynamics and monetary policy. Speech at the Philip Gamble Memorial Lecture, University of Massachusetts, Amherst, Amherst, Massachusetts, September 24, 2015. 1. This note is a shorter and less technical version of Matteo Luciani (2019). “Common and idiosyncratic inflation,” Finance and Economics Discussion Series 2020-024. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2020.024.Return to text 2. In March 2017 the price index for wireless telephone services plunged 52% (at an annual rate), shaving off about 8 basis points from the monthly percent change in core PCE prices. The plunge was due to both a methodological change to the measurement of wireless services in the CPI and the fact that in late February of 2017 both Verizon and AT&T (which in March 2017 accounted for nearly 70% of wireless subscriptions in the US) brought back unlimited data plans. Return to text 3. The benchmark specification includes one common factor, and each disaggregated price can load the common factor in a time window of three months. Return to text 4. An example is the PCE price index for "New Domestic Autos" (Item: 7), and the PCE price index for "New Foreign Autos" (Item: 8), which are both constructed out of the CPI for "New cars." Return to text 5. For example, we combine the new domestic and new foreign auto sub-indexes into one sub-index on new autos. Return to text 6. A time series suffers from residual seasonality when a predictable pattern occurs over the year, despite the series being previously seasonal adjusted. Return to text	2020-03-29T04:03:05	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4202120900154114, "perplexity": 2147.384741815524}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370493684.2/warc/CC-MAIN-20200329015008-20200329045008-00050.warc.gz"}
http://dlmf.nist.gov/8.27	# §8.27(i) Incomplete Gamma Functions • DiDonato (1978) gives a simple approximation for the function $F(p,x)=x^{-p}e^{x^{2}/2}\int_{x}^{\infty}e^{-t^{2}/2}t^{p}dt$ (which is related to the incomplete gamma function by a change of variables) for real $p$ and large positive $x$. This takes the form $F(p,x)=4x/h(p,x)$, approximately, where $h(p,x)=3(x^{2}-p)+\sqrt{(x^{2}-p)^{2}+8(x^{2}+p)}$ and is shown to produce an absolute error $\mathop{O\/}\nolimits\!\left(x^{-7}\right)$ as $x\to\infty$. • Luke (1975, §4.3) gives Padé approximation methods, combined with a detailed analysis of the error terms, valid for real and complex variables except on the negative real $z$-axis. See also Temme (1994b, §3). • Luke (1969b, pp. 25, 40–41) gives Chebyshev-series expansions for $\mathop{\Gamma\/}\nolimits\!\left(a,\omega z\right)$ (by specifying parameters) with $1\leq\omega<\infty$, and $\mathop{\gamma\/}\nolimits\!\left(a,\omega z\right)$ with $0\leq\omega\leq 1$; see also Temme (1994b, §3). • Luke (1969b, p. 186) gives hypergeometric polynomial representations that converge uniformly on compact subsets of the $z$-plane that exclude $z=0$ and are valid for $\left\|\mathop{\mathrm{ph}\/}\nolimits z\right\|<\pi$. # §8.27(ii) Generalized Exponential Integral • Luke (1975, p. 103) gives Chebyshev-series expansions for $\mathop{E_{1}\/}\nolimits\!\left(x\right)$ and related functions for $x\geq 5$. • Luke (1975, p. 106) gives rational and Padé approximations, with remainders, for $\mathop{E_{1}\/}\nolimits\!\left(z\right)$ and $z^{-1}\int_{0}^{z}t^{-1}(1-e^{-t})dt$ for complex $z$ with $\left\|\mathop{\mathrm{ph}\/}\nolimits z\right\|\leq\pi$. • Verbeeck (1970) gives polynomial and rational approximations for $\mathop{E_{p}\/}\nolimits\!\left(x\right)=(e^{-x}/x)P(z)$, approximately, where $P(z)$ denotes a quotient of polynomials of equal degree in $z=x^{-1}$.	2014-10-25T05:35:48	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 24, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9835667610168457, "perplexity": 943.8216817804242}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414119647778.29/warc/CC-MAIN-20141024030047-00002-ip-10-16-133-185.ec2.internal.warc.gz"}
https://www.aimsciences.org/article/doi/10.3934/mbe.2009.6.261	Article Contents Article Contents # The estimation of the effective reproductive number from disease outbreak data • We consider a single outbreak susceptible-infected-recovered (SIR) model and corresponding estimation procedures for the effective reproductive number $\mathcal{R}(t)$. We discuss the estimation of the underlying SIR parameters with a generalized least squares (GLS) estimation technique. We do this in the context of appropriate statistical models for the measurement process. We use asymptotic statistical theories to derive the mean and variance of the limiting (Gaussian) sampling distribution and to perform post statistical analysis of the inverse problems. We illustrate the ideas and pitfalls (e.g., large condition numbers on the corresponding Fisher information matrix) with both synthetic and influenza incidence data sets. Mathematics Subject Classification: Primary: 62G05, 93E24, 49Q12, 37N25; Secondary: 62H12, 62N02. Citation: Open Access Under a Creative Commons license	2022-12-08T04:09:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.2882329225540161, "perplexity": 669.9010640951304}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711232.54/warc/CC-MAIN-20221208014204-20221208044204-00555.warc.gz"}
http://www.legisquebec.gouv.qc.ca/en/showversion/cr/I-0.2.1,%20r.%203?code=se:24_3&pointInTime=20201120	### I-0.2.1, r. 3 - Québec Immigration Regulation 24.3. A foreign national and the family members referred to in section 24.1 pass the assessment referred to in the first paragraph of section 24.2 if they adequately answer to a minimum of 75% of the assessment questions. In case of failure, it is possible to again take the assessment, on the conditions set out in section 24.4 and in compliance with the time period provided for in the first paragraph of section 24.5. Despite the foregoing, 2 weeks must elapse before a person referred to in the first paragraph may again take the assessment. O.C. 1030-2019, s. 2. In force: 2020-01-01 24.3. A foreign national and the family members referred to in section 24.1 pass the assessment referred to in the first paragraph of section 24.2 if they adequately answer to a minimum of 75% of the assessment questions. In case of failure, it is possible to again take the assessment, on the conditions set out in section 24.4 and in compliance with the time period provided for in the first paragraph of section 24.5. Despite the foregoing, 2 weeks must elapse before a person referred to in the first paragraph may again take the assessment. O.C. 1030-2019, s. 2.	2021-01-17T04:13:22	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8201155066490173, "perplexity": 628.039454342988}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703509104.12/warc/CC-MAIN-20210117020341-20210117050341-00739.warc.gz"}
https://zbmath.org/authors/?q=ai%3Arousseau.christiane	## Rousseau, Christiane Compute Distance To: Author ID: rousseau.christiane Published as: Rousseau, Christiane; Rousseau, C.; Russo, K.; Rousseau, Christian; Rousseau, Christine more...less Homepage: http://dms.umontreal.ca/fr/repertoire-departement/professeurs/portrait/rousseac External Links: MGP · ORCID · Wikidata · Math-Net.Ru · GND · IdRef Documents Indexed: 96 Publications since 1978, including 3 Books 2 Contributions as Editor · 3 Further Contributions Biographic References: 2 Publications Co-Authors: 46 Co-Authors with 72 Joint Publications 1,169 Co-Co-Authors all top 5 ### Co-Authors 27 single-authored 7 Christopher, Colin J. 7 Dumortier, Freddy 7 Patera, Jiří 6 Roussarie, Robert 5 Mardešić, Pavao 5 Schlomiuk, Dana I. 4 Lambert, Caroline 3 Antaya, Hélène 3 Ascah-Coallier, Isabelle 3 Klimeš, Martin 3 Li, Chengzhi 3 Saint-Aubin, Yvan 3 Toni, Bourama 3 Zhu, Huaiping 2 Guimond, Louis-Sébastien 2 Guzmán, Ana 2 Hurtubise, Jacques C. 2 Ilyashenko, Yulij Sergeevich 2 Kaper, Hans G. 2 Krauskopf, Bernd 2 Lopez, Salvatore 2 Teyssier, Loïc 2 Żołądek, Henryk 1 Arriagada-Silva, Waldo 1 Blows, Terence R. 1 Bröcker, Jochen 1 Calderhead, Ben 1 Cheraghi, Davoud 1 Colli, Eduardo 1 Cotter, Colin John 1 Coutu, Caroline 1 Crisan, Dan O. 1 del Olmo, Mariano A. 1 El Morsalani, Mohamed 1 Etoua, Remy Magloire 1 Freiberger, Marianne 1 Gagnon, Jean-François 1 Hénot, Olivier 1 Holm, Darryl D. 1 Joyal, Pierre 1 Khibnik, Alexander I. 1 Koh, In-Guy 1 Koh, In-Gyu 1 Kuna, Tobias 1 La Sala, G. 1 Lamontagne, Yann 1 Laurin, Sophie 1 Moser-Jauslin, Lucy 1 Nemenzo, Fidel Ronquillo 1 Pelloni, Beatrice 1 Peterson, Ivar 1 Polthier, Konrad 1 Raachandran R. 1 Rodriquez, M. A. 1 Sabidussi, Gert 1 Shan, Chunhua 1 Shepherd, Ted 1 Świrszcz, Grzegorz M. 1 Thibaudeau, Pierre 1 Wang, Xian 1 Weller, Hilary 1 Ziegler, Günter Matthias all top 5 ### Serials 20 Journal of Differential Equations 7 Nonlinearity 6 Journal of Mathematical Physics 6 Qualitative Theory of Dynamical Systems 6 Moscow Mathematical Journal 4 Journal of Dynamical and Control Systems 3 Annales des Sciences Mathématiques du Québec 3 Canadian Mathematical Bulletin 3 Notices of the American Mathematical Society 2 Canadian Journal of Mathematics 2 Journal of Pure and Applied Algebra 2 Ergodic Theory and Dynamical Systems 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 International Journal of Structural Stability and Dynamics 2 Springer Undergraduate Texts in Mathematics and Technology 1 Advances in Mathematics 1 Annales de l’Institut Fourier 1 Annales Polonici Mathematici 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Bulletin Mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie. Nouvelle Série 1 Transactions of the Moscow Mathematical Society 1 Comptes Rendus Mathématiques de l’Académie des Sciences 1 Publicacions Matemàtiques 1 IMRN. International Mathematics Research Notices 1 Journal of Physics A: Mathematical and General 1 Journal of Dynamics and Differential Equations 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Conformal Geometry and Dynamics 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Communications on Pure and Applied Analysis 1 NATO Science Series II: Mathematics, Physics and Chemistry 1 Nonlinear Analysis. Theory, Methods & Applications 1 Other Titles in Applied Mathematics 1 Advanced Textbooks in Mathematics 1 Springer-Lehrbuch all top 5 ### Fields 55 Ordinary differential equations (34-XX) 47 Dynamical systems and ergodic theory (37-XX) 13 Several complex variables and analytic spaces (32-XX) 11 General and overarching topics; collections (00-XX) 6 Nonassociative rings and algebras (17-XX) 6 Category theory; homological algebra (18-XX) 6 Geophysics (86-XX) 5 History and biography (01-XX) 5 Mathematical logic and foundations (03-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Topological groups, Lie groups (22-XX) 4 Functions of a complex variable (30-XX) 4 Biology and other natural sciences (92-XX) 4 Mathematics education (97-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Combinatorics (05-XX) 2 Special functions (33-XX) 2 Partial differential equations (35-XX) 2 Differential geometry (53-XX) 2 Mechanics of deformable solids (74-XX) 2 Quantum theory (81-XX) 2 Systems theory; control (93-XX) 2 Information and communication theory, circuits (94-XX) 1 Measure and integration (28-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX) 1 Mechanics of particles and systems (70-XX) ### Citations contained in zbMATH Open 73 Publications have been cited 1,038 times in 650 Documents Cited by Year Linearization of isochronous centers. Zbl 0830.34023 Mardešić, P.; Rousseau, C.; Toni, B. 1995 Hilbert’s 16th problem for quadratic vector fields. Zbl 0802.34028 Dumortier, F.; Roussarie, R.; Rousseau, C. 1994 Cubic Liénard equations with linear damping. Zbl 0716.58023 Dumortier, Freddy; Rousseau, Christiane 1990 Normalizable, integrable, and linearizable saddle points for complex quadratic systems in $$\mathbb{C}^2$$. Zbl 1022.37035 Christopher, C.; Mardešić, P.; Rousseau, C. 2003 Local bifurcations of critical periods in the reduced Kukles system. Zbl 0885.34033 Rousseau, C.; Toni, B. 1997 Bifurcation analysis of a predator-prey system with generalised Holling type III functional response. Zbl 1160.34047 Lamontagne, Yann; Coutu, Caroline; Rousseau, Christiane 2008 Bifurcation at infinity in polynomial vector fields. Zbl 0778.34024 Blows, T. R.; Rousseau, C. 1993 Darboux linearization and isochronous centers with a rational first integral. Zbl 0881.34041 Mardešić, P.; Moser-Jauslin, L.; Rousseau, C. 1997 Local bifurcation of critical periods in vector fields with homogeneous nonlinearities of the third degree. Zbl 0792.58030 Rousseau, C.; Toni, B. 1993 Elementary graphics of cyclicity 1 and 2. Zbl 0855.58043 Dumortier, F.; Roussarie, R.; Rousseau, C. 1994 Bifurcation analysis of a generalized Gause model with prey harvesting and a generalized Holling response function of type III. Zbl 1217.34080 Etoua, Remy Magloire; Rousseau, Christiane 2010 Saddle quantities and applications. Zbl 0684.34033 Joyal, Pierre; Rousseau, Christian 1989 A system with three limit cycles appearing in a Hopf bifurcation and dying in a homoclinic bifurcation: The cusp of order 4. Zbl 0684.34048 Li, Chengzhi; Rousseau, Christine 1989 Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type. Zbl 1012.34028 Zhu, Huaiping; Rousseau, Christiane 2002 Normalizable, integrable and linearizable saddle points in the Lotka-Volterra system. Zbl 1100.34022 Christopher, Colin; Rousseau, Christiane 2004 Hilbert’s 16th problem for quadratic systems and cyclicity of elementary graphics. Zbl 0895.58046 Dumortier, F.; El Morsalani, M.; Rousseau, C. 1996 Global study of a family of cubic Liénard equations. Zbl 0920.58034 Khibnik, Alexander I.; Krauskopf, Bernd; Rousseau, Christiane 1998 Nondegenerate linearizable centres of complex planar quadratic and symmetric cubic systems in $$\mathbb C^2$$. Zbl 0984.34023 Christopher, C.; Rousseau, C. 2001 Zeroes of complete elliptic integrals for 1:2 resonance. Zbl 0738.33014 Rousseau, Christiane; Żołądek, Henryk 1991 The centres in the reduced Kukles system. Zbl 0830.34025 Rousseau, Christiane; Schlomiuk, Dana; Thibaudeau, Pierre 1995 Cubic vector fields symmetric with respect to a center. Zbl 0839.34035 Rousseau, C.; Schlomiuk, D. 1995 Modulus of analytic classification for unfoldings of generic parabolic diffeomorphisms. Zbl 1077.37035 Mardešić, P.; Roussarie, R.; Rousseau, C. 2004 Codimension-three unfoldings of reflectionally symmetric planar vector fields. Zbl 0904.34025 Krauskopf, Bernd; Rousseau, Christiane 1997 Codimension 2 symmetric homoclinic bifurcations and application to 1:2 resonance. Zbl 0714.58039 Li, Chengzhi; Rousseau, Christiane 1990 Modulus of analytic classification for the generic unfolding of a codimension 1 resonant diffeomorphism or resonant saddle. Zbl 1127.37039 Rousseau, Christiane; Christopher, Colin 2007 Complete system of analytic invariants for unfolded differential linear systems with an rank $$k$$ irregular singularity of Poincaré. Zbl 1302.34131 Hurtubise, Jacques; Lambert, Caroline; Rousseau, Christiane 2014 PP-graphics with a nilpotent elliptic singularity in quadratic systems and Hilbert’s 16th problem. Zbl 1046.34055 Rousseau, Christiane; Zhu, Huaiping 2004 Complete system of analytic invariants for unfolded differential linear systems with an irregular singularity of Poincaré rank 1. Zbl 1263.34127 Lambert, Caroline; Rousseau, Christiane 2012 Analytical moduli for unfoldings of saddle-node vector fields. Zbl 1165.37016 Rousseau, Christiane; Teyssier, Loïc 2008 Clebsch-Gordan coefficients for $$E_ 6$$ and SO(10) unification models. Zbl 0556.22011 Koh, In-Guy; Patera, J.; Rousseau, C. 1984 Complex orthogonal and symplectic matrices depending on parameters. Zbl 0495.17007 Patera, J.; Rousseau, C. 1982 Almost planar homoclinic loops in $$\mathbb{R}^ 3$$. Zbl 0849.34036 Roussarie, Robert; Rousseau, Christiane 1996 Generalized Hopf bifurcations and applications to planar quadratic systems. Zbl 0666.34035 Rousseau, C.; Schlomiuk, D. 1988 Genericity conditions for finite cyclicity of elementary graphics. Zbl 0930.34020 Guzmán, Ana; Rousseau, Christiane 1999 Normalizability, synchronicity, and relative exactness for vector fields in $$\mathbb C^2$$. Zbl 1068.37030 Christopher, C.; Mardešić, P.; Rousseau, C. 2004 Modulus of orbital analytic classification for a family unfolding a saddle-node. Zbl 1089.37018 Rousseau, Christiane 2005 Versal deformations of elements of classical Jordan algebras. Zbl 0523.17001 Patera, J.; Rousseau, C. 1983 The moduli space of germs of generic families of analytic diffeomorphisms unfolding of a codimension one resonant diffeomorphism or resonant saddle. Zbl 1204.37048 Rousseau, Christiane 2010 Example of a quadratic system with two cycles appearing in a homoclinic loop bifurcation. Zbl 0626.34021 Rousseau, Christiane 1987 Normal forms near a saddle-node and applications to finite cyclicity of graphics. Zbl 1013.37044 Dumortier, F.; Ilyashenko, Y.; Rousseau, C. 2002 Organizing center for the bifurcation analysis of a generalized Gause model with prey harvesting and Holling response function of type III. Zbl 1236.34059 Laurin, Sophie; Rousseau, Christiane 2011 Topos theory and complex analysis. Zbl 0433.32003 Rousseau, Christiane 1979 The Stokes phenomenon in the confluence of the hypergeometric equation using Riccati equation. Zbl 1147.34064 Lambert, Caroline; Rousseau, Christiane 2008 Improving stability in the time-stepping analysis of structural nonlinear dynamics. Zbl 1205.74182 Lopez, Salvatore; Russo, K. 2008 The bifurcation diagram of cubic polynomial vector fields on $$\mathbb{C}\mathbb{P}^1$$. Zbl 1372.37095 Rousseau, C. 2017 Study of the cyclicity of some degenerate graphics inside quadratic systems. Zbl 1170.34020 Dumortier, Freddy; Rousseau, Christiane 2009 Clebsch-Gordan coefficients for SU(5)$$\supset SU(3)\times SU(2)\times U(1)$$ theories. Zbl 0552.22008 Koh, In-Gyu; Patera, J.; Rousseau, C. 1983 Analytic moduli for unfoldings of germs of generic analytic diffeomorphisms with a codimension $$k$$ parabolic point. Zbl 1308.32018 Rousseau, C. 2015 Moduli space of unfolded differential linear systems with an irregular singularity of Poincaré rank 1. Zbl 1292.34085 Lambert, Caroline; Rousseau, Christiane 2013 A simple proof for the unicity of the limit cycle in the Bogdanov-Takens system. Zbl 0706.34026 Li, Chengzhi; Rousseau, Christiane; Wang, Xian 1990 Generic $$2$$-parameter perturbations of parabolic singular points of vector fields in $$\mathbb C$$. Zbl 1403.37057 Klimeš, Martin; Rousseau, Christiane 2018 Versal deformations of elements of real classical Lie algebras. Zbl 0507.17006 Patera, J.; Rousseau, C.; Schlomiuk, D. 1982 Clebsch-Gordan coefficients for SU(5) unification models. Zbl 0617.22020 del Olmo, Mariano A.; Patera, J.; Rodriquez, M. A.; Rousseau, C. 1987 Bifurcation methods in polynomial systems. Zbl 0791.58080 Rousseau, Christiane 1993 Cyclicity of graphics with semi-hyperbolic points inside quadratic systems. Zbl 0989.37047 Rousseau, C.; Świrszcz, G.; Żołądek, H. 1998 Normal forms for germs of analytic families of planar vector fields unfolding a generic saddle-node or resonant saddle. Zbl 1103.34024 Rousseau, Christiane 2006 Hilbert’s 16-th problem for quadratic vector fields and cyclicity of graphics. Zbl 0895.34025 Rousseau, Christiane 1997 Moduli space for generic unfolded differential linear systems. Zbl 1361.34099 Hurtubise, Jacques; Rousseau, Christiane 2017 Topos theory and complex analysis. Zbl 0378.02028 Rousseau, Christiane 1978 Dimensions of orbits and strata in complex and real classical Lie algebras. Zbl 0488.22037 Patera, J.; Rousseau, C.; Schlomiuk, D. 1982 The root extraction problem. Zbl 1118.37016 Rousseau, C. 2007 The modulus of analytic classification for the unfolding of the codimension-one flip and Hopf bifurcations. Zbl 1242.58021 Arriagada-Silva, Waldo; Rousseau, Christiane 2011 The moduli space of germs of generic families of analytic diffeomorphisms unfolding a parabolic fixed point. Zbl 1351.37192 Christopher, Colin; Rousseau, Christiane 2014 The moduli space of germs of generic families of analytic diffeomorphisms unfolding a parabolic fixed point. Zbl 1134.37021 Christopher, Colin; Rousseau, Christiane 2007 Spiderweb central configurations. Zbl 1454.70005 Hénot, Olivier; Rousseau, Christiane 2019 Finite cyclicity of some graphics through a nilpotent point of saddle type inside quadratic systems. Zbl 1345.34078 Rousseau, Christiane; Shan, Chunhua; Zhu, Huaiping 2016 An approach to statical and quasi-statical nonlinear analysis of structures in small strains and finite rotations hypotheses. Zbl 1359.74424 Lopez, S.; Russo, K.; La Sala, G. 2013 Finite cyclicity of some center graphics through a nilpotent point inside quadratic systems. Zbl 1334.34077 Roussarie, Robert; Rousseau, Christiane 2015 Nombres réels et complexes dans les topos spatiaux. Zbl 0411.18004 Rousseau, Christiane 1979 Mathematics and technology. With the collaboration of Hélène Antaya and Isabelle Ascah-Coallier. (Mathématiques et technologie.) Zbl 1172.00001 Rousseau, Christiane; Saint-Aubin, Yvan 2008 The modulus of unfoldings of cusps in conformal geometry. Zbl 1234.58009 Rousseau, C. 2012 Finite cyclicity of nilpotent graphics of pp-type surrounding a center. Zbl 1165.34019 Roussarie, R.; Rousseau, C. 2008 Finite cyclicity of elementary graphics surrounding a focus or center in quadratic systems. Zbl 1042.34062 Dumortier, F.; Guzmán, A.; Rousseau, C. 2002 Spiderweb central configurations. Zbl 1454.70005 Hénot, Olivier; Rousseau, Christiane 2019 Generic $$2$$-parameter perturbations of parabolic singular points of vector fields in $$\mathbb C$$. Zbl 1403.37057 Klimeš, Martin; Rousseau, Christiane 2018 The bifurcation diagram of cubic polynomial vector fields on $$\mathbb{C}\mathbb{P}^1$$. Zbl 1372.37095 Rousseau, C. 2017 Moduli space for generic unfolded differential linear systems. Zbl 1361.34099 Hurtubise, Jacques; Rousseau, Christiane 2017 Finite cyclicity of some graphics through a nilpotent point of saddle type inside quadratic systems. Zbl 1345.34078 Rousseau, Christiane; Shan, Chunhua; Zhu, Huaiping 2016 Analytic moduli for unfoldings of germs of generic analytic diffeomorphisms with a codimension $$k$$ parabolic point. Zbl 1308.32018 Rousseau, C. 2015 Finite cyclicity of some center graphics through a nilpotent point inside quadratic systems. Zbl 1334.34077 Roussarie, Robert; Rousseau, Christiane 2015 Complete system of analytic invariants for unfolded differential linear systems with an rank $$k$$ irregular singularity of Poincaré. Zbl 1302.34131 Hurtubise, Jacques; Lambert, Caroline; Rousseau, Christiane 2014 The moduli space of germs of generic families of analytic diffeomorphisms unfolding a parabolic fixed point. Zbl 1351.37192 Christopher, Colin; Rousseau, Christiane 2014 Moduli space of unfolded differential linear systems with an irregular singularity of Poincaré rank 1. Zbl 1292.34085 Lambert, Caroline; Rousseau, Christiane 2013 An approach to statical and quasi-statical nonlinear analysis of structures in small strains and finite rotations hypotheses. Zbl 1359.74424 Lopez, S.; Russo, K.; La Sala, G. 2013 Complete system of analytic invariants for unfolded differential linear systems with an irregular singularity of Poincaré rank 1. Zbl 1263.34127 Lambert, Caroline; Rousseau, Christiane 2012 The modulus of unfoldings of cusps in conformal geometry. Zbl 1234.58009 Rousseau, C. 2012 Organizing center for the bifurcation analysis of a generalized Gause model with prey harvesting and Holling response function of type III. Zbl 1236.34059 Laurin, Sophie; Rousseau, Christiane 2011 The modulus of analytic classification for the unfolding of the codimension-one flip and Hopf bifurcations. Zbl 1242.58021 Arriagada-Silva, Waldo; Rousseau, Christiane 2011 Bifurcation analysis of a generalized Gause model with prey harvesting and a generalized Holling response function of type III. Zbl 1217.34080 Etoua, Remy Magloire; Rousseau, Christiane 2010 The moduli space of germs of generic families of analytic diffeomorphisms unfolding of a codimension one resonant diffeomorphism or resonant saddle. Zbl 1204.37048 Rousseau, Christiane 2010 Study of the cyclicity of some degenerate graphics inside quadratic systems. Zbl 1170.34020 Dumortier, Freddy; Rousseau, Christiane 2009 Bifurcation analysis of a predator-prey system with generalised Holling type III functional response. Zbl 1160.34047 Lamontagne, Yann; Coutu, Caroline; Rousseau, Christiane 2008 Analytical moduli for unfoldings of saddle-node vector fields. Zbl 1165.37016 Rousseau, Christiane; Teyssier, Loïc 2008 The Stokes phenomenon in the confluence of the hypergeometric equation using Riccati equation. Zbl 1147.34064 Lambert, Caroline; Rousseau, Christiane 2008 Improving stability in the time-stepping analysis of structural nonlinear dynamics. Zbl 1205.74182 Lopez, Salvatore; Russo, K. 2008 Mathematics and technology. With the collaboration of Hélène Antaya and Isabelle Ascah-Coallier. (Mathématiques et technologie.) Zbl 1172.00001 Rousseau, Christiane; Saint-Aubin, Yvan 2008 Finite cyclicity of nilpotent graphics of pp-type surrounding a center. Zbl 1165.34019 Roussarie, R.; Rousseau, C. 2008 Modulus of analytic classification for the generic unfolding of a codimension 1 resonant diffeomorphism or resonant saddle. Zbl 1127.37039 Rousseau, Christiane; Christopher, Colin 2007 The root extraction problem. Zbl 1118.37016 Rousseau, C. 2007 The moduli space of germs of generic families of analytic diffeomorphisms unfolding a parabolic fixed point. Zbl 1134.37021 Christopher, Colin; Rousseau, Christiane 2007 Normal forms for germs of analytic families of planar vector fields unfolding a generic saddle-node or resonant saddle. Zbl 1103.34024 Rousseau, Christiane 2006 Modulus of orbital analytic classification for a family unfolding a saddle-node. Zbl 1089.37018 Rousseau, Christiane 2005 Normalizable, integrable and linearizable saddle points in the Lotka-Volterra system. Zbl 1100.34022 Christopher, Colin; Rousseau, Christiane 2004 Modulus of analytic classification for unfoldings of generic parabolic diffeomorphisms. Zbl 1077.37035 Mardešić, P.; Roussarie, R.; Rousseau, C. 2004 PP-graphics with a nilpotent elliptic singularity in quadratic systems and Hilbert’s 16th problem. Zbl 1046.34055 Rousseau, Christiane; Zhu, Huaiping 2004 Normalizability, synchronicity, and relative exactness for vector fields in $$\mathbb C^2$$. Zbl 1068.37030 Christopher, C.; Mardešić, P.; Rousseau, C. 2004 Normalizable, integrable, and linearizable saddle points for complex quadratic systems in $$\mathbb{C}^2$$. Zbl 1022.37035 Christopher, C.; Mardešić, P.; Rousseau, C. 2003 Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type. Zbl 1012.34028 Zhu, Huaiping; Rousseau, Christiane 2002 Normal forms near a saddle-node and applications to finite cyclicity of graphics. Zbl 1013.37044 Dumortier, F.; Ilyashenko, Y.; Rousseau, C. 2002 Finite cyclicity of elementary graphics surrounding a focus or center in quadratic systems. Zbl 1042.34062 Dumortier, F.; Guzmán, A.; Rousseau, C. 2002 Nondegenerate linearizable centres of complex planar quadratic and symmetric cubic systems in $$\mathbb C^2$$. Zbl 0984.34023 Christopher, C.; Rousseau, C. 2001 Genericity conditions for finite cyclicity of elementary graphics. Zbl 0930.34020 Guzmán, Ana; Rousseau, Christiane 1999 Global study of a family of cubic Liénard equations. Zbl 0920.58034 Khibnik, Alexander I.; Krauskopf, Bernd; Rousseau, Christiane 1998 Cyclicity of graphics with semi-hyperbolic points inside quadratic systems. Zbl 0989.37047 Rousseau, C.; Świrszcz, G.; Żołądek, H. 1998 Local bifurcations of critical periods in the reduced Kukles system. Zbl 0885.34033 Rousseau, C.; Toni, B. 1997 Darboux linearization and isochronous centers with a rational first integral. Zbl 0881.34041 Mardešić, P.; Moser-Jauslin, L.; Rousseau, C. 1997 Codimension-three unfoldings of reflectionally symmetric planar vector fields. Zbl 0904.34025 Krauskopf, Bernd; Rousseau, Christiane 1997 Hilbert’s 16-th problem for quadratic vector fields and cyclicity of graphics. Zbl 0895.34025 Rousseau, Christiane 1997 Hilbert’s 16th problem for quadratic systems and cyclicity of elementary graphics. Zbl 0895.58046 Dumortier, F.; El Morsalani, M.; Rousseau, C. 1996 Almost planar homoclinic loops in $$\mathbb{R}^ 3$$. Zbl 0849.34036 Roussarie, Robert; Rousseau, Christiane 1996 Linearization of isochronous centers. Zbl 0830.34023 Mardešić, P.; Rousseau, C.; Toni, B. 1995 The centres in the reduced Kukles system. Zbl 0830.34025 Rousseau, Christiane; Schlomiuk, Dana; Thibaudeau, Pierre 1995 Cubic vector fields symmetric with respect to a center. Zbl 0839.34035 Rousseau, C.; Schlomiuk, D. 1995 Hilbert’s 16th problem for quadratic vector fields. Zbl 0802.34028 Dumortier, F.; Roussarie, R.; Rousseau, C. 1994 Elementary graphics of cyclicity 1 and 2. Zbl 0855.58043 Dumortier, F.; Roussarie, R.; Rousseau, C. 1994 Bifurcation at infinity in polynomial vector fields. Zbl 0778.34024 Blows, T. R.; Rousseau, C. 1993 Local bifurcation of critical periods in vector fields with homogeneous nonlinearities of the third degree. Zbl 0792.58030 Rousseau, C.; Toni, B. 1993 Bifurcation methods in polynomial systems. Zbl 0791.58080 Rousseau, Christiane 1993 Zeroes of complete elliptic integrals for 1:2 resonance. Zbl 0738.33014 Rousseau, Christiane; Żołądek, Henryk 1991 Cubic Liénard equations with linear damping. Zbl 0716.58023 Dumortier, Freddy; Rousseau, Christiane 1990 Codimension 2 symmetric homoclinic bifurcations and application to 1:2 resonance. Zbl 0714.58039 Li, Chengzhi; Rousseau, Christiane 1990 A simple proof for the unicity of the limit cycle in the Bogdanov-Takens system. Zbl 0706.34026 Li, Chengzhi; Rousseau, Christiane; Wang, Xian 1990 Saddle quantities and applications. Zbl 0684.34033 Joyal, Pierre; Rousseau, Christian 1989 A system with three limit cycles appearing in a Hopf bifurcation and dying in a homoclinic bifurcation: The cusp of order 4. Zbl 0684.34048 Li, Chengzhi; Rousseau, Christine 1989 Generalized Hopf bifurcations and applications to planar quadratic systems. Zbl 0666.34035 Rousseau, C.; Schlomiuk, D. 1988 Example of a quadratic system with two cycles appearing in a homoclinic loop bifurcation. Zbl 0626.34021 Rousseau, Christiane 1987 Clebsch-Gordan coefficients for SU(5) unification models. Zbl 0617.22020 del Olmo, Mariano A.; Patera, J.; Rodriquez, M. A.; Rousseau, C. 1987 Clebsch-Gordan coefficients for $$E_ 6$$ and SO(10) unification models. Zbl 0556.22011 Koh, In-Guy; Patera, J.; Rousseau, C. 1984 Versal deformations of elements of classical Jordan algebras. Zbl 0523.17001 Patera, J.; Rousseau, C. 1983 Clebsch-Gordan coefficients for SU(5)$$\supset SU(3)\times SU(2)\times U(1)$$ theories. Zbl 0552.22008 Koh, In-Gyu; Patera, J.; Rousseau, C. 1983 Complex orthogonal and symplectic matrices depending on parameters. Zbl 0495.17007 Patera, J.; Rousseau, C. 1982 Versal deformations of elements of real classical Lie algebras. Zbl 0507.17006 Patera, J.; Rousseau, C.; Schlomiuk, D. 1982 Dimensions of orbits and strata in complex and real classical Lie algebras. Zbl 0488.22037 Patera, J.; Rousseau, C.; Schlomiuk, D. 1982 Topos theory and complex analysis. Zbl 0433.32003 Rousseau, Christiane 1979 Nombres réels et complexes dans les topos spatiaux. Zbl 0411.18004 Rousseau, Christiane 1979 Topos theory and complex analysis. Zbl 0378.02028 Rousseau, Christiane 1978 all top 5 ### Cited by 591 Authors 43 Llibre, Jaume 37 Romanovskiĭ, Valeriĭ Georgievich 33 Rousseau, Christiane 32 Giné, Jaume 28 Han, Maoan 25 Liu, Yirong 23 Valls Anglés, Cláudia 22 Algaba, Antonio 20 Huang, Wentao 20 Villadelprat, Jordi 18 Chen, Hebai 18 Chen, Xingwu 16 Zhang, Weinian 14 Dumortier, Freddy 13 Huang, Jicai 13 Wu, Yusen 13 Zhao, Liqin 12 García, Cristóbal 12 Gasull, Armengol 12 Tang, Yilei 11 Oliveira, Regilene D. S. 10 Li, Chengzhi 10 Reyes, Manuel 10 Torregrosa, Joan 10 Wu, Yuhai 10 Zhu, Huaiping 9 Christopher, Colin J. 9 Gaiko, Valery A. 9 García, Isaac A. 9 Liu, Changjian 9 Rodríguez-Luis, Alejandro J. 8 Ferčec, Brigita 8 Mañosas, Francesc 8 Patera, Jiří 8 Wang, Zhaoxia 8 Yu, Pei 7 Chavarriga, Javier 7 Freire Macías, Emilio 7 Sabatini, Marco 7 Xiao, Dongmei 7 Zhang, Zhifen 6 Artés, Joan Carles 6 Gamero, Estanislao 6 Gavrilov, Lubomir 6 Grau, Maite 6 Klimeš, Martin 6 Ruan, Shigui 6 Wang, Qinlong 6 Zhang, Tonghua 6 Zhang, Xiang 6 Zhao, Yulin 5 Asheghi, Rasoul 5 Aziz, Waleed 5 Feng, Zhaosheng 5 Fernandes, Wilker 5 Huzak, Renato 5 Iliev, Iliya Dimov 5 Lu, Min 5 Merino, Manuel 5 Peng, Linping 5 Ponce, Enrique 5 Schlomiuk, Dana I. 5 Yang, Jihua 5 Zangeneh, Hamid R. Z. 5 Zhang, Qi 4 Bonckaert, Patrick 4 Caubergh, Magdalena 4 Chen, Haibo 4 Chung, Kwok-Wai 4 Colak, Ilker E. 4 De Maesschalck, Peter 4 Dukarić, Maša 4 Jarque, Xavier 4 Jiang, Jiao 4 Li, Weigu 4 Lloyd, Noel Glynne 4 Marín Pérez, David 4 Pearson, Jane Margaret 4 Qin, Bo-Wei 4 Sergeichuk, Vladimir Vasil’evich 4 Shafer, Douglas S. 4 Shan, Chunhua 4 Sun, Xianbo 4 Zhang, Cui 4 Zhang, Xinan 4 Żołądek, Henryk 3 Anderson, Gregory W. 3 Arriagada-Silva, Waldo 3 Blažek, Tomáš 3 Buică, Adriana 3 Cima, Anna 3 Corbera, Montserrat 3 Dmytryshyn, Andrii R. 3 Dong, Guangfeng 3 Du, Chaoxiong 3 Edneral, Victor F. 3 Futorny, Vyacheslav M. 3 Garijo, Antonio 3 Homburg, Ale Jan 3 Hu, Zhaoping ...and 491 more Authors all top 5 ### Cited in 121 Serials 103 Journal of Differential Equations 66 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 39 Journal of Mathematical Analysis and Applications 31 Qualitative Theory of Dynamical Systems 23 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 21 Applied Mathematics and Computation 20 Chaos, Solitons and Fractals 15 Bulletin des Sciences Mathématiques 15 Nonlinear Analysis. Real World Applications 13 Computers & Mathematics with Applications 13 Nonlinear Dynamics 12 Journal of Mathematical Physics 12 Physica D 12 Discrete and Continuous Dynamical Systems. Series B 10 Advances in Difference Equations 9 Journal of Dynamics and Differential Equations 9 Journal of Dynamical and Control Systems 8 Journal of Computational and Applied Mathematics 8 Discrete and Continuous Dynamical Systems 7 Acta Mathematica Sinica. English Series 7 Nonlinear Analysis. Theory, Methods & Applications 6 Proceedings of the American Mathematical Society 5 Acta Mathematicae Applicatae Sinica. English Series 5 Applied Mathematics Letters 5 Science in China. Series A 5 Linear Algebra and its Applications 5 Journal of Nonlinear Science 5 SIAM Journal on Applied Dynamical Systems 4 Advances in Mathematics 4 Journal of Symbolic Computation 4 Communications on Pure and Applied Analysis 4 Journal of Applied Analysis and Computation 3 Nonlinearity 3 Annales de l’Institut Fourier 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 Transactions of the American Mathematical Society 3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 3 Journal of Mathematical Sciences (New York) 3 Journal of Difference Equations and Applications 3 Abstract and Applied Analysis 3 Discrete Dynamics in Nature and Society 3 Journal of Nonlinear Mathematical Physics 3 Dynamical Systems 3 International Journal of Biomathematics 2 Bulletin of the Australian Mathematical Society 2 Rocky Mountain Journal of Mathematics 2 Programming and Computer Software 2 Results in Mathematics 2 Ergodic Theory and Dynamical Systems 2 Applied Mathematics and Mechanics. (English Edition) 2 Mathematical and Computer Modelling 2 Bulletin of the American Mathematical Society. New Series 2 Boletín de la Sociedad Matemática Mexicana. Third Series 2 Differential Equations and Dynamical Systems 2 Regular and Chaotic Dynamics 2 Journal of Biological Systems 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Applied Mathematics and Computing 2 Mediterranean Journal of Mathematics 2 Mathematical Modelling of Natural Phenomena 2 Discrete and Continuous Dynamical Systems. Series S 2 International Journal of Structural Stability and Dynamics 1 International Journal of Modern Physics A 1 Communications in Mathematical Physics 1 International Journal of Theoretical Physics 1 Israel Journal of Mathematics 1 Journal of Engineering Mathematics 1 Journal of Mathematical Biology 1 Letters in Mathematical Physics 1 Mathematical Biosciences 1 Mathematical Methods in the Applied Sciences 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Physics Letters. A 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Fuzzy Sets and Systems 1 International Journal of Mathematics and Mathematical Sciences 1 International Journal for Numerical Methods in Engineering 1 Journal of Pure and Applied Algebra 1 Journal of Soviet Mathematics 1 The Journal of Symbolic Logic 1 Mathematics and Computers in Simulation 1 Quaestiones Mathematicae 1 Quarterly of Applied Mathematics 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Siberian Mathematical Journal 1 Transactions of the Moscow Mathematical Society 1 Acta Applicandae Mathematicae 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Revista Matemática Iberoamericana 1 Dynamics and Stability of Systems 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Journal on Applied Mathematics 1 Expositiones Mathematicae 1 Acta Mathematica Sinica. New Series 1 Acta Mechanica Sinica. (English Edition) 1 Chinese Science Bulletin 1 Applied Mathematics. Series B (English Edition) 1 Calculus of Variations and Partial Differential Equations 1 Electronic Journal of Differential Equations (EJDE) 1 Doklady Mathematics ...and 21 more Serials all top 5 ### Cited in 43 Fields 554 Ordinary differential equations (34-XX) 232 Dynamical systems and ergodic theory (37-XX) 88 Biology and other natural sciences (92-XX) 12 Several complex variables and analytic spaces (32-XX) 11 Mechanics of particles and systems (70-XX) 10 Partial differential equations (35-XX) 10 Numerical analysis (65-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 9 Computer science (68-XX) 8 Topological groups, Lie groups (22-XX) 7 Nonassociative rings and algebras (17-XX) 7 Global analysis, analysis on manifolds (58-XX) 6 Operator theory (47-XX) 6 Quantum theory (81-XX) 5 Mathematical logic and foundations (03-XX) 5 Mechanics of deformable solids (74-XX) 4 Algebraic geometry (14-XX) 4 Category theory; homological algebra (18-XX) 4 Functions of a complex variable (30-XX) 4 Systems theory; control (93-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Differential geometry (53-XX) 3 Probability theory and stochastic processes (60-XX) 3 Fluid mechanics (76-XX) 3 Statistical mechanics, structure of matter (82-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Commutative algebra (13-XX) 2 Real functions (26-XX) 2 Special functions (33-XX) 2 Difference and functional equations (39-XX) 2 Geometry (51-XX) 2 Optics, electromagnetic theory (78-XX) 2 Geophysics (86-XX) 1 General and overarching topics; collections (00-XX) 1 Field theory and polynomials (12-XX) 1 Group theory and generalizations (20-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistics (62-XX) 1 Classical thermodynamics, heat transfer (80-XX) ### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2022-07-06T07:38:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6244028806686401, "perplexity": 7915.695341106375}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104668059.88/warc/CC-MAIN-20220706060502-20220706090502-00313.warc.gz"}
https://gea.esac.esa.int/archive/documentation/GDR2/Data_analysis/chap_cu8par/sec_cu8par_process/ssec_cu8par_process_priamteff.html	# 8.3.1 Effective temperatures Author(s): René Andrae We estimate stellar effective temperatures, $T_{\rm eff}$, from the two distance-independent colours $G_{\rm BP}-G$ and $G-G_{\rm RP}$. These two colours are rather degenerate, as is obvious from the tight locus in Figure 8.1. Nonetheless, the synthetic photometry shown in Figure 8.1a reveals a clear dependence of colours on temperature with $T_{\rm eff}$, which is confirmed by the colours of real Gaia stars with literature estimates of $T_{\rm eff}$ shown in Figure 8.2. It is possible to form a third colour, $G_{\mathrm{BP}}-G_{\mathrm{RP}}$, but this is not independent of the other two colours. More importantly, $G_{\mathrm{BP}}-G_{\mathrm{RP}}$ is noisier than the other two colours since it does not contain the $G$-band which has higher signal-to-noise ratio because the astrometric field has more CCDs (Gaia Collaboration et al. 2016). All three possible colours exhibit monotonic colour-temperature relations, as shown in Figure 8.3. As an aside, let us emphasise that Figure 8.3 also demonstrates that gold-standard and silver-standard photometry indeed provide the same colour-temperature relations. This is an independent validation of the gold and silver photometric system (Riello et al. 2018). For our temperature estimation, we refrain from using a simplistic polynomial model, which would make too restrictive a-priori assumptions about the mathematical form of the colour-temperature relation. Instead, we use $G_{\rm BP}-G$ and $G-G_{\rm RP}$ as features to estimate $T_{\rm eff}$ using extremely randomised trees (Geurts et al. 2006, hereafter ExtraTrees). This machine-learning algorithm comes up with a non-parametric model for the colour-temperature relation, which is far more general than a model of polynomial class. We do ExtraTrees regression with an ensemble of 201 trees, whose median value provides the parameter estimate. Further ExtraTrees regression parameters are $k=2$ random trials per split and $n_{\textrm{min}}=5$ minimal stars per leaf node. Furthermore, as uncertainty estimates, we provide the 16th and 84th percentiles of the ExtraTrees ensemble, which form a central 68% confidence interval. These uncertainty estimates in general form an asymmetric confidence interval. Note that we do not propagate the flux errors through ExtraTrees such that the reported uncertainty interval is solely due to the degeneracy of $T_{\rm eff}$ with the colours as well as the intrinsic spread of the ExtraTrees ensemble. However, off-line testing has shown that propagating the flux errors through ExtraTrees has only little impact on the resulting parameter or uncertainty estimates. Let us also emphasise that ExtraTrees are incapable of extrapolation, i.e. if its training sample has a limited range of labels, ExtraTrees can never produce parameter or uncertainty estimates outside this training label range. Since the real in-flight instrument differs from the nominal pre-launch prescription (Jordi et al. 2010), we cannot train ExtraTrees on synthetic photometry. Instead, we train on 32 602 real stars with observed Gaia photometry and $T_{\rm eff}$ labels provided by the literature. The empirical training sample is restricted to the range 3000K$-$10 000K, since outside this interval there are not enough stars with literature estimates of $T_{\rm eff}$ to train good ExtraTrees models. Since ExtraTrees cannot extrapolate, this implies that there are no sources in Gaia DR2 with with $T_{\rm eff}<3000$K or $T_{\rm eff}>10\,000$K. Since this training sample is empirical, the real stars have non-zero extinctions which are estimated from the literature (where available) in Table 8.2. Evidently, the properties of this empirical training sample – its limited range, the details of its $T_{\rm eff}$ distribution, but also the non-zero extinction – will all have an impact on the resulting temperature estimates. For further details see Andrae et al. (2018).	2018-10-19T19:49:37	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 23, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8187333345413208, "perplexity": 1189.2600715222075}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583512434.71/warc/CC-MAIN-20181019191802-20181019213302-00117.warc.gz"}
http://mathonline.wikidot.com/the-empty-universal-and-identity-relations-on-a-set	The Empty, Universal, and Identity Relations on a Set Table of Contents # The Empty, Universal, and Identity Relations on a Set Recall from the Relations on Sets page that if $X$ is a set then a relation $R$ on $X$ is a subset of the Cartesian product $X \times X$ where if $(x, y) \in R$ then we write $x \: R \: y$ and say "$x$ relates $y$ and if $(x, y) \not \in R$ then we write $x \: \not R \: y$ and say $x$ does not relate $y$. We will now look at three rather basic relations on a set $X$. Definition: Let $X$ be a set. The Empty Relation $\emptyset$ on $X$ is defined to be the relation where for all $x, y \in X$ we have that $x \: \not R \: y$. For example, consider the set of integers $\mathbb{Z}$ and let $R$ be the relation such that for $x, y \in \mathbb{Z}$ we have that $x \: R \: y$ if both $x + y$ is even and $x + y$ is odd. Clearly the sum $x + y$ cannot both be even and odd, and so $R$ is the empty relation since for all $x, y \in X$ we have that $x \: \not R \: y$, i.e., $R = \emptyset$. Definition: Let $X$ be a set. The Universal Relation or Full Relation $\mathcal U$ on $\mathbb{Z}$ is defined to be the relation where for all $x, y \in X$ we have that $x \: \mathcal U \: y$. For example, consider the set of integers $\mathbb{Z}$ again. Define $R$ to be the relation such that for $x, y \in \mathbb{Z}$ we have that $x \: R \: y$ if $x + y \in \mathbb{Z}$. The sum of any two integers is always going to be an integer, and so for all $x, y \in \mathbb{Z}$ we have that $x \: R \: y$ so $R$ is the universal relation on $X$ so $R = \mathcal U$ Definition: Let $X$ be a set. The Identity Relation $\mathcal I$ on $\mathbb{Z}$ is defined to be the relation where for all $x, y \in X$ we have that $x \: \mathcal I \: y$ if and only if $x = y$. For example, consider the set of integers $\mathbb{Z} \setminus \{ 0 \}$. Define $R$ to be the relation such that for $x, y \in \mathbb{Z}$ we have that $x \: R \: y$ if $\frac{x}{y} = 1$. If $x \: R \: y$ then $\frac{x}{y} = 1$ so $x = y$. Conversely, if $x, y \in \mathbb{Z} \setminus \{0 \}$ and $x = y$ then $\frac{x}{y} = 1$ so $x \: R \: y$. Therefore $R$ is the identity relation on $\mathbb{Z} \setminus \{ 0 \}$ so $R = \mathcal I$. Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License	2018-06-19T15:59:35	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9750313758850098, "perplexity": 43.84871154153389}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267863100.8/warc/CC-MAIN-20180619154023-20180619174023-00244.warc.gz"}
http://pdglive.lbl.gov/DataBlock.action?node=S067NUS	# (C) Other neutrino mixing results The LSND collaboration reported in AGUILAR 2001 a signal which is consistent with ${{\overline{\mathit \nu}}_{{\mu}}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{e}}}$ oscillations. In a three neutrino framework, this would be a measurement of $\theta _{12}$ and $\Delta \mathit m{}^{2}_{21}$. This does not appear to be consistent with most of the other neutrino data. The MiniBooNE experiment, reported in AGUILAR-AREVALO 2007 , does a two-neutrino analysis which, assuming $\mathit CP$ conservation, rules out AGUILAR 2001 . However, the MiniBooNE antineutrino data reported in AGUILAR-AREVALO 2013A are consistent with the signal reported in AGUILAR 2001 . The following listings include results which might be relevant towards understanding these observations. They include searches for ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{e}}}$ , ${{\overline{\mathit \nu}}_{{\mu}}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{e}}}$ , sterile neutrino oscillations, and $\mathit CPT$ violation. # Search for ${{\boldsymbol \nu}_{{\mu}}}$ or ${{\boldsymbol \nu}_{{e}}}$ $\rightarrow$ ${{\boldsymbol \nu}_{{s}}}$ INSPIRE search VALUE CL% DOCUMENT ID TECN COMMENT • • • We do not use the following data for averages, fits, limits, etc. • • • $<0.4$ 90 1 2017 B ICCB IceCube-DeepCore $<8 \times 10^{-3}$ 95 2 2017 T $\beta$ decay $<0.01$ 90 3 2017 NEOS $<0.02$ 90 4 2016 ICCB IceCube $<4.5 \times 10^{-4}$ 95 5 2016 B MINOS, DayaBay $<0.086$ 95 6 2016 C MINS $<0.011$ 95 7 2016 B DAYA 8 2001 MCRO matter effects 9 2000 SKAM neutral currents + matter effects 1 AARTSEN 2017B uses three years of upward-going atmospheric neutrino data in the energy range of 10-60 GeV to constrain their disappearance into light sterile neutrinos. The reported limit sin$^2\theta _{24}$ $<$ 0.11 at 90$\%$ C.L. is for $\Delta$m${}^{2}_{41}$ = 1.0 eV${}^{2}$. We convert the result to sin$^22\theta _{24}$ for the listing. AARTSEN 2017B also reports cos $^2\theta _{24}\cdot{}$sin$^2\theta _{34}$ $<$ 0.15 at 90$\%$ C.L. for $\Delta$m${}^{2}_{41}$ = 1.0 eV${}^{2}$. 2 ABDURASHITOV 2017 use the Troitsk nu-mass experiment to search for sterile neutrinos with mass 0.1 - 2 keV. We convert the reported limit from $\mathit U{}^{2}_{e4}<$0.002 to sin$^22\theta _{14}<$0.008 assume $\mathit U_{e4}\sim{}$ sin$\theta _{14}$. The stated limit corresponds to the smallest $\mathit U{}^{2}_{e4}$. The exclusion curve begins at $\mathit U{}^{2}_{e4}$ of 0.02 for m$_{4}$ = 0.1 keV. 3 KO 2017 reports on short baseline reactor oscillation search ( ${{\overline{\mathit \nu}}_{{e}}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{s}}}$ ), motivated be the so-called "reactor antineutrino anomaly". The experiment is conducted at 23.7 m from the core of unit 5 of the Hanbit Nuclear Power Complex in Korea. the reported limited on sin$^2(2\theta _{41})$ for sterile neutrinos was determined using the reactor antineutrino spectrum determined by the Daya Bay experiment for $\Delta$m${}^{2}_{14}$ around 0.55 eV${}^{2}$ where the sensitivity is maximal. A fraction of the parameter space derived from the "reactor antineutrino anomaly" is excluded by this work. Compared to reactor models an event excess is observed at about 5 MeV, in agreement with other experiments. 4 AARTSEN 2016 use one year of upward-going atmospheric muon neutrino data in the energy range of 320 GeV to 20 TeV to constrain their disappearance into light sterile neutrinos. Sterile neutrinos are expected to produce distinctive zenith distribution for these energies for 0.01 ${}\leq{}\Delta$m${}^{2}{}\leq{}$10 eV${}^{2}$. The stated limit is for sin$^22\theta _{24}$ at $\Delta$m${}^{2}$ around 0.3 eV${}^{2}$. 5 ADAMSON 2016B combine the results of AN 2016B, ADAMSON 2016C, and Bugey-3 reactor experiments to constrain ${{\mathit \nu}_{{\mu}}}$ to ${{\mathit \nu}_{{e}}}$ mixing through oscillations into light sterile neutrinos. The stated limit for sin$^22\theta _{ {{\mathit \mu}} {{\mathit e}} }$ is at $\vert \Delta$m${}^{2}_{41}\vert$ = 1.2 eV${}^{2}$. 6 ADAMSON 2016C use the NuMI beam and exposure of $10.56 \times 10^{20}$ protons on target to search for the oscillation of ${{\mathit \nu}_{{\mu}}}$ dominated beam into light sterile neutrinos with detectors at 1.04 and 735 km. The reported limit sin$^2(\theta _{24})$ $<$ 0.022 at 95$\%$ C.L. is for $\vert \Delta$m${}^{2}_{41}\vert$ = 0.5 eV${}^{2}$. We convert the result to sin$^2(2\theta _{24})$ for the listing. 7 AN 2016B utilize 621 days of data to place limits on the ${{\overline{\mathit \nu}}_{{e}}}$ disappearance into a light sterile neutrino. The stated limit corresponds to the smallest sin$^2(2\theta _{14})$ at $\vert \Delta$m${}^{2}_{41}\vert$ $\sim{}$ $0.03$ eV${}^{2}$ (obtained from Figure 3 in AN 2016B). The exclusion curve begins at $\vert \Delta$m${}^{2}_{41}\vert \sim{}1.5 \times 10^{-4}$ eV${}^{2}$ and extends to $\sim{}0.25$ eV${}^{2}$. The analysis assumes sin$^2(2\theta _{12})$ = $0.846$ $\pm0.021$, $\Delta$m${}^{2}_{21}$ = ($7.53$ $\pm0.18$) $\times 10^{-5}$ eV${}^{2}$, and $\vert \Delta$m${}^{2}_{32}\vert$ = $0.00244$ $\pm0.00006$ eV${}^{2}$. 8 AMBROSIO 2001 tested the pure 2-flavor ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{s}}}$ hypothesis using matter effects which change the shape of the zenith-angle distribution of upward through-going muons. With maximum mixing and $\Delta$m${}^{2}$around $0.0024~$eV${}^{2}$, the ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{s}}}$ oscillation isdisfavored with 99$\%$ confidence level with respect to the ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{\tau}}}$ hypothesis. 9 FUKUDA 2000 tested the pure 2-flavor ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{s}}}$ hypothesis using three complementary atmospheric-neutrino data samples. With this hypothesis, zenith-angle distributions are expected to show characteristic behavior due to neutral currents and matter effects. In the $\Delta$m${}^{2}$ and sin$^22\theta$region preferred by the Super-Kamiokande data, the ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{s}}}$ hypothesis isrejected at the 99$\%$ confidence level, while the ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{\tau}}}$ hypothesis consistently fits all of the data sample. References: AARTSEN 2017B PR D95 112002 Search for Sterile Neutrino Mixing using Three Years of IceCube DeepCore Data ABDURASHITOV 2017 JETPL 105 753 First Measeurements in Search for keV-Sterile Neutrino in Tritium beta-Decay by Troitsk nu-Mass Experiment KO 2017 PRL 118 121802 Sterile Neutrino Search at the NEOS Experiment AARTSEN 2016 PRL 117 071801 Searches for Sterile Neutrinos with the IceCube Detector PRL 85 3999 ${{\mathit \tau}}$ Neutrinos Favored over Sterile Neutrinos in Atmospheric Muon Neutrino Oscillations	2019-03-20T06:00:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7955403923988342, "perplexity": 4269.027167525758}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202299.16/warc/CC-MAIN-20190320044358-20190320070358-00376.warc.gz"}
https://par.nsf.gov/biblio/10371870-evidence-galaxy-assembly-bias-sdss-dr7-galaxy-samples-from-count-statistics	skip to main content Evidence of galaxy assembly bias in SDSS DR7 galaxy samples from count statistics ABSTRACT We present observational constraints on the galaxy–halo connection, focusing particularly on galaxy assembly bias from a novel combination of counts-in-cylinders statistics, P(NCIC), with the standard measurements of the projected two-point correlation function wp(rp), and number density ngal of galaxies. We measure ngal, wp(rp), and P(NCIC) for volume-limited, luminosity-threshold samples of galaxies selected from SDSS DR7, and use them to constrain halo occupation distribution (HOD) models, including a model in which galaxy occupation depends upon a secondary halo property, namely halo concentration. We detect significant positive central assembly bias for the Mr < −20.0 and Mr < −19.5 samples. Central galaxies preferentially reside within haloes of high concentration at fixed mass. Positive central assembly bias is also favoured in the Mr < −20.5 and Mr < −19.0 samples. We find no evidence of central assembly bias in the Mr < −21.0 sample. We observe only a marginal preference for negative satellite assembly bias in the Mr < −20.0 and Mr < −19.0 samples, and non-zero satellite assembly bias is not indicated in other samples. Our findings underscore the necessity of accounting for galaxy assembly bias when interpreting galaxy survey data, and demonstrate the potential of count statistics in extracting information more » Authors: ; ; ; ; ; ; Publication Date: NSF-PAR ID: 10371870 Journal Name: Monthly Notices of the Royal Astronomical Society Volume: 516 Issue: 3 Page Range or eLocation-ID: p. 4003-4024 ISSN: 0035-8711 Publisher: Oxford University Press Sponsoring Org: National Science Foundation ##### More Like this 1. ABSTRACT The combination of galaxy–galaxy lensing (GGL) and galaxy clustering is a powerful probe of low-redshift matter clustering, especially if it is extended to the non-linear regime. To this end, we use an N-body and halo occupation distribution (HOD) emulator method to model the redMaGiC sample of colour-selected passive galaxies in the Dark Energy Survey (DES), adding parameters that describe central galaxy incompleteness, galaxy assembly bias, and a scale-independent multiplicative lensing bias Alens. We use this emulator to forecast cosmological constraints attainable from the GGL surface density profile ΔΣ(rp) and the projected galaxy correlation function wp, gg(rp) in the final (Year 6) DES data set over scales $r_p=0.3\!-\!30.0\, h^{-1} \, \mathrm{Mpc}$. For a $3{{\ \rm per\ cent}}$ prior on Alens we forecast precisions of $1.9{{\ \rm per\ cent}}$, $2.0{{\ \rm per\ cent}}$, and $1.9{{\ \rm per\ cent}}$ on Ωm, σ8, and $S_8 \equiv \sigma _8\Omega _m^{0.5}$, marginalized over all halo occupation distribution (HOD) parameters as well as Alens. Adding scales $r_p=0.3\!-\!3.0\, h^{-1} \, \mathrm{Mpc}$ improves the S8 precision by a factor of ∼1.6 relative to a large scale ($3.0\!-\!30.0\, h^{-1} \, \mathrm{Mpc}$) analysis, equivalent to increasing the survey area by a factor of ∼2.6. Sharpening the Alens prior to $1{{\more » 2. ABSTRACT We describe our non-linear emulation (i.e. interpolation) framework that combines the halo occupation distribution (HOD) galaxy bias model with N-body simulations of non-linear structure formation, designed to accurately predict the projected clustering and galaxy–galaxy lensing signals from luminous red galaxies in the redshift range 0.16 < z < 0.36 on comoving scales 0.6 < rp < 30$h^{-1} \, \text{Mpc}$. The interpolation accuracy is ≲ 1–2 per cent across the entire physically plausible range of parameters for all scales considered. We correctly recover the true value of the cosmological parameter S8 = (σ8/0.8228)(Ωm/0.3107)0.6 from mock measurements produced via subhalo abundance matching (SHAM)-based light-cones designed to approximately match the properties of the SDSS LOWZ galaxy sample. Applying our model to Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 14 (DR14) LOWZ galaxy clustering and galaxy-shear cross-correlation measurements made with Sloan Digital Sky Survey (SDSS) Data Release 8 (DR8) imaging, we perform a prototype cosmological analysis marginalizing over wCDM cosmological parameters and galaxy HOD parameters. We obtain a 4.4 per cent measurement of S8 = 0.847 ± 0.037, in 3.5σ tension with the Planck cosmological results of 1.00 ± 0.02. We discuss the possibility of underestimated systematic uncertainties or astrophysical effects that could explain this discrepancy. 3. ABSTRACT We test different implementations of the halo occupation distribution (HOD) model to reconstruct the spatial distribution of galaxies as predicted by a version of the L-GALAXIES semi-analytical model (SAM). We compare the measured two-point correlation functions of the HOD mock catalogues and the SAM samples to quantify the fidelity of the reconstruction. We use fixed number density galaxy samples selected according to stellar mass or star formation rate (SFR). We develop three different schemes to populate haloes with galaxies with increasing complexity, considering the scatter of the satellite HOD as an additional parameter in the modelling. We modify the SAM output, removing assembly bias and using a standard Navarro–Frenk–White density profile for the satellite galaxies as the target to reproduce with our HOD mocks. We find that all models give similar reproductions of the two-halo contribution to the clustering signal, but there are differences in the one-halo term. In particular, the HOD mock reproductions work equally well using either the HOD of central and satellites separately or using a model that also accounts for whether or not the haloes contain a central galaxy. We find that the HOD scatter does not have an important impact on the clustering predictionsmore » 4. ABSTRACT Galaxy–galaxy lensing is a powerful probe of the connection between galaxies and their host dark matter haloes, which is important both for galaxy evolution and cosmology. We extend the measurement and modelling of the galaxy–galaxy lensing signal in the recent Dark Energy Survey Year 3 cosmology analysis to the highly non-linear scales (∼100 kpc). This extension enables us to study the galaxy–halo connection via a Halo Occupation Distribution (HOD) framework for the two lens samples used in the cosmology analysis: a luminous red galaxy sample (redmagic) and a magnitude-limited galaxy sample (maglim). We find that redmagic (maglim) galaxies typically live in dark matter haloes of mass log10(Mh/M⊙) ≈ 13.7 which is roughly constant over redshift (13.3−13.5 depending on redshift). We constrain these masses to${\sim}15{{\ \rm per\ cent}}\$, approximately 1.5 times improvement over the previous work. We also constrain the linear galaxy bias more than five times better than what is inferred by the cosmological scales only. We find the satellite fraction for redmagic (maglim) to be ∼0.1−0.2 (0.1−0.3) with no clear trend in redshift. Our constraints on these halo properties are broadly consistent with other available estimates from previous work, large-scale constraints, and simulations. The framework built in this paper willmore » 5. Abstract Applying halo models to analyze the small-scale clustering of galaxies is a proven method for characterizing the connection between galaxies and their host halos. Such works are often plagued by systematic errors or limited to clustering statistics that can be predicted analytically. In this work, we employ a numerical mock-based modeling procedure to examine the clustering of Sloan Digital Sky Survey DR7 galaxies. We apply a standard halo occupation distribution (HOD) model to dark matter only simulations with a ΛCDM cosmology. To constrain the theoreStical models, we utilize a combination of galaxy number density and selected scales of the projected correlation function, redshift-space correlation function, group multiplicity function, average group velocity dispersion, mark correlation function, and counts-in-cells statistics. We design an algorithm to choose an optimal combination of measurements that yields tight and accurate constraints on our model parameters. Compared to previous work using fewer clustering statistics, we find a significant improvement in the constraints on all parameters of our halo model for two different luminosity-threshold galaxy samples. Most interestingly, we obtain unprecedented high-precision constraints on the scatter in the relationship between galaxy luminosity and halo mass. However, our best-fit model results in significant tension (>4σ) for both samples,more »	2023-03-23T22:52:54	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32760414481163025, "perplexity": 4178.068328875365}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945218.30/warc/CC-MAIN-20230323225049-20230324015049-00658.warc.gz"}
https://www-cdf.fnal.gov/physics/exotic/run2/EMTiming_analysis/reblessed2/note.html	# Search for Photons from Long-Lived Particles at CDF - Reblessed Tables and Figures for the PRL - M. Goncharov, V. Krutelyov, E. Lee, D. Toback, P. Wagner Texas A&M University We present the first search for heavy, long-lived particles that decay to photons at a hadron collider. We use a sample of gamma+jet+missing transverse energy events in $p{\bar p}$ collisions at \sqrt{s}=1.96 TeV taken with the CDF II detector. Candidate events are selected based on the arrival time of the photon at the detector. Using an integrated luminosity of 570 pb-1 of collision data, we observe 2 events, consistent with the background estimate of 1.3$\pm$0.7 events. While our search strategy does not rely on model-specific dynamics, we set cross section limits in a supersymmetric model with chi10-> gamma+gravitino and place the world-best 95\% C.L. lower limit on the \none\ mass of 101 GeV/c^2 at \tau_{chi10} = 5 ns. Draft submitted to Phys Rev Lett: FERMILAB-PUB-07-075-E Public Note: CDF 8378 Reblessed Tables and Figures: • The time distribution of background, signal and observed data in the time window containing all control regions. • The table with the efficiencies of each requirement. • The cross section limit as a function of neutralino mass and lifetime. • The expected and the observed exclusion region of the GMSB model as a function of neutralino mass and lifetime.	2020-02-17T10:04:11	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7497504949569702, "perplexity": 3531.076923499422}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875141806.26/warc/CC-MAIN-20200217085334-20200217115334-00233.warc.gz"}
https://gateway.ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1mXWo6uco/wiki/Schur_polynomial.html	# Schur polynomial In mathematics, Schur polynomials, named after Issai Schur, are certain symmetric polynomials in n variables, indexed by partitions, that generalize the elementary symmetric polynomials and the complete homogeneous symmetric polynomials. In representation theory they are the characters of polynomial irreducible representations of the general linear groups. The Schur polynomials form a linear basis for the space of all symmetric polynomials. Any product of Schur functions can be written as a linear combination of Schur polynomials with non-negative integral coefficients; the values of these coefficients is given combinatorially by the Littlewood–Richardson rule. More generally, skew Schur polynomials are associated with pairs of partitions and have similar properties to Schur polynomials. ## Definition Schur polynomials are indexed by integer partitions. Given a partition λ = (λ1, λ2, ,λn), where λ1λ2λn, and each λj is a non-negative integer, the functions are alternating polynomials by properties of the determinant. A polynomial is alternating if it changes sign under any transposition of the variables. Since they are alternating, they are all divisible by the Vandermonde determinant, The Schur polynomials are defined as the ratio This is a symmetric function because the numerator and denominator are both alternating, and a polynomial since all alternating polynomials are divisible by the Vandermonde determinant. ## Properties The degree d Schur polynomials in n variables are a linear basis for the space of homogeneous degree d symmetric polynomials in n variables. For a partition λ = (λ1, λ2, ..., λn), the Schur polynomial is a sum of monomials, where the summation is over all semistandard Young tableaux T of shape λ. The exponents t1, ..., tn give the weight of T, in other words each ti counts the occurrences of the number i in T. This can be shown to be equivalent to the definition from the first Giambelli formula using the Lindström–Gessel–Viennot lemma (as outlined on that page). Schur polynomials can be expressed as linear combinations of monomial symmetric functions mμ with non-negative integer coefficients Kλμ called Kostka numbers, The Kostka numbers Kλμ are given by the number of semi-standard Young tableaux of shape λ and weight μ. ### Jacobi−Trudi identities The first Jacobi−Trudi formula expresses the Schur polynomial as a determinant in terms of the complete homogeneous symmetric polynomials, [1] where hi := s(i). The second Jacobi-Trudi formula expresses the Schur polynomial as a determinant in terms of the elementary symmetric polynomials, [2] where ei := s(1i). and λ' is the conjugate partition to λ. These two formulae are known as determinantal identities. ### The Giambelli identity Another determinantal identity is Giambelli's formula, which expresses the Schur function for an arbitrary partition in terms of those for the hook partitions contained within the Young diagram. In Frobenius' notation, the partition is denoted where, for each diagonal element in position ii, ai denotes the number of boxes to the right in the same row and bi denotes the number of boxes beneath it in the same column (the arm and leg lengths, respectively). The Giambelli identity expresses the partition as the determinant . ### The Cauchy identity The Cauchy identities for the Schur functions (now in infinitely many variables), states that and where the sum is taken over all partitions λ. There are many generalizations of these identities, for example, Hall-Littlewood polynomials, Schubert polynomials and Grothendieck polynomials admit Cauchy-like identities. ### The Murnaghan−Nakayama rule The Murnaghan–Nakayama rule expresses a product of a power-sum symmetric function with a Schur polynomial, in terms of Schur polynomials: where the sum is over all partitions μ such that μ/λ is a rim-hook of size r and ht(μ/λ) is the number of rows in the diagram μ/λ. ### The Littlewood-Richardson rule and Pieri's formula The Littlewood–Richardson coefficients depend on three partitions, say , of which and describe the Schur functions being multiplied, and gives the Schur function of which this is the coefficient in the linear combination; in other words they are the coefficients such that The Littlewood–Richardson rule states that is equal to the number of Littlewood–Richardson tableaux of skew shape and of weight . Pieri's formula is a special case of the Littlewood-Richardson rule, which expresses the product in terms of Schur polynomials. The dual version expresses in terms of Schur polynomials. ### Specializations Evaluating the Schur polynomial sλ in (1,1,...,1) gives the number of semi-standard Young tableaux of shape λ with entries in 1, 2, ..., n. One can show, by using the Weyl character formula for example, that In this formula, λ, the tuple indicating the width of each row of the Young diagram, is implicitly extended with zeros until it has length n. The sum of the elements λi is d. See also the Hook length formula which computes the same quantity for fixed λ. ## Example The following extended example should help clarify these ideas. Consider the case n = 3, d = 4. Using Ferrers diagrams or some other method, we find that there are just four partitions of 4 into at most three parts. We have and so on. Summarizing: Every homogeneous degree-four symmetric polynomial in three variables can be expressed as a unique linear combination of these four Schur polynomials, and this combination can again be found using a Gröbner basis for an appropriate elimination order. For example, is obviously a symmetric polynomial which is homogeneous of degree four, and we have ## Relation to representation theory The Schur polynomials occur in the representation theory of the symmetric groups, general linear groups, and unitary groups. The Weyl character formula implies that the Schur polynomials are the characters of finite-dimensional irreducible representations of the general linear groups, and helps to generalize Schur's work to other compact and semisimple Lie groups. Several expressions arise for this relation, one of the most important being the expansion of the Schur functions sλ in terms of the symmetric power functions . If we write χλ ρ for the character of the representation of the symmetric group indexed by the partition λ evaluated at elements of cycle type indexed by the partition ρ, then where ρ = (1r1, 2r2, 3r3, ...) means that the partition ρ has rk parts of length k. A proof of this can be found in R. Stanley's Enumerative combinatoric II, Corollary 7.17.5. The integers χλ ρ can be computed using the Murnaghan–Nakayama rule. ## Skew Schur functions Skew Schur functions sλ/μ depend on two partitions λ and μ, and can be defined by the property Here, the inner product is the Hall inner product, for which the Schur polynomials form an orthonormal basis. Similar to the ordinary Schur polynomials, there are numerous ways to compute these. The corresponding Jacobi-Trudi identities are , . There is also a combinatorial interpretation of the skew Schur polynomials, namely it is a sum over all semi-standard Young tableaux (or column-strict tableaux) of the skew shape . The skew Schur polynomials expands positively in Schur polynomials. A rule for the coefficients is given by the Littlewood-Richardson rule. ## Generalizations There are numerous generalizations of Schur polynomials: • Hall–Littlewood polynomials • Shifted Schur polynomials • Factorial Schur polynomials • Flagged Schur polynomials • Double Schur polynomials • Schubert polynomials • Stanley symmetric functions (also known as stable Schubert polynomials) • Key polynomials (also known as Demazure characters) • Quasi-symmetric Schur polynomials • Jack polynomials • Modular Schur polynomials • Macdonald polynomials • Schur polynomials for the symplectic and orthogonal group. • k-Schur functions • Loop Schur functions • Grothendieck polynomials (K-theoretical analogue of Schur polynomials) • LLT polynomials ### Double Schur polynomials The double Schur polynomials[3] can be seen as a generalization of the shifted Schur polynomials. These polynomials are also closely related to the factorial Schur polynomials. Given a partition λ, and a sequence a1, a2, one can define the double Schur polynomial sλ(x \|\| a) as where the sum is taken over all reverse semi-standard Young tableaux T of shape λ, and integer entries in 1,,n. Here T(α) denotes the value in the box α in T and c(α) is the content of the box. A combinatorial rule for the Littlewood-Richardson coefficients (depending on the sequence a), is given by A.I Molev in.[3] In particular, this implies that the shifted Schur polynomials have non-negative Littlewood-Richardson coefficients. The shifted Schur polynomials, s*λ(y) , can be obtained from the double Schur polynomials by specializing ai=-i and yi=xi+i. The double Schur polynomials are special cases of the double Schubert polynomials. ### Factorial Schur polynomials The factorial Schur polynomials may be defined as follows. Given a partition λ, and a doubly infinite sequence ,a-1, a0, a1, one can define the factorial Schur polynomial sλ(x\|a) as where the sum is taken over all semi-standard Young tableaux T of shape λ, and integer entries in 1,,n. Here T(α) denotes the value in the box α in T and c(α) is the content of the box. There is also a determinant formula, where (y\|a)k = (y-a1)... (y-ak). It is clear that if we let ai=0 for all i, we recover the usual Schur polynomial sλ. The double Schur polynomials and the factorial Schur polynomials in n variables are related via the identity sλ(x\|\|a) = sλ(x\|u) where an-i+1 = ui. ## References 1. Formula A.5 in Fulton, William; Harris, Joe (1991). Representation theory. A first course. Graduate Texts in Mathematics, Readings in Mathematics. 129. New York: Springer-Verlag. ISBN 978-0-387-97495-8. MR 1153249, ISBN 978-0-387-97527-6. 2. Formula A.6 in Fulton, William; Harris, Joe (1991). Representation theory. A first course. Graduate Texts in Mathematics, Readings in Mathematics. 129. New York: Springer-Verlag. ISBN 978-0-387-97495-8. MR 1153249, ISBN 978-0-387-97527-6. 3. Molev, A.I. (June 2009). "Littlewood–Richardson polynomials". Journal of Algebra. 321 (11): 3450–3468. doi:10.1016/j.jalgebra.2008.02.034. This article is issued from Wikipedia - version of the 11/16/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.	2022-05-26T11:55:49	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9095973968505859, "perplexity": 738.9420051807249}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662604794.68/warc/CC-MAIN-20220526100301-20220526130301-00445.warc.gz"}
http://gams.cam.nist.gov/20.9	# §20.9(i) Elliptic Integrals With $k$ defined by 20.9.1 $k={\mathop{\theta_{2}\/}\nolimits^{2}}\!\left(0\middle\|\tau\right)/{\mathop{% \theta_{3}\/}\nolimits^{2}}\!\left(0\middle\|\tau\right)$ Symbols: $\mathop{\theta_{j}\/}\nolimits\!\left(z\middle\|\tau\right)$: theta function, $\tau$: lattice parameter and $k$: modulus Referenced by: §20.11(iii), §20.9(ii), §23.6(ii) Permalink: http://dlmf.nist.gov/20.9.E1 Encodings: TeX, pMML, png and the notation of §19.2(ii), the complete Legendre integrals of the first kind may be expressed as theta functions: 20.9.2 $\displaystyle\mathop{K\/}\nolimits\!\left(k\right)$ $\displaystyle=\tfrac{1}{2}\pi{\mathop{\theta_{3}\/}\nolimits^{2}}\!\left(0% \middle\|\tau\right),$ $\displaystyle{\mathop{K\/}\nolimits^{\prime}}\!\left(k\right)$ $\displaystyle=-i\tau\mathop{K\/}\nolimits\!\left(k\right),$ together with (22.2.1). In the case of the symmetric integrals, with the notation of §19.16(i) we have 20.9.3 $\mathop{R_{F}\/}\nolimits\!\left(\frac{{\mathop{\theta_{2}\/}\nolimits^{2}}\!% \left(z,q\right)}{{\mathop{\theta_{2}\/}\nolimits^{2}}\!\left(0,q\right)},% \frac{{\mathop{\theta_{3}\/}\nolimits^{2}}\!\left(z,q\right)}{{\mathop{\theta_% {3}\/}\nolimits^{2}}\!\left(0,q\right)},\frac{{\mathop{\theta_{4}\/}\nolimits^% {2}}\!\left(z,q\right)}{{\mathop{\theta_{4}\/}\nolimits^{2}}\!\left(0,q\right)% }\right)=\frac{{\mathop{\theta_{1}\/}\nolimits^{\prime}}\!\left(0,q\right)}{% \mathop{\theta_{1}\/}\nolimits\!\left(z,q\right)}z,$ 20.9.4 $\mathop{R_{F}\/}\nolimits\!\left(0,{\mathop{\theta_{3}\/}\nolimits^{4}}\!\left% (0,q\right),{\mathop{\theta_{4}\/}\nolimits^{4}}\!\left(0,q\right)\right)=% \tfrac{1}{2}\pi,$ 20.9.5 $\mathop{\exp\/}\nolimits\!\left(-\frac{\pi\mathop{R_{F}\/}\nolimits\!\left(0,k% ^{2},1\right)}{\mathop{R_{F}\/}\nolimits\!\left(0,{k^{\prime}}^{2},1\right)}% \right)=q.$ # §20.9(ii) Elliptic Functions and Modular Functions See §§22.2 and 23.6(i) for the relations of Jacobian and Weierstrass elliptic functions to theta functions. The relations (20.9.1) and (20.9.2) between $k$ and $\tau$ (or $q$) are solutions of Jacobi’s inversion problem; see Baker (1995) and Whittaker and Watson (1927, pp. 480–485). As a function of $\tau$, $k^{2}$ is the elliptic modular function; see Walker (1996, Chapter 7) and (23.15.2), (23.15.6). # §20.9(iii) Riemann Zeta Function See Koblitz (1993, Ch. 2, §4) and Titchmarsh (1986b, pp. 21–22). See also §§20.10(i) and 25.2.	2014-09-30T18:10:40	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 45, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9397719502449036, "perplexity": 6152.5884295133465}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1412037663060.18/warc/CC-MAIN-20140930004103-00189-ip-10-234-18-248.ec2.internal.warc.gz"}
https://gea.esac.esa.int/archive/documentation/GDR3/Data_analysis/chap_cu8par/sec_cu8par_apsis/ssec_cu8par_apsis_smsgen.html	# 11.3.1 Sampled Mean Spectrum generator (SMSgen) Author(s): René Andrae ## Goals SMSgen is a purely technical module, running first in the Apsis chain. Its tasks comprise the following: First and foremost, SMSgen provides sampled low-resolution BP/RP spectra as input to the Apsis modules. More specifically, SMSgen provides the integrated fluxes and the flux uncertainties in 120 pixels per BP and RP spectrum. Second, SMSgen applies the correction to the flux in the $G$ band as proposed by Riello et al. (2021), see Section 11.2.2. Third, SMSgen applies the zero-point correction to the parallax, see Section 11.2.1. ## Inputs SMSgen uses the continuous representation of internally calibrated BP/RP spectra in terms of coefficients and a table of pre-defined physical wavelengths (converted to pixel position with the applicable dispersion relation from CU5). All 55 coefficients for both, BP and RP, are used, i.e. SMSgen does not use the truncation methods proposed in Carrasco et al. (2021). ## Method Given the basis definition for the continuous representation of internally calibrated BP/RP spectra chosen by CU5, SMSgen computes a “design matrix” $D$ which provides the integrated flux of each basis function in all 120 pixels. These pixels cover the wavelength ranges for non-zero transmission in BP and RP, as is shown in Figure 11.5. For a given coefficient vector $\boldsymbol{c}$, the sampled BP/RP spectrum $\boldsymbol{s}$ is then given by the simple matrix product $\boldsymbol{s}=D\cdot\boldsymbol{c}$. This is done for BP and RP coefficients separately, providing sampled spectra for BP and RP, respectively, each having 120 pixels. The flux uncertainties are propagated from the coefficient covariance matrix $\Sigma_{\textrm{coeffs}}$ provided by CU5. SMSgen computes the full pixel covariance matrix $\Sigma_{\textrm{spec}}=D\cdot\Sigma_{\textrm{coeffs}}\cdot D^{T}$. However, the full pixel covariance matrices for BP and RP each have format $120\times 120$ and thus consume a lot of memory. Since in DR3 no Apsis module actually accounts for correlated errors in pixel fluxes, SMSgen only provides the standard deviations for each pixel, i.e. the square-roots of the diagonal elements in $\Sigma_{\textrm{spec}}$. Besides, with only 55 coefficients provided by CU5 for each BP and RP, $\Sigma_{\textrm{spec}}$ cannot have full rank and thus could not be inverted for usage in a $\chi^{2}$. ## Scope SMSgen does not provide any outputs in DR3. It produced sampled BP/RP spectra for all sources for internal usage only by Apsis processing.	2022-08-08T04:07:37	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 11, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7844860553741455, "perplexity": 2223.6725630792394}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882570765.6/warc/CC-MAIN-20220808031623-20220808061623-00687.warc.gz"}
http://ptruchon.wordpress.com/tag/mathscience/	# Posts Tagged ‘math/science’ ## Synthetic Biology Posted by Patrick on November 30, 2012 Last week, Quirks and Quarks had a segment about synthetic biology [1]: a new branch of science whose goal is to design and construct new biological functions and systems not found in nature. [2] The explicit assumption of this branch of science is that DNA is a kind of computing code. Indeed, Canadian researcher Andrew Hessel says that DNA is a “tremendous medium for encoding information: it’s far more robust and compact than even electronic data storage, and it’s really the code of life. So we’re looking at it through the lens of computing [...], which I think is a remarkable shift. [1, 2:17] Seen through this lens, these researchers want to reprogram living organisms to make them do new and useful things. Imagine, for example, “bacteria that breath CO2 and pee straight diesel fuel” [1, 2:58]. These researchers believe that this technology could save the world. Whether or not you get excited by the possibilities that we may finally live in harmony with nature (by controlling it even more drastically), two things concern me. The first is implicitly outlined in one of Hessel’s comments: “I think this is the most powerful technology we’ve ever made. The only thing that I think compares to it is electronic computing. And really, we’ve seen how electronic computing has revolutionized and continues to revolutionize the world. I think this is even more powerful because now we’re talking about programming not electronic processors, but living processors.” [1, 3:48] This technology is the most powerful we’ve ever made… Are we wise enough to foresee all the consequences of reprogrammed organisms? At one level, DNA works like computer code and new (and better programs) can be written, but biological organisms also interact with one another and evolve. Do we seriously think we’re smart enough to understand all these interactions? Taken as a whole, this new field would be orders of magnitudes more complex than the entire Internet, which is by no means simple. This time though, programming “bugs” may be more dangerous than simple computer glitches. Maybe you think that spreading FUD is not the most compelling line of reasoning. After all, the same has been said about other fields of science before. Nuclear physics was supposed to lead to global planetary destruction, and we’re still here. Fare enough. Maybe we are (or will become) smart enough… My second concern is not so much about the technology itself but the legal infrastructure surrounding it: we live in a world where companies like Apple Inc. patent things like “rectangle with rounded corners”. [3] Patents on software are just as ridiculous and detrimental for innovation since: [They] block individuals from taking part in [...] development and distribution [...] This may not seem relevant to most people but it’s the same as the freedom to write a book. Most people will never write a book, but some people will and society as a whole benefits from what is made by the few [...] [4] If the evolution of synthetic biology is inevitable, I hope it doesn’t follow the insane route that commercial software and electronic devices have taken. Exploring such a powerful science requires openness, collaboration, and governmental oversight, not secrecy and commercial control. If we are going to engage in geo-engineering and massive biological reprogramming, the legal model of the Free Software Foundation [5] is probably the best place to start, if not the only one that will be safe and sustainable. 1. Quirks and Quarks: Using DNA to Save the World, <http://www.cbc.ca/quirks/episode/2012/11/24/november-24-2012/#4> 2. Wikipedia: Synthetic Biology, <https://en.wikipedia.org/wiki/Synthetic_biology> 3. The Verge: Apple finally gets its patent on a rectangle with rounded corners, <http://www.theverge.com/2012/11/7/3614506/apple-patents-rectangle-with-rounded-corners> 4. End Software Patents, <http://endsoftpatents.org/> 5. Patrick Truchon, Free Software, <http://ptruchon.pagekite.me/wiki/doku.php?id=freesoftware> ## Math Games: Simulators and Instruments Posted by Patrick on September 6, 2012 I’m in the process of changing my mind about a topic I don’t know much about: the gamification of learning, in particular, the gamification of mathematics learning. Here’s my preconceived idea about math games: it’s sugar coating. There’s something you have to practice; it’s hard, and you’re not very interested. So to make it less painful, we’ll add points you can earn for each correct answer (or better yet, monsters you can defeat by factoring polynomials, with cool graphics and stuff). Hopefully, you’ll want to sit in front of your computer 10 minutes longer than with your textbook to practice your math. In my opinion: • The math in these games has nothing to do with the context of the game (which is often true of textbook questions too mind you [2]). • These games do nothing to foster internal motivation and appreciation of mathematics. • They focus on skills, not mathematical and conceptual thinking. • They are really just fancy worksheets with blinking lights and noise to keep you awake. I’m realizing now that that idea is a bit of a Straw Man. In a Webinar [1] he presented back in January, Keith Devlin (@profkeithdevlin) clarifies what math games have been, are, and can be. He uses the analogy of a flight simulator, or a music instrument to convince us that well designed math games could be invaluable tools to help students investigate abstract ideas in a world that makes them more concrete. He doesn’t want math games to replace instructions, instead he wants them to be a complimentary tool of discovery, where students can think mathematically without having to worry about the notation. In one of his previous books, Devlin argues that what makes math hard is its level of abstraction. The logic is often simpler than that of a soap opera. [3] Now to extrapolate a little bit from Devlin’s presentation, it seems to me that a good way to teach mathematics would be to: 1. Use well designed games to explore mathematical thinking and logic in a context that is intuitive and non-symbolic. 2. Slowly introduce symbols and layers of abstraction. 3. Practice on synthesizing these two aspects. 4. Repeat with new concepts… There’s a catch though, which Devlin mentions briefly: It makes no sense to test students on the second part if they are still on the first part. Can you imagine if part of the assessment process was to have students play a game so we could see what they struggle with? 1. Keith Devlin, Game-Based Learning Webinar Recording <http://www.instantpresenter.com/WebConference/RecordingDefault.aspx?c_psrid=E955DD80854D> 2. Dan Meyer, [PS] Critical Thinking, <http://blog.mrmeyer.com/?p=12582> 3. Keith Devlin, The Math Gene, <http://www.amazon.com/The-Math-Gene-Mathematical-Thinking/dp/0465016197> ## Driving Me Nuts Posted by Patrick on February 16, 2012 Yesterday, Peter (@polarisdotca) asked this question: Why does tying knot in strip of paper form a regular pentagon? Why not 6, 7,…? Why regular? Anyone have intuitive explanation? #wcydwt [1] Being a rock climber, I like knots; I DEPEND on knots! Being a math and physics teacher, I like puzzles; I DEPEND on puzzles. So naturally, this one peaked my interest. Here’s what I’ve got so far: The first step was to recreate the experiment, so I started by making a regular knot (actually called the “Overhand knot” [2]) with a strip of paper: Then, I tried to flatten it as tightly as possible without breaking it: It’s a little loose at the “exit points”, but we can easily imagine that the “ideal case” would indeed be a regular pentagon (regular because all sides are the same lengths; pentagon because it has five sides). So now: why is that? Intuitively, I think there can only be five sides because there are three folds and two exit points, for a total of five. That’s how the knot is made, by folding the rope three times onto itself: Here’s what it looks like when unfolded: Three of the sides are from folding, and two of the sides are just the edge of the strip of paper, which correspond to the exit points. Why does it have to be regular though? Is it because that’s the most compact configuration? Is this shape the solution to some optimization problem (like greatest ratio of SurfaceArea-to-Perimeter, which minimizes some energy function or something…) My next question was: how would a Figure-Eight knot [3] behave? I was not only interested in this knot because I probably use it more often than the overhand knot, but because my trick to make it is to start it like an overhand knot, then finish it an extra half turn later (ie. that would add an extra fold in the strip of paper!) Could this lead to a 6-sided figure? Here it is loose: And flattened: Yeap: four folds and two exit points. Here’s the weird thing though: one of those exit point is not even “connected” to the other sides: Why is that?! Also if I could make it perfectly, would it also be a regular polygon? or is it intrinsically elongated? Thanks Peter! This puzzle is driving me nuts! 1. Peter Newbury’s Tweet: 2. Animated Knots, Overhand Knot, <http://www.animatedknots.com/overhand/index.php> 3. Animated Knots, Figure 8 Bend, <http://www.animatedknots.com/fig8join/index.php> Posted in Uncategorized \| Tagged: \| 1 Comment » ## CO2 Levels (a depressing story) Posted by Patrick on November 27, 2011 A few days ago, I listened to an ABC radio podcast on All in the Mind entitled “The case for moral enhancement”. [1] I was expecting the ethical minefield of eugenics to be discussed (which it was), but I was surprised by the turn of the conversation towards the end: 0ne of the reasons why we’d want to enhance our moral compass is because we didn’t evolve to deal with problems that affect the entire population of the planet. In particular, one of the professors grimly said that “it’s wishful thinking to think that people are going to voluntarily deal with climate change”. Heavy stuff! Today it was CBC radio’s Quirks and Quarks turn to tackle the issue of climate change. [2] Again, it was nothing short of depressing. Very… Depressing… One of the guests said that our inability to deal with the problem not only means that we’ll face catastrophic repercussions, but it also says something pretty grim about ourselves: “Can we not deal with an ethical issue about the lives of billions of people around this planet?” Because I like to understand the information contained in graphs, I clicked on the one posted on the Quirks page [2], which led me to its source on wikipedia [3], which lead me to the source of the raw data [4]. I decided to import that data into a spreadsheet to see what information I could extract from it. Using two simple functions, and a method called “least squares” [5] to scale them properly, I managed to find the proper parameters that model the CO2 concentration as a function of time. Visually, the orange graph (the model) follows the blue graph (the data) pretty well, so the model I found is pretty good (within that range of time anyways). I found the equation of the model (the orange graph) to be: $\LARGE \text{C} = 270+2.7\sin\big(2\pi(t-0.06)\big)+45 \cdot 2^{(t-1958.208)/37}$ It looks complicated, but there’s basically three pieces to this function, each with their own particular meaning. The first part is just the number 270. What it means is that if we go back in time by more than a few hundred years, the average CO2 concentration in the atmosphere would have been around 270 ppmv (compare that to today’s 390 ppmv !) The second part is responsible for the oscillation of the concentration due to seasons. The number 2.7 in front of the sine function means that the concentration increases from its average value by 2.7 ppmv in the winter and decreases by 2.7 ppmv in the summer. So the total variation (of about 5.4 ppmv) is pretty small (compared to the average increase). The third part is what we’re responsible for. It says that the difference in CO2 from the ancient average of 270 ppmv will double every 37 years. This is a bit tricky so here it is again: if you look at the concentration of CO2 today and subtract that from what it was hundreds of years ago, that difference will double in 37 years time. For example: • The concentration was around 315 ppmv in 1958, which is a difference of 45 ppmv from 270 ppmv. • 37 years later (in 1995), the concentration was 360 ppmv, which is a difference of 90 ppmv from 270 ppmv (double the previous difference of 45 ppmv) • Another 37 years later (in 2032), the concentration should be (if the trend continues) 450 ppmv, because there should be a difference of 180 ppmv from 270 ppmv ( double the previous difference of 90 ppmv) • And in 2069? 720 ppmv, because it’ll be 360 ppmv more than 270 ppmv… So according to this model, if the trend continues (ie, we keep doing what we’re doing now), the atmosphere will reach levels of CO2 comparable to that of the Eocene–Oligocene extinction event 34 million years ago (which were around 760 ppmv) [3] in a time scale of a few 37-year periods! And I thought the podcasts were depressing… The next graph shows this extrapolation in both direction. The model (in orange) is graphed (without the seasonal variations) between 1750 and 2100 with the actual data (in blue). The future looks completely crazy, but other data suggest that the past is actually pretty spot on. [3] Now, to be fair, the assumption that “we keep doing what we’re doing now” implies at least two things that are very unlikely: 1. Our population will continue to grow exponentially. 2. Our resources of fossil fuels will continue to match our growing demands. In reality, we’ll either find ways to turn this around, or we’ll suffer from other problems that will curb our population explosion and our ability to consume so much fossil full. One thing is certain: we can’t let that orange curve go that high. 1. All in the Mind, The case for moral enhancement, <http://www.abc.net.au/rn/allinthemind/stories/2011/3360688.htm> 2. Quirks and Quarks, The Rocky Road to Durban, 3. Wikipedia, Mauna Loa Carbon Dioxide-en.svg <https://en.wikipedia.org/wiki/File:Mauna_Loa_Carbon_Dioxide-en.svg> 4. NOAA ESRL DATA, <ftp://ftp.cmdl.noaa.gov/ccg/co2/trends/co2_mm_mlo.txt> 5. Wikipedia, Least Squares, <https://en.wikipedia.org/wiki/Least_squares> Posted in Uncategorized \| Tagged: , \| 1 Comment » ## Conceptualizing Physics Posted by Patrick on June 27, 2011 The following two videos address one of the questions that I ponder the most: what are the best ways to help students understand concepts in mathematics and physics? Although both speakers reach similar conclusions, they each reveal many other insights that are also very important. Here are a few lessons that I take from each. Derek Muller (@veritasium) shows that: • Students new to physics come with misconceptions they think are true (about the world of physics). • Because of this, they don’t pay their utmost attention to the videos (which might as well be traditional lectures). • Which causes them to think that what is being presented is the same as what they think. • So they don’t learn anything. • While getting more confident in their misconception. But his interviews with the students also showed something else: • Students are bad at judging how much a video (or lecture) is helping them learn. This part I found very interesting. Indeed, the “clear” videos didn’t help them learn as much as the “confusing” ones. Although Derek doesn’t make that leap, I think this applies equally well to traditional classroom lectures. Further more, it also suggests that students’ evaluations of teachers are (at best) an incomplete metric of teachers effectiveness, if not a completely bad one. Of course, it doesn’t mean that the way to help students is to be as confusing as possible, but now I’m wondering if the good feedback I tended to get about my teaching was such a good thing… In essence, Derek says that for students to really learn physics, they have to engage and struggle with the concepts on their own terms. Delivering information is not sufficient for learning. Dr. Eric Mazur (@eric_mazur) also comes to the same conclusion but in the context of the lecture hall: This time, Dr. Mazur breaks down learning into two parts [3]: 1. Delivery of information 2. Synthesis of information Traditionally, classroom lectures have focused on the first part, but it is the second part that constitute true learning. Thus, he assigns readings ahead of time (or finds other ways for students to get the information before they enter the classroom) so that students can spend more time in class synthesizing information instead of being passive recipients. Dr. Mazur also reaches a second conclusion: Conceptual understanding leads to good problem solving abilities, but good problem solving abilities doesn’t necessarily implies conceptual understanding. This strikes at the heart of traditional assessment methods. Simply giving problems to solve doesn’t discriminate between those who understand what’s going on, and those who have memorized an algorithm they don’t really understand. In my practice, I always try to emphasize the “why” of things over the “how” (mainly because I have a bad memory myself). It’s encouraging to see research that validates that philosophy, and enlightening to see the various methods used by these inspiring educators. • Update: I added a reference relating to Howard Gardner that is very relevant to this post. [4] • Update 2: I added a reference to an article describing the results of team of researchers at UBC that supports what Dr. Mazur is doing. [5] 1. Veritasium, Khan Academy and the Effectiveness of Science Videos , 2. Eric Mazur, Memorization or understanding: are we teaching the right thing? 3. Mazur Group Publication, Peer Instruction: Making Science Engaging, <http://mazur.harvard.edu/publications.php?function=display&rowid=538> 4. The Daily Riff, Misconceptions About Learning & Teaching <http://www.thedailyriff.com/articles/howard-gardner-shares-his-just-released-97.php> 5. ScienceNOW, A Better Way to Teach? <http://news.sciencemag.org/sciencenow/2011/05/a-better-way-to-teach.html> ## How to Imagine More Than 3D Posted by Patrick on August 18, 2009 This summer, a friend of mine and I were talking about science fiction, and how one interpretation of quantum mechanics (as we understand it) says that everything that can happen does in parallel universes. In his book, “The Elegant Universe”, Brian Green attempts to explain in layman terms the ideas of String Theory. Green also made a good documentary about this subject. In the “Multiple Dimensions” segment of the documentary [1], he explains that the mathematics of String Theory requires 6 extra dimensions to the 3D of space and 1D of time that we feel, and that the only difference between these extra dimensions and the three we know is their “shape”. I’ve watch this documentary several times over the past few years, and I’ve never really been able to “picture” these extra dimensions in my mind, until (maybe) today. Rob Bryanton, author of “Imagining the Tenth Dimension” has this really clear animation on his website [2]. Basically: • Then draw another point somewhere else and connect them to get a line in 1D. • Then draw another point somewhere off the line to get a different direction thus creating a 2D space. • Then instead of imagining “height”, stay in this flatland and imagine a “worm whole” that takes you from one point on this sheet to another without traveling on the sheet. You’d have to travel in the 3rd dimension to do that. • Now imagine this 3D environment as if it were a point traveling in a straight line (through time), that’s the 4th dimension, which looks like the 1D line from above except the “points” it connects are actually 3D spaces. (Now we’re in 4D) • If you imagine an alternate future to the one you actually have, you’re imagining a different ending point which is off the line your drew, so you’re creating a 2D space of possible universes (We’re now in 5D). • If you jump from any of those points in these possible universes without traveling in this 2D space of possibilities, you’d need an extra dimension (We’re now at 6D). • Now imagine all of these possible universes with all their different endings as a single point. It seems that we can’t imagine much more than that. I mean, what else is there than the sum of all possible universes? Well, all these universes started from the same Bigbang, so now we can imagine a different Bigbang with all its different possible endings. We draw a line between these two sets of universes to get a line in 7D. • We imagine another Bigbang and its endings off that line to get a 2D space of different Bigbang-with-alternate-endings points (Now we’re in 8D). • Again, if we travel from one of these points to another without touching the surface of that 2D space, we’re using an extra dimension to do it (Now we’re in 9D) • Finally, we’re done. We have imagined all possible beginnings, with their respective possible endings, and every ways to travel between them as a 9D space. We can step back and look at that space as if it were a point now residing in 10D. This seems to be a very different picture than the one Green tried to explain in the Nova documentary, but in the “Parallel Universes” segment Green explains how the extra dimensions maybe used to contain the other universes. Maybe, they’re all talking about the same thing then… I really have no idea though. As much as I love thinking about all that stuff, I really have no expertise in any of it. So, if any of you ever become string theorist, please invite me for lunch one day to tell me what’s really going on. 1. Nova, The Elegant Universe, <http://www.pbs.org/wgbh/nova/elegant/program.html> 2. Imagining the Tenth Dimension, <http://tenthdimension.com/medialinks.php> ## Ideas Too Powerful to Handle? Posted by Patrick on June 17, 2009 Pre-reflection Today in Math 11 we will be watching a documentary [1] about four scientists who had such powerful ideas that they went crazy (some of them even committed suicide). Before we find out more about what these people saw, I’d like you to think about the following questions. • Scientific laws govern (or describe?) how the universe operates. These laws are expressed mathematically. What do you think is the relationship between mathematics and the universe we live in? • Do you think mathematics is discovered or invented? Think of the slope of the tangent at a point (using the slope of a secant when we let ∆x -> 0). This idea is at the centre of Calculus. Was it invented or discovered? Think of a computer algorithm (which is just a complicated set of logical operations). Are computer programs invented or discovered? • Do you believe there is an built-in limitation to mathematics’ ability to explain (or describe?) the universe? Do you think there’s a built-in limitation to what computer programs can do? • Do you believe there is an built-in limitation in our (human) ability to understand mathematics and its consequences. • Do you think a perfectly logical being could deduce all the laws of mathematics, or does it take something more (intuition, imagination, etc…) ============================================= ============================================= Preview of five great mathematicians, physicists, and philosophers: Georg Cantor (1845-1918) [2] realized that there are different “sizes” of infinities. In fact, he proved that there is an infinity of infinities. For example, there are an infinite number of integer numbers, but between any two intergers, there’s an infinite number of fractions, and between any two fractions, and infinite number of irrational numbers… Cantor tried his whole life to find the relationship between the sizes of infinite sets in the form of what is now called the “continuum hypothesis”. He never succeeded to prove or disprove it. Ludwig Boltzmann (1844-1906) [3] was the founder of statistical mechanics and thermodynamics. He shook the world of physics because instead of assuming a deterministic model of the universe, he allowed for probabilistic laws. He pioneered the concept of entropy, and his theories gave time a direction. “Boltzmann had in essence, captured mortality in an equation”. Kurt Gödel (1906-1978) [4] came up with two “incompleteness theorems” which prove that any complex systems of arithmetic has inherent limitations. In these systems, there will always be true statements which can’t be proven true, and it’s impossible to know which one they are. Alan Turing (1912-1954) [5] made Gödel’s abstract ideas more concrete by thinking about the inherent limits of computers (since they are bound by logic). All four of these men felt a deep connection between the abstract questions they were investigating and the big questions of consciousness and “ultimate reality”. In contrast, Richard Feynman (1918-1988) [6], one of the greatest quantum physicists, was very comfortable with the unknowable and didn’t do physics to discover the “ultimate reality”, but simply to “find out more about the world”. [7] The videos: Watch BBC’s Dangerous Knowledge [1] first and end with Feynman’s. [7] • How are your opinions about mathematics, logic, and human consciousness clearer, or more confused now? • Compare and contrast Cantor, Boltzmann, Gödel, and Turing’s attitude about their questions with Feynman’s. What is your opinion on how a “good scientist” should approach a problem? 2. Wikipedia: Georg Cantor, <http://en.wikipedia.org/wiki/Georg_Cantor#Continuum_hypothesis> 3. Wikipedia: Ludwig Boltzmann, <http://en.wikipedia.org/wiki/Boltzmann> 4. Wikipedia: Incompleteness Theorem, <http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems> 5. Wikipedia: Alan Turing, <http://en.wikipedia.org/wiki/Alan_Turing#University_and_his_work_on_computability> 6. Wikipedia: Richard Feynman, <http://en.wikipedia.org/wiki/Richard_Feynman> Posted in Uncategorized \| Tagged: \| 2 Comments » ## I, Robot and Game Theory Posted by Patrick on April 8, 2009 Cover of I, Robot illustrates the story “Runaround”. I, Robot , by Isaac Asimov [1], is a collection of nine short stories where robots and positronic computers follow three laws [2] supposed to protect humans: 1. A robot may not injure a human being or, through inaction, allow a human being to come to harm. 2. A robot must obey orders given to it by human beings, except where such orders would conflict with the First Law. 3. A robot must protect its own existence as long as such protection does not conflict with the First or Second Law. The theme of the movie was probably based mostly on the last story, called The Evitable Conflict [3]. In this story, powerful positronic computers around the world have the task of optimizing the world’s economy. Naturally, such a complex problem cannot be solved without making trade offs and sacrificing the well being of some individuals for the greater good. As such, the machines come to generalize the First Law to mean: “No robot may injure humanity or, through inaction, allow humanity to come to harm.” The three laws, which were supposed to prevent robots from taking over, in essence, dictate them to do so (for our own good). In the movie, the detective uncovers this scheme soon enough, and with the help of a non-three-laws robot, manages to shutdown the main computer in time. In the book, however, humans realize that the solutions the machines are implementing are the best, and any deviation from their scheme would leave us worse off overall. And so, they come to accept the benevolent (and selfless) dictatorship of the machines. When I read this story, I wondered if a “best solution” could exist to such complex problems as “optimizing the world’s economy”. I was recently reminded of this question after watching political scientist Bruce Bueno de Mesquita speak at TED [4] about how game theory [5] can be used to predict the most likely outcome of a situation where many players are trying to optimize their own self interest. In the language of game theory, it seems that Asimov’s machines were finding some kind of equilibria. But with all the machines cooperating not for their own self interest, but for that of humanity, would game theory be the proper tool to use? Finally, Cory Doctorow puts a spin on things with his I, Robot [6], and imagines a world divided into two: In the West, robots are bound by the three laws; in the East, the are not. Maybe because of this division, his three-laws-bound robots don’t seem to generalize the first law. His non-three-laws robots, however, open up a whole new set of possibilities… 1. Wikipedia: I, Robot, <http://en.wikipedia.org/wiki/I_robot> 2. Wikipedia: Three Laws of Robotics, <http://en.wikipedia.org/wiki/Three_Laws_of_Robotics> 3. Wikipedia: The Evitable Conflict, <http://en.wikipedia.org/wiki/The_Evitable_Conflict> 4. TED: , <http://www.ted.com/index.php/talk/bruce_bueno_de_mesquita_predicts_iran_s_future.html> 5. Wikipedia: Game Theory, <http://en.wikipedia.org/wiki/Game_theory> 7. Wikimedia File, <http://en.wikipedia.org/wiki/File:I_Robot_-_Runaround.jpg> ## Hiding money… Posted by Patrick on March 12, 2009 How much money do you think you’d be able to hide in your room? What do you think 1 million US$looks like compared to 1 billion US$ or even 1 trillion US\$ ? 1. Pagetutor, <http://www.pagetutor.com/trillion/index.html> ## Mandelbrot Set (the song)… Posted by Patrick on February 26, 2009 This started with a song by Jonathan Coulton [1] that I didn’t really understand. After exploring a few wikipedia and youtube pages, I thought I’d share my results so that you too can appreciate the talent of this geeky musician…The idea is simple: What is the shape below, where does it come from, and how is it drawn? Picture of the Mandelbrot Set from Wikimedia Commons [2] First, here are a few things to notice about this picture: it’s a fractal, which means that if you zoom in on the edge of the shape, you’ll always see some kind of spiky “structure”, no matter how close you get. The animation that follows illustrates this very well. From Wikipedia: Regardless of the extent to which one zooms in on a Mandelbrot set, there is always additional detail to see. During the twelve-second zoom in the animation [below], the set becomes magnified eleven-million fold. Thus, assuming the first frame is life-size at 45 mm across, a carbon atom would comprise 36 pixels in the final frame. [3] 11 million fold zoom in. From Wikipedia [3] Also, you’ll notice that the axes are not the typical x-axis and y-axis we are used to seeing in a Cartesian coordinate plane. While the horizontal axis holds the good ol’ real numbers we all know, the vertical axis holds weird imaginary numbers. These numbers are called imaginary because they are no-where to be found on the real number line, but they are still useful (somehow). Indeed, these numbers arise from trying to find what number multiplied by itself gives -1 ? The same question could be framed algebraically as: What is x so that: $x^2 = -1$ Clearly, x = 1 doesn’t work, but neither does x = -1 since two negative numbers multiplied together give a positive number. So, since no real numbers answer that question, mathematicians invented (or discovered?) an imaginary number that would do it, and they called it “i”. So now we have: $i^2 = -1$ meaning that: $i = \sqrt{-1}$ To understand how the Mandelbrot fractal is painted, we have to understand how to multiply and add imaginary and real numbers together. By adding real and imaginary numbers (as if they were different terms) we can make complex numbers that can be plotted in the complex plane. For example, the number 3 + 2i would be plotted as the point (3, 2).To multiply two complex numbers together, we use the same algebraic rules, but we keep in mind that i squared is -1. For example: $i (a+ib)^2 = (a+ib)(a+ib)$ $i (a+ib)^2 =a^2 + 2iab + i^2b^2$ $i (a+ib)^2 = a^2 - b^2 - 2iab$ Now we are ready to describe the rule that governs the drawing of the Mandelbrot Fractal. The idea is to ask if individual points should be painted black, or left white (ie, ask if the point is in the Mandelbrot set or not). To find out, take the point you want to test (let’s call it “c”) and square it. Then you add c to the result, and square it again. Then add c and square again. And so on. If you can do this forever without the answer going to infinity, then that point is in the Mandelbrot set and should be painted black. Mathematically, I think this could be said like:let: $z_1 = c$ $z_n = z_{n-1}^2 + c$ If $\left\| z_\infty \right\| < \infty$ , then c is in the Mandelbrot set. After you’ve “tested” all points in the plane, you get the Mandelbrot Fractal… An easy example of this would be to start with a real number. Imagine c = 0.2 $z_1 = 0.2$ $z_2 = z_1^2 + 0.2 =0.24$ $z_3 = z_2^2 + 0.2 = 0.2576$ $z_4 = z_3^2 + 0.2 = 0.2664...$ $z_5 = z_4^2 + 0.2 = 0.271...$ $z_6 = 0.273...$ $z_7 = 0.275...$ $z_8 = 0.276...$ $z_9 = 0.276...$ and so on… Since the sequence doesn’t blow up to infinity, the point 0.2 is in the Mandelbrot set. The point i is also in the Mandelbrot set: $z_0 = 0$ $z_1 = i$ $z_2 = i^2 + i = -1 + i$ $z_3 = (-1 + i)^2 + i = \left( (-1)^2 - 2i - 1 \right) + i = -i$ $z_4 = (-i)^2 + i = -1 + i = z_2 ...$ But the point 1 isn’t: $z_1 = 1$ $z_2 = 1^2 + 1 = 2$ $z_3 = 2^2 + 1 = 5$ $z_4 = 5^2 + 1 = 26$ $z_5 = 26^2 + 1 =$ BIG Finally, it’s time to appreciate the song. To further help visualize the lyrics, a Cornell University student made a really cool “black board animation” . Enjoy! Discretion Advise: The following song contains some coarse language. “Mandelbrot Set” by Jonathan Coulton [1], is licensed Creative Commons [4]	2013-06-19T07:51:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 28, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4462965428829193, "perplexity": 1289.7856044382797}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368708144156/warc/CC-MAIN-20130516124224-00009-ip-10-60-113-184.ec2.internal.warc.gz"}
https://pos.sissa.it/256/073/	Volume 256 - 34th annual International Symposium on Lattice Field Theory (LATTICE2016) - Nonzero Temperature and Density Viscosity of the pure SU(3) gauge theory revisited A. Pasztor,* S. Borsanyi, Z. Fodor, M. Giordano, S.D. Katz, S. Mages, A. Schaefer, B. Toth *corresponding author Full text: pdf Pre-published on: January 30, 2017 Published on: March 24, 2017 Abstract We compute the Euclidean correlators of the energy-momentum tensor in Yang-Mills theory at finite temperature at zero and finite spatial momenta with lattice simulations. We perform continuum extrapolations of these quantities using $N_{\tau}$ = 10,12,16 lattices. We use these correlators to estimate the shear viscosity of the gluon plasma in the deconfined phase DOI: https://doi.org/10.22323/1.256.0073 How to cite Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete. Open Access Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.	2020-12-05T04:56:47	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5003735423088074, "perplexity": 5264.662345483141}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141746320.91/warc/CC-MAIN-20201205044004-20201205074004-00102.warc.gz"}
https://read.dukeupress.edu/demography/article/58/3/901/173291/Stop-Go-What-Can-We-Learn-About-Family-Planning	## Abstract We revisit the discussion on family limitation through stopping and spacing behavior before and during the fertility transition with a sample of 12,800 settler women's birth histories in nineteenth- and twentieth-century South Africa. Using cure models that allow us to separate those who stop childbearing from those who continue, we find no evidence of parity-specific spacing before the transition. We do find evidence of non-parity-based birth postponement before the transition. Increased stopping and parity-independent postponement characterized the beginning of the fertility transition, with increased parity-specific spacing following later in the transition phase. ## Introduction Analyses of the drivers of fertility transitions often frame the discussion in terms of whether a society is ready, willing, and able (RWA) to begin limiting conception to limit family size (Coale 1973; Lesthaeghe and Vanderhoeft 2001: chapter 8). Ready implies that the economic, social, and cultural climate has an impact on a society's preference for children. Yet, although people may see the advantage of having fewer children, they are willing to limit family size only after that preference has become the norm in their society. Finally, they are able to implement actions to limit family size only if they know effective techniques. Typical evidence of readiness, willingness, and ability includes feelings regarding having a certain number of children (e.g., Fisher 2000a, 2000b; Fisher and Szreter 2003; Szreter and Fisher 2010: chapter 6) or knowledge of the kinds of birth control available (e.g., McDonald and Moyle 2018). Our ability to investigate these issues, however, is limited. McLaren (1984:3) noted that purely demographic studies cannot directly measure the contextual environment that would inform our knowledge of RWA. We may not be able to definitively outline the circumstantial impact on readiness, we may never know willingness without access to individual details, and we may not know ability without access to explicit mentions of it. However, an empirical exploration of birth histories can shed light on characteristics of the fertility transition. Whether and how quickly couples continue to have children following a first birth determine the final number of children they have. Changes to these patterns do inform our understanding of the fertility transition. A robust debate in the historical demography literature concerns whether the first fertility transition was characterized by an increase in stopping behavior or an increase in the intentional spacing of subsequent births (Anderton and Bean 1985; Guinnane 2011; Knodel 1987). The dominance of one theory over the other has important implications for understanding the causes of the fertility transition. If the transition was dominated by stopping, it suggests an innovation in the approach to birth control that was absent before the transition as the main mechanism through which the transition was implemented: an increase in ability, with readiness and willingness potentially already present. Conversely, if spacing dominated the transition, it suggests increased use of known behaviors to adjust family size given some change in preferences: an adaptation in response to readiness and willingness, with ability already present (Carlsson 1966). The consensus for many years had been that the transition was characterized and perhaps even defined by a new awareness of the ability to choose and manage family size as couples moved away from natural fertility (Coale 1986). New lower fertility rates were brought about by ceasing childbearing when the desired family size had been reached (Knodel 1987; Knodel and van de Walle 1979; van de Walle 1992), and it appeared that the fertility transition was implemented through birth control innovation. Later studies revisited this question. A substantial literature has argued for a change in intentional spacing behavior as a feature of the transition, thereby suggesting that the transition was a form of adaptation in response to a changing physical, social, economic, and cultural environment (Anderton and Bean 1985; Crafts 1984; David et al. 1988; David and Mroz 1989; Dribe et al. 2017; Garrett et al. 2001:288; Haines 1989; Szreter and Garrett 2000). These studies suggest that we think beyond intentional behavior and beyond the fertility transition as being a structural break in birth control behavior (Szreter and Garrett 2000). Indeed, evidence points to geographic, economic, and social differences in fertility rates before the transition (Anderton and Bean 1985; Bengtsson and Dribe 2006; Dribe and Scalone 2010). Some researchers have argued for evidence of pretransitional parity-dependent fertility control through spacing (Anderton and Bean 1985; Cinnirella et al. 2017; David et al. 1988; van Bavel 2004; van Bavel and Kok 2010). Most have used a variety of techniques assuming that observed fertility outcomes are intentional (Johnson-Hanks 2007; Timæus and Moultrie 2008, 2013). Yet Fisher (2000a, 2000b), Fisher and Szreter (2003), and Szreter and Fisher (2010:236–242) found little communication between partners regarding family size outcomes, although they did find that partners used techniques to avoid conception—techniques that originated long before the transition. Specifically, Timæus and Moultrie (2008), Moultrie et al. (2012), and Timæus and Moultrie (2013) discussed the importance of unintentional fertility control through postponement due to circumstances unrelated to family size as a third way that fertility outcomes may be eventuated. They noted that take-up of this idea in studies of historical fertility transitions has been fairly limited and that ignoring this option may result in misidentifying parity-dependent spacing both before and during the transition (Timæus and Moultrie 2013). The debate remains far from resolved, and our country-wide data set of complete birth histories of White South African women from 1835 to 1950 allows us to enter the fray. Settler South Africa was in many respects similar to other settler communities on the periphery. South Africa during the nineteenth century was largely rural, land-abundant, and labor-scarce, much like the frontiers in the United States and Canada and like much of Australia and New Zealand. Industrialization began late in the nineteenth century, taking off in the early twentieth century. The fertility transition among the settlers in South Africa began in the late 1870s to women born in the 1850s, a timing similar to other settler fertility transitions as well as several European transitions (Cilliers and Mariotti 2019). Our econometric technique is a mixed population model, known as a cure model in the biomedical literature. Cure models are increasingly popular in demographic analyses because they take into account that some women may never go on to experience an event, a point that traditional event-history models do not consider. Our goal is modest. We use our data to analyze features of fertility behavior before and during the demographic transition in South Africa. We remain agnostic about intentions regarding family size beyond what our estimation technique is able to provide. We stratify our sample into four periods: 1835–1859, 1860–1884, 1885–1909, and 1910–1950. Looking at only those women who have had at least one child, we find that before the transition, a woman's physiology was the prime determinant of the space between her consecutive children as well as when she had her final child. That is, age and fecundity mattered most. Social and economic characteristics arguably played a small role in all three types of fertility behavior: there is some evidence of postponement but no evidence of achieving desired family size through stopping or spacing. The incidence of stopping and postponement began to increase from 1885 onward, and parity-dependent spacing increased from 1910 onward. Crucially, this means that we do not find evidence of parity-dependent spacing before the fertility transition. Quite the contrary, women at high parities before the transition had the least variation in birth interval length, which we interpret as evidence of higher fecundity. Although it is by now very clear that pretransitional couples were able to affect the timing of conception to avoid an inconveniently timed birth, they were not consistently using this strategy to control ultimate family size. Postponement will ultimately affect final family size because of women's finite childbearing window, but it does not imply conscious family planning. Regarding “ready, willing, and able,” the evidence we find points to early readiness and ability at the onset of the transition, followed by an increase in willingness, which led to community-wide longer birth intervals later. ## Intentional and Unintentional Family Size Control If we can show that women/couples intentionally stopped having children at lower parities during the transition, then we will have some evidence of an improved ability to stop childbearing relative to pretransition periods. This evidence would suggest that a preference for smaller families may have always existed but that the transition was the first time that large sections of the population were able to successfully implement strategies to prevent childbearing (Carlsson 1966; Okun 1994). If we do not find evidence of increased stopping—and instead see evidence of increased time between successive births—then, the literature argues, we are simply seeing a change in preferences being implemented with birth control techniques that humankind has always known. Given women's finite childbearing window, increased birth spacing will also result in lower numbers of children ever born (Anderton and Bean 1985). Both concepts—stopping and spacing—allude to conscious efforts to limit final family size, referred to as parity-dependent fertility decisions. Timæus and Moultrie (2008) noted a third possibility: postponing the birth of a child, not because of the number and ages of existing children but rather because of a preference not to have a child under the current circumstances (e.g., war, famine, health, other uncertainty, educational attainment, career, and so on; Johnson-Hanks 2004). The investigation of birth stopping and spacing and, later, postponement before and during the demographic transition has evolved tremendously in the 60 or so years that demographers have been studying historical fertility. Methodological innovations, improvements in computing power, and access to better data have allowed a revisiting of this issue, and the debate remains far from resolved. The earliest investigations concluded that couples made little attempt to limit fertility before the transition and that any deviations of the pretransition fertility rates between groups had more to do with factors such as cultural practices and seasonal migration (Henry 1961; Knodel and van de Walle 1979). It followed that the fertility transition must have been driven largely by an intentional increase in stopping rates once couples had achieved their desired family size. The Coale and Trusell m index (Coale and Trussell 1974) was instrumental in reaching this conclusion. The index, however, is limited in that it was constructed specifically to detect parity-dependent stopping rather than spacing (Knodel 1987; Okun 1994). Okun (1994) and Guinnane et al. (1994) noted that the Coale and Trussell index cannot accurately identify small proportions of fertility controllers in a population. Family limitation through spacing may well have been taking place but could not be detected. David et al. (1988) subsequently developed the cohort parity analysis technique specifically to identify spacing behavior, yet Okun (1994) noted that it, too, is unreliable in certain cases. This technique also has large data requirements. Data advances, particularly the use of family genealogies and family reconstitution data, allow a more precise look at the length of time between consecutive births both before and during the fertility transition. A growing literature accepts that the transition was at least in part characterized by changes to birth interval length and not just by family limitation (Anderton and Bean 1985; Crafts 1984; David and Mroz 1989; Dribe et al. 2017; Garrett et al. 2001:288; Haines 1989; Reher et al. 2017; Reher and Sanz-Gimeno 2007; Szreter and Garrett 2000).1 Another literature has examined evidence of parity-specific spacing before the transition (Cinnirella et al. 2017; van Bavel 2004; van Bavel and Kok 2010). This effort is important: evidence of spacing to limit family size would clearly show that couples already knew how to achieve their desired family size and that they were doing so before the transition. The conclusion would then be that the transition itself was a result of changing family size preferences in response to a change in external conditions in the late-nineteenth century. Exploiting the use of event-history models—in particular, Cox proportional hazards models—and using family reconstitution data, these studies all found evidence of parity-dependent control: longer birth intervals at higher parities, after controlling for age, before the transition.2 Moreover, they found differences in birth interval lengths based on occupation, region of residence, religion, language, and other variables that are unlikely to change much over the adult lifetime. The conclusion is that couples were able to limit family size before the transition. A limitation of the search for pretransitional spacing is that it contains a sometimes implicit assumption that the observed outcome of smaller family sizes and longer birth intervals must be driven by an intention to limit family size. The debate doesn't allow for a change to birth interval lengths driven by something other than parity dependence (Johnson-Hanks 2007; Moultrie et al. 2012; Timæus and Moultrie 2008). Furthermore, the debate assumes some kind of explicit agreement within a partnership on the intended size of the family, something that Fisher (2000a, 2000b), Fisher and Szreter (2003), and Szreter and Fisher (2010: chapter 6) found not to be the case, even though they found evidence of pretransitional birth control. In a recent dramatic twist in the debate, Clark and Cummins (2019) argued that the parity-dependent control that Cinnirella et al. (2017) observed is an artifact of the estimation method and that no parity-dependent control exists in pretransition England.3 Offering further support for this argument, Clark et al. (2019) argued that the unexpected arrival of twins led to an increase in the total number of children by almost one, concluding that couples did not respond to the additional unexpected birth. Separately, Yamaguchi and Ferguson (1995), Li and Choe (1997), Alter et al. (2007), Gray et al. (2010), and Alter (2019) argued that Cox proportional hazards models are inappropriate for this type of event-history analysis because the technique assumes that all women will at some point experience a subsequent birth when in reality, some stop having children. The suggestion is that the data may not satisfy the proportionality assumption needed to obtain unbiased estimates using the Cox model. A debate that began about whether the transition was driven by stopping or spacing, and that has not yet ended in consensus, has shifted to an investigation of whether couples practiced conscious spacing before the transition. This second debate has culminated in substantial disagreement on the appropriate use of methodology given limitations to family reconstitution data. It is at this stage in the debate that our study enters the fray. With data spanning 100 years and armed with event-history models that look simultaneously at stopping, spacing, and postponement, we investigate fertility outcomes both before and during the transition.4 ## Data We use South African Families (SAF), a genealogical registry of all settler families living in the eighteenth, nineteenth, and early twentieth centuries.5 It is one of very few registries in the world that is known to have documented a full population of immigrants and their families over several generations, and its vast scope over nearly three centuries is well suited to the study of demographic responses over the long run.6 Individuals in SAF are reported patrilineally, with children appearing exclusively in their father's lineage. As such, children are not directly linked to their mothers.7 Every male to immigrate to South Africa begins a new lineage in the data. These family trees contain as much as was known about each family member and typically include birth, baptism, marriage, and death dates and locations, as well as region of origin for progenitors. The spouse's name (maiden name, where applicable) and vital information are also listed. Ideally, all entries would be complete for all life history events, but this is not always the case.8 We restrict the sample to women with complete birth histories (i.e., we know the birthdates of the children they registered) and limit the analysis to marital childbearing, given that children born out of wedlock were rarely recorded in any of the source documents used by the genealogists who compiled the family lineages. The analysis does not include women with no children recorded under their husbands because it is unclear whether these women truly had no children or their children simply were not recorded. Our data contain limited information on infant and childhood mortality. Some births in our data have no death dates, and it is feasible that some of these are infant or early childhood deaths that were not recorded correctly. We cannot exclude births for which we have no death date because doing so would require the exclusion of entire families, which would substantially reduce the sample. We expect the erroneous recording of infant deaths to decline over time with declines in the infant mortality rate.9 Later, in the discussion of our results, we consider the implications of a reduction in infant mortality or the reporting thereof for our model. A woman's reproductive life is taken to be between the ages of 15 and 49. We include all women who we know lived at least until age 50 or for whom we have either their death date or their husband's death date. We exclude women for whom we have none of this information. We follow 12,800 women who gave birth to a total of 61,871 children between 1835 and 1950. ### Representativeness By virtue of the mere size and scope of SAF, many sources of potential bias are mitigated. However, some remain because of the missing or incomplete entries we alluded to earlier. Chiefly concerning among these are (1) a misrepresentation of the age, regional, or socioeconomic distribution of women in our sample, and (2) the selective noninclusion of childless women and women with incomplete birth histories. Each of these warrants further discussion. To discern any sample composition biases, Cilliers and Mariotti (2019) compared the SAF data with available aggregate census returns for the Cape Colony. The sample captures census distributions reasonably accurately. In general, we do not believe that the SAF systematically under- or oversamples certain groups of the population with respect to gender, and it likewise appears to provide an accurate representation of the age structure of the full population if not by district. Thus, we believe that any differential birth timing by age or region captured by our model is indicative of behavioral differences rather than a function of sample composition. To ensure that this is the case, we add controls for region in our estimation. We also consider the socioeconomic structure of the sample, as proxied for by the household head's occupation.10 This variable is particularly poorly recorded, as we will show later. However, because the analysis does not predominantly focus on this variable, we include it purely to address correlation between occupation and other explanatory variables; we do not interpret it in the analysis. A comparison between women dropped from our sample because they had no recorded children or because they had incomplete birth histories and the remaining women is informative to the question of bias arising from their exclusion. The former have poor records in general. It is unclear why they would have a substantially different number of children than the women in our sample and whether their birth timing would substantially differ from that of the women in our sample. For our findings to be incorrect, these excluded women would need completely different patterns of childbearing to shift the averages we find. We see no logical reason why their pattern of childbearing would be correlated with the quality of their other records. ### Periodization We split the sample into four periods to coincide with the timing of changes in settlement patterns and economic developments, as well as indicators of the onset of the fertility transition.11Cilliers and Mariotti (2019) showed that the onset of the settler fertility transition was driven by women born in the 1850s, who began having children in the 1870s. Our first period, 1835–1859, therefore consists of children born before the fertility transition began. These children were born predominantly in the Cape Colony; they resided either in Cape Town—which we denote Old Urban—or in what was then, and still largely is, a rural region that extended north and east from Cape Town, exceeding to some extent the boundary of the Cape Colony to the north—Old Rural. This period coincides with the start of the Great Trek, the movement of Afrikaans speakers from largely the eastern portion of the Cape Colony into the interior of what was to become South Africa. We call these newly settled regions New Rural; they span essentially all of modern South Africa that excludes Old Rural and the urban areas. That is, New Rural contains the two independent Boer Republics, the British colony of Natal, and the far northern districts of what came to be the Cape Colony under the British. Our second period is 1860–1884, a combination of pretransition and transition births. With the Great Trek, we begin to see the establishment of small urban pockets along the east coast as well as in the interior during this period. We label these urban areas New Urban. These areas were initially small but began to grow with the development of the mining industry in the interior in the last quarter of the nineteenth century. Our third period covers 1885–1909, when the fertility transition was well underway. These births coincide with the discovery of gold on the Witwatersrand, the slow advent of industrialization into the early twentieth century, and the Boer War (1899–1902). The settlers began a slow urbanization late in the nineteenth century, with the pace increasing because of the Boer War and the subsequent growth of the mining industry around Johannesburg in the early twentieth century (Giliomee 2003:323). Our final period is from 1910 through 1950. The major economic developments during this time were the intensification of gold mining on the Witwatersrand coupled with industrialization and the growth of manufacturing in the 1920s and 1930s. ## Sample Characteristics We turn now to look at mother's and birth interval characteristics over our sample period, as shown in Table 1. Panel A reports means and standard deviations for the number of children ever born, age at marriage, first birth, and last birth, and birth interval lengths. The average number of children ever born is 7.61 in the first period, exhibiting a barely discernible decrease in the second period before it begins to decrease in the third period, culminating in 4.13 children for women giving birth in the last period. Figure 1 shows this result in more detail by looking at the distribution of children ever born by women giving birth in the four periods we examine. The first two periods exhibit largely the same distribution of children ever born, with most women having between 1 and 10 children. The third period shows higher shares of women with seven or fewer children and a faster decline in share as the number of children increased. We observe a big change in the final period: a large increase in the proportion of women with smaller families and much more concentration around low numbers of children. Average age at marriage increased throughout the period of study: it increased by four years between the first period and the last, with the largest increases coming between the third and fourth periods. We see a similar increase in age at conception of the first child throughout the period of study. Age at last birth increased slightly before the transition before decreasing again slightly during the transition. Finally, looking at average birth interval lengths, we see increases in each period, with a final large increase between the third and fourth periods to an average interval length of 39.59 months. We explore the increase in birth interval length in greater detail in Figure 2, which plots mean birth interval lengths and their standard deviations by period over parity.12 In the two early periods, birth interval lengths were slightly shorter than 30 months—the same length that Menken and Sheps (1972) predicted for a pretransitional society. Birth intervals increased slightly at higher parities but were never more than 30 months. They decreased again at the highest parities, most likely because of the dominance of the highly fecund at these parities. Interval length increased at all parities in the two transition periods, particularly at the lower parities. Figure 2 is strongly suggestive of some form of birth interval length changes—whether spacing or postponement changes—playing a role in the transition, especially in the later stages. Figure 3 explores interval length in yet further detail, looking at period as well as children ever born over parity. The figure plots mean birth interval lengths (given by the symbols) and their standard deviations (given by the bars) for 1835–1859 and 1910–1950 by whether the total number of children ever born was three, five, or eight; the figure thereby captures average family sizes before the transition and at the end of the analysis period. Unsurprisingly, we find that smaller numbers of children ever born are correlated with larger birth intervals regardless of period, as must be the case if there was limited stopping.13 We see increases in birth interval length between periods when holding constant the number of children ever born. That is, the birth interval lengths for families with three or five children ever born were shorter in the 1835–1859 period than in the 1910–1950 period, showing an increase in spacing or postponement behavior over time and suggesting that only limited spacing behavior took place before the transition. Finally, we see very little change in the interval lengths at low parities for women with eight children between the two periods: an increase in interval length for the younger group is evident only after the fifth child. This is to be expected: there is not much time to waste on spacing or postponing if there will be eight children. Table 1, panel B reports shares for demographic, economic, and cultural characteristics. Mother's age is her age at the conception of each child. The number of observations here is the number of birth intervals, shown in the final row of the table. Just over 30% of all the birth intervals occurred for mothers aged 24 and younger, with this number decreasing to 14% over time. We see increases in the percentage of birth intervals for mothers aged 30–34, 35–39, and 40 or older—a finding that signifies changes in the timing of births across intervals. The decrease in share at the youngest age suggests a later start to childbearing as well as an increase in birth interval length once childbearing has started. The proportion of final birth intervals increased from 10.34% for the 1835–1859 period to 32.11 % for the post-1910 period. The increase is predominantly between the third and fourth periods. As can be seen for each economic and cultural characteristic in the table, there is a somewhat high percentage of unknowns. Because some selection bias is likely correlated with the unknowns, we include them in the subsequent analysis (although we do not report them in the analysis). The registration documents seldom required the husband to report his occupation, and hence the occupation information available in the sample is subject to some bias, as noted earlier. With respect to region, births in the first period were predominantly located in the Cape Colony, particularly in the rural areas, as expected, given that this was a largely rural colony. As the settlers began to migrate, the percentage in the Cape Colony dropped, and the percentage in the interior and of unknowns increased.14 We continue to see increases in the percentage of the sample from outside the Cape Colony and, in particular, an increase in the proportion of the sample in the New Rural area over time. The sample is dominated by women born locally but also consists of a large proportion of unknowns and is most likely skewed toward the local-born. As to be expected given the late arrival of British migrants, the dominant home language of the early cohorts is Afrikaans. This dominance abates somewhat over the century due to increasing migration from Britain. ## Simultaneous Determination of Stopping and Spacing Table 1 and the figures show substantial changes in child numbers, the distribution of children ever born, and interval lengths over time, but they cannot separate spacing, postponement, and stopping behavior during the transition and thus cannot pick up intentional family limitation before the transition. For this, we turn to the empirical analysis. A typical survival model, such as a Cox proportional hazards model, might suffice to evaluate the time until marriage or time until first birth if all the observations in the data experience the event. Such a model is inadequate when evaluating time until subsequent births because not all women have additional births. The problem with a standard survival model is that it amalgamates the speed of progression to the next event with the proportion progressing; it assumes that everyone in the data is at some point subject to the event (Schmidt and Witte 1989). In fertility analysis, this simply is not the case: some women will drop out of the analysis of time to subsequent birth because they stop having children. Furthermore, factors affecting the speed to progression of a subsequent child may differ from the factors affecting whether a woman does progress to have a subsequent child. One final concern is censoring in the data, whereby some individuals are classified as not experiencing the event because they did not experience it under the period of observation. This misclassification may lead to bias in a Cox model (Li and Choe 1997). Methodologically, split population models, also known as cure models in the biomedical literature, have been used to evaluate stopping and transition rates in demographic research (Alter 2019; Alter et al. 2007; Bremhorst et al. 2016; Gray et al. 2010; Li and Choe, 1997; Yamaguchi and Ferguson 1995). The advantage of these models over other event-history models is that they allow for women to leave the duration estimation if they have stopped having children. The intuition is that we want to estimate the proportion of the population surviving until some time, t—that is, not having a subsequent birth by t. This proportion includes two groups of women: (1) women who never have another child, termed stoppers, with proportion denoted p; and (2) those who have not yet had another child but will eventually, sometimes termed movers. Mathematically, we write this as $S(y)=p(x)+(1–p(x))Sm(t, y, z),$ (1) where p(x) is the proportion of stoppers (those who never have another child) estimated from the following logistic regression: $Li,t=lnpi,t1−pi,t=βXi,t+εi,t,$ (2) where ln ( pi,t / 1 – pi,t) is the log transformation of the probability that no subsequent child is born after the observed birth, and X is a vector of explanatory variables. Sm(t, y, z), the duration model, is the probability that women who do have another birth have not had one by time t. Using the log normal distribution, the survivor function of movers is as follows: $Sm(t,y,z)=1−Φ(ln(t)−μσ)=1−Φ(ln(t)−βyYi,tβzZi,t),$ (3) where Φ() is the cumulative distribution function of the standard normal distribution, ln(t) is the log of time until the next birth, and Yi,t and Zi,t are the explanatory variables. Following Yamaguchi and Ferguson (1995), we use an accelerated failure-time regression specification for the duration model rather than a proportional hazards model. Notice that covariates appear both in our estimate of µ, the mean of the distribution of the log of duration, as well as in the estimate of σ, the standard deviation of the log of duration. We refer to the estimate of the mean as the “scale” parameter, and the estimate of the standard deviation is the “shape” parameter in our results. The scale parameter measures the mean of a birth interval conditional on the number of existing children. We can think of the mean as measuring the population's socially accepted time interval between births. If the mean at a particular parity increases, then the society has adopted longer birth intervals at that parity. The scale parameter therefore measures parity-dependent birth spacing. The shape parameter, in contrast, is an indication of non-parity-specific postponement. Econometrically, it picks up variation in the time to the next child. That is, it measures changes in individual behavior that do not impact the mean. These changes would be decisions to have or not to have another birth because of temporary personal circumstances, such as the state of the local economy or individual income and health reasons. An increase in the variance in the duration to the next child therefore shows only some people making postponement decisions and not a shift for the whole society (Timæus and Moultrie 2008). It is perhaps elucidatory to reiterate what we mean by parity-dependent spacing and parity-independent postponement. Parity-dependent spacing may be directly related to influencing the final number of children, or it may be related to new preferences for the time between successive children without any desire to limit final numbers. Longer birth intervals due to either one of these explanations are termed parity-dependent spacing in that the decision about when to have a child depends on when the last child was born. If there is a population-wide shift in birth interval lengths, then we pick this up as an increase in the mean interval length. Parity-independent postponement is the decision that at a specific moment in time, having another child is not a good idea because of circumstances unrelated to the age of the last child and with no intention to limit family size ultimately or to change the experienced birth interval length. Of course, the consequence of postponement may well be a reduction in the total number of children, given a woman's constraint on the ability to conceive as she ages. If there is no population-wide change in preferences but there is individual-level postponement, then we see a change in the variance of interval length rather than in the mean. If many in the population postpone, then we should indeed see an increase in the mean length. Because our data come from all over South Africa, there is only one uniform shock—the 1899–1902 Boer War—that may result in postponement showing up as a societal lengthening of birth intervals. In our data, external circumstances resulting in postponement should show up in the shape parameter but not the scale. Finally, some of those who postpone, and even those who intentionally increase spacing, could quite possibly be seen as having stopped because they will have run out of time to have another child. We discuss how this influences our findings in the Results section. Our primary measure of interest is a dummy variable for period, given that we explore the relationship between period and the birth interval structure. We include both the supply of children and the demand for them in the explanatory variables to reduce the bias arising from the relationship between these variables and the period. On the supply side, we control for fecundity by accounting for the age at conception of the current birth, given that age is highly associated with fecundity. On the demand side, we include region controls, the husband's occupation, whether the mother was born in South Africa or abroad (Europe), and whether the home language was English or Afrikaans. ## Results Table 2 provides the results of the cure regression discussed in the empirical section. The table is divided into three panels. Panel A shows log odds coefficients for the fraction of women who stop having children, called the cure fraction; coefficients larger than 0 indicate an increased log odds of not having another child given the current birth interval. Panel B shows the coefficients indicating mean length of time until the next birth for the women who continue to have children, indicating intentional spacing. In this panel, a positive coefficient suggests an increased hazard of having another birth, which can be thought of as resulting in shorter birth intervals. A negative coefficient suggests a decreased hazard of having another birth—a lengthening of the birth interval (Li and Choe 1997). Finally, panel C shows the variation in the mean length of time until the next birth, or postponement; a negative coefficient suggests an increase in the variation in the time between two successive births. Each of the seven columns in Table 2 represents a move from one parity level to the next. We begin with the age variables (panel A): how old a mother was when the current observed child was conceived. The reference age category is 30–34. The coefficients on ages younger than 30 are almost all negative and significant; women younger than 30 were less likely than women aged 30–34 to stop having children at a given parity level. Women aged 35–39 were more likely to not have another child at parity levels 4 and higher relative to younger women. We find no significant results for women older than 40, most likely because of the low number of observations in that group. These age results are as expected given the decreased likelihood of conception as women age. We now look at the probability of stopping over time, our main variable of interest. The reference period is 1835–1859. We see no significant differences in stopping for the period 1860–1884 relative to the period before at parities 2 and higher. We begin to see an increase in stopping probabilities relative to the reference group for the 1885–1909 period, and these increase between 1910 and 1950. Panel B of Table 2 shows mean birth interval length. Relative to those aged 30–34, younger women have shorter intervals, and older women have longer intervals, as expected given a woman's reduced physiological ability to conceive as she ages. Relative to interval lengths between 1835 and 1859, longer mean intervals are evident only beginning in the 1910–1950 period. The evidence suggests that no parity-dependent spacing occurred before the fertility transition and that this behavior began only in the later stages of the transition. In the next section, we argue further why the regressions do not show parity-dependent spacing in the pretransition group.15 Finally, in panel C, we look at changes in the variation of birth interval lengths that result from postponement. We find a higher variance for older women relative to women aged 30–34, evidence of a decline in fecundity driven by age. We see less variance for women at parities 5 and higher in the period 1860–1884. Recall that the transition had just begun during this period and therefore that a decrease in family size implies that only the most fecund women were likely to have had children at these higher parities. By nature, their intervals will be shorter and less diverse. It is quite possible that some who chose to postpone found themselves unintentionally stopping if they waited too long for the next conception. We would not see this behavior in the shape parameters but rather in the cure fraction parameters. In the worst-case scenario, our cure fraction picks up only unintentional stoppers. Converting the stopping coefficients in panel A of Table 2 to parity progression ratios allows a deeper investigation of this problem. We plot the parity progression ratios predicted by the model in Table 2 in Figure A1 (online appendix). The model predicts increased stopping behavior in the final period relative to the first three. The increasingly concave curve over successive periods, particularly the last two, suggests intentional stopping. Progression to the third and fourth births drops more rapidly than progression to higher-order births (Brass and Juarez 1983; Brass et al. 1997; Timæus and Moultrie 2020). Given age at first birth, unintentional stopping is more likely to occur at higher parities, and the stopping we see at lower parities is more likely to be made up of intentional stoppers. If stopping were dominated by endless postponers, the parity progression ratios would exhibit a more linear decline. As noted, Table 2 does not report interactions of period of birth with socioeconomic characteristics. We provide these results in Table A1 in the online appendix. The results with the interactions are weaker as a result of smaller numbers of observations in each category. We still see a higher probability of stopping for the last period, but the coefficients in the third period are insignificant (although still positive). ### Looking Deeper Into Parity Dependent Control The regression results in Table 2 and the online appendix tables do not bring to light any parity-dependent control before the fertility transition. We agree with Timæus and Moultrie (2013), Cinnirella et al. (2017), and Clark and Cummins (2019) that individual- and couple-level heterogeneity may be masking parity-dependent fertility control and that we need to consider this. It is theoretically possible that our reference group, births in the period 1835–1859, exhibits parity-dependent spacing behavior and that subsequent periods exhibit precisely the same kind of parity-dependent spacing behavior. The spacing results we find are not significant at parities higher than the transition from parity 3 to 4. Thus, if parity-dependent spacing occurred at higher parities, it would not have changed over time even though the number of children ever born decreased over time. Because we can estimate stopping-, spacing-, and postponement-induced variation simultaneously, when we look at spacing and postponement at higher parities, we are really looking at only those people who reached those parities. Over time, the higher parities will be increasingly dominated by the highly fecund as more people stopped having children earlier—and yet we see no change in spacing. Is that because the highly fecund who would have had narrower intervals in the pretransition period began increasing their spacing in a way that kept the interval length exactly the same as when there was more heterogeneity at higher parities? That would be remarkable: it would suggest a degree of spacing that would not allow women to reach high parities in the first place. What we do see is a reduction in variance induced through postponement for the period 1860–1884 at higher parities. This reduction in variance is suggestive of more consistency in birth interval length, as one might expect at parities dominated by the highly fertile. This finding is supply-side evidence of fecundity and not demand-side evidence based on parity. Nevertheless, we investigate this finding further. Following Clark and Cummins (2019), we first look at whether women who married younger and began having children earlier experienced faster fertility declines than those who married later, as parity-dependent control would suggest. We look at women who married at ages 15–19, 20–24, and 25–29. We set their fertility rates at ages 30–34 equal to 1 and plot their subsequent average fertility indexes at ages 35–39, 40–44, and 45–49. If there is parity-dependent fertility control, we should see a steeper decline in the fertility rates of those who married earlier. Figure 4 plots the fertility rates for the three marriage ages at four age groups for the period 1835–1859. We do not find any pattern in the fertility rate decrease. If anything, women marrying later had the fastest fertility decrease. We conduct this exercise for each of the four periods and find no evidence of parity-dependent fertility control until the last period, when the rate of fertility decline matches the hypothesis (Figures A1–A3, online appendix). This finding is as expected, given that this period is situated in the fertility transition. We next explore the change in fertility by age group for all women who married at ages 20–24. We look at the birth rates of these women in the early stages of marriage (at ages 25–29) and split them into three groups: parity 1, parity 2, and parity 3 or higher. We assume that those with parity 1 are the least fecund and that those with parity 3 or higher are the most fecund. If there is parity-dependent control, then we would expect to see those with parity 3 or higher at ages 25–29 exhibit a faster rate of fertility decrease from ages 30 to 49. Again, we set the fertility rate at ages 30–34 equal to 1 and calculate subsequent fertility indexes relative to that. Figure 5 shows very similar rates of fertility decrease for the three parity groups. This finding raises concern about the role of the least fecund. Within this group are women/couples who do not conceive easily. Because their fertility rate would be expected to be lower at all ages, they too would bias the finding of parity-dependent spacing. Indeed, they bias the result toward a finding of parity-dependent spacing. Ultimately, which scenario dominates is hard to say. Once the transition had begun, we again see the expected ordering of the fertility rate decline (Figures A4–A6, online appendix). This set of evidence should assuage concerns regarding the role of individual-level heterogeneity in masking the evidence of parity-specific control. These data show no evidence of parity-specific spacing before the transition. ## Conclusion This study examines the fertility experience of settler women in nineteenth-century South Africa. The period we study, 1835–1950, covers the pretransition period, the transition period, and an overall period of extensive geographic, cultural, economic, and social change. Our data, which comprise women's complete birth histories, are well suited to event-history analysis techniques, and we use mixed population models to allow for both ongoing procreation and the cessation of childbearing. We look at the mean and variance of the length of time between consecutive births and the likelihood of stopping after a certain number of children have been born. Our estimation shows that a woman's own physiology and fecundity are the main determinants of both when a woman stopped having children and birth interval lengths before the transition. We do not find evidence of explicit parity-dependent control for either stopping or spacing, although we do see some evidence of variation in birth interval lengths driven by postponement. During the transition, we first see an increase in both stopping behavior and variation in birth interval length driven by postponement, followed in the last period by an increase in spacing. Our findings show a role for both stopping and spacing in the fertility transition, finding common cause with the literature advocating for family limitation (Knodel 1987) as well as birth interval timing (Dribe et al. 2017). The results show that an empirical examination of a representative data set can shed light on reproductive behavior and compensate to some extent for the lack of direct evidence on people's reproductive intentions. Our methodology allows us to show that couples were able to limit their childbearing toward the end of the nineteenth century. That these couples did limit their childbearing shows that their society perceived the benefits of smaller families, had evolved away from the conservative large-family model, and knew how to implement its preferences. ## Acknowledgments The authors thank the three anonymous referees, the Editor, George Alter, Gregory Clark, Martin Dribe, and Timothy Hatton for valuable guidance. We also thank participants at the Joint APEBH 2019 and All-UC Group in Economic History Conference, the Economic History seminar at UC Davis, and the Centre for Economic History ANU workshop on Fertility Transitions: Past and Present. All errors remain our own. ## Notes 1 This list is by no means comprehensive. See Dribe et al. (2017) for a deeper discussion of the findings. 2 See Alter (2019) for a critique of these methods. 3 Cinnirella et al. (2019) provided a rejoinder to the Clark and Cummins (2019) argument. 4 Bengtsson and Dribe (2006) and Dribe and Scalone (2010) are among the few that looked at short-run shocks that may result in the postponement of a subsequent birth independent of the number and age of existing children. 5 The registers were compiled from the baptism records (which contain birthdates) and marriage records of the Dutch Reformed Church, marriage documents obtained from various courts and magistrates offices, and a number of notable genealogical publications and individual family histories. See Gouws (1987) for a more detailed description of the origins of these data. See Cilliers and Fourie (2012) and Cilliers and Mariotti (2019) for a full account of the transcription of the SAF into a database fit for use in demographic analysis. 6 Although the data contain all known families, they do not always contain all members of these families. 7 For example, if settler A1 (male) has two children, A1B1 (male) and A1B2 (female), both of whom then marry and have a number children of their own, only the children of A1B1 will appear in settler A1’s lineage (because these children share their paternal grandfather’s surname). The children of A1B2 will appear in her husband’s lineage. See Cilliers and Mariotti (2019) for details on our construction of a data set of mothers from these patrilineages. 8 See Cilliers and Mariotti (2019) for an extensive discussion of the implications of missing data on SAF sample representativeness when studying fertility behavior in this population. 9 Simkins and Van Heyningen (1989), however, suggested White infant mortality rates that were substantially higher than in Australia during the fertility transition. 10 We use husband’s occupation here because women rarely had reported occupations in the genealogical data and the censuses. 11 Inclusion in a given period is conditional on a first birth for the couple in that period. 12 Figure 2 does not take into account the number of children ever born, and hence at higher parities over time, it is dominated by an increasingly small proportion of women with large numbers of children—women we may deem to be highly fecund relative to the average. 13 The intervals indicated by the solid black circles and triangles are larger than those indicated by the hollow circles and solid diamonds. 14 It is quite likely that as the settlers migrated, the quality of the records deteriorated. The implications of this for the purposes of analysis are discussed at length in Cilliers and Mariotti (2019). 15 Although our data do not allow a study of the role of infant mortality on birth curtailment and interval length, we offer a brief discussion of what this role might be given the importance of the decline in mortality rates in the European fertility transition (Reher et al. 2017; Reher and Sanz-Gimeno 2007). As noted, we do have many recorded births without corresponding death dates. If some of these are children who died in infancy, then our findings are consistent with longer birth intervals reflecting a decline in infant mortality rates. If children who died in infancy or childhood remain completely unrecorded, then a decrease in the infant mortality rate should be associated with a reduction in birth interval lengths. Between two surviving children, we now have a third survivor who previously would have been unrecorded, thereby reducing the length of the observed interval. Because we don’t see a decline in intervals, one of two scenarios is possible: (1) all deceased children are unrecorded, the infant mortality rate is not changing, and fertility declines for other reasons; or (2) some of the children with missing death dates died in childhood, the infant mortality rate may have declined, and the latter is part of the cause of the fertility decline. We think that the second scenario is more likely. ## References Alter, G., Oris, M., & Tyurin, K. ( 2007 , March ). The shape of a fertility transition: An analysis of birth intervals in eastern Belgium . Paper presented at the annual meeting of the Population Association of America , New York, NY . Alter, G. C. ( 2019 ). The evolution of models in historical demography . Journal of Interdisciplinary History , 50 , 325 362 . Anderton, D. L., & Bean, L. 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https://pdglive.lbl.gov/DataBlock.action?node=S054EQS	#### Limits for Excited ${{\mathit q}}$ (${{\mathit q}^{}}$ ) from Single Production These limits are from ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit q}^{}}{{\overline{\mathit q}}}$ , ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit q}^{}}$ X, or ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}$ X and depend on transition magnetic couplings between ${{\mathit q}}$ and ${{\mathit q}^{}}$ . Assumptions about ${{\mathit q}^{}}$ decay mode are given in the footnotes and comments. VALUE (GeV) CL% DOCUMENT ID TECN COMMENT $\bf{ > 6700}$ OUR LIMIT $\bf{\text{none 2000 - 6700}}$ 95 1 2020 T ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}{{\mathit X}}$ , ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit q}}{{\mathit g}}$ $\text{none 1250 - 3200}$ 95 1 2020 T ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit b}^{}}{{\mathit X}}$ , ${{\mathit b}^{}}$ $\rightarrow$ ${{\mathit b}}{{\mathit g}}$ , ${{\mathit b}}{{\mathit \gamma}}$ , ${{\mathit b}}{{\mathit Z}}$ , ${{\mathit t}}{{\mathit W}}$ $\text{none 1800 - 6300}$ 95 2 2020 AI CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}{{\mathit X}}$ , ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit q}}{{\mathit g}}$ $\text{none 1500 - 2600}$ 95 3 2018 AB ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit b}^{}}{{\mathit X}}$ , ${{\mathit b}^{}}$ $\rightarrow$ ${{\mathit b}}{{\mathit g}}$ $\text{none 1500 - 5300}$ 95 4 2018 BA ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}{{\mathit X}}$ , ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit q}}{{\mathit \gamma}}$ $\text{none 1000 - 5500}$ 95 5 2018 AG CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}{{\mathit X}}$ , ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit q}}{{\mathit \gamma}}$ $\text{none 1000 - 1800}$ 95 6 2018 AG CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit b}^{}}{{\mathit X}}$ , ${{\mathit b}^{}}$ $\rightarrow$ ${{\mathit b}}{{\mathit \gamma}}$ $\text{none 600 - 6000}$ 95 7 2018 BO CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}$ ${{\mathit X}}$ , ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit q}}{{\mathit g}}$ $\text{none 1200 - 5000}$ 95 8 2018 P CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}{{\mathit X}}$ , ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit q}}{{\mathit W}}$ $\text{none 1200 - 4700}$ 95 8 2018 P CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}{{\mathit X}}$ , ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit q}}{{\mathit Z}}$ $> 6000$ 95 9 2017 AK ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}{{\mathit X}}$ , ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit q}}{{\mathit g}}$ • • We do not use the following data for averages, fits, limits, etc. • • $> 2600$ 95 10 2021 AG CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit b}^{}}{{\mathit X}}$ , ${{\mathit b}^{}}$ $\rightarrow$ ${{\mathit t}}{{\mathit W}}$ $\text{none 600 - 5400}$ 95 11 2017 W CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}{{\mathit X}}$ , ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit q}}{{\mathit g}}$ $\text{none 1100 - 2100}$ 95 12 2016 ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit b}^{}}{{\mathit X}}$ , ${{\mathit b}^{}}$ $\rightarrow$ ${{\mathit b}}{{\mathit g}}$ $> 1500$ 95 13 2016 AH ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit b}^{}}{{\mathit X}}$ , ${{\mathit b}^{}}$ $\rightarrow$ ${{\mathit t}}{{\mathit W}}$ $> 4400$ 95 14 2016 AI ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}{{\mathit X}}$ , ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit q}}{{\mathit \gamma}}$ 15 2016 AV ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}{{\mathit X}}$ , ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit W}}{{\mathit b}}$ $> 5200$ 95 16 2016 S ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}{{\mathit X}}$ , ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit q}}{{\mathit g}}$ $> 1390$ 95 17 2016 I CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit b}^{}}{{\mathit X}}$ , ${{\mathit b}^{}}$ $\rightarrow$ ${{\mathit t}}{{\mathit W}}$ $> 5000$ 95 18 2016 K CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}{{\mathit X}}$ , ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit q}}{{\mathit g}}$ $\text{none 500 - 1600}$ 95 19 2016 L CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}{{\mathit X}}$ , ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit q}}{{\mathit g}}$ $> 4060$ 95 20 2015 V ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}{{\mathit X}}$ , ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit q}}{{\mathit g}}$ $> 3500$ 95 21 2015 V CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}{{\mathit X}}$ , ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit q}}{{\mathit g}}$ $> 3500$ 95 22 2014 A ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}{{\mathit X}}$ , ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit q}}{{\mathit \gamma}}$ $> 3200$ 95 23 2014 CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}{{\mathit X}}$ , ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit q}}{{\mathit W}}$ $> 2900$ 95 24 2014 CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}{{\mathit X}}$ , ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit q}}{{\mathit Z}}$ $\text{none 700 - 3500}$ 95 25 2014 J CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}{{\mathit X}}$ , ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit q}}{{\mathit \gamma}}$ $> 2380$ 95 26 2013 AJ CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}{{\mathit X}}$ , ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit q}}{{\mathit W}}$ $> 2150$ 95 27 2013 AJ CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit q}^{}}{{\mathit X}}$ , ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit q}}{{\mathit Z}}$ 1 AAD 2020T search for resonances decaying into dijets in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. Assume ${{\mathit \Lambda}}$ = ${\mathit m}_{{{\mathit q}^{}}}$, ${{\mathit f}_{{s}}}$ = ${{\mathit f}}$ = ${{\mathit f}^{\,'}}$ = 1. 2 SIRUNYAN 2020AI search for resonances decaying into dijets in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. Assume ${{\mathit \Lambda}}$ = ${\mathit m}_{{{\mathit q}^{}}}$, ${{\mathit f}_{{s}}}$ = ${{\mathit f}}$ = ${{\mathit f}^{\,'}}$ = 1. 3 AABOUD 2018AB assume ${{\mathit \Lambda}}$ = ${\mathit m}_{{{\mathit b}^{}}}$, ${{\mathit f}_{{s}}}$ = ${{\mathit f}}$ = ${{\mathit f}^{\,'}}$ = 1. The contact interactions are not included in ${{\mathit b}^{}}$ production and decay amplitudes. 4 AABOUD 2018BA search for first-generation excited quarks (${{\mathit u}^{}}$ and ${{\mathit d}^{}}$ ) with degenerate mass, assuming ${{\mathit \Lambda}}$ = ${\mathit m}_{{{\mathit q}^{}}}$, ${{\mathit f}_{{s}}}$ = ${{\mathit f}}$ = ${{\mathit f}^{\,'}}$ = 1. The contact interactions are not included in ${{\mathit q}^{}}$ production and decay amplitudes. 5 SIRUNYAN 2018AG search for first-generation excited quarks (${{\mathit u}^{}}$ and ${{\mathit d}^{}}$ ) with degenerate mass, assuming ${{\mathit \Lambda}}$ = ${\mathit m}_{{{\mathit q}^{}}}$, ${{\mathit f}_{{s}}}$ = ${{\mathit f}}$ = ${{\mathit f}^{\,'}}$ = 1. 6 SIRUNYAN 2018AG search for excited ${{\mathit b}}$ quark assuming ${{\mathit \Lambda}}$ = ${\mathit m}_{{{\mathit q}^{}}}$, ${{\mathit f}_{{s}}}$ = ${{\mathit f}}$ = ${{\mathit f}^{\,'}}$ = 1. 7 SIRUNYAN 2018BO assume ${{\mathit \Lambda}}$ = ${\mathit m}_{{{\mathit q}^{}}}$, ${{\mathit f}_{{s}}}$ = ${{\mathit f}}$ = ${{\mathit f}^{\,'}}$ = 1. The contact interactions are not included in ${{\mathit q}^{}}$ production and decay amplitudes. 8 SIRUNYAN 2018P use the hadronic decay of ${{\mathit W}}$ or ${{\mathit Z}}$ , assuming ${{\mathit \Lambda}}$ = ${\mathit m}_{{{\mathit q}^{}}}$, ${{\mathit f}_{{s}}}$ = ${{\mathit f}}$ = ${{\mathit f}^{\,'}}$ = 1. 9 AABOUD 2017AK assume $\Lambda$ = ${\mathit m}_{{{\mathit q}^{}}}$, ${{\mathit f}_{{s}}}$ = ${{\mathit f}}$ = ${{\mathit f}^{\,'}}$ = 1. The contact interactions are not included in ${{\mathit q}^{}}$ production and decay amplitudes. Only the decay of ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit g}}{{\mathit u}}$ and ${{\mathit q}^{}}$ $\rightarrow$ ${{\mathit g}}{{\mathit d}}$ is simulated as the benchmark signals in the analysis. 10 SIRUNYAN 2021AG search for ${{\mathit b}^{}}$ decaying to ${{\mathit t}}{{\mathit W}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. The limit quoted above assumes ${{\mathit \kappa}_{{L}}^{b}}$ = ${{\mathit g}_{{L}}}$ = 1, ${{\mathit \kappa}_{{R}}^{b}}$ = ${{\mathit g}_{{R}}}$ = 0. The limit becomes ${\mathit m}_{{{\mathit b}^{}}}$ $>$ 2.8 TeV ($>$ 3.1 TeV) if we assume ${{\mathit \kappa}_{{L}}^{b}}$ = ${{\mathit g}_{{L}}}$ = 0, ${{\mathit \kappa}_{{R}}^{b}}$ = ${{\mathit g}_{{R}}}$ = 1 (${{\mathit \kappa}_{{L}}^{b}}$ = ${{\mathit g}_{{L}}}$ = ${{\mathit \kappa}_{{R}}^{b}}$ = ${{\mathit g}_{{R}}}$ = 1). See their Fig. 5 for limits on $\sigma \cdot{}B$. 11 KHACHATRYAN 2017W assume $\Lambda$ = ${\mathit m}_{{{\mathit q}^{}}}$, ${{\mathit f}_{{s}}}$ = ${{\mathit f}}$ = ${{\mathit f}^{\,'}}$ = 1. The contact interactions are not included in ${{\mathit q}^{}}$ production and decay amplitudes. 12 AABOUD 2016 assume $\Lambda$ = ${\mathit m}_{{{\mathit b}^{}}}$, ${{\mathit f}_{{s}}}$ = ${{\mathit f}}$ = ${{\mathit f}^{\,'}}$ = 1. The contact interactions are not included in the ${{\mathit b}^{}}$ production and decay amplitudes. 13 AAD 2016AH search for ${{\mathit b}^{}}$ decaying to ${{\mathit t}}{{\mathit W}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV. ${{\mathit f}_{{g}}}$ = ${{\mathit f}_{{L}}}$ = ${{\mathit f}_{{R}}}$ = 1 are assumed. See their Fig. 12b for limits on $\sigma \cdot{}\mathit B$. 14 AAD 2016AI assume $\Lambda$ = ${\mathit m}_{{{\mathit q}^{}}}$, ${{\mathit f}_{{s}}}$ = ${{\mathit f}}$ = ${{\mathit f}^{\,'}}$ = 1. 15 AAD 2016AV search for single production of vector-like quarks decaying to ${{\mathit W}}{{\mathit b}}$ in ${{\mathit p}}{{\mathit p}}$ collisions. See their Fig. 8 for the limits on couplings and mixings. 16 AAD 2016S assume $\Lambda$ = ${\mathit m}_{{{\mathit q}^{}}}$, ${{\mathit f}_{{s}}}$ = ${{\mathit f}}$ = ${{\mathit f}^{\,'}}$ = 1. The contact interactions are not included in ${{\mathit q}^{}}$ production and decay amplitudes. 17 KHACHATRYAN 2016I search for ${{\mathit b}^{}}$ decaying to ${{\mathit t}}{{\mathit W}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV. ${{\mathit \kappa}_{{L}}^{b}}$ = ${{\mathit g}_{{L}}}$ = 1, ${{\mathit \kappa}_{{R}}^{b}}$ = ${{\mathit g}_{{R}}}$ = 0 are assumed. See their Fig. 8 for limits on $\sigma \cdot{}\mathit B$. 18 KHACHATRYAN 2016K assume ${{\mathit \Lambda}}$ = ${\mathit m}_{{{\mathit q}^{}}}$, ${{\mathit f}_{{s}}}$ = ${{\mathit f}}$ = ${{\mathit f}^{\,'}}$ = 1. The contact interactions are not included in ${{\mathit q}^{}}$ production and decay amplitudes. 19 KHACHATRYAN 2016L search for resonances decaying to dijets in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV using the data scouting technique which increases the sensitivity to the low mass resonances. 20 AAD 2015V assume ${{\mathit \Lambda}}$ = ${\mathit m}_{{{\mathit q}^{}}}$, ${{\mathit f}_{{s}}}$ = ${{\mathit f}}$ = ${{\mathit f}^{\,'}}$ = 1. The contact interactions are not included in ${{\mathit q}^{}}$ production and decay amplitudes. 21 KHACHATRYAN 2015V assume ${{\mathit \Lambda}}$ = ${\mathit m}_{{{\mathit q}^{}}}$, ${{\mathit f}_{{s}}}$ = ${{\mathit f}}$ = ${{\mathit f}^{\,'}}$ = 1. The contact interactions are not included in ${{\mathit q}^{}}$ production and decay amplitudes. 22 AAD 2014A assume ${{\mathit \Lambda}}$ = ${\mathit m}_{{{\mathit q}^{}}}$, ${{\mathit f}_{{s}}}$ = ${{\mathit f}}$ = ${{\mathit f}^{\,'}}$ = 1. 23 KHACHATRYAN 2014 use the hadronic decay of ${{\mathit W}}$ , assuming ${{\mathit \Lambda}}$ = ${\mathit m}_{{{\mathit q}^{}}}$, ${{\mathit f}_{{s}}}$ =${{\mathit f}}$ =${{\mathit f}^{\,'}}$ = 1. 24 KHACHATRYAN 2014 use the hadronic decay of ${{\mathit Z}}$ , assuming ${{\mathit \Lambda}}$ = ${\mathit m}_{{{\mathit q}^{}}}$, ${{\mathit f}_{{s}}}$ =${{\mathit f}}$ =${{\mathit f}^{\,'}}$ = 1. 25 KHACHATRYAN 2014J assume ${{\mathit f}_{{s}}}$ = ${{\mathit f}}$ = ${{\mathit f}^{\,'}}$ = ${{\mathit \Lambda}}$ $/$ ${\mathit m}_{{{\mathit q}^{}}}$. 26 CHATRCHYAN 2013AJ use the hadronic decay of ${{\mathit W}}$ . 27 CHATRCHYAN 2013AJ use the hadronic decay of ${{\mathit Z}}$ . 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Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector JHEP 1602 110 Search for the Production of Single Vector-Like and Excited Quarks in the ${{\mathit W}}{\mathit {\mathit t}}$ Final State in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector JHEP 1603 041 Search for New Phenomena with Photon $+$ Jet Events in Proton-Proton Collisions at $\sqrt {s }$ = 13 TeV with the ATLAS Detector PL B754 302 Search for New Phenomena in Dijet Mass and Angular Distributions from ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 13 TeV with the ATLAS Detector KHACHATRYAN 2016L PRL 117 031802 Search for Narrow Resonances in Dijet Final States at $\sqrt {s }$ = 8 TeV with the Novel CMS Technique of Data Scouting KHACHATRYAN 2016K PRL 116 071801 Search for Narrow Resonances Decaying to Dijets in Proton-Proton Collisions at $\sqrt {s }$ = 13 TeV KHACHATRYAN 2016I JHEP 1601 166 Search for the Production of an Excited Bottom Quark Decaying to ${{\mathit t}}{{\mathit W}}$ in Proton-Proton Collisions at $\sqrt {s }$ = 8 TeV PR D91 052007 Search for New Phenomena in the Dijet Mass Distribution using ${{\mathit p}}{{\mathit p}}$ Collision Data at $\sqrt {s }$ = 8 TeV with the ATLAS Detector PR D91 052009 Search for Resonances and Quantum Black Holes using Dijet Mass Spectra in Proton-Proton Collisions at $\sqrt {s }$ = 8 TeV PL B728 562 Search for New Phenomena in Photon + Jet Events Collected in Proton$−$Proton Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector JHEP 1408 173 Search for Massive Resonances in Dijet Systems Containing Jets Tagged as ${{\mathit W}}$ or ${{\mathit Z}}$ Boson Decays in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV PL B738 274 Search for Excited Quarks in the ${{\mathit \gamma}}$ + Jet Final State in Proton-Proton Collisions at $\sqrt {s }$ = 8 TeV PL B723 280 Search for Heavy Resonances in the ${{\mathit W}}$ /${{\mathit Z}}$ -Tagged Dijet Mass Spectrum in ${{\mathit p}}{{\mathit p}}$ Collisions at 7 TeV	2023-03-25T04:16:48	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9615508317947388, "perplexity": 692.5921251972086}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": 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https://indico.fnal.gov/event/19348/contributions/186525/	Indico search will be reestablished in the next version upgrade of the software: https://getindico.io/roadmap/ # Neutrino 2020 June 22, 2020 to July 2, 2020 US/Central timezone ## Sensitivity study of KM3NeT-ORCA to Sterile Neutrinos Not scheduled 10m Poster ### Speaker Dr Tarak Thakore (University of Cincinnati) ### Description The KM3NeT is a next generation neutrino telescope under construction in the Mediterranean sea. The primary goal of the low energy configuration, ORCA, is to measure oscillation parameters with atmospheric neutrinos, in particular the Neutrino Mass Ordering (NMO). In addition to this primary goal, ORCA will also be capable of constraining a number of non-standard physics scenarios such as sterile neutrinos. In this contribution, we will present ORCA's sensitivity to sterile neutrino parameters $U_{e4}$, $U_{\mu4}$ and $U_{\tau4}$ over a wide range of $\Delta m^2_{41}$ ~ $10^{-5} - 10^2$ $\rm{eV}^2$. ### Mini-abstract Searching for sterile neturinos with the upcoming KM3NeT-ORCA neutrino telescope Experiment/Collaboration KM3NeT ### Primary author Dr Tarak Thakore (University of Cincinnati) ### Co-authors Dr Alba Domi (Erlangen Centre for Astroparticle Physics) Dr Joao Coelho (Université Paris-Saclay, CNRS/IN2P3)	2021-11-27T16:50:00	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.40807899832725525, "perplexity": 11412.244774188246}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358208.31/warc/CC-MAIN-20211127163427-20211127193427-00337.warc.gz"}
https://lammps.sandia.gov/doc/fix_lb_fluid.html	# fix lb/fluid command ## Syntax fix ID group-ID lb/fluid nevery LBtype viscosity density keyword values ... • ID, group-ID are documented in fix command • lb/fluid = style name of this fix command • nevery = update the lattice-Boltzmann fluid every this many timesteps • LBtype = 1 to use the standard finite difference LB integrator, 2 to use the LB integrator of Ollila et al. • viscosity = the fluid viscosity (units of mass/(timelength)). • density = the fluid density. • zero or more keyword/value pairs may be appended • keyword = setArea or setGamma or scaleGamma or dx or dm or a0 or noise or calcforce or trilinear or D3Q19 or read_restart or write_restart or zwall_velocity or bodyforce or printfluid setArea values = type node_area type = atom type (1-N) node_area = portion of the surface area of the composite object associated with the particular atom type (used when the force coupling constant is set by default). setGamma values = gamma gamma = user set value for the force coupling constant. scaleGamma values = type gammaFactor type = atom type (1-N) gammaFactor = factor to scale the setGamma gamma value by, for the specified atom type. dx values = dx_LB = the lattice spacing. dm values = dm_LB = the lattice-Boltzmann mass unit. a0 values = a_0_real = the square of the speed of sound in the fluid. noise values = Temperature seed Temperature = fluid temperature. seed = random number generator seed (positive integer) calcforce values = N forcegroup-ID N = output the force and torque every N timesteps forcegroup-ID = ID of the particle group to calculate the force and torque of trilinear values = none (used to switch from the default Peskin interpolation stencil to the trilinear stencil). D3Q19 values = none (used to switch from the default D3Q15, 15 velocity lattice, to the D3Q19, 19 velocity lattice). read_restart values = restart file = name of the restart file to use to restart a fluid run. write_restart values = N = write a restart file every N MD timesteps. zwall_velocity values = velocity_bottom velocity_top = velocities along the y-direction of the bottom and top walls (located at z=zmin and z=zmax). bodyforce values = bodyforcex bodyforcey bodyforcez = the x,y and z components of a constant body force added to the fluid. printfluid values = N = print the fluid density and velocity at each grid point every N timesteps. ## Examples fix 1 all lb/fluid 1 2 1.0 1.0 setGamma 13.0 dx 4.0 dm 10.0 calcforce sphere1 fix 1 all lb/fluid 1 1 1.0 0.0009982071 setArea 1 1.144592082 dx 2.0 dm 0.3 trilinear noise 300.0 8979873 ## Description Implement a lattice-Boltzmann fluid on a uniform mesh covering the LAMMPS simulation domain. The MD particles described by group-ID apply a velocity dependent force to the fluid. The lattice-Boltzmann algorithm solves for the fluid motion governed by the Navier Stokes equations, $\begin{split}\partial_t \rho + \partial_{\beta}\left(\rho u_{\beta}\right)= & 0 \\ \partial_t\left(\rho u_{\alpha}\right) + \partial_{\beta}\left(\rho u_{\alpha} u_{\beta}\right) = & \partial_{\beta}\sigma_{\alpha \beta} + F_{\alpha} + \partial_{\beta}\left(\eta_{\alpha \beta \gamma \nu}\partial_{\gamma} u_{\nu}\right)\end{split}$ with, $\eta_{\alpha \beta \gamma \nu} = \eta\left[\delta_{\alpha \gamma}\delta_{\beta \nu} + \delta_{\alpha \nu}\delta_{\beta \gamma} - \frac{2}{3}\delta_{\alpha \beta}\delta_{\gamma \nu}\right] + \Lambda \delta_{\alpha \beta}\delta_{\gamma \nu}$ where $$\rho$$ is the fluid density, u is the local fluid velocity, $$\sigma$$ is the stress tensor, F is a local external force, and $$\eta$$ and $$\Lambda$$ are the shear and bulk viscosities respectively. Here, we have implemented $\sigma_{\alpha \beta} = -P_{\alpha \beta} = -\rho a_0 \delta_{\alpha \beta}$ with $$a_0$$ set to $$\frac{1}{3} \frac{dx}{dt}^2$$ by default. The algorithm involves tracking the time evolution of a set of partial distribution functions which evolve according to a velocity discretized version of the Boltzmann equation, $\left(\partial_t + e_{i\alpha}\partial_{\alpha}\right)f_i = -\frac{1}{\tau}\left(f_i - f_i^{eq}\right) + W_i$ where the first term on the right hand side represents a single time relaxation towards the equilibrium distribution function, and $$\tau$$ is a parameter physically related to the viscosity. On a technical note, we have implemented a 15 velocity model (D3Q15) as default; however, the user can switch to a 19 velocity model (D3Q19) through the use of the D3Q19 keyword. This fix provides the user with the choice of two algorithms to solve this equation, through the specification of the keyword LBtype. If LBtype is set equal to 1, the standard finite difference LB integrator is used. If LBtype is set equal to 2, the algorithm of Ollila et al. is used. Physical variables are then defined in terms of moments of the distribution functions, $\begin{split}\rho = & \displaystyle\sum\limits_{i} f_i \\ \rho u_{\alpha} = & \displaystyle\sum\limits_{i} f_i e_{i\alpha}\end{split}$ Full details of the lattice-Boltzmann algorithm used can be found in Mackay et al.. The fluid is coupled to the MD particles described by group-ID through a velocity dependent force. The contribution to the fluid force on a given lattice mesh site j due to MD particle $$\alpha$$ is calculated as: ${\bf F}_{j \alpha} = \gamma \left({\bf v}_n - {\bf u}_f \right) \zeta_{j\alpha}$ where $$\mathbf{v}_n$$ is the velocity of the MD particle, $$\mathbf{u}_f$$ is the fluid velocity interpolated to the particle location, and $$\gamma$$ is the force coupling constant. $$\zeta$$ is a weight assigned to the grid point, obtained by distributing the particle to the nearest lattice sites. For this, the user has the choice between a trilinear stencil, which provides a support of 8 lattice sites, or the immersed boundary method Peskin stencil, which provides a support of 64 lattice sites. While the Peskin stencil is seen to provide more stable results, the trilinear stencil may be better suited for simulation of objects close to walls, due to its smaller support. Therefore, by default, the Peskin stencil is used; however the user may switch to the trilinear stencil by specifying the keyword, trilinear. By default, the force coupling constant, $$\gamma$$, is calculated according to $\gamma = \frac{2m_um_v}{m_u+m_v}\left(\frac{1}{\Delta t_{collision}}\right)$ Here, $$m_v$$ is the mass of the MD particle, $$m_u$$ is a representative fluid mass at the particle location, and $$\Delta t_{collision}$$ is a collision time, chosen such that $$\frac{\tau}{\Delta t_{collision}} = 1$$ (see Mackay and Denniston for full details). In order to calculate $$m_u$$, the fluid density is interpolated to the MD particle location, and multiplied by a volume, node_area $$dx_{LB}$$, where node_area represents the portion of the surface area of the composite object associated with a given MD particle. By default, node_area is set equal to $$dx_{LB}^2$$; however specific values for given atom types can be set using the setArea keyword. The user also has the option of specifying their own value for the force coupling constant, for all the MD particles associated with the fix, through the use of the setGamma keyword. This may be useful when modelling porous particles. See Mackay et al. for a detailed description of the method by which the user can choose an appropriate $$\gamma$$ value. Note while this fix applies the force of the particles on the fluid, it does not apply the force of the fluid to the particles. When the force coupling constant is set using the default method, there is only one option to include this hydrodynamic force on the particles, and that is through the use of the lb/viscous fix. This fix adds the hydrodynamic force to the total force acting on the particles, after which any of the built-in LAMMPS integrators can be used to integrate the particle motion. However, if the user specifies their own value for the force coupling constant, as mentioned in Mackay et al., the built-in LAMMPS integrators may prove to be unstable. Therefore, we have included our own integrators fix lb/rigid/pc/sphere, and fix lb/pc, to solve for the particle motion in these cases. These integrators should not be used with the lb/viscous fix, as they add hydrodynamic forces to the particles directly. In addition, they can not be used if the force coupling constant has been set the default way. Note if the force coupling constant is set using the default method, and the lb/viscous fix is NOT used to add the hydrodynamic force to the total force acting on the particles, this physically corresponds to a situation in which an infinitely massive particle is moving through the fluid (since collisions between the particle and the fluid do not act to change the particle’s velocity). Therefore, the user should set the mass of the particle to be significantly larger than the mass of the fluid at the particle location, in order to approximate an infinitely massive particle (see the dragforce test run for an example). Inside the fix, parameters are scaled by the lattice-Boltzmann timestep, $$dt_{LB}$$, grid spacing, $$dx_{LB}$$, and mass unit, $$dm_{LB}$$. $$dt_{LB}$$ is set equal to $$\mathrm{nevery}\cdot dt_{MD}$$, where $$dt_{MD}$$ is the MD timestep. By default, $$dm_{LB}$$ is set equal to 1.0, and $$dx_{LB}$$ is chosen so that $$\frac{\tau}{dt} = \frac{3\eta dt}{\rho dx^2}$$ is approximately equal to 1. However, the user has the option of specifying their own values for $$dm_{LB}$$, and $$dx_{LB}$$, by using the optional keywords dm, and dx respectively. Note Care must be taken when choosing both a value for $$dx_{LB}$$, and a simulation domain size. This fix uses the same subdivision of the simulation domain among processors as the main LAMMPS program. In order to uniformly cover the simulation domain with lattice sites, the lengths of the individual LAMMPS sub-domains must all be evenly divisible by $$dx_{LB}$$. If the simulation domain size is cubic, with equal lengths in all dimensions, and the default value for $$dx_{LB}$$ is used, this will automatically be satisfied. Physical parameters describing the fluid are specified through viscosity, density, and a0. If the force coupling constant is set the default way, the surface area associated with the MD particles is specified using the setArea keyword. If the user chooses to specify a value for the force coupling constant, this is set using the setGamma keyword. These parameters should all be given in terms of the mass, distance, and time units chosen for the main LAMMPS run, as they are scaled by the LB timestep, lattice spacing, and mass unit, inside the fix. The setArea keyword allows the user to associate a surface area with a given atom type. For example if a spherical composite object of radius R is represented as a spherical shell of N evenly distributed MD particles, all of the same type, the surface area per particle associated with that atom type should be set equal to $$\frac{4\pi R^2}{N}$$. This keyword should only be used if the force coupling constant, $$\gamma$$, is set the default way. The setGamma keyword allows the user to specify their own value for the force coupling constant, $$\gamma$$, instead of using the default value. The scaleGamma keyword should be used in conjunction with the setGamma keyword, when the user wishes to specify different $$\gamma$$ values for different atom types. This keyword allows the user to scale the setGamma $$\gamma$$ value by a factor, gammaFactor, for a given atom type. The dx keyword allows the user to specify a value for the LB grid spacing. The dm keyword allows the user to specify the LB mass unit. If the a0 keyword is used, the value specified is used for the square of the speed of sound in the fluid. If this keyword is not present, the speed of sound squared is set equal to $$\frac{1}{3}\left(\frac{dx_{LB}}{dt_{LB}}\right)^2$$. Setting $$a0 > (\frac{dx_{LB}}{dt_{LB}})^2$$ is not allowed, as this may lead to instabilities. If the noise keyword is used, followed by a positive temperature value, and a positive integer random number seed, a thermal lattice-Boltzmann algorithm is used. If LBtype is set equal to 1 (i.e. the standard LB integrator is chosen), the thermal LB algorithm of Adhikari et al. is used; however if LBtype is set equal to 2 both the LB integrator, and thermal LB algorithm described in Ollila et al. are used. If the calcforce keyword is used, both the fluid force and torque acting on the specified particle group are printed to the screen every N timesteps. If the keyword trilinear is used, the trilinear stencil is used to interpolate the particle nodes onto the fluid mesh. By default, the immersed boundary method, Peskin stencil is used. Both of these interpolation methods are described in Mackay et al.. If the keyword D3Q19 is used, the 19 velocity (D3Q19) lattice is used by the lattice-Boltzmann algorithm. By default, the 15 velocity (D3Q15) lattice is used. If the keyword write_restart is used, followed by a positive integer, N, a binary restart file is printed every N LB timesteps. This restart file only contains information about the fluid. Therefore, a LAMMPS restart file should also be written in order to print out full details of the simulation. Note When a large number of lattice grid points are used, the restart files may become quite large. In order to restart the fluid portion of the simulation, the keyword read_restart is specified, followed by the name of the binary lb_fluid restart file to be used. If the zwall_velocity keyword is used y-velocities are assigned to the lower and upper walls. This keyword requires the presence of walls in the z-direction. This is set by assigning fixed boundary conditions in the z-direction. If fixed boundary conditions are present in the z-direction, and this keyword is not used, the walls are assumed to be stationary. If the bodyforce keyword is used, a constant body force is added to the fluid, defined by it’s x, y and z components. If the printfluid keyword is used, followed by a positive integer, N, the fluid densities and velocities at each lattice site are printed to the screen every N timesteps. For further details, as well as descriptions and results of several test runs, see Mackay et al.. Please include a citation to this paper if the lb_fluid fix is used in work contributing to published research. Restart, fix_modify, output, run start/stop, minimize info: Due to the large size of the fluid data, this fix writes it’s own binary restart files, if requested, independent of the main LAMMPS binary restart files; no information about lb_fluid is written to the main LAMMPS binary restart files. None of the fix_modify options are relevant to this fix. No global or per-atom quantities are stored by this fix for access by various output commands. No parameter of this fix can be used with the start/stop keywords of the run command. This fix is not invoked during energy minimization. ## Restrictions This fix is part of the USER-LB package. It is only enabled if LAMMPS was built with that package. See the Build package doc page for more info. This fix can only be used with an orthogonal simulation domain. Walls have only been implemented in the z-direction. Therefore, the boundary conditions, as specified via the main LAMMPS boundary command must be periodic for x and y, and either fixed or periodic for z. Shrink-wrapped boundary conditions are not permitted with this fix. This fix must be used before any of fix lb/viscous, fix lb/momentum, fix lb/rigid/pc/sphere, and/ or fix lb/pc , as the fluid needs to be initialized before any of these routines try to access its properties. In addition, in order for the hydrodynamic forces to be added to the particles, this fix must be used in conjunction with the lb/viscous fix if the force coupling constant is set by default, or either the lb/viscous fix or one of the lb/rigid/pc/sphere or lb/pc integrators, if the user chooses to specify their own value for the force coupling constant. ## Default By default, the force coupling constant is set according to $\gamma = \frac{2m_um_v}{m_u+m_v}\left(\frac{1}{\Delta t_{collision}}\right)$ and an area of $$dx_{LB}^2$$ per node, used to calculate the fluid mass at the particle node location, is assumed. dx is chosen such that $$\frac{\tau}{dt_{LB}} = \frac{3\eta dt_{LB}}{\rho dx_{LB}^2}$$ is approximately equal to 1. dm is set equal to 1.0. a0 is set equal to $$\frac{1}{3}\left(\frac{dx_{LB}}{dt_{LB}}\right)^2$$. The Peskin stencil is used as the default interpolation method. The D3Q15 lattice is used for the lattice-Boltzmann algorithm. If walls are present, they are assumed to be stationary. (Ollila et al.) Ollila, S.T.T., Denniston, C., Karttunen, M., and Ala-Nissila, T., Fluctuating lattice-Boltzmann model for complex fluids, J. Chem. Phys. 134 (2011) 064902. (Mackay et al.) Mackay, F. E., Ollila, S.T.T., and Denniston, C., Hydrodynamic Forces Implemented into LAMMPS through a lattice-Boltzmann fluid, Computer Physics Communications 184 (2013) 2021-2031. (Mackay and Denniston) Mackay, F. E., and Denniston, C., Coupling MD particles to a lattice-Boltzmann fluid through the use of conservative forces, J. Comput. Phys. 237 (2013) 289-298. (Adhikari et al.) Adhikari, R., Stratford, K., Cates, M. E., and Wagner, A. J., Fluctuating lattice Boltzmann, Europhys. Lett. 71 (2005) 473-479.	2020-06-01T17:32:45	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6546381711959839, "perplexity": 1186.6476310801193}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347419056.73/warc/CC-MAIN-20200601145025-20200601175025-00170.warc.gz"}
https://finalfantasy.fandom.com/wiki/Holy_(ability)	## FANDOM 37,128 Pages Relm: I couldn't miss the chance to practice my drawing! Light our way! Yuna, Final Fantasy X Holy (ホーリー, Hōrī?), also known as Fade, White, or Pearl, is usually a powerful spell made up of pure energy that deals holy-elemental damage. Despite being one of the most powerful offensive spells, it is classified as White Magic and can often only be cast by White Mages. It is often a counterpart to the Black Magic spells Flare, Meteor or Ultima, and the spells often have similar graphics. Undead are usually weak to holy magic. In some games, characters or enemies may have access to an upgraded version, Holyja. ## Appearances Edit ### Final Fantasy Edit Damages all foes with holy light. Description Holy (FADE on the NES due to censorship) is a level 8 White Magic spell that inflicts heavy damage against all enemies. The total damage depends on the caster's Intellect. It is one of the most powerful offensive spells, second only to Flare. The spell can be bought at Gaia and be learned by the White Wizard. In the Dawn of Souls and 20th Anniversary Edition releases it costs 50 MP to cast. If a character wields the Sage's Staff when they cast this spell, the damage will be doubled. ### Final Fantasy II Edit Deals holy damage. Description Holy is a non-elemental White Magic spell learned from its respective scroll/tome. It can be bought at Mysidia and from the secret merchant underneath the waterfall in the Unknown Cave. Holy XVI can be used by Deumion and the Light Emperor. ### Final Fantasy III Edit Holy is a level 8 White Magic spell bought for 60,000 gil in Eureka. It deals light-elemental damage and can be used by the Devout and Sage. Unei can also cast Holy when she joins the party as a guest in the 3D versions, and the spell can be used through the item White Musk. It has a base power of 160. ### Final Fantasy IV Edit Causes holy damage. Description In the 2D versions Holy (White on the SNES due to censorship) can inflict Sap if the target is weak against it. In the 3D versions, Holy costs 50 MP, and has a spell power of 140 with 100% accuracy. It has a casting time of 3, cost 46 MP, spell power of 340 with a 75% accuracy. It is learned by Rosa (level 55 (2D) or level 60 (3D)), Porom (level 52), and Fusoya (default). The weapons Holy Lance and Asura's Rod cast Holy when used as an item, while the Lightbringer randomly casts it after attacking (though the latter two are only available in the GBA/PSP versions). Deathmask is the only enemy capable of casting this spell. In the Easy Type version, the casting time was reduced to 2. #### Final Fantasy IV -Interlude- Edit Holy is a White Magic spell learned by Rosa (level 55) and Porom (level 52). It deals major Holy-elemental damage to a single target at the cost of 46 MP. #### Final Fantasy IV: The After Years Edit Holy deals high Holy-elemental damage for 46 MP. It can be used by Porom (level 52), Leonora (level 70), Rosa (level 60), and Fusoya (default). There are some Band abilities that seem to use Holy, including Holy Burst and Holy Ray. ### Final Fantasy V Edit Holy is a level 6 White Magic spell that costs 20 MP to cast. It is obtained in the physical side of the Fork Tower after defeating Minotaur. When Minotaur is defeated, he attempts to use the spell, but fails due to having no MP. If the player uses an Ether on Minotaur, he will cast the spell. Holy can be properly cast by Barrier, Enuo, Exdeath in the final battle, Famed Mimic Gogo, Halicarnassus, and Neo Exdeath. The player may also use Holy by catching and releasing a Mini Dragon. Holy is one of the spells that can be cast from the Wonder Wand for free. ### Final Fantasy VI Edit Attacks with holy energy. Description Holy is classified as an Attack spell with a power of 108, a hit rate of 150, and is vulnerable to Runic. It can be learned by Terra (level 57) and Celes (level 72). Alexander teaches the spell at a rate of x2. It costs 40 MP to cast. Holy may be randomly cast when attacking with the Holy Rod, Holy Lance, or Lightbringer. Holy can be cast by Dullahan, Holy Dragon, Level 60 Magic, Level 80 Magic, Cherry, Magic, Master Tonberry, Behemoth King (Living), Warlock, Kaiser Dragon, and Tonberries. In the SNES/PS version, Holy was translated as "Pearl", but this may have had as much to do with Ted Woolsey's creative translations as censorship, as the spell White Wind was translated as "Pearl Wind". ### Final Fantasy VII Edit Holy serves as a plot device and cannot be used by the player in battle. Known as the "Ultimate White Magic" and summoned through the White Materia held by Aerith Gainsborough, it is the only spell capable of stopping Meteor, the "Ultimate Black Magic" summoned through the Black Materia that would destroy the world. Thus, it is more of a defensive spell than its other incarnations. Holy causes the Lifestream to attack a threat to the planet directly. Alexander's summon is the only holy-based attack, and summoning or connecting his Summon Materia to an Elemental Materia is the only other way to inflict holy-elemental damage. ### Final Fantasy VIII Edit Holy spell inflicts heavy holy-elemental damage on one opponent. It is a rare spell only drawn from bosses with the exception of Elnoyle. The player can also get one Holy spell from Zell's "love quest" if they give Fish & Blue as the answers to a "survey" held by girls at the library, and later return for the results. Holy is one of the best spells to junction onto HP and Magic. It can also be junctioned onto Elem-Atk-J and Elem-Def-J and can protect from certain status effects when junctioned onto ST-Def-J. The spell can also be used through the Holy Stone item. Casting Holy in battle increases compatibility with Alexander by 2, with Carbuncle and Leviathan by 1, with Eden by 0.4 and with Bahamut by 0.2, but lowers compatibility with Doomtrain by 2. ### Final Fantasy IX Edit Causes Holy damage. Description Holy is a White Magic spell for Eiko, learned through the White Robe or the Angel Flute, Eiko's ultimate weapon. Beatrix can cast the spell during the short time she is a playable character. Quina learns Lv. 4 Holy as Blue Magic, which deals Holy damage to enemies whose levels are multiples of four. Holy costs 36 MP to cast and has a power of 113. It can be reflected and works with Return Magic. The formula for Holy is as follows: $Base = Spell Power - Targets Magic Defense$ $Bonus = Mag ... [(Lv + Mag) / 8] + Mag$ $Damage = Base * Bonus$ The bosses Trance Kuja, Ozma, and Necron can use the spell. #### Tetra Master Edit Tetra Master #057 Location: Treno, Card Stadium Lindblum, Freak/Boy ### Final Fantasy X Edit Holy is a White Magic spell and the final ability in Yuna's section of the standard Sphere Grid; it is also at the end of Yuna's expert Sphere Grid, though it is obstructed by two sphere locks. It has a spell power of 100 and costs 85 MP to cast. Holy can be cast by Cindy and Ultima Weapon. It deals strong Holy damage to a single opponent. #### Final Fantasy X-2 Edit Holy can only be used by equipping the Supreme Light or Sacred Beast Garment Grids and spherechanging through the colored gates. Holy scores eight hits, though each causes less damage than the original. It costs 85 MP to cast. Holy can be cast by Haizhe (Oversoul - Fiend Arena), King VERMIN! (Oversoul), Paragon (Oversoul) and Stalwart (Oversoul). #### Final Fantasy X-2: Last Mission Edit Holy is a unique ability used by anyone using the White Mage dressphere as the main dress. It deals holy damage to one enemy and its range is three tiles ahead of the character, and costs 8 MP to cast. This section about an ability in Final Fantasy X-2: Last Mission is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it. ### Final Fantasy XI Edit Holy MP 100 Effect Deals Light-elemental damage; lowers Defense of undead. Duration Unknown (for undead defense reduction) Casting Time 0.75 sec Recast Time 60 sec Magic Type Divine Magic Element Light Jobs WHM 50 Light Spirit 50 PLD 55 Holy is a form of White Magic in the Divine Magic category. It is usable by White Mages and Paladins, but is not very strong. At a cost of 100 MP, the spell often deals only about 300 damage even to weak foes, unless a White Mage exploits Afflatus Misery. Holy II is cast by very high level White Mages and Paladins and Proto-Ultima and Alexander (high-level Notorious Monsters), the latter of which also has an attack called Mega Holy; these spells are rather powerful. ### Final Fantasy XII Edit In the original versions Holy is a Level 7 White Magick spell on the License Board. It requires 55 LP to unlock and 60 MP to cast. It deals Holy-elemental damage against a single target and has the maximum Effect Capacity, which means no other spell or Technick can be performed simultaneously. Holy can be purchased at Balfonheim Port after the events at the Pharos for 11,200 gil. In the Zodiac versions, Holy is a White Magick 11 license, and is obtained from a treasure at the Pharos's First Ascent/Wellspring Ravel. It used by White Mage and Monk job classes, though Monks can only learn it after getting the Esper Chaos license. It now costs 48 MP to cast. Reddas can use Holy when he joins as a guest. The Effect Capacity mechanic has been done away with. The Undying uses Piercing Holy, which penetrates a character's Reflect status. #### Final Fantasy XII: Revenant Wings Edit Holy is a spell that Penelo, the Esper Zalera, the Judge of Wings, White Mages, and Feolthanos can use. The spell deals damage to one foe. Zombies and vampyrs take extra damage from it. Penelo learns Holy at level 42. Zalera uses Holy as his regular attack. ### Final Fantasy XIV Edit Holy appeared in the original Final Fantasy XIV after the release of Patch 1.21. It was a White Mage spell available after completing the "Wheel of Disaster" job quest at level 45. The player would consume all of their MP to deal high damage to all enemies near the user and would inflict the bind status. Holy appears in the relaunch as a White Mage ability after completing the "Yearn for the Urn" job quest at level 45. Holy has a casting time of 3 seconds and has a recast time of 2.5 seconds. The spell inflicted damage with a potency of 200 to all enemies in range and inflicted the stun status for 4 seconds. As of the release of Final Fantasy XIV: Heavensward, Holy deals damage with full potency for the first enemy, damage dealt is now decreased by 10% for the second, 20% for the third, 30% for the fourth, 40% for the fifth, and 50% for all remaining enemies. Casting multiple times does not make the spell do diminishing damage, the damage instead cascades with the first target receiving 200, the second 180 and so on, to a minimum of 100 potency per enemy. At the initial release, Holy had a potency of 240 and a 4 second stun effect. After the release of patch 2.1, Holy had its potency lowered to 200 for game balance. ### Final Fantasy XV Edit Noctis smites foes with sacred energy and deals holy damage to nearby enemies when dodging their attacks with the Ring of the Lucii equipped in the weapon slot, and when in Armiger Unleashed mode. The ring can be equipped in Chapter 13 and Holy is the second spell Noctis learns on it. Armiger Unleashed can be obtained in the Windows and Royal Editions from the Keycatrich ruins' statue after Noctis has collected all 13 royal arms. Damage scales with Noctis's Magic and level. Holy is activated by tapping or holding the Phase/Defense button, and is a counterattack. Should the Phase/Defense button be held without Noctis being attacked, he will walk cautiously like in Phase Mode, but will be in a focused state to ready the spell when pressed to do so. Doing this gradually drains his MP at a rate of 10% per second. If Noctis successfully counters an enemy with Holy, he will recover 15% of his maximum MP (10% before Patch 1.06). Unlike phasing, this does not work against bullets. Blinking (timing the dodge perfectly) casts an especially strong Holy that deals 15 times more damage (thus it almost always hits the damage cap) and recovers 40% of Noctis's max MP. If far away, Noctis will teleport close to the enemy. This frequently puts enemies into a vulnerable state. If equipped with the Ardyn's Ensemble attire, it is easy to hit the damage cap with a Magic-built Noctis even without precisely timing the Holy, although the staggering effect of the special Holy is still useful. In earlier versions, Holy was noticeably louder. After patch 1.06, Holy's normal damage was halved, but its MP recovery was boosted by 50% and the recovery time between casts was removed. The patch adds the improved Holy activated via blinking. In the Windows and Royal Editions, dodging while in Armiger Unleashed also uses Holy. It naturally breaks the damage limit, unlike the Holy from the ring. Spamming Holy in Armiger Unleashed can put Noctis into Stasis. Holy (either from the Ring of the Lucii or Armiger Unleashed) will cancel out any active elemental effect on the field. ### Final Fantasy Tactics Edit White Magick that attacks the target with sacred light. Description Bright light, shine down on bloody impurity! Holy! Upon casting (PlayStation) Holy is a White Magic ability learned by the White Mage and costs 600 JP to learn. It costs 56 MP to use and has a speed of 17. Holy ignores the target's magic evasion unless the target has immunity against holy-elemental. Holy is considered the best attack spell to be calculated. ### Final Fantasy Tactics Advance Edit Emits a holy light to deal damage. Description Holy can be learned by Bishops through the Nirvana. It is usable by bangaa, but hume Paladins can learn a ranged weapon skill born of the spell called Holy Blade, which allows the player to attack with a double damage Holy-elemental weapon attack. A monster called Titania (Tactics Advance) can use a form of Holy magic called LV?D Holy that deals harsh Holy damage to all units with a level equal to the current day. Holy costs 32 MP to cast, has a Magic Power of 50, and has a range of 3. It can be retargeted back at the user through Return Magic and is stealable through the ability Steal: Ability. Holy cannot be reflected, but MP can be absorbed whenever it is cast. #### Final Fantasy Tactics A2: Grimoire of the Rift Edit Holy can be learned by Bishops through the Nirvana, has 3 range and costs 32 MP to cast. It deals holy damage and needs 400 AP to be mastered. There is also another ability called Holy Strike learned by Master Monks through the Sanjiegun. Unlike Holy, it uses Strength, costs no MP, but only has 1 range. Likewise, it deals holy damage and requires 350 AP to be mastered. ### Final Fantasy Tactics S Edit This section about an ability in Final Fantasy Tactics S is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it. ### Final Fantasy Type-0 Edit Holy casts a white sphere of energy that homes into the nearest opponent and renders them to stone upon death. It can be learned by completing Dominating the Dragon's Nest on Finis difficulty. It requires a Defense Magic stat of 95. ### Final Fantasy Crystal Chronicles Edit Holy is cast by combining any Fire, Blizzard, or Thunder Magicite with one Life Magicite, the latter being in the second command slot. It inflicts major Holy damage and also deals major damage to invisible enemies. #### Final Fantasy Crystal Chronicles: Ring of Fates Edit Holy deals a heavy amount of Holy damage to nearby enemies. It is cast by piling Cure, Clear, and Raise. #### Final Fantasy Crystal Chronicles: My Life as a King Edit Holy is the only holy spell ability, exclusive to the White Mage class, and caps at level 100. Its description falsely states that it deals damage to a single enemy but it actually deals holy-elemental damage to all enemies. It can be used once per battle, and up to five times a day. #### Final Fantasy Crystal Chronicles: Echoes of Time Edit Holy deals a heavy amount of Holy damage to nearby enemies. It is cast by stacking Cure and Raise target rings. It also makes traversing the library easier as it can destroy white orbs. ### Final Fantasy Mystic Quest Edit White is a powerful non-elemental Wizard Magic spell that can destroy all enemies quickly. It can be repelled. It can be used by Phoebe, Reuben, and Benjamin. It is second only to Flare. ### Final Fantasy Legend III Edit White is a non-elemental White Magic spell. It cost 36 MP to use, and it can be bought for 25000 GP in Dwelg Town (Underworld). It is much less powerful than Nuke and several Lost Magic spells. This loophole allows it to circumvent resistances. It was turned against the party by Agron after the death of Dion. It is Borgin's most powerful spell and a useful choice for him against the final boss, Xagor, who resists all elemental damage. ### Bravely Default Edit Holy is a level 6 White Magic spell that deals major light damage to one target. It costs 80 MP to use. It can be bought in Grandship for 6400 pg. Holy is a level 6 Sword Magic that imbues a weapon with a high-power light effect for ten turns. This will raise attack power by the amount of the magic effect. It costs 80 MP to use. It can be bought in Grandship (ch 5) for 6400 pg. #### Bravely Second: End Layer Edit Holy is a level 6 White Magic for the White Mage. It deals light-based elemental damage to one target. It costs 80 MP to use. It can be bought in Caldisla and Chompshire for 12800 pg. ### Final Fantasy Dimensions Edit Holy is a level 8 White Magic spell, learned and used by the White Mage and Seer and only usable by other jobs through the White Magic Lv. 8 job command. The player needs to complete the Mysidia Cavern before using the spell. Holy deals major Light elemental damage to a single target and costs 42 MP to use. Holy is one of the abilities needed for the Fusion Ability Final Heaven, along Earthshatter. ### Final Fantasy Dimensions II Edit Holy I-III are magic attacks available only for Aemo to use. The spells can only be learned from the White Mage signet. All Holy spells deal heavy light-elemental magic damage to an enemy and inflict more damage against undead and demon enemies. The spell costs 85 MP to use. In the original free-to-play versions, two versions of Holy were available. Holy I-IV could be used by any party member equipped with the Eiko signet. Lastly, Holy Z-Ω could also be used by any party member equipped with the White Mage god-type signet. The abilities functioned the same as Holy in the premium release. Each version dealt more damage depending on the summon's rank and had increased MP costs for each version of the spell. ### Dissidia Final Fantasy (2008) Edit Holy is a Bravery attack for Bartz and Terra, which they shoot five orbs of light that track opponents and begin a Chase Sequence. Terra's Holy costs 20 CP to equip and 140 AP to master, while Bartz's Holy costs 25 CP and 120 AP. Terra has a variation of Holy called Holy Combo, where she casts Holy and follows up by firing several Flare fireballs if it connects. Holy Combo costs 30 CP to equip and 300 AP to master. When Terra double-casts Holy or Holy Combo while in EX-Mode, she will fire two sets of three orbs each. Bartz's Holy can chain into Flare, while Terra's Holy Combo can chain into Ultima. Bartz knows Holy initially, while Terra learns Holy at Level 10 and Holy Combo at Level 19. Kuja has a variation of Holy called Ring Holy, where he fires three slow-moving rings of energy that track opponents. It costs 20 CP to equip and 120 AP to master. Kuja is able to use Ring Holy in the air initially and learns to use it on the ground at Level 33. Onion Knight casts Holy in his EX Burst as a Sage, where he summons a burst of light around his opponent. Kuja's HP attack Seraphic Star is based on the Holy spell's appearance in Final Fantasy IX, and is named "Holy Star" in the Japanese version of the game. The attack throws a sphere of light forward to trap and stun opponents before exploding. Kuja is able to cast it on the ground initially and learns to use it in the air at Level 9. It costs 40 CP to equip and 180 AP to master. In addition, the descriptions for Kuja's Strike Energy and Snatch Blow abilities state that he casts them by using holy. #### Dissidia 012 Final Fantasy Edit Aerith using Holy In addition to the Holy spells present in Dissidia, there are two new variants used by new characters. One is a Bravery attack usable by Prishe, and the other is an HP attack usable by the Assist-exclusive Aerith. Prishe's Holy fires an orb of white light that tracks the opponent. Prishe learns the attack at Level 15, and it costs 30 CP to use and 150 AP to master. Aerith's Holy is her HP attack when called as an Assist in the air. She charges energy for a period of time, then consumes the opponent in a blast of light. The attack has a long charge time, but is entirely unavoidable upon execution, striking directly around the opponent wherever they are. #### Dissidia Final Fantasy NT Edit Along with many characters retaining their Holy spells, Y'shtola also has Holy as an HP attack, directly lifted from her game's version of it, with the addition of it being able to draw in opponents before dealing damage. She also has a trap variation called Holy Snare which acts as a landmine that triggers when an enemy wanders within its proximity. This section about an ability in Dissidia Final Fantasy NT is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it. #### Dissidia Final Fantasy Opera Omnia Edit This section about an ability in Dissidia Final Fantasy Opera Omnia is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it. ### Theatrhythm Final Fantasy Curtain Call Edit Holy is a reactive ability that costs 25 CP to equip. It is activated just once in Battle Music Sequences (BMS) when the player makes a chain of 40 hits. It deals extra strength magic damage. It is learned by Rosa (level 95), Aerith (level 95), Eiko (level 80), Yuna (level 65), Y'shtola (level 90), and Benjamin (level 95). ### Theatrhythm Final Fantasy All-Star Carnival Edit This section about an ability in Theatrhythm Final Fantasy All-Star Carnival is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it. ### Pictlogica Final Fantasy Edit Holy XVI appears as a Premium Skill used by Minwu. This section about a spell in Pictlogica Final Fantasy is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it. #### Pictlogica Final Fantasy ≒ Edit This section about an ability in Pictlogica Final Fantasy ≒ is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it. ### Final Fantasy Airborne Brigade Edit This section about an ability in Final Fantasy Airborne Brigade is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it. ### Final Fantasy Artniks Edit This section about an ability in Final Fantasy Artniks is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it. ### Final Fantasy All the Bravest Edit Holy is the ability that the Devout used during battle. It is also an enemy ability that is used by the Deathmask during battle. ### Final Fantasy Record Keeper Edit Holy is a White Magic ability with a Rarity of 5☆. It deals four hits of massive holy elemental damage to one target, it can initially be used two twice and it can be honed to Rank 5. It can be made using Major White Orb x10, Major Ice Orb x6, Major Holy Orb x6, and 50000 gil. This section about an ability in Final Fantasy Record Keeper is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it. ### Final Fantasy Explorers Edit Concentrate holy energy in front of you and trigger a massive blast of light. Description This section about a spell in Final Fantasy Explorers is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it. ### Final Fantasy Brave Exvius Edit Deals light damage to one enemy. Description (Magic Spell) Holy is a Lv. 7 White Magic spell that costs 35 MP to use. It deals Light-elemental magic damage to one target, with a damage multiplier of x2.3. A handful of characters, such as Y'shtola, Eiko, and Trance Terra learn it, but it can also be obtained as an equippable ability via Trust Master Reward from Exdeath, and any character who equips the Holy Wand will also be granted the ability to use Holy along with the ability to cast white magic twice in a turn. Holy is also present through the Ring of the Lucii accessory, the Trust Master Reward of Noctis. Holy increases the unit's physical evasion by 25%, and when activated deals light-element magic damage to the attacker and restores 15 MP to the user. #### War of the Visions: Final Fantasy Brave ExviusEdit This section about an ability in War of the Visions: Final Fantasy Brave Exvius is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it. ### Mobius Final Fantasy Edit Holy is the Ultimate for Imam, and its upgraded forms, Avatar and Hierophant. This section about a spell in Mobius Final Fantasy is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it. ### World of Final Fantasy Edit Holy is a tier three light spell. It is used by Holy Dragon and Paleberry King and can be unlocked by having 2 members in a stack with tier two light spells. Enna Kros uses two variations of Holy: Kinda Sorta Holy and Pretty Strong Holy. ### Chocobo no Fushigi na Dungeon Edit This section about a spell in Chocobo no Fushigi na Dungeon is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it. #### Chocobo's Dungeon 2 Edit This section about a spell in Chocobo's Dungeon 2 is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it. ### Final Fantasy Fables: Chocobo's Dungeon Edit This section about a spell in Final Fantasy Fables: Chocobo's Dungeon is empty or needs to be expanded. You can help the Final Fantasy Wiki by expanding it. ### Final Fantasy Trading Card Game Edit Eiko's card featuring her FMV appearance uses W-White [Holy]. The ability allows the player to select up to two Forwards and deal them 8000 damage, but can only be used if the player has taken at least 5 damage. To use W-White [Holy], the player must Dull Eiko, discard another Eiko card, and pay two Earth CP. Porom's Amano art card can use Holy. For one Water CP, the discard of another Porom card, and Dulling Porom, Holy deals 2000 damage per card in the player's hand to a Forward of their choice. ## Non-Final Fantasy guest appearances Edit ### Ehrgeiz: God Bless the Ring Edit Holy Materia. Description Holy is a magic spell within the Forsaken Dungeon. The Basic Magic version attempts to confuse an enemy and consume one Magic Stone when used. The Ultra Magic version attempts to confuse multiple enemies, it consumes three Magic Stones when used. ### Chrono Cross Edit Casts a holy circle (annihilates undead). Description HolyLight is called Holy in the Japanese version. Any character can use this element, dealing both damage and inflicting the Fatigue statue effect on the intended target. Targets that are Undead are immediately annihilated. ### Kingdom Hearts series Edit Holy, also called Faith and Pearl, appears as a recurring light-based attack and is often one of the strongest attacks available. It calls on one or more pillars of light to damage enemies. In Chain of Memories and Re:Chain of Memories, Sora can learn Holy. In Kingdom Hearts II, King Mickey uses Pearl as an action ability and Queen Minnie can use Faith as a Reaction Command. In 358/2 Days, Holy appears as Mickey's Limit Break. In Birth by Sleep, Ventus can create Faith through Command Melding. In Re:coded, Data-Sora can purchase Faith. In Dream Drop Distance, both Sora and Riku can purchase Faith as Ability Links. In Kingdom Hearts χ, players can use Holy with a SR+ King Mickey card. ### Mario Hoops 3-on-3 Edit Holy Shot is the special shot of the unlockable White Mage character. ### Mario Sports Mix Edit White Mage's special shot consists of her yelling "Holy!" and then using it to rapidly shoot the item she has at an opponent. ### Valkyrie Anatomia Edit Holy appears as a spell used by Aemo. ## Names in other languages Edit • Italian: Sancta - Latin word for "holy" • Spanish: Sanctus • French: Sidéral (meaning "Sidereal"), Sacre (meaning "Coronation"), or Lumière (meaning "Light") • German: Sanctus ## Gallery Edit This gallery is incomplete and requires Final Fantasy X-2: Last Mission, Final Fantasy Type-0 and Final Fantasy Crystal Chronicles: My Life as a King added. You can help the Final Fantasy Wiki by uploading images. ## Etymology Edit A pearl is a hard object produced within the soft tissue (specifically the mantle) of a living shelled mollusk. Just like the shell of a clam, a pearl is composed of calcium carbonate in minute crystalline form, which has been deposited in concentric layers. The ideal pearl is perfectly round and smooth, but many other shapes (baroque pearls) occur. The finest quality natural pearls have been highly valued as gemstones and objects of beauty for many centuries. Because of this, pearl has become a metaphor for something rare, fine, admirable and valuable. 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https://zbmath.org/authors/?q=ai%3Asaad.yousef	Compute Distance To: Documents Indexed: 195 Publications since 1974, including 4 Books 4 Contributions as Editor Co-Authors: 124 Co-Authors with 149 Joint Publications 3,083 Co-Co-Authors all top 5 ### Co-Authors 45 single-authored 15 Xi, Yuanzhe 10 Chelikowsky, James R. 10 Li, Ruipeng 8 Chen, Jie 8 Chow, Edmond G. W. 7 Schultz, Martin H. 6 Wu, Kesheng 6 Zhou, Yunkai 5 Kalantzis, Vassilis 5 Soulaimani, Azzeddine 5 Stathopoulos, Andreas 5 Ubaru, Shashanka 5 Zhang, Jun 4 Bellalij, Mohammed 4 Sosonkina, Maria 4 Tiago, Murilo L. 3 Bollhöfer, Matthias 3 Brown, Peter N. 3 Chan, Tony Fan-Cheong 3 Fang, Haw-ren 3 Gallopoulos, Efstratios 3 Li, Na 3 Li, Zhongze 3 Little, Leigh 3 MacLachlan, Scott P. 3 Osei-Kuffuor, Daniel 3 Polizzi, Eric 3 Sameh, Ahmed H. 3 Seghouane, Abd-Krim 3 Sosonkina, Masha 3 Vecharynski, Eugene 2 Chapman, Andrew M. 2 de Hoop, Maarten V. 2 Erlandson, Lucas 2 Giraud, Luc 2 Gowda, Shivaraju B. 2 Jain, Manish Kumar 2 Ngo, T. T. 2 Philippe, Bernard J. 2 Sadok, Hassane 2 Saylor, Paul E. 2 Sidje, Roger B. 2 Tang, Jok M. 2 Truhlar, Donald G. 2 Van der Vorst, Henk Albertus 2 Yang, Chao 2 Yeung, Man-Chung 2 Zheng, Qingqing 1 Alemany, M. M. G. 1 Anderson, Edward 1 Anitescu, Mihai 1 Arbenz, Peter 1 Aurentz, Jared Lee 1 Axelsson, Axel Owe Holger 1 Bekas, Constantine 1 Bekas, Costas 1 Ben Salah, Nizar 1 Boley, Daniel L. 1 Brezinski, Claude 1 Cai, Difeng 1 Cai, Xiao-Chuan 1 Calgaro, Caterina 1 Castillo, Paul E. 1 Chehab, Jean-Paul 1 Choi, Hyoung Gwon 1 Collins, Lee A. 1 D’Ambra, Pasqua 1 De La Grandmaison, Emmanuel Lorin 1 Dillon, Geoffrey 1 Duff, Iain S. 1 El-Guide, Mohamed 1 Elman, Howard C. 1 Erhel, Jocelyne 1 Froese Fischer, Charlotte 1 Gear, Charles William 1 Giannakis, Georgios B. 1 Grama, Ananth Y. 1 Guillaume, Philippe 1 Guyomarc’h, Frédéric 1 Haidar, Azzam 1 Hénon, Pascal 1 Ilić, Miloš 1 Ipsen, Ilse C. F. 1 Jay, Laurent-Olivier 1 Johnsson, S. Lennart 1 Kechroud, Riyad 1 Kerkhoven, Thomas 1 Kestyn, James 1 Keyes, David Elliot 1 Kim, Hanchul 1 Kronik, Leeor 1 Le Calvez, Caroline 1 Lin, Lin 1 Liu, Xiao 1 Ma, Sangback 1 Mazumdar, Arya 1 Melson, John T. 1 Międlar, Agnieszka 1 Moreau, Stéphane 1 Nath Datta, Biswa ...and 24 more Co-Authors all top 5 ### Serials 34 SIAM Journal on Scientific Computing 23 Numerical Linear Algebra with Applications 17 SIAM Journal on Matrix Analysis and Applications 11 SIAM Journal on Scientific and Statistical Computing 7 Computer Physics Communications 6 Journal of Computational and Applied Mathematics 6 SIAM Journal on Numerical Analysis 6 Applied Numerical Mathematics 6 Linear Algebra and its Applications 6 ETNA. Electronic Transactions on Numerical Analysis 4 Mathematics of Computation 4 Parallel Computing 4 SIAM Review 3 Computer Methods in Applied Mechanics and Engineering 3 Neural Computation 3 Numerical Algorithms 2 International Journal for Numerical Methods in Fluids 2 Journal of Computational Physics 2 Numerische Mathematik 2 Journal of Scientific Computing 2 International Journal of High Speed Computing 1 Computers & Mathematics with Applications 1 IEEE Transactions on Information Theory 1 BIT 1 IEEE Transactions on Automatic Control 1 Mathematics and Computers in Simulation 1 Operations Research 1 IEEE Transactions on Signal Processing 1 Pattern Recognition 1 SIAM Journal on Optimization 1 Engineering Analysis with Boundary Elements 1 International Journal of Computational Fluid Dynamics 1 Journal of Machine Learning Research (JMLR) 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 1 Classics in Applied Mathematics 1 Numerical Mathematics: Theory, Methods and Applications 1 S$$\vec{\text{e}}$$MA Journal all top 5 ### Fields 184 Numerical analysis (65-XX) 23 Partial differential equations (35-XX) 20 Linear and multilinear algebra; matrix theory (15-XX) 14 Computer science (68-XX) 14 Fluid mechanics (76-XX) 7 Statistical mechanics, structure of matter (82-XX) 5 General and overarching topics; collections (00-XX) 5 Operations research, mathematical programming (90-XX) 4 Probability theory and stochastic processes (60-XX) 4 Systems theory; control (93-XX) 3 Combinatorics (05-XX) 3 Quantum theory (81-XX) 3 Information and communication theory, circuits (94-XX) 2 Special functions (33-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 History and biography (01-XX) 1 Ordinary differential equations (34-XX) 1 Approximations and expansions (41-XX) 1 Statistics (62-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX) ### Citations contained in zbMATH Open 172 Publications have been cited 9,670 times in 6,485 Documents Cited by Year GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. Zbl 0599.65018 1986 Parallel iterative methods for sparse linear systems. Zbl 1002.65042 2001 Iterative methods for sparse linear systems. 2nd ed. Zbl 1031.65046 2003 A flexible inner-outer preconditioned GMRES algorithm. Zbl 0780.65022 1993 Iterative methods for sparse linear systems. Zbl 1031.65047 1996 Numerical methods for large eigenvalue problems. Zbl 0991.65039 1992 Numerical methods for large eigenvalue problems. Revised ed. Zbl 1242.65068 2011 Hybrid Krylov methods for nonlinear systems of equations. Zbl 0708.65049 1990 Analysis of some Krylov subspace approximations to the matrix exponential operator. Zbl 0749.65030 1992 ILUT: A dual threshold incomplete LU factorization. Zbl 0838.65026 1994 Krylov subspace methods for solving large unsymmetric linear systems. Zbl 0474.65019 1981 Efficient solution of parabolic equations by Krylov approximation methods. Zbl 0757.65101 1992 Variations on Arnoldi’s method for computing eigenelements of large unsymmetric matrices. Zbl 0456.65017 1980 Convergence theory of nonlinear Newton-Krylov algorithms. Zbl 0814.65048 1994 Iterative solution of linear systems in the 20th century. Zbl 0965.65051 Saad, Yousef; van der Vorst, Henk A. 2000 Approximate inverse preconditioners via sparse-sparse iterations. Zbl 0922.65034 1998 On the rates of convergence of the Lanczos and the block-Lanczos methods. Zbl 0456.65016 1980 Two classes of multisecant methods for nonlinear acceleration. Zbl 1224.65134 2009 Experimental study of ILU preconditioners for indefinite matrices. Zbl 0891.65028 1997 Chebyshev acceleration techniques for solving nonsymmetric eigenvalue problems. Zbl 0539.65013 1984 The Lanczos biorthogonalization algorithm and other oblique projection methods for solving large unsymmetric systems. Zbl 0483.65022 1982 Numerical methods for electronic structure calculations of materials. Zbl 1185.82004 Saad, Yousef; Chelikowsky, James R.; Shontz, Suzanne M. 2010 Deflated and augmented Krylov subspace techniques. Zbl 0889.65028 1997 Practical use of polynomial preconditionings for the conjugate gradient method. Zbl 0601.65019 1985 A deflated version of the conjugate gradient algorithm. Zbl 0955.65021 Saad, Y.; Yeung, M.; Erhel, J.; Guyomarc’h, F. 2000 ILUM: A multi-elimination ILU preconditioner for general sparse matrices. Zbl 0858.65029 1996 Krylov subspace methods on supercomputers. Zbl 0693.65028 1989 Conjugate gradient-like algorithms for solving nonsymmetric linear systems. Zbl 0566.65019 1985 On the Lanczos method for solving symmetric linear systems with several right-hand sides. Zbl 0615.65038 1987 Dynamic thick restarting of the Davidson, and the implicitly restarted Arnoldi methods. Zbl 0924.65028 Stathopoulos, Andreas; Saad, Yousef; Wu, Kesheng 1998 Approximate inverse techniques for block-partitioned matrices. Zbl 0888.65035 1997 Arnoldi methods for large Sylvester-like observer matrix equations, and an associated algorithm for partial spectrum assignment. Zbl 0734.65037 1991 ARMS: an algebraic recursive multilevel solver for general sparse linear systems. Zbl 1071.65001 2002 Crout versions of ILU for general sparse matrices. Zbl 1042.65025 Li, Na; Saad, Yousef; Chow, Edmond 2003 Preconditioning techniques for nonsymmetric and indefinite linear systems. Zbl 0662.65028 1988 Analysis of augmented Krylov subspace methods. Zbl 0871.65026 1997 Self-consistent-field calculations using Chebyshev-filtered subspace iteration. Zbl 1105.65111 Zhou, Yunkai; Saad, Yousef; Tiago, Murilo L.; Chelikowsky, James R. 2006 BILUM: Block versions of multielimination and multilevel ILU preconditioner for general sparse linear systems. Zbl 0956.65026 1999 Efficient estimation of eigenvalue counts in an interval. Zbl 1413.65092 Di Napoli, Edoardo; Polizzi, Eric; Saad, Yousef 2016 Iterative solution of linear equations in ODE codes. Zbl 0541.65051 1983 A parallel block cyclic reduction algorithm for the fast solution of elliptic equations. Zbl 0676.65098 1989 Numerical methods in Markov chain modeling. Zbl 0764.65095 Philippe, Bernard; Saad, Youcef; Stewart, William J. 1992 Distributed Schur complement techniques for general sparse linear systems. Zbl 0955.65020 2000 An estimator for the diagonal of a matrix. Zbl 1123.65026 Bekas, C.; Kokiopoulou, E.; Saad, Y. 2007 A probing method for computing the diagonal of a matrix inverse. Zbl 1274.65132 2012 BILUTM: A domain-based multilevel block ILUT preconditioner for general sparse matrices. Zbl 0942.65045 1999 Projection and deflation methods for partial pole assignment in linear state feedback. Zbl 0641.93031 1988 Approximating spectral densities of large matrices. Zbl 1338.15026 Lin, Lin; Saad, Yousef; Yang, Chao 2016 Practical use of some Krylov subspace methods for solving indefinite and nonsymmetric linear systems. Zbl 0539.65012 1984 Preconditioning Helmholtz linear systems. Zbl 1190.65048 2010 A filtered Lanczos procedure for extreme and interior eigenvalue problems. Zbl 1253.65053 2012 A hybrid Chebyshev Krylov subspace algorithm for solving nonsymmetric systems of linear equations. Zbl 0613.65031 Elman, Howard C.; Saad, Youcef; Saylor, Paul E. 1986 Trace optimization and eigenproblems in dimension reduction methods. Zbl 1249.65075 Kokiopoulou, E.; Chen, Jie; Saad, Yousef 2011 Multilevel preconditioners constructed from inverse-based ILUs. Zbl 1104.65037 2006 An arbitrary Lagrangian-Eulerian finite element method for solving three-dimensional free surface flows. Zbl 0948.76043 1998 Numerical solution of large nonsymmetric eigenvalue problems. Zbl 0798.65053 1989 Least squares polynomials in the complex plane and their use for solving nonsymmetric linear systems. Zbl 0619.65022 1987 Restarting techniques for the (Jacobi-)Davidson symmetric eigenvalue method. Zbl 0912.65027 1998 Shanks sequence transformations and Anderson acceleration. Zbl 1395.65001 Brezinski, Claude; Redivo-Zaglia, Michela; Saad, Yousef 2018 A thick-restart Lanczos algorithm with polynomial filtering for Hermitian eigenvalue problems. Zbl 1348.65071 Li, Ruipeng; Xi, Yuanzhe; Vecharynski, Eugene; Yang, Chao; Saad, Yousef 2016 An algebraic multilevel preconditioner with low-rank corrections for sparse symmetric matrices. Zbl 1376.65036 Xi, Yuanzhe; Li, Ruipeng; Saad, Yousef 2016 Preconditioning techniques for the solution of the Helmholtz equation by the finite element method. Zbl 1059.65105 2004 High-order ILU preconditioners for CFD problems. Zbl 0959.76077 Chapman, Andrew; Saad, Yousef; Wigton, Larry 2000 A Chebyshev-Davidson algorithm for large symmetric eigenproblems. Zbl 1151.65321 2007 pARMS: a parallel version of the algebraic recursive multilevel solver. Zbl 1071.65532 Li, Zhongze; Saad, Yousef; Sosonkina, Masha 2003 Fast estimation of $$\mathrm{tr}(f(A))$$ via stochastic Lanczos quadrature. Zbl 1386.65125 Ubaru, Shashanka; Chen, Jie; Saad, Yousef 2017 Overlapping domain decomposition algorithms for general sparse matrices. Zbl 0851.65083 1996 Solving sparse triangular linear systems on parallel computers. Zbl 0726.65026 1989 Complex shift and invert strategies for real matrices. Zbl 0623.65045 1987 Robust preconditioning of large, sparse, symmetric eigenvalue problems. Zbl 0857.65040 Stathopoulos, Andreas; Saad, Yousef; Fischer, Charlotte F. 1995 On the tensor SVD and the optimal low rank orthogonal approximation of tensors. Zbl 1184.65043 2009 On acceleration methods for coupled nonlinear elliptic systems. Zbl 0724.65095 1992 Block Krylov-Schur method for large symmetric eigenvalue problems. Zbl 1153.65330 2008 The trace ratio optimization problem. Zbl 1251.65090 Ngo, T. T.; Bellalij, M.; Saad, Y. 2012 Inexact Newton preconditioning techniques for large symmetric eigenvalue problems. Zbl 0916.65035 Wu, Kesheng; Saad, Yousef; Stathopoulos, Andreas 1998 Schur complement-based domain decomposition preconditioners with low-rank corrections. Zbl 1399.65238 Li, Ruipeng; Xi, Yuanzhe; Saad, Yousef 2016 A spectrum slicing method for the Kohn-Sham problem. Zbl 1264.82014 2012 Divide and conquer low-rank preconditioners for symmetric matrices. Zbl 1362.65036 2013 Chebyshev-filtered subspace iteration method free of sparse diagonalization for solving the Kohn-Sham equation. Zbl 1351.82098 Zhou, Yunkai; Chelikowsky, James R.; Saad, Yousef 2014 Solution of large eigenvalue problems in electronic structure calculations. Zbl 0862.65059 Saad, Y.; Stathopoulos, A.; Chelikowsky, J.; Wu, K.; Öǧüt, S. 1996 MIQR: a multilevel incomplete QR preconditioner for large sparse least-squares problems. Zbl 1113.65036 2006 Incremental incomplete LU factorizations with applications. Zbl 1240.65091 Calgaro, Caterina; Chehab, Jean-Paul; Saad, Yousef 2010 Low-rank correction methods for algebraic domain decomposition preconditioners. Zbl 1371.65029 2017 On the relations between ILUs and factored approximate inverses. Zbl 1017.65019 2002 Computing partial spectra with least-squares rational filters. Zbl 1351.65026 2016 Iterative solution of indefinite symmetric linear systems by methods using orthogonal polynomials over two disjoint intervals. Zbl 0547.65028 1983 Enhanced multi-level block ILU preconditioning strategies for general sparse linear systems. Zbl 1010.65014 2001 Multilevel ILU with reorderings for diagonal dominance. Zbl 1091.65034 2005 A greedy strategy for coarse-grid selection. Zbl 1154.65016 2007 Fast approximate $$k$$NN graph construction for high dimensional data via recursive Lanczos bisection. Zbl 1235.68137 Chen, Jie; Fang, Haw-Ren; Saad, Yousef 2009 Electronic structure calculations for plane-wave codes without diagonalization. Zbl 1001.65038 Jay, Laurent O.; Kim, Hanchul; Saad, Yousef; Chelikowsky, James R. 1999 Domain decomposition and multi-level type techniques for general sparse linear systems. Zbl 0909.65020 Saad, Yousef; Sosonkina, Maria; Zhang, Jun 1998 Data communication in parallel architectures. Zbl 0681.68007 1989 ILUS: An incomplete LU preconditioner in sparse skyline format. Zbl 0896.76037 1997 Complexity of dense-linear-system solution on a multiprocessor ring. Zbl 0587.65022 Ipsen, Ilse C. F.; Saad, Youcef; Schultz, Martin H. 1986 Alternating direction methods on multiprocessors. Zbl 0625.65105 Johnsson, S. Lennart; Saad, Youcef; Schultz, Martin H. 1987 A parallel multistage ILU factorization based on a hierarchical graph decomposition. Zbl 1126.65028 2006 The trace ratio optimization problem for dimensionality reduction. Zbl 1209.65063 Ngo, T. T.; Bellalij, M.; Saad, Y. 2010 Crout versions of ILU factorization with pivoting for sparse symmetric matrices. Zbl 1075.65045 2005 Diagonal threshold techniques in robust multi-level ILU preconditioners for general sparse linear systems. Zbl 0982.65057 1999 A power Schur complement low-rank correction preconditioner for general sparse linear systems. Zbl 07340707 Zheng, Qingqing; Xi, Yuanzhe; Saad, Yousef 2021 Solving the three-dimensional high-frequency Helmholtz equation using contour integration and polynomial preconditioning. Zbl 1434.65234 Liu, Xiao; Xi, Yuanzhe; Saad, Yousef; de Hoop, Maarten V. 2020 A rational approximation method for solving acoustic nonlinear eigenvalue problems. Zbl 1464.76086 El-Guide, Mohamed; Miȩdlar, Agnieszka; Saad, Yousef 2020 Iterative methods for linear systems of equations: a brief historical journey. Zbl 1477.65063 2020 Multicolor low-rank preconditioner for general sparse linear systems. Zbl 1474.65070 Zheng, Qingqing; Xi, Yuanzhe; Saad, Yousef 2020 The eigenvalues slicing library (EVSL): algorithms, implementation, and software. Zbl 1420.65050 Li, Ruipeng; Xi, Yuanzhe; Erlandson, Lucas; Saad, Yousef 2019 Shanks sequence transformations and Anderson acceleration. Zbl 1395.65001 Brezinski, Claude; Redivo-Zaglia, Michela; Saad, Yousef 2018 Beyond automated multilevel substructuring: domain decomposition with rational filtering. Zbl 1394.65030 Kalantzis, Vassilis; Xi, Yuanzhe; Saad, Yousef 2018 A hierarchical low rank Schur complement preconditioner for indefinite linear systems. Zbl 1392.65027 Dillon, Geoffrey; Kalantzis, Vassilis; Xi, Yuanzhe; Saad, Yousef 2018 Domain decomposition approaches for accelerating contour integration eigenvalue solvers for symmetric eigenvalue problems. Zbl 06986991 Kalantzis, Vassilis; Kestyn, James; Polizzi, Eric; Saad, Yousef 2018 Phase retrieval via reweighted amplitude flow. Zbl 1415.94269 Wang, Gang; Giannakis, Georgios B.; Saad, Yousef; Chen, Jie 2018 SMASH: structured matrix approximation by separation and hierarchy. Zbl 07031743 Cai, Difeng; Chow, Edmond; Erlandson, Lucas; Saad, Yousef; Xi, Yuanzhe 2018 Fast estimation of $$\mathrm{tr}(f(A))$$ via stochastic Lanczos quadrature. Zbl 1386.65125 Ubaru, Shashanka; Chen, Jie; Saad, Yousef 2017 Low-rank correction methods for algebraic domain decomposition preconditioners. Zbl 1371.65029 2017 A rational function preconditioner for indefinite sparse linear systems. Zbl 1368.65044 2017 Low rank approximation and decomposition of large matrices using error correcting codes. Zbl 1374.94851 Ubaru, Shashanka; Mazumdar, Arya; Saad, Yousef 2017 Cucheb: a GPU implementation of the filtered Lanczos procedure. Zbl 1411.65005 Aurentz, Jared L.; Kalantzis, Vassilis; Saad, Yousef 2017 Efficient estimation of eigenvalue counts in an interval. Zbl 1413.65092 Di Napoli, Edoardo; Polizzi, Eric; Saad, Yousef 2016 Approximating spectral densities of large matrices. Zbl 1338.15026 Lin, Lin; Saad, Yousef; Yang, Chao 2016 A thick-restart Lanczos algorithm with polynomial filtering for Hermitian eigenvalue problems. Zbl 1348.65071 Li, Ruipeng; Xi, Yuanzhe; Vecharynski, Eugene; Yang, Chao; Saad, Yousef 2016 An algebraic multilevel preconditioner with low-rank corrections for sparse symmetric matrices. Zbl 1376.65036 Xi, Yuanzhe; Li, Ruipeng; Saad, Yousef 2016 Schur complement-based domain decomposition preconditioners with low-rank corrections. Zbl 1399.65238 Li, Ruipeng; Xi, Yuanzhe; Saad, Yousef 2016 Computing partial spectra with least-squares rational filters. Zbl 1351.65026 2016 Spectral Schur complement techniques for symmetric eigenvalue problems. Zbl 1352.65118 Kalantzis, Vassilis; Li, Ruipeng; Saad, Yousef 2016 Matrix reordering using multilevel graph coarsening for ILU preconditioning. Zbl 1315.65033 Osei-Kuffuor, Daniel; Li, Ruipeng; Saad, Yousef 2015 Spectral recycling strategies for the solution of nonlinear eigenproblems in thermoacoustics. Zbl 1374.65090 Salas, Pablo; Giraud, Luc; Saad, Yousef; Moreau, Stéphane 2015 Chebyshev-filtered subspace iteration method free of sparse diagonalization for solving the Kohn-Sham equation. Zbl 1351.82098 Zhou, Yunkai; Chelikowsky, James R.; Saad, Yousef 2014 Preconditioned Krylov subspace methods for sampling multivariate Gaussian distributions. Zbl 1296.60087 2014 Graph partitioning using matrix values for preconditioning symmetric positive definite systems. Zbl 1290.65025 Vecharynski, Eugene; Saad, Yousef; Sosonkina, Masha 2014 Divide and conquer low-rank preconditioners for symmetric matrices. Zbl 1362.65036 2013 A probing method for computing the diagonal of a matrix inverse. Zbl 1274.65132 2012 A filtered Lanczos procedure for extreme and interior eigenvalue problems. Zbl 1253.65053 2012 The trace ratio optimization problem. Zbl 1251.65090 Ngo, T. T.; Bellalij, M.; Saad, Y. 2012 A spectrum slicing method for the Kohn-Sham problem. Zbl 1264.82014 2012 Modification and compensation strategies for threshold-based incomplete factorizations. Zbl 1241.65032 Maclachlan, S.; Osei-Kuffuor, D.; Saad, Yousef 2012 Numerical methods for large eigenvalue problems. Revised ed. Zbl 1242.65068 2011 Trace optimization and eigenproblems in dimension reduction methods. Zbl 1249.65075 Kokiopoulou, E.; Chen, Jie; Saad, Yousef 2011 Computing $$f(A)b$$ via least squares polynomial approximations. Zbl 1234.65027 Chen, Jie; Anitescu, Mihai; Saad, Yousef 2011 Domain-decomposition-type methods for computing the diagonal of a matrix inverse. Zbl 1232.65048 2011 Rational approximation to the Fermi-Dirac function with applications in density functional theory. Zbl 1211.65026 2011 Numerical methods for electronic structure calculations of materials. Zbl 1185.82004 Saad, Yousef; Chelikowsky, James R.; Shontz, Suzanne M. 2010 Preconditioning Helmholtz linear systems. Zbl 1190.65048 2010 Incremental incomplete LU factorizations with applications. Zbl 1240.65091 Calgaro, Caterina; Chehab, Jean-Paul; Saad, Yousef 2010 The trace ratio optimization problem for dimensionality reduction. Zbl 1209.65063 Ngo, T. T.; Bellalij, M.; Saad, Y. 2010 Further analysis of the Arnoldi process for eigenvalue problems. Zbl 1210.65085 2010 Computing $$exp(-\tau A) b$$ with Laguerre polynomials. Zbl 1205.65165 Sheehan, Bernard N.; Saad, Yousef; Sidje, Roger B. 2010 Sparse approximations of the Schur complement for parallel algebraic hybrid solvers in 3D. Zbl 1240.65093 Giraud, L.; Haidar, A.; Saad, Y. 2010 Two classes of multisecant methods for nonlinear acceleration. Zbl 1224.65134 2009 On the tensor SVD and the optimal low rank orthogonal approximation of tensors. Zbl 1184.65043 2009 Fast approximate $$k$$NN graph construction for high dimensional data via recursive Lanczos bisection. Zbl 1235.68137 Chen, Jie; Fang, Haw-Ren; Saad, Yousef 2009 Enhanced graph-based dimensionality reduction with repulsion Laplaceans. Zbl 1176.68182 2009 Block Krylov-Schur method for large symmetric eigenvalue problems. Zbl 1153.65330 2008 Computation of large invariant subspaces using polynomial filtered Lanczos iterations with applications in density functional theory. Zbl 1159.65319 Bekas, C.; Kokiopoulou, E.; Saad, Yousef 2008 Analysis of some Krylov subspace methods for normal matrices via approximation theory and convex optimization. Zbl 1171.65019 2008 An estimator for the diagonal of a matrix. Zbl 1123.65026 Bekas, C.; Kokiopoulou, E.; Saad, Y. 2007 A Chebyshev-Davidson algorithm for large symmetric eigenproblems. Zbl 1151.65321 2007 A greedy strategy for coarse-grid selection. Zbl 1154.65016 2007 On correction equations and domain decomposition for computing invariant subspaces. Zbl 1173.65320 2007 Greedy coarsening strategies for nonsymmetric problems. Zbl 1149.65022 2007 Self-consistent-field calculations using Chebyshev-filtered subspace iteration. Zbl 1105.65111 Zhou, Yunkai; Saad, Yousef; Tiago, Murilo L.; Chelikowsky, James R. 2006 Multilevel preconditioners constructed from inverse-based ILUs. Zbl 1104.65037 2006 MIQR: a multilevel incomplete QR preconditioner for large sparse least-squares problems. Zbl 1113.65036 2006 A parallel multistage ILU factorization based on a hierarchical graph decomposition. Zbl 1126.65028 2006 SchurRAS: A restricted version of the overlapping Schur complement preconditioner. Zbl 1099.65034 2006 Filtered conjugate residual-type algorithms with applications. Zbl 1120.65046 2006 Multilevel ILU with reorderings for diagonal dominance. Zbl 1091.65034 2005 Crout versions of ILU factorization with pivoting for sparse symmetric matrices. Zbl 1075.65045 2005 Computation of smallest eigenvalues using spectral Schur complements. Zbl 1091.65035 2005 Efficient computation of the coupling matrix in time-dependent density functional theory. Zbl 1196.65188 De La Grandmaison, Emmanuel Lorin; Gowda, Shivaraju B.; Saad, Yousef; Tiago, Murilo L.; Chelikowsky, James R. 2005 Preconditioning techniques for the solution of the Helmholtz equation by the finite element method. Zbl 1059.65105 2004 Variations on algebraic recursive multilevel solvers (ARMS) for the solution of CFD problems. Zbl 1112.76054 Saad, Yousef; Soulaimani, Azzeddine; Touihri, Ridha 2004 Iterative methods for sparse linear systems. 2nd ed. Zbl 1031.65046 2003 Crout versions of ILU for general sparse matrices. Zbl 1042.65025 Li, Na; Saad, Yousef; Chow, Edmond 2003 pARMS: a parallel version of the algebraic recursive multilevel solver. Zbl 1071.65532 Li, Zhongze; Saad, Yousef; Sosonkina, Masha 2003 Finding exact and approximate block structures for ILU preconditioning. Zbl 1034.65020 2003 Block LU preconditioners for symmetric and nonsymmetric saddle point problems. Zbl 1042.65026 Little, Leigh; Saad, Yousef; Smoch, Laurent 2003 Block preconditioners for saddle point problems. Zbl 1030.65036 2003 ARMS: an algebraic recursive multilevel solver for general sparse linear systems. Zbl 1071.65001 2002 On the relations between ILUs and factored approximate inverses. Zbl 1017.65019 2002 A factored approximate inverse preconditioner with pivoting. Zbl 0999.65027 2002 Enhanced GMRES acceleration techniques for some CFD problems. Zbl 1007.76071 Souläimani, Azzeddine; Ben Salah, Nizar; Saad, Yousef 2002 pARMS: A package for solving general sparse linear systems on parallel computers. Zbl 1057.65523 2002 Parallel iterative methods for sparse linear systems. Zbl 1002.65042 2001 Enhanced multi-level block ILU preconditioning strategies for general sparse linear systems. Zbl 1010.65014 2001 An edge-based stabilized finite element method for solving compressible flows: formulation and parallel implementation. Zbl 1116.76391 Soulaimani, Azzeddine; Saad, Yousef; Rebaine, Ali 2001 Iterative solution of linear systems in the 20th century. Zbl 0965.65051 Saad, Yousef; van der Vorst, Henk A. 2000 A deflated version of the conjugate gradient algorithm. Zbl 0955.65021 Saad, Y.; Yeung, M.; Erhel, J.; Guyomarc’h, F. 2000 Distributed Schur complement techniques for general sparse linear systems. Zbl 0955.65020 2000 High-order ILU preconditioners for CFD problems. Zbl 0959.76077 Chapman, Andrew; Saad, Yousef; Wigton, Larry 2000 Further analysis of minimum residual iterations. Zbl 0983.65035 2000 Preconditioning strategies for linear systems arising in tire design. Zbl 1051.65060 Sosonkina, Maria; Melson, John T.; Saad, Yousef; Watson, Layne T. 2000 BILUM: Block versions of multielimination and multilevel ILU preconditioner for general sparse linear systems. Zbl 0956.65026 1999 BILUTM: A domain-based multilevel block ILUT preconditioner for general sparse matrices. Zbl 0942.65045 1999 Electronic structure calculations for plane-wave codes without diagonalization. Zbl 1001.65038 Jay, Laurent O.; Kim, Hanchul; Saad, Yousef; Chelikowsky, James R. 1999 Diagonal threshold techniques in robust multi-level ILU preconditioners for general sparse linear systems. Zbl 0982.65057 1999 Preserving symmetry in preconditioned Krylov subspace methods. Zbl 0928.65042 Chan, T. F.; Chow, E.; Saad, Y.; Yeung, M. C. 1999 Modified Krylov acceleration for parallel environments. Zbl 0927.65049 1999 Non-standard parallel solution strategies for distributed sparse linear systems. Zbl 0931.65024 1999 Approximate inverse preconditioners via sparse-sparse iterations. Zbl 0922.65034 1998 Dynamic thick restarting of the Davidson, and the implicitly restarted Arnoldi methods. Zbl 0924.65028 Stathopoulos, Andreas; Saad, Yousef; Wu, Kesheng 1998 ...and 72 more Documents all top 5 ### Cited by 8,536 Authors 70 Reichel, Lothar 70 Tezduyar, Tayfun E. 64 Saad, Yousef 62 Huang, Ting-Zhu 44 Axelsson, Axel Owe Holger 40 Khojasteh Salkuyeh, Davod 39 Vuik, Cornelis 36 Cai, Xiao-Chuan 36 Zhang, Guofeng 36 Zhang, Jun 34 Simoncini, Valeria 33 Jia, Zhongxiao 33 Takizawa, Kenji 33 Toutounian, Faezeh 32 Benzi, Michele 32 Jbilou, Khalide 31 Bai, Zhongzhi 30 Gu, Xian-Ming 29 Antoine, Xavier 29 Bazilevs, Yuri 29 Knoll, Dana A. 27 Cao, Yang 26 Hughes, Thomas J. R. 25 Liang, Zhaozheng 25 Sadok, Hassane 24 Ferronato, Massimiliano 24 Wathen, Andrew John 22 Carpentieri, Bruno 22 Mohanty, Ranjan Kumar 21 Niu, Qiang 20 Elman, Howard C. 20 Ma, Changfeng 20 Wei, Yimin 20 Wu, Gang 20 Wu, Shiliang 19 Jing, Yanfei 19 Li, Rencang 19 Stoll, Martin 19 Szyld, Daniel B. 19 Van der Vorst, Henk Albertus 18 Chacón, Luis 18 Helsing, Johan 18 Keyes, David Elliot 18 Pini, Giorgio 17 Beik, Fatemeh Panjeh Ali 17 Benner, Peter 17 Calvetti, Daniela 17 Grigori, Laura 17 Nataf, Frédéric 17 Novati, Paolo 17 Serra-Capizzano, Stefano 17 Shadid, John N. 17 Wu, Yujiang 16 Gravvanis, George A. 16 Gu, Tongxiang 16 Hwang, Fengnan 16 Il’in, Valeriĭ Pavlovich 16 Janna, Carlo 16 Mittal, Sanjay 16 Quarteroni, Alfio M. 16 Sleijpen, Gerard L. G. 16 Van Gijzen, Martin Bastiaan 16 Wen, Chun 16 Xi, Yuanzhe 15 Brezinski, Claude 15 Chien, Cheng-Sheng 15 Hayami, Ken 15 Li, Cuixia 15 Li, Liang 15 Lu, Linzhang 15 Sadkane, Miloud 15 Sun, Haiwei 15 Zhang, Shao-Liang 14 Bergamaschi, Luca 14 Cao, Zhihao 14 Darve, Eric 14 Gambolati, Giuseppe 14 Geuzaine, Christophe A. 14 Gu, Chuanqing 14 Meurant, Gérard A. 14 Min, Chohong 14 Neytcheva, Maya G. 14 Raydan, Marcos 14 Sogabe, Tomohiro 14 Yang, Haijian 14 Ying, Lexing 14 Zhang, Lei-Hong 13 Behr, Marek A. 13 Castelletto, Nicola 13 Dumbser, Michael 13 Gazzola, Silvia 13 Giraud, Luc 13 Imakura, Akira 13 John, Volker 13 Liu, Xingping 13 Magoulès, Frédéric 13 Miao, Cun-Qiang 13 Najafi, H. Saberi 13 Soulaimani, Azzeddine 13 Tchelepi, Hamdi A. ...and 8,436 more Authors all top 5 ### Cited in 434 Serials 726 Journal of Computational Physics 457 Journal of Computational and Applied Mathematics 361 Computer Methods in Applied Mechanics and Engineering 266 Computers & Mathematics with Applications 254 Applied Mathematics and Computation 246 SIAM Journal on Scientific Computing 208 Linear Algebra and its Applications 204 Applied Numerical Mathematics 191 Numerical Algorithms 172 Numerical Linear Algebra with Applications 167 Computers and Fluids 133 Journal of Scientific Computing 127 BIT 111 International Journal for Numerical Methods in Engineering 110 Engineering Analysis with Boundary Elements 105 SIAM Journal on Matrix Analysis and Applications 98 International Journal of Computer Mathematics 90 Computational Mechanics 70 International Journal for Numerical Methods in Fluids 67 Numerische Mathematik 62 Journal of Fluid Mechanics 58 Computer Physics Communications 54 Computational and Applied Mathematics 47 Mathematics of Computation 45 Applied Mathematics Letters 45 Advances in Computational Mathematics 40 Mathematics and Computers in Simulation 37 Computational Optimization and Applications 36 Japan Journal of Industrial and Applied Mathematics 36 ETNA. Electronic Transactions on Numerical Analysis 35 Mathematical Problems in Engineering 35 Computational Geosciences 34 International Journal of Computational Fluid Dynamics 33 Communications in Numerical Methods in Engineering 32 Applied Mathematical Modelling 30 Archives of Computational Methods in Engineering 27 Calcolo 26 SIAM Journal on Numerical Analysis 25 Journal of Applied Mathematics and Computing 25 Communications in Computational Physics 24 Optimization Methods & Software 22 Mathematical and Computer Modelling 21 East Asian Journal on Applied Mathematics 20 Computing 20 Physics of Fluids 20 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 19 Journal of Optimization Theory and Applications 18 Computational Mathematics and Mathematical Physics 17 Numerical Functional Analysis and Optimization 17 COMPEL 17 Multiscale Modeling & Simulation 15 SIAM Review 15 SIAM Journal on Optimization 15 Journal of Mathematical Sciences (New York) 15 Journal of Numerical Mathematics 15 International Journal of Computational Methods 14 Numerical Methods for Partial Differential Equations 14 Computing and Visualization in Science 14 Journal of Applied Mathematics 14 Journal of Computational Acoustics 14 SIAM Journal on Imaging Sciences 14 Science China. Mathematics 13 Advances in Applied Mathematics and Mechanics 12 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 12 Abstract and Applied Analysis 12 Computational Methods in Applied Mathematics 11 Inverse Problems 11 Automatica 11 Physica D 11 Mathematical Programming. Series A. Series B 11 Journal of Machine Learning Research (JMLR) 10 Journal of Engineering Mathematics 10 International Journal of Numerical Methods for Heat & Fluid Flow 10 Combustion Theory and Modelling 10 Comptes Rendus. Mathématique. Académie des Sciences, Paris 10 Advances in Difference Equations 10 International Journal for Numerical Methods in Biomedical Engineering 9 Discrete Applied Mathematics 9 Linear and Multilinear Algebra 9 Applied Mathematics and Mechanics. (English Edition) 9 Russian Journal of Numerical Analysis and Mathematical Modelling 9 Parallel Algorithms and Applications 9 Statistics and Computing 9 Numerical Algebra, Control and Optimization 8 Bulletin of Mathematical Biology 8 Acta Numerica 8 Optimization Letters 8 SIAM/ASA Journal on Uncertainty Quantification 7 International Journal for Numerical and Analytical Methods in Geomechanics 7 International Journal of Solids and Structures 7 ACM Transactions on Mathematical Software 7 Systems & Control Letters 7 Parallel Computing 7 Annals of Operations Research 7 European Journal of Operational Research 7 Engineering Computations 7 Matematicheskoe Modelirovanie 7 AIMS Mathematics 7 Results in Applied Mathematics 6 Communications on Pure and Applied Mathematics ...and 334 more Serials all top 5 ### Cited in 53 Fields 5,011 Numerical analysis (65-XX) 1,552 Fluid mechanics (76-XX) 1,116 Partial differential equations (35-XX) 601 Mechanics of deformable solids (74-XX) 581 Linear and multilinear algebra; matrix theory (15-XX) 301 Operations research, mathematical programming (90-XX) 247 Optics, electromagnetic theory (78-XX) 238 Computer science (68-XX) 200 Biology and other natural sciences (92-XX) 159 Calculus of variations and optimal control; optimization (49-XX) 156 Statistical mechanics, structure of matter (82-XX) 146 Ordinary differential equations (34-XX) 137 Systems theory; control (93-XX) 129 Geophysics (86-XX) 116 Classical thermodynamics, heat transfer (80-XX) 106 Statistics (62-XX) 100 Probability theory and stochastic processes (60-XX) 95 Quantum theory (81-XX) 92 Information and communication theory, circuits (94-XX) 82 Integral equations (45-XX) 75 Operator theory (47-XX) 62 Combinatorics (05-XX) 52 Dynamical systems and ergodic theory (37-XX) 47 Approximations and expansions (41-XX) 44 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 35 Mechanics of particles and systems (70-XX) 25 Real functions (26-XX) 21 Harmonic analysis on Euclidean spaces (42-XX) 17 Functions of a complex variable (30-XX) 17 Astronomy and astrophysics (85-XX) 16 Potential theory (31-XX) 11 Special functions (33-XX) 11 Functional analysis (46-XX) 10 Global analysis, analysis on manifolds (58-XX) 8 General and overarching topics; collections (00-XX) 8 Integral transforms, operational calculus (44-XX) 6 History and biography (01-XX) 5 Differential geometry (53-XX) 4 Difference and functional equations (39-XX) 4 Sequences, series, summability (40-XX) 4 Convex and discrete geometry (52-XX) 4 Relativity and gravitational theory (83-XX) 3 Measure and integration (28-XX) 2 Mathematical logic and foundations (03-XX) 2 Number theory (11-XX) 2 Mathematics education (97-XX) 1 Field theory and polynomials (12-XX) 1 $$K$$-theory (19-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Geometry (51-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) ### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2022-07-07T11:32:12	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5991377830505371, "perplexity": 8249.01433249591}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104690785.95/warc/CC-MAIN-20220707093848-20220707123848-00242.warc.gz"}
https://lammps.sandia.gov/doc/fix_evaporate.html	# fix evaporate command ## Syntax fix ID group-ID evaporate N M region-ID seed • ID, group-ID are documented in fix command • evaporate = style name of this fix command • N = delete atoms every this many timesteps • M = number of atoms to delete each time • region-ID = ID of region within which to perform deletions • seed = random number seed to use for choosing atoms to delete • zero or more keyword/value pairs may be appended keyword = molecule molecule value = no or yes ## Examples fix 1 solvent evaporate 1000 10 surface 49892 fix 1 solvent evaporate 1000 10 surface 38277 molecule yes ## Description Remove M atoms from the simulation every N steps. This can be used, for example, to model evaporation of solvent particles or molecules (i.e. drying) of a system. Every N steps, the number of atoms in the fix group and within the specified region are counted. M of these are chosen at random and deleted. If there are less than M eligible particles, then all of them are deleted. If the setting for the molecule keyword is no, then only single atoms are deleted. In this case, you should insure you do not delete only a portion of a molecule (only some of its atoms), or LAMMPS will soon generate an error when it tries to find those atoms. LAMMPS will warn you if any of the atoms eligible for deletion have a non-zero molecule ID, but does not check for this at the time of deletion. If the setting for the molecule keyword is yes, then when an atom is chosen for deletion, the entire molecule it is part of is deleted. The count of deleted atoms is incremented by the number of atoms in the molecule, which may make it exceed M. If the molecule ID of the chosen atom is 0, then it is assumed to not be part of a molecule, and just the single atom is deleted. As an example, if you wish to delete 10 water molecules every N steps, you should set M to 30. If only the water’s oxygen atoms were in the fix group, then two hydrogen atoms would be deleted when an oxygen atom is selected for deletion, whether the hydrogens are inside the evaporation region or not. Note that neighbor lists are re-built on timesteps that atoms are removed. Thus you should not remove atoms too frequently or you will incur overhead due to the cost of building neighbor lists. Note If you are monitoring the temperature of a system where the atom count is changing due to evaporation, you typically should use the compute_modify dynamic yes command for the temperature compute you are using. Restart, fix_modify, output, run start/stop, minimize info: No information about this fix is written to binary restart files. None of the fix_modify options are relevant to this fix. This fix computes a global scalar, which can be accessed by various output commands. The scalar is the cumulative number of deleted atoms. The scalar value calculated by this fix is “intensive”. No parameter of this fix can be used with the start/stop keywords of the run command. This fix is not invoked during energy minimization. ## Restrictions This fix is part of the MISC package. It is only enabled if LAMMPS was built with that package. See the Build package doc page for more info. ## Default The option defaults are molecule = no.	2018-09-20T13:05:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5678359866142273, "perplexity": 1879.6853515141293}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156471.4/warc/CC-MAIN-20180920120835-20180920141235-00040.warc.gz"}
https://phys.libretexts.org/Bookshelves/College_Physics/Book%3A_College_Physics_(OpenStax)/28%3A_Special_Relativity	$$\require{cancel}$$ # 28: Special Relativity Modern relativity is divided into two parts. Special relativity deals with observers who are moving at constant velocity. General relativity deals with observers who are undergoing acceleration. Einstein is famous because his theories of relativity made revolutionary predictions. Most importantly, his theories have been verified to great precision in a vast range of experiments, altering forever our concept of space and time. • 28.0: Prelude to Special Relativity It is important to note that although classical mechanics, in general, and classical relativity, in particular, are limited, they are extremely good approximations for large, slow-moving objects. Otherwise, we could not use classical physics to launch satellites or build bridges. In the classical limit (objects larger than submicroscopic and moving slower than about 1% of the speed of light), relativistic mechanics becomes the same as classical mechanics. • 28.1: Einstein’s Postulates Relativity is the study of how different observers measure the same event. Modern relativity is correct in all circumstances and, in the limit of low velocity and weak gravitation, gives the same predictions as classical relativity. An inertial frame of reference is a reference frame in which a body at rest remains at rest and a body in motion moves at a constant speed in a straight line unless acted on by an outside force. Modern relativity is based on Einstein’s two postulates. • 28.2: Simultaneity and Time Dilation Two simultaneous events are not necessarily simultaneous to all observers—simultaneity is not absolute. Time dilation is the phenomenon of time passing slower for an observer who is moving relative to another observer. Observers moving at a relative velocity do not measure the same elapsed time for an event. Proper time is measured by an observer at rest relative to the event being observed and implies that relative velocity cannot exceed the speed of light. • 28.3: Length Contraction All observers agree upon relative speed. Distance depends on an observer’s motion. Proper length is the distance between two points measured by an observer who is at rest relative to both of the points. Earth-bound observers measure proper length when measuring the distance between two points that are stationary relative to the Earth. Length contraction is the shortening of the measured length of an object moving relative to the observer’s frame. • 28.4: Relativistic Addition of Velocities With classical velocity addition, velocities add vectorially. Relativistic velocity addition describes the velocities of an object moving at a relativistic speed. An observer of electromagnetic radiation sees relativistic Doppler effects if the source of the radiation is moving relative to the observer. The wavelength of the radiation is longer than that emitted by the source when the source moves away from the observer and shorter when the source moves toward the observer. • 28.5: Relativistic Momentum The law of conservation of momentum is valid whenever the net external force is zero and for relativistic momentum. Relativistic momentum is classical momentum multiplied by the relativistic factor. At low velocities, relativistic momentum is equivalent to classical momentum. Relativistic momentum approaches infinity as uu approaches cc . This implies that an object with mass cannot reach the speed of light. Relativistic momentum is conserved, just as classical momentum is conserved. • 28.6: Relativistic Energy Conservation of energy is one of the most important laws in physics. Not only does energy have many important forms, but each form can be converted to any other. We know that classically the total amount of energy in a system remains constant. Relativistically, energy is still conserved, provided its definition is altered to include the possibility of mass changing to energy, as in the reactions that occur within a nuclear reactor. • 28.E: Special Relativity (Exercise) Thumbnail: A diagrammatic representation of spacetime. Image use with permission (CC-BY-SA 3.0; Stib).	2021-10-17T22:04:17	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8088737726211548, "perplexity": 414.3665071536114}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585183.47/warc/CC-MAIN-20211017210244-20211018000244-00537.warc.gz"}
http://dlmf.nist.gov/14.6	# §14.6(i) Nonnegative Integer Orders For $m=0,1,2,\dots$, 14.6.1 $\displaystyle\mathop{\mathsf{P}^{m}_{\nu}\/}\nolimits\!\left(x\right)$ $\displaystyle=(-1)^{m}\left(1-x^{2}\right)^{m/2}\frac{{d}^{m}\mathop{\mathsf{P% }_{\nu}\/}\nolimits\!\left(x\right)}{{dx}^{m}},$ 14.6.2 $\displaystyle\mathop{\mathsf{Q}^{m}_{\nu}\/}\nolimits\!\left(x\right)$ $\displaystyle=(-1)^{m}\left(1-x^{2}\right)^{m/2}\frac{{d}^{m}\mathop{\mathsf{Q% }_{\nu}\/}\nolimits\!\left(x\right)}{{dx}^{m}}.$ 14.6.3 $\displaystyle\mathop{P^{m}_{\nu}\/}\nolimits\!\left(x\right)$ $\displaystyle=\left(x^{2}-1\right)^{m/2}\frac{{d}^{m}\mathop{P_{\nu}\/}% \nolimits\!\left(x\right)}{{dx}^{m}},$ 14.6.4 $\displaystyle\mathop{Q^{m}_{\nu}\/}\nolimits\!\left(x\right)$ $\displaystyle=\left(x^{2}-1\right)^{m/2}\frac{{d}^{m}\mathop{Q_{\nu}\/}% \nolimits\!\left(x\right)}{{dx}^{m}},$ 14.6.5 $\left(\nu+1\right)_{m}\mathop{\boldsymbol{Q}^{m}_{\nu}\/}\nolimits\!\left(x% \right)=(-1)^{m}\left(x^{2}-1\right)^{m/2}\frac{{d}^{m}\mathop{\boldsymbol{Q}_% {\nu}\/}\nolimits\!\left(x\right)}{{dx}^{m}}.$ # §14.6(ii) Negative Integer Orders For $m=1,2,3,\dots$, 14.6.6 $\displaystyle\mathop{\mathsf{P}^{-m}_{\nu}\/}\nolimits\!\left(x\right)$ $\displaystyle=\left(1-x^{2}\right)^{-m/2}\int_{x}^{1}\!\dots\!\int_{x}^{1}% \mathop{P_{\nu}\/}\nolimits\!\left(x\right)\left(\!dx\right)^{m}.$ 14.6.7 $\displaystyle\mathop{P^{-m}_{\nu}\/}\nolimits\!\left(x\right)$ $\displaystyle=\left(x^{2}-1\right)^{-m/2}\int_{1}^{x}\!\dots\!\int_{1}^{x}% \mathop{P_{\nu}\/}\nolimits\!\left(x\right)\left(\!dx\right)^{m},$ 14.6.8 $\displaystyle\mathop{Q^{-m}_{\nu}\/}\nolimits\!\left(x\right)$ $\displaystyle=(-1)^{m}\left(x^{2}-1\right)^{-m/2}\*\int_{x}^{\infty}\!\dots\!% \int_{x}^{\infty}\mathop{Q_{\nu}\/}\nolimits\!\left(x\right)\left(\!dx\right)^% {m}.$ For connections between positive and negative integer orders see (14.9.3), (14.9.4), and (14.9.13).	2014-11-28T13:22:44	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 75, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5126855969429016, "perplexity": 12201.060641752802}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931010402.68/warc/CC-MAIN-20141125155650-00214-ip-10-235-23-156.ec2.internal.warc.gz"}
https://indico.fnal.gov/event/15949/contributions/34749/	# 36th Annual International Symposium on Lattice Field Theory Jul 22 – 28, 2018 Kellogg Hotel and Conference Center EST timezone ## Roper State from Overlap Fermion Jul 26, 2018, 12:00 PM 20m 105 (Kellogg Hotel and Conference Center) ### 105 #### Kellogg Hotel and Conference Center 219 S Harrison Rd, East Lansing, MI 48824 Hadron Spectroscopy and Interactions ### Speaker Prof. Keh-Fei Liu (University of Kentucky) ### Description Variational method with valence overlap fermion is employed to calculate the Roper state on the $24^3 \times 64$ domain-wall fermion lattice at a = 0.114 and 330 MeV pion mass. It is found that the results are consistent with those from the sequential empirical Bayes (SEB) method. They are about 300 MeV lower than those with the clover fermion at comparable lattice spacing and pion mass. To understand the difference, we study the would-be $\eta-\pi$ ghost state in the isovector scalar channel with the $\bar{q}q$ interpolation field in the quenched approximation for both the overlap and Wilson fermions to compare their couplings to the two hadron state with the single hadron interpolation field. ### Primary author Prof. Keh-Fei Liu (University of Kentucky) ### Co-authors Gen Wang (University of Kentucky) Dr Mingyang Sun (University of Kentucky) Slides	2022-10-01T20:55:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4129049777984619, "perplexity": 5760.139895240411}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030336921.76/warc/CC-MAIN-20221001195125-20221001225125-00574.warc.gz"}
http://siba-ese.unile.it/index.php/quadecon/issue/view/908	## A Note on Income Share Elasticity and Stochastic Dominance - 2002 Corrado Benassi , Alessandra Chirico Full Version (PDF) (Quaderni del Dipartimento di Scienze Economiche e Matematico-Statistiche dell'Università del Salento - Collana di Economia, 36/18 / 2002) Esteban (1986) introduced the notion of income share elasticity as a function $\pi$ which can describe the size distribution of income. On the other hand, indices of first or second order stochastic dominance are widely used to describe shifts in income distribution, to which inequality measures are attached. The paper draws a link between the two, by providing conditions such that a given shift to $\pi$ is equivalent to a first or second order stochastic dominance shift of the distribution of income. Introduction PDF Corrado Benassi , Alessandra Chirco 2-6 Income share elasticity and income dispersion PDF Corrado Benassi , Alessandra Chirco 2-6 Concluding remarks PDF Corrado Benassi , Alessandra Chirco 6-6 Bibliography PDF 6a-6a Questo sito utilizza un cookie tecnico per consentire la corretta navigazione. Se vuoi saperne di più consulta l'informativa estesa. This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.	2021-05-08T00:40:12	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33834946155548096, "perplexity": 9425.354018676166}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988831.77/warc/CC-MAIN-20210508001259-20210508031259-00260.warc.gz"}
https://finalfantasy.fandom.com/wiki/Cure_(Final_Fantasy_VII)	## FANDOM 38,294 Pages Restores HP Description Cure is a restore magic spell in Final Fantasy VII. It is granted by the Restore Materia at level one, and is the basic curative spell below Cure2 and Cure3, which heals a target's HP. ## StatsEdit Magic Materia Restore, Master Magic Heal a small amount of HP. 5 Added Cut, All, Final Attack, HP Absorb, Magic Counter, MP Absorb, MP Turbo, Quadra Magic, Sneak Attack, Steal as well Yes Cure heals in the following formula: $(5 * 22) + [ (Level + Magical Attack) * 6 ]$ where "Level" is the caster's current level and "Magical Attack" is their Magic atk stat. ## UseEdit Cure can be used by characters with the Restore Materia at level 1. At early levels, it restores a large amount of HP, more than a Potion, but its MP cost means it should not be used too regularly. Cure remains useful throughout the game for its low MP-cost healing, especially in-between battles. Cure can be amplified by pairing the Restore Materia with All. This allows a character to heal all allies at once, which grants Cure another edge over Potion and can be important to rescue the party from dire situations. Though Cure can be paired with other Support Materia, most are better paired with other Materia that provide attack magic. In addition to being used for healing, Cure can be used to damage undead enemies. Cure is cast by the enemies Adamantaimai and Rude. However, Adamantaimai's version results in a glitch. Community content is available under CC-BY-SA unless otherwise noted.	2020-07-11T06:25:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3432837128639221, "perplexity": 12513.876073984087}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655921988.66/warc/CC-MAIN-20200711032932-20200711062932-00411.warc.gz"}
https://zbmath.org/authors/?q=ai%3Ablass.andreas-raphael	# zbMATH — the first resource for mathematics ## Blass, Andreas Raphael Compute Distance To: Author ID: blass.andreas-raphael Published as: Blass, Andreas; Blass, A. R.; Blass, Andreas R.; Blass, A. Homepage: http://www.math.lsa.umich.edu/~ablass/ External Links: MGP · Math-Net.Ru · Wikidata · MathOverflow · ResearchGate · dblp · GND Documents Indexed: 228 Publications since 1968, including 6 Books all top 5 #### Co-Authors 88 single-authored 67 Gurevich, Yuri 9 Shelah, Saharon 8 Irwin, John M. 6 Harary, Frank 6 Stanojević, Časlav V. 5 Dershowitz, Nachum 3 Di Nasso, Mauro 3 Hindman, Neil 3 Rossman, Benjamin 3 Sagan, Bruce Eli 3 Scedrov, Andre 2 Baldwin, John T. 2 Bergelson, Vitaly 2 Exoo, Geoffrey 2 Jiarasuksakun, Thiradet 2 Pambuccian, Victor V. 2 Reisig, Wolfgang 2 Rosenzweig, Dean 2 Ščedrov, Andrej 2 Van den Bussche, Jan 2 Zhang, Yi 1 Adelman, Murray 1 Banakh, Taras Onufrievich 1 Beklemishev, Lev D. 1 Bjørner, Nikolaj S. 1 Blair, David G. 1 Bocharov, Alex 1 Braun, Gábor 1 Brendle, Jörg 1 Brian, William Rea 1 Cenzer, Douglas 1 Dimitriou, Ioanna Matilde 1 Dobrinen, Natasha L. 1 Erdős, Pál 1 Falcao, L. 1 Finkbeiner, Bernd 1 Forti, Marco 1 Frankiewicz, Ryszard 1 Gao, Su 1 Glass, Andrew M. W. 1 Göbel, Rüdiger 1 Hamkins, Joel David 1 Hardy, Michael 1 Hirst, Jeffry Lynn 1 Hrušák, Michael 1 Hudis, Efim 1 Jech, Thomas J. 1 Jin, Renling 1 Kister, James M. 1 Kozen, Dexter C. 1 Kreinovich, Vladik Yakovlevich 1 Kueker, David W. 1 Laflamme, Claude 1 Larson, Paul B. 1 Longpré, Luc 1 Löwe, Benedikt 1 Mildenberger, Heike 1 Miller, Zevi 1 Mitavskiy, Boris S. 1 Moche, Gugu 1 Nachmanson, Lev 1 Neumann, Peter Michael 1 Plebanek, Grzegorz 1 Raghavan, Dilip 1 Ryll-Nardzewski, Czesław 1 Schlitt, Greg M. 1 Schulte, Wolfram 1 Simpson, Stephen G. 1 Taylor, Alan D. 1 Veanes, Margus 1 Verner, Jonathan L. 1 Weiss, Gary all top 5 #### Serials 19 The Journal of Symbolic Logic 18 Bulletin of the European Association for Theoretical Computer Science EATCS 10 Proceedings of the American Mathematical Society 10 Transactions of the American Mathematical Society 10 Annals of Pure and Applied Logic 8 ACM Transactions on Computational Logic 6 Fundamenta Mathematicae 4 Communications in Algebra 4 Journal of Graph Theory 4 Journal of Pure and Applied Algebra 4 Topology and its Applications 3 American Mathematical Monthly 3 SIAM Journal on Computing 3 Journal of Algebraic Combinatorics 2 Discrete Mathematics 2 Information Processing Letters 2 Journal of Mathematical Physics 2 Advances in Mathematics 2 Algebra Universalis 2 Information and Control 2 Notre Dame Journal of Formal Logic 2 Information and Computation 2 Topology Proceedings 2 The Electronic Journal of Combinatorics 2 The Bulletin of Symbolic Logic 2 Contemporary Mathematics 2 Lecture Notes in Computer Science 2 Logical Methods in Computer Science 1 Archiv für Mathematische Logik und Grundlagenforschung 1 Israel Journal of Mathematics 1 Mathematica Balkanica 1 Annals of Mathematical Logic 1 Geometriae Dedicata 1 Journal of Algebra 1 Journal of Combinatorics, Information & System Sciences 1 Journal of Combinatorial Theory. Series A 1 Journal of Combinatorial Theory. Series B 1 Journal of Computer and System Sciences 1 Journal of the London Mathematical Society. Second Series 1 Mathematica Japonica 1 Memoirs of the American Mathematical Society 1 Michigan Mathematical Journal 1 Pacific Journal of Mathematics 1 Proceedings of the London Mathematical Society. Third Series 1 Rendiconti del Seminario Matemàtico e Fisico di Milano 1 Rivista di Matematica della Università di Parma. Serie IV 1 Theoretical Computer Science 1 CWI Quarterly 1 Bulletin of the European Association for Theoretical Computer Science (EATCS) 1 MSCS. Mathematical Structures in Computer Science 1 Elemente der Mathematik 1 Bulletin of the Polish Academy of Sciences, Mathematics 1 Archive for Mathematical Logic 1 Indagationes Mathematicae. New Series 1 Mathematical Logic Quarterly (MLQ) 1 Logic Journal of the IGPL 1 East-West Journal of Mathematics 1 Journal of Mathematical Logic 1 Journal of Universal Computer Science 1 Scientiae Mathematicae Japonicae 1 Bulletin de l’Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques 1 Matematichki Vesnik. New Series all top 5 #### Fields 154 Mathematical logic and foundations (03-XX) 63 Computer science (68-XX) 29 Combinatorics (05-XX) 25 Category theory; homological algebra (18-XX) 22 Group theory and generalizations (20-XX) 19 General topology (54-XX) 8 Quantum theory (81-XX) 7 Order, lattices, ordered algebraic structures (06-XX) 7 General algebraic systems (08-XX) 6 General and overarching topics; collections (00-XX) 5 Probability theory and stochastic processes (60-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Associative rings and algebras (16-XX) 3 Functional analysis (46-XX) 3 Information and communication theory, circuits (94-XX) 2 History and biography (01-XX) 2 Number theory (11-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Measure and integration (28-XX) 2 Operator theory (47-XX) 2 Geometry (51-XX) 1 Field theory and polynomials (12-XX) 1 Topological groups, Lie groups (22-XX) 1 Sequences, series, summability (40-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Global analysis, analysis on manifolds (58-XX) #### Citations contained in zbMATH Open 152 Publications have been cited 1,311 times in 1,025 Documents Cited by Year Combinatorial cardinal characteristics of the continuum. Zbl 1198.03058 Blass, Andreas 2010 There may be simple $$P_{\aleph _ 1}$$- and $$P_{\aleph _ 2}$$-points and the Rudin-Keisler ordering may be downward directed. Zbl 0634.03047 Blass, Andreas; Shelah, Saharon 1987 A game semantics for linear logic. Zbl 0763.03008 Blass, Andreas 1992 On the unique satisfiability problem. Zbl 0543.03027 Blass, Andreas; Gurevich, Yuri 1982 Henkin quantifiers and complete problems. Zbl 0618.03016 Blass, Andreas; Gurevich, Yuri 1986 A partition theorem for perfect sets. Zbl 0472.03038 Blass, Andreas 1981 Ultrafilters with small generating sets. Zbl 0681.03033 Blass, Andreas; Shelah, Saharon 1989 Möbius functions of lattices. Zbl 0872.06004 Blass, Andreas; Sagan, Bruce E. 1997 Consistency results about filters and the number of inequivalent growth types. Zbl 0673.03038 Blass, Andreas; Laflamme, Claude 1989 Partition theorems for spaces of variable words. Zbl 0809.04005 Bergelson, Vitaly; Blass, Andreas; Hindman, Neil 1994 Near coherence of filters. I: Cofinal equivalence of models of arithmetic. Zbl 0622.03040 Blass, Andreas 1986 Selctive ultrafilters and homogeneity. Zbl 0649.03036 Blass, Andreas 1988 Properties of almost all graphs and complexes. Zbl 0418.05050 Blass, Andreas; Harary, Frank 1979 The Rudin-Keisler ordering of P-points. Zbl 0269.02025 Blass, Andreas 1973 Near coherence of filters. III: A simplified consistency proof. Zbl 0702.03030 Blass, Andreas; Shelah, Saharon 1989 Characteristic and Ehrhart polynomials. Zbl 0899.05003 Blass, Andreas; Sagan, Bruce E. 1998 Paley graphs satisfy all first-order adjacency axioms. Zbl 0472.05058 Blass, Andreas; Exoo, Geoffrey; Harary, Frank 1981 Injectivity, projectivity, and the axiom of choice. Zbl 0426.03053 Blass, Andreas 1979 Ultrafilters: Where topological dynamics = algebra = combinatorics. Zbl 0856.54042 Blass, Andreas 1993 On strongly summable ultrafilters and union ultrafilters. Zbl 0643.03032 Blass, Andreas; Hindman, Neil 1987 Choiceless polynomial time. Zbl 0936.03037 Blass, Andreas; Gurevich, Yuri; Shelah, Saharon 1999 A zero-one law for logic with a fixed-point operator. Zbl 0608.68077 Blass, Andreas; Gurevich, Yuri; Kozen, Dexter 1985 Near coherence of filters. II: Applications to operator ideals, the Stone-Čech remainder of a half-line, order ideals of sequences, and slenderness of groups. Zbl 0647.03043 Blass, Andreas 1987 Applications of superperfect forcing and its relatives. Zbl 0683.03029 Blass, Andreas 1989 Ramsey’s theorem in the hierarchy of choice principles. Zbl 0374.02037 Blass, Andreas 1978 On the cofinality of ultrapowers. Zbl 0930.03060 Blass, Andreas; Mildenberger, Heike 1999 Infinitary combinatorics and modal logic. Zbl 0699.03008 Blass, Andreas 1990 Classifying topoi and finite forcing. Zbl 0516.03042 Blass, Andreas; Scedrov, Andrej 1983 A note on extensions of asymptotic density. Zbl 0992.28002 Blass, A.; Frankiewicz, R.; Plebanek, G.; Ryll-Nardzewski, C. 2001 Degrees of indeterminacy of games. Zbl 0234.90066 Blass, Andreas 1972 Graphs with unique maximal clumpings. Zbl 0377.05036 Blass, Andreas 1978 Ultrafilter mappings and their Dedekind cuts. Zbl 0305.02065 Blass, Andreas 1974 Which trees are link graphs? Zbl 0448.05028 Blass, Andreas; Harary, Frank; Miller, Zevi 1980 Matrix transformation is complete for the average case. Zbl 0828.68078 Blass, Andreas; Gurevich, Yuri 1995 On polynomial time computation over unordered structures. Zbl 1020.03038 Blass, Andreas; Gurevich, Yuri; Shelah, Saharon 2002 Abstract state machines capture parallel algorithms. Zbl 1365.68253 Blass, Andreas; Gurevich, Yuri 2003 A model without ultrafilters. Zbl 0365.02054 Blass, Andreas 1977 Cardinal characteristics and the product of countably many infinite cyclic groups. Zbl 0816.20047 Blass, Andreas 1994 Two closed categories of filters. Zbl 0357.18004 Blass, Andreas 1977 Play to test. Zbl 1183.68176 Blass, Andreas; Gurevich, Yuri; Nachmanson, Lev; Veanes, Margus 2006 Seven trees in one. Zbl 0846.18002 Blass, Andreas 1995 Complexity of winning strategies. Zbl 0243.90052 Blass, Andreas 1972 A ”natural” theory without a prime model. Zbl 0273.02033 Baldwin, J. T.; Blass, A. R.; Glass, A. M. W.; Kueker, D. W. 1973 Bijective proofs of two broken circuit theorems. Zbl 0592.05022 Blass, Andreas; Sagan, Bruce Eli 1986 Ultrafilters related to Hindman’s finite-unions theorem and its extensions. Zbl 0634.03045 Blass, Andreas 1987 Existential fixed-point logic. Zbl 0647.03018 Blass, Andreas; Gurevich, Yuri 1987 Freyd’s models for the independence of the axiom of choice. Zbl 0687.03031 Blass, Andreas; Scedrov, Andre 1989 Groupwise density and related cardinals. Zbl 0706.03036 Blass, Andreas 1990 Existence of bases implies the axiom of choice. Zbl 0557.03030 Blass, Andreas 1984 Exact functors and measurable cardinals. Zbl 0348.18007 Blass, Andreas 1976 Questions and answers – a category arising in linear logic, complexity theory, and set theory. Zbl 0823.03039 Blass, Andreas 1995 A characterization and sum decomposition for operator ideals. Zbl 0414.47017 Blass, Andreas; Weiss, Gary 1978 Prime ideals yield almost maximal ideals. Zbl 0609.06006 Blass, Andreas 1987 Logical analysis of some theorems of combinatorics and topological dynamics. Zbl 0652.03040 Blass, Andreas R.; Hirst, Jeffry L.; Simpson, Stephen G. 1987 Quasi-selective ultrafilters and asymptotic numerosities. Zbl 1270.03105 Blass, Andreas; Di Nasso, Mauro; Forti, Marco 2012 An application of universal algebra in group theory. Zbl 0292.20033 Blass, Andreas; Neumann, Peter M. 1974 Algorithms: a quest for absolute definitions. Zbl 1169.68408 Blass, Andreas; Gurevich, Yuri 2003 Simple cardinal characteristics of the continuum. Zbl 0828.03019 Blass, Andreas 1993 Interactive small-step algorithms. I: Axiomatization. Zbl 1132.68029 Blass, Andreas; Gurevich, Yuri; Rosenzweig, Dean; Rossman, Benjamin 2007 Program termination and well partial orderings. Zbl 1367.68061 Blass, Andreas; Gurevich, Yuri 2008 An axiomatic approach to rank in model theory. Zbl 0298.02055 Baldwin, J. T.; Blass, Andreas 1974 End extensions, conservative extensions, and the Rudin-Frolik ordering. Zbl 0362.02052 Blass, Andreas 1977 Reductions between cardinal characteristics of the continuum. Zbl 0838.03036 Blass, Andreas 1996 The logic of choice. Zbl 0973.03007 Blass, Andreas; Gurevich, Yuri 2000 The model of set theory generated by countably many generic reals. Zbl 0482.03022 Blass, Andreas 1981 Randomizing reductions of search problems. Zbl 0789.68056 Blass, Andreas; Gurevich, Yuri 1993 On strong $$P$$-points. Zbl 1302.03050 Blass, Andreas; Hrušák, Michael; Verner, Jonathan 2013 Ordinary interactive small-step algorithms. I. Zbl 1367.68094 Blass, Andreas; Gurevich, Yuri 2006 The next best thing to a P-point. Zbl 1367.03078 Blass, Andreas; Dobrinen, Natasha; Raghavan, Dilip 2015 Equivalence of two strong forms of determinacy. Zbl 0336.02048 Blass, Andreas 1975 Cohomology detects failures of the axiom of choice. Zbl 0532.04002 Blass, Andreas 1983 The number of near-coherence classes of ultrafilters is either finite or $$2^{\mathfrak c}$$. Zbl 1182.03076 Banakh, Taras; Blass, Andreas 2006 A model-theoretic view of some special ultrafilters. Zbl 0439.03031 Blass, Andreas 1978 Strong extension axioms and Shelah’s zero-one law for choiceless polynomial time. Zbl 1045.03039 Blass, Andreas; Gurevich, Yuri 2003 Amalgamation of nonstandard models of arithmetic. Zbl 0381.03050 Blass, Andreas 1978 Natural endomorphisms of Burnside rings. Zbl 0417.20006 Blass, Andreas 1979 When are two algorithms the same? Zbl 1192.03021 Blass, Andreas; Dershowitz, Nachum; Gurevich, Yuri 2009 Some questions arising from Hindman’s theorem. Zbl 1084.05008 Blass, Andreas 2005 Abstract state machines capture parallel algorithms: correction and extension. Zbl 1367.68097 Blass, Andreas; Gurevich, Yuri 2008 Equivalence relations, invariants, and normal forms. Zbl 0545.68035 Blass, Andreas; Gurevich, Yuri 1984 Cores of $$\Pi^1_1$$ sets of reals. Zbl 0295.02038 Blass, Andreas; Cenzer, Douglas 1975 On certain types and models for arithmetic. Zbl 0296.02031 Blass, Andreas 1974 Boolean classifying topoi. Zbl 0504.03030 Blass, Andreas; Scedrov, Andrej 1983 Background, reserve, and Gandy machines. Zbl 0973.03053 Blass, Andreas; Gurevich, Yuri 2000 Free subgroups of the Baer-Specker group. Zbl 1022.20025 Blass, Andreas; Irwin, John 2001 On the Egoroff property of pointwise convergent sequences of functions. Zbl 0601.54004 Blass, Andreas; Jech, Thomas 1986 Free subgroups of the homeomorphism group of the reals. Zbl 0604.57015 Blass, Andreas; Kister, James M. 1986 Specker’s theorem for Nöbeling’s group. Zbl 0998.20047 Blass, Andreas 2002 Random orders and gambler’s ruin. Zbl 1075.05004 Blass, Andreas; Braun, Gábor 2005 Optimal ancilla-free Pauli+V circuits for axial rotations. Zbl 1333.81067 Blass, Andreas; Bocharov, Alex; Gurevich, Yuri 2015 Partitions and permutation groups. Zbl 1247.03108 Blass, Andreas 2011 Existential fixed-point logic, universal quantifiers, and topoi. Zbl 1287.03085 Blass, Andreas 2010 Pairwise testing. Zbl 1169.68352 Blass, Andreas; Gurevich, Yuri 2002 Ultrafilters and set theory. Zbl 1269.03048 Blass, Andreas 2010 The linear time hierarchy theorems for abstract state machines and RAMs. Zbl 0960.68070 Blass, Andreas; Gurevich, Yuri 1997 Needed reals and recursion in generic reals. Zbl 0980.03055 Blass, Andreas 2001 Abstract state machines and computationally complete query languages. Zbl 0976.68061 Blass, Andreas; Gurevich, Yuri; Van den Bussche, Jan 2000 Baer meets Baire: Applications of category arguments and descriptive set theory to $$\mathbb{Z}^{\aleph_ 0}$$. Zbl 0870.20037 Blass, Andreas R.; Irwin, John 1996 Conservative extensions of models of arithmetic. Zbl 0453.03072 Blass, Andreas 1980 The underlying logic of Hoare logic. Zbl 1012.03514 Blass, Andreas; Gurevich, Yuri 2001 Who needs category theory? Zbl 1409.68095 Blass, Andreas; Gurevich, Yuri 2018 On quantum computation, anyons, and categories. Zbl 1439.81028 Blass, Andreas; Gurevich, Yuri 2016 The next best thing to a P-point. Zbl 1367.03078 Blass, Andreas; Dobrinen, Natasha; Raghavan, Dilip 2015 Optimal ancilla-free Pauli+V circuits for axial rotations. Zbl 1333.81067 Blass, Andreas; Bocharov, Alex; Gurevich, Yuri 2015 Finite embeddability of sets and ultrafilters. Zbl 1382.03068 Blass, Andreas; Di Nasso, Mauro 2015 Negative probability. Zbl 1416.60013 Blass, Andreas; Gurevich, Yuri 2015 Ancilla-approximable quantum state transformations. Zbl 1322.81015 Blass, Andreas; Gurevich, Yuri 2015 On strong $$P$$-points. Zbl 1302.03050 Blass, Andreas; Hrušák, Michael; Verner, Jonathan 2013 Quasi-selective ultrafilters and asymptotic numerosities. Zbl 1270.03105 Blass, Andreas; Di Nasso, Mauro; Forti, Marco 2012 Partitions and permutation groups. Zbl 1247.03108 Blass, Andreas 2011 Combinatorial cardinal characteristics of the continuum. Zbl 1198.03058 Blass, Andreas 2010 Existential fixed-point logic, universal quantifiers, and topoi. Zbl 1287.03085 Blass, Andreas 2010 Ultrafilters and set theory. Zbl 1269.03048 Blass, Andreas 2010 Content-dependent chunking for differential compression, the local maximum approach. Zbl 1201.68015 Bjørner, Nikolaj; Blass, Andreas; Gurevich, Yuri 2010 Hilbertian deductive systems, infon logic, and Datalog. Zbl 1275.03127 Blass, Andreas; Gurevich, Yuri 2010 Fields of logic and computation. Essays dedicated to Yuri Gurevich on the occasion of his 70th birthday. Zbl 1194.03003 Blass, Andreas; Dershowitz, Nachum; Reisig, Wolfgang 2010 When are two algorithms the same? Zbl 1192.03021 Blass, Andreas; Dershowitz, Nachum; Gurevich, Yuri 2009 Homogeneous sets from several ultrafilters. Zbl 1202.05145 Blass, Andreas 2009 Program termination and well partial orderings. Zbl 1367.68061 Blass, Andreas; Gurevich, Yuri 2008 Abstract state machines capture parallel algorithms: correction and extension. Zbl 1367.68097 Blass, Andreas; Gurevich, Yuri 2008 Basic subgroups and freeness, a counterexample. Zbl 1192.20039 Blass, Andreas; Shelah, Saharon 2008 Why sets? Zbl 1133.03347 Blass, Andreas; Gurevich, Yuri 2008 Interactive small-step algorithms. I: Axiomatization. Zbl 1132.68029 Blass, Andreas; Gurevich, Yuri; Rosenzweig, Dean; Rossman, Benjamin 2007 Ordinary interactive small-step algorithms. II. Zbl 1367.68095 Blass, Andreas; Gurevich, Yuri 2007 Inaccessible cardinals without the axiom of choice. Zbl 1116.03045 Blass, Andreas; Dimitriou, Ioanna M.; Löwe, Benedikt 2007 Interactive small-step algorithms. II: Abstract state machines and the characterization theorem. Zbl 1132.68030 Blass, Andreas; Gurevich, Yuri; Rosenzweig, Dean; Rossman, Benjamin 2007 Ordinary interactive small-step algorithms. III. Zbl 1367.68096 Blass, Andreas; Gurevich, Yuri 2007 Play to test. Zbl 1183.68176 Blass, Andreas; Gurevich, Yuri; Nachmanson, Lev; Veanes, Margus 2006 Ordinary interactive small-step algorithms. I. Zbl 1367.68094 Blass, Andreas; Gurevich, Yuri 2006 The number of near-coherence classes of ultrafilters is either finite or $$2^{\mathfrak c}$$. Zbl 1182.03076 Banakh, Taras; Blass, Andreas 2006 Algorithms: a quest for absolute definitions. Zbl 1110.03023 Blass, Andreas; Gurevich, Yuri 2006 Some questions arising from Hindman’s theorem. Zbl 1084.05008 Blass, Andreas 2005 Random orders and gambler’s ruin. Zbl 1075.05004 Blass, Andreas; Braun, Gábor 2005 Special families of sets and Baer-Specker groups. Zbl 1090.03026 Blass, Andreas; Irwin, John 2005 Unsplit families, dominating families, and ultrafilters. Zbl 1084.03038 Blass, Andreas 2005 Pairwise testing. Zbl 1065.68032 Blass, Andreas; Gurevich, Yuri 2004 Algorithms: a quest for absolute definitions. Zbl 1065.68052 Blass, Andreas; Gurevich, Yuri 2004 Abstract state machines capture parallel algorithms. Zbl 1365.68253 Blass, Andreas; Gurevich, Yuri 2003 Algorithms: a quest for absolute definitions. Zbl 1169.68408 Blass, Andreas; Gurevich, Yuri 2003 Strong extension axioms and Shelah’s zero-one law for choiceless polynomial time. Zbl 1045.03039 Blass, Andreas; Gurevich, Yuri 2003 Homotopy and homology of finite lattices. Zbl 1025.06002 Blass, Andreas 2003 Resource consciousness in classical logic. Zbl 1038.03009 Blass, Andreas 2003 On polynomial time computation over unordered structures. Zbl 1020.03038 Blass, Andreas; Gurevich, Yuri; Shelah, Saharon 2002 Specker’s theorem for Nöbeling’s group. Zbl 0998.20047 Blass, Andreas 2002 Pairwise testing. Zbl 1169.68352 Blass, Andreas; Gurevich, Yuri 2002 Finite preimages under the natural map from $$\beta(\mathbb N\times\mathbb N)$$ to $$\beta\mathbb N\times\beta\mathbb N$$. Zbl 1083.54014 Blass, Andreas; Moche, Gugu 2002 Algorithms vs. machines. Zbl 1024.68101 Blass, Andreas; Gurevich, Yuri 2002 Nearly adequate sets. Zbl 1013.03054 Blass, Andreas 2002 Abstract state machines and computationally complete query languages. Zbl 1009.68030 Blass, Andreas; Gurevich, Yuri; Van den Bussche, Jan 2002 A note on extensions of asymptotic density. Zbl 0992.28002 Blass, A.; Frankiewicz, R.; Plebanek, G.; Ryll-Nardzewski, C. 2001 Free subgroups of the Baer-Specker group. Zbl 1022.20025 Blass, Andreas; Irwin, John 2001 Needed reals and recursion in generic reals. Zbl 0980.03055 Blass, Andreas 2001 The underlying logic of Hoare logic. Zbl 1012.03514 Blass, Andreas; Gurevich, Yuri 2001 Inadequacy of computable loop invariants. Zbl 1365.68315 Blass, Andreas; Gurevich, Yuri 2001 The logic of choice. Zbl 0973.03007 Blass, Andreas; Gurevich, Yuri 2000 Background, reserve, and Gandy machines. Zbl 0973.03053 Blass, Andreas; Gurevich, Yuri 2000 Abstract state machines and computationally complete query languages. Zbl 0976.68061 Blass, Andreas; Gurevich, Yuri; Van den Bussche, Jan 2000 The underlying logic of Hoare logic. Zbl 1012.03047 Blass, Andreas; Gurevich, Yuri 2000 Abstract state machines and pure mathematics. Zbl 0976.03046 Blass, Andreas 2000 Choiceless polynomial time. Zbl 0936.03037 Blass, Andreas; Gurevich, Yuri; Shelah, Saharon 1999 On the cofinality of ultrapowers. Zbl 0930.03060 Blass, Andreas; Mildenberger, Heike 1999 Purity and Reid’s theorem. Zbl 0939.20056 Blass, Andreas; Irwin, John 1999 Basic subgroups and a freeness criterion for torsion-free Abelian groups. Zbl 0943.20052 Blass, Andreas; Irwin, John 1999 Characteristic and Ehrhart polynomials. Zbl 0899.05003 Blass, Andreas; Sagan, Bruce E. 1998 Möbius functions of lattices. Zbl 0872.06004 Blass, Andreas; Sagan, Bruce E. 1997 The linear time hierarchy theorems for abstract state machines and RAMs. Zbl 0960.68070 Blass, Andreas; Gurevich, Yuri 1997 Reductions between cardinal characteristics of the continuum. Zbl 0838.03036 Blass, Andreas 1996 Baer meets Baire: Applications of category arguments and descriptive set theory to $$\mathbb{Z}^{\aleph_ 0}$$. Zbl 0870.20037 Blass, Andreas R.; Irwin, John 1996 Subgroups of the Baer-Specker group with few endomorphisms but large dual. Zbl 0851.20052 Blass, Andreas; Göbel, Rüdiger 1996 On the group of eventually divisible integer sequences. Zbl 0872.20047 Blass, Andreas R. 1996 Matrix transformation is complete for the average case. Zbl 0828.68078 Blass, Andreas; Gurevich, Yuri 1995 Seven trees in one. Zbl 0846.18002 Blass, Andreas 1995 Questions and answers – a category arising in linear logic, complexity theory, and set theory. Zbl 0823.03039 Blass, Andreas 1995 Some abelian groups with free duals. Zbl 0843.20046 Blass, Andreas; Irwin, John; Schlitt, Greg 1995 Partition theorems for spaces of variable words. Zbl 0809.04005 Bergelson, Vitaly; Blass, Andreas; Hindman, Neil 1994 Cardinal characteristics and the product of countably many infinite cyclic groups. Zbl 0816.20047 Blass, Andreas 1994 Is game semantics necessary? Zbl 0953.03066 Blass, A. 1994 Ultrafilters: Where topological dynamics = algebra = combinatorics. Zbl 0856.54042 Blass, Andreas 1993 Simple cardinal characteristics of the continuum. Zbl 0828.03019 Blass, Andreas 1993 Randomizing reductions of search problems. Zbl 0789.68056 Blass, Andreas; Gurevich, Yuri 1993 A game semantics for linear logic. Zbl 0763.03008 Blass, Andreas 1992 On the reduction theory for average case complexity. Zbl 0789.68068 Blass, Andreas; Gurevich, Yuri 1991 Infinitary combinatorics and modal logic. Zbl 0699.03008 Blass, Andreas 1990 Groupwise density and related cardinals. Zbl 0706.03036 Blass, Andreas 1990 Sums of ultrafilters and the Rudin-Keisler and Rudin-Frolik orders. Zbl 0704.54003 Blass, Andreas; Hindman, Neil 1990 Ultrafilters with small generating sets. Zbl 0681.03033 Blass, Andreas; Shelah, Saharon 1989 Consistency results about filters and the number of inequivalent growth types. Zbl 0673.03038 Blass, Andreas; Laflamme, Claude 1989 Near coherence of filters. III: A simplified consistency proof. Zbl 0702.03030 Blass, Andreas; Shelah, Saharon 1989 Applications of superperfect forcing and its relatives. Zbl 0683.03029 Blass, Andreas 1989 Freyd’s models for the independence of the axiom of choice. Zbl 0687.03031 Blass, Andreas; Scedrov, Andre 1989 Selctive ultrafilters and homogeneity. Zbl 0649.03036 Blass, Andreas 1988 The logic in computer science column - topoi and computation. Zbl 0681.03044 Blass, Andreas 1988 There may be simple $$P_{\aleph _ 1}$$- and $$P_{\aleph _ 2}$$-points and the Rudin-Keisler ordering may be downward directed. Zbl 0634.03047 Blass, Andreas; Shelah, Saharon 1987 On strongly summable ultrafilters and union ultrafilters. Zbl 0643.03032 Blass, Andreas; Hindman, Neil 1987 Near coherence of filters. II: Applications to operator ideals, the Stone-Čech remainder of a half-line, order ideals of sequences, and slenderness of groups. Zbl 0647.03043 Blass, Andreas 1987 Ultrafilters related to Hindman’s finite-unions theorem and its extensions. Zbl 0634.03045 Blass, Andreas 1987 Existential fixed-point logic. Zbl 0647.03018 Blass, Andreas; Gurevich, Yuri 1987 Prime ideals yield almost maximal ideals. Zbl 0609.06006 Blass, Andreas 1987 Logical analysis of some theorems of combinatorics and topological dynamics. Zbl 0652.03040 Blass, Andreas R.; Hirst, Jeffry L.; Simpson, Stephen G. 1987 Well-ordering and induction in intuitionistic logic and topoi. Zbl 0655.03039 Blass, Andreas 1987 ...and 52 more Documents all top 5 #### Cited by 1,028 Authors 64 Shelah, Saharon 37 Blass, Andreas Raphael 25 Tsaban, Boaz 25 Zdoms’kyĭ, Lyubomyr Sergiĭovych 21 Brendle, Jörg 17 Hrušák, Michael 17 Mildenberger, Heike 15 Gurevich, Yuri 15 Japaridze, Giorgi 14 Banakh, Taras Onufrievich 12 Repovš, Dušan D. 12 Tachtsis, Eleftherios 11 Hindman, Neil 11 Raghavan, Dilip 9 Dobrinen, Natasha L. 9 Dow, Alan S. 9 Fischer, Vera 9 Garti, Shimon 9 Guzmán González, Osvaldo 9 Sagan, Bruce Eli 9 Todorcevic, Stevo B. 8 Caramello, Olivia 8 Laflamme, Claude 8 Miller, Arnold W. 7 Brian, William Rea 7 Goldstern, Martin Robert 7 Hemaspaandra, Lane A. 7 Keremedis, Kyriakos 7 Protasov, Igor Volodymyrovych 6 Dawar, Anuj 6 García-Ferreira, Salvador 6 Geschke, Stefan 6 Hamkins, Joel David 6 Kanellopoulos, Vassilis 5 Brunner, Norbert 5 Di Nasso, Mauro 5 Dodos, Pandelis 5 Friedman, Sy-David 5 Grädel, Erich 5 Hallam, Joshua W. 5 Howard, Paul E. 5 Johnstone, Peter T. 5 Karagila, Asaf 5 Kellner, Jakob 5 Montoya, Diana Carolina 5 Ramos-García, Ulises Ariet 5 Santocanale, Luigi 5 Scheepers, Marion 5 Sevenster, Merlijn 5 Steprāns, Juris 4 Anderson, Daron 4 Banaschewski, Bernhard 4 Bezhanishvili, Guram 4 Dershowitz, Nachum 4 Fernández Bretón, David José 4 Forti, Marco 4 Glaßer, Christian 4 Göbel, Rüdiger 4 Grohe, Martin 4 Herrlich, Horst 4 Kolaitis, Phokion G. 4 Kurilić, Miloš S. 4 Larson, Paul B. 4 Leivant, Daniel M. 4 Marcone, Alberto 4 Mejía, Diego Alejandro 4 Minami, Hiroaki 4 Rodríguez Ruiz, José 4 Rossman, Benjamin 4 Schewe, Klaus-Dieter 4 Shore, Richard A. 4 Sobota, Damian 4 Solecki, Sławomir 4 Strauss, Dona 4 Szewczak, Piotr 4 Thomas, Hugh Ross 4 Tomita, Artur Hideyuki 4 Tran, Tan Nhat 4 Verner, Jonathan L. 4 Yoshinaga, Masahiko 3 Aguilera, Juan Pablo 3 Bankston, Paul 3 Bartoszynski, Tomek 3 Borodulin-Nadzieja, Piotr 3 Carlucci, Lorenzo 3 Chatterjee, Krishnendu 3 Chodounský, David 3 Compton, Kevin J. 3 Esakia, Leo 3 Farah, Ilijas 3 Farkas, Barnabás 3 Farmaki, Vassiliki 3 Gottlob, Georg 3 Hall, Eric Joseph 3 Hathaway, Dan 3 Judah, Haim I. 3 Kunisada, Ryoichi 3 Leinster, Tom 3 Li, Xueliang 3 Machura, Michal ...and 928 more Authors all top 5 #### Cited in 182 Serials 99 Annals of Pure and Applied Logic 69 The Journal of Symbolic Logic 67 Topology and its Applications 56 Archive for Mathematical Logic 49 Proceedings of the American Mathematical Society 46 Theoretical Computer Science 41 Transactions of the American Mathematical Society 23 Discrete Mathematics 21 Israel Journal of Mathematics 21 Advances in Mathematics 21 The Bulletin of Symbolic Logic 20 Journal of Pure and Applied Algebra 17 Information and Computation 16 Journal of Computer and System Sciences 15 Fundamenta Mathematicae 15 Mathematical Logic Quarterly (MLQ) 13 Journal of Combinatorial Theory. Series A 13 Studia Logica 10 Algebra Universalis 8 Notre Dame Journal of Formal Logic 8 Semigroup Forum 8 Order 7 Discrete Applied Mathematics 7 Journal of Algebra 6 Journal of Mathematical Analysis and Applications 5 Information Processing Letters 5 Czechoslovak Mathematical Journal 5 Monatshefte für Mathematik 5 European Journal of Combinatorics 5 Advances in Applied Mathematics 5 Journal of Mathematical Sciences (New York) 5 The Electronic Journal of Combinatorics 5 Journal of Mathematical Logic 5 Logical Methods in Computer Science 4 Communications in Algebra 4 Mathematical Proceedings of the Cambridge Philosophical Society 4 Commentationes Mathematicae Universitatis Carolinae 4 Journal of Combinatorial Theory. Series B 4 Journal of Philosophical Logic 4 Mathematica Slovaca 4 Siberian Mathematical Journal 4 Acta Mathematica Hungarica 4 Journal of Algebraic Combinatorics 4 Topology Proceedings 4 Theory of Computing Systems 4 The Review of Symbolic Logic 3 Artificial Intelligence 3 Archiv für Mathematische Logik und Grundlagenforschung 3 Rocky Mountain Journal of Mathematics 3 Journal of Number Theory 3 Mathematical Systems Theory 3 Quaestiones Mathematicae 3 Synthese 3 Graphs and Combinatorics 3 MSCS. Mathematical Structures in Computer Science 3 Combinatorics, Probability and Computing 3 Séminaire Lotharingien de Combinatoire 3 Journal of Applied Analysis 3 Journal of the European Mathematical Society (JEMS) 3 Journal of Applied Logic 3 Science China. Mathematics 2 Compositio Mathematica 2 Integral Equations and Operator Theory 2 Journal of Functional Analysis 2 Journal of Graph Theory 2 Journal of the Mathematical Society of Japan 2 Mathematische Annalen 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Programming and Computer Software 2 Rendiconti del Seminario Matematico della Università di Padova 2 Journal of Complexity 2 Algorithmica 2 Journal of the American Mathematical Society 2 Mathematical and Computer Modelling 2 Formal Aspects of Computing 2 International Journal of Foundations of Computer Science 2 Bulletin of the American Mathematical Society. New Series 2 Bulletin of the Polish Academy of Sciences, Mathematics 2 Indagationes Mathematicae. New Series 2 Computational Complexity 2 Applied Categorical Structures 2 Journal of Combinatorial Designs 2 Annals of Mathematics and Artificial Intelligence 2 Annals of Combinatorics 2 Natural Computing 2 Central European Journal of Mathematics 2 ACM Transactions on Computational Logic 2 Mediterranean Journal of Mathematics 2 Journal of Logical and Algebraic Methods in Programming 1 Acta Informatica 1 American Mathematical Monthly 1 Bulletin of the Australian Mathematical Society 1 Communications in Mathematical Physics 1 International Journal of Theoretical Physics 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Biology 1 Mathematical Notes 1 Periodica Mathematica Hungarica 1 Problems of Information Transmission 1 Studia Mathematica ...and 82 more Serials all top 5 #### Cited in 46 Fields 654 Mathematical logic and foundations (03-XX) 207 General topology (54-XX) 200 Computer science (68-XX) 177 Combinatorics (05-XX) 75 Order, lattices, ordered algebraic structures (06-XX) 61 Group theory and generalizations (20-XX) 55 Category theory; homological algebra (18-XX) 37 Topological groups, Lie groups (22-XX) 36 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 32 Measure and integration (28-XX) 32 Functional analysis (46-XX) 22 Convex and discrete geometry (52-XX) 19 Number theory (11-XX) 19 Real functions (26-XX) 17 Dynamical systems and ergodic theory (37-XX) 13 General and overarching topics; collections (00-XX) 12 Associative rings and algebras (16-XX) 11 History and biography (01-XX) 11 General algebraic systems (08-XX) 11 Information and communication theory, circuits (94-XX) 10 Commutative algebra (13-XX) 10 Probability theory and stochastic processes (60-XX) 9 Manifolds and cell complexes (57-XX) 7 Operator theory (47-XX) 7 Quantum theory (81-XX) 6 Algebraic topology (55-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 4 Operations research, mathematical programming (90-XX) 4 Biology and other natural sciences (92-XX) 3 Nonassociative rings and algebras (17-XX) 3 Sequences, series, summability (40-XX) 3 Geometry (51-XX) 2 Field theory and polynomials (12-XX) 2 Algebraic geometry (14-XX) 2 Partial differential equations (35-XX) 1 $$K$$-theory (19-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Difference and functional equations (39-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Numerical analysis (65-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) 1 Systems theory; control (93-XX) #### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2021-07-25T20:25:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.454767107963562, "perplexity": 7723.490671665314}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046151760.94/warc/CC-MAIN-20210725174608-20210725204608-00009.warc.gz"}
https://www.usgs.gov/center-news/volcano-watch-whats-mauna-loa	Volcano Watch — What's up with Mauna Loa? Release Date: Of the more than 30 eruptions of Mauna Loa in the last hundred years, the 1975 and 1984 eruptions are the first events for which we have detailed seismic and deformation data. Thus, we consider the 1975 and 1984 data sets important standards against which future unrest can be compared and interpreted. The July 1975 eruption was preceded by at least a year of increased seismic activity and inflation of the summit magma chamber. Civil authorities were briefed on the activity in the fall of 1974, and Big Island residents were alerted to the possibility of an eruption through extensive news media reports. The eruption lasted only one day, and the summit magma chamber began to inflate immediately thereafter. The inflation continued steadily, and the rate of intermediate-depth earthquakes began to increase in the early 1980s. In late 1983, microseismicity beneath Mauna Loa increased sharply, prompting HVO to forecast an eruption within the next two years. In early March 1984, shallow earthquake activity beneath the summit caldera dramatically increased, and the eruption started several weeks later. Our capability to detect unrest at Mauna Loa has increased significantly since its last eruption. To monitor seismicity, we have added new seismic stations along the southwest rift zone, as well as state-of-the-art seismic instrumentation at several other locations on the island that will aid in the monitoring of Mauna Loa. To track the deformation of the ground surface, we have installed three electronic tiltmeters and three extremely sensitive strainmeters into 130 m (425 ft) deep boreholes and positioned four continuously-recording GPS instruments on Mauna Loa. All the instruments relay data to HVO via radio modems and satellite links, so that we can look at changes occurring on the volcano within one to ten minutes. In addition, we survey over 50 benchmarks on the volcano yearly with GPS to determine the overall pattern of deformation, and we do additional tilt and leveling surveys at the summit to measure vertical changes. When magma is accumulating beneath Mauna Loa, we observe swelling of the ground surface. Monitoring stations move away from the area above the summit magma chamber, and we measure increases in distance between benchmarks, increases in their elevation, and a radial pattern of tilt away from the locus of inflation. Conversely, during an eruption, the deformation patterns are reversed as magma leaves the reservoir to move to the surface. Modeling of data gathered over the last two eruption cycles of Mauna Loa reveals that the top of the magma reservoir is located about 3 km (1.9 miles) below the southeastern part of Mokuaweoweo, the summit caldera. The reservoir started re-inflating immediately after the 1984 eruption and, by 1993, had filled with as much magma as was accumulated between the 1975 and 1984 eruptions. However, the rate of inflation slowed considerably after 1993, and results from both continuously recording instruments and recent surveys confirm that magma is not currently accumulating beneath the summit. Furthermore, we have not observed any dramatic increase in the level of seismic activity since 1984. If the pre-eruptive patterns of 1975 and 1984 are any indication of what we can expect, we should observe an increase in the number and size of earthquakes, and renewed inflation of the summit at least a year prior to the next eruption. While those of us living on the slopes of Mauna Loa might be relieved that the next eruption does not appear to be right around the corner, we should realize this is a temporary reprieve. Let's all take advantage of it to plan and prepare for the inevitable. Volcano Activity Update Eruptive activity of Kīlauea Volcano continued unabated at the Puu Oo vent during the past week. Lavamoves away from the vent toward the ocean in a network of tubes and descends Pulama pali in several separate tubes. Breakouts from the tube system feed surface flows above and on the pali. Many surface flows, mainly from breakouts of the ocean entry tubes, are also observed in the coastal flats. Lava continues to enter the ocean at Kamoamoa and the area east of Kupapa`u. The public is reminded that the benches of the two ocean entries are very hazardous, with possible collapses of the new land. The steam clouds are extremely hot, highly acidic, and laced with glass particles. Swimming at the black sand beaches of the benches can be a blistering or even deadly venture. There were no earthquakes reported felt during the week ending on October 18.	2020-09-28T06:50:34	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3892032504081726, "perplexity": 2558.762394112292}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401585213.82/warc/CC-MAIN-20200928041630-20200928071630-00332.warc.gz"}
https://pos.sissa.it/390/418/	Volume 390 - 40th International Conference on High Energy physics (ICHEP2020) - Parallel: Quark and Lepton Flavour Physics Results and Prospects of Radiative and Electroweak Penguin Decays at Belle II Y. Sato Full text: Not available Abstract Radiative and electroweak penguin mediated decays of $B$ mesons are a great probe for physics beyond the standard model of particle physics. Furthermore, recently anomalies on exclusive $b\to s\ell^+\ell^-$ processes which may imply lepton flavor universality violation, have been observed. Belle II experiment sheds light on the anomalies with the measurement of an inclusive analysis in this mode. Thanks to smaller hadronic uncertainties compared with exclusive modes, complementary information can be provided. Belle II is also a unique experiment to search for processes involving neutrinos such as $B\to K^{()}\nu\bar{\nu}$. We report the results and prospects of an inclusive $B\to X_s \ell^+\ell^-$ analysis and a search for $B\to K^{()}\nu\bar{\nu}$. How to cite Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete. Open Access Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.	2020-11-29T10:41:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.587094783782959, "perplexity": 2203.718948106499}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141197593.33/warc/CC-MAIN-20201129093434-20201129123434-00112.warc.gz"}
https://wiki.bnl.gov/eic/index.php?title=PYTHIA&diff=364&oldid=363	# Difference between revisions of "PYTHIA" ## Documentation on PYTHIA: #### Pythia processes important in ep Subprocess # Description soft VMD V N → V N 91 elastic VMD V N → V X 92 single-diffractive VMD V N → XN 93 single-diffractive VMD V N → XX 94 double-diffractive VMD V N → X 95 soft non-diffractive VMD low-pT QCD 2→2 96 semihard QCD 2→2 RESOLVED (hard VMD and anomalous) qq → qq 11 QCD 2 → 2(q) q qbar → q qbar 12 q qbar → gg 13 gq → gq 28 qg → qg 28 QCD 2 → 2(g) gg → q qbar 53 gg → gg 68 DIRECT γ∗q → q 99 LO DIS γ∗T q → qg 131 (transverse) QCDC γ∗L q → qg 132 (longitudinal) QCDC γ∗T g → q qbar 135 (transverse) PGF γ∗L g → q qbar 136 (longitudinal) PGF VMD: Vector Meson Dominance, describing the elastic diffractive production of Vector Mesons QCDC: QCD-Compton, radiation of a gluon from incoming or outgoing quark lines PGF: Photon Gluon Fusion ## Running PYTHIA the code can be found on the afs directory for EIC at BNL "/afs/rhic.bnl.gov/eic/PACKAGES/PYTHIA-RAD-CORR" this is code is based on PYTHIA 6.4.13 and was modified to include radiative corrections using RadGen. The main program is in the same directory and called pyMaineRHIC_v1.f, several other routines are needed which are in the same directory. The executable is in the same directory and called pythiaeRHIC There are several steer files (named: input.data. XXXXX.eic) provided in this directory to run PYTHIA and get reasonable output ### How to Run the Code pythiaeRHIC < input.data_noradcor.eic > XXX.log input.data_noradcor.eic is one of the steer file examples in the directory to run PYTHIA with settings tuned for Hermes, and/or H1 and ZEUS. If you want to run only elastic vector meson production the example steer file is "input.data_noradcor.VM.eic" • create a directory called radgen in the area you want to run the code • you either need to generate the lookup table for your cuts and beam energy settings first pythiaeRHIC < input.data_make-radcor.eic • or you can use one of the files already generated the directories are in "/afs/rhic.bnl.gov/eic/PACKAGES/PYTHIA-RAD-CORR" • to run the code than with radiative corrections simply change the steer file to either input.data_radcor.eic or input.data_radcor.VM.eic and type pythiaeRHIC < input.data_radcor.eic > XXX.log ### Output file structure the output file is in a text format which has the following structure. • 1st line: PYTHIA EVENT FILE • 2nd line: "============================================" • 3rd line: information which is valid for the event I: 0 (line index) ievent: eventnumber running from 1 to XXX genevent: trials to generate this event subprocess: pythia subprocess (MSTI(1)), for details see table above nucleon: hadron beam type (MSTI(12)) targetparton: parton hit in the target (MSTI(16)) xtargparton: x of target parton (PARI(34)) beamparton: in case of resolved photon processes and soft VMD the virtual photon has a hadronic structure. This gives the info which parton interacted with the target parton (MSTI(15)) xbeamparton: x of beam parton (PARI(33)) thetabeamparton: theta of beam parton (PARI(53)) truey, trueQ2, truex, trueW2, trueNu: are the kinematic variables of the event. If radiative corrections are turned on they are different from what is calculated from the scattered lepton. If radiative corrections are turned off they are the same as what is calculated from the scattered lepton leptonphi: phi of the lepton (VINT(313)) s_hat: shat of the process (PARI(14)) t_hat: Mandelstam t (PARI(15)) u_hat: Mandelstm u (PARI(16)) pt2_hat: pthat^2 of the hard scattering (PARI(18)) Q2_hat: Q2hat of the hard scattering (PARI(22)), F2, F1, R, sigma_rad, SigRadCor: information used and needed in the radiative correction code EBrems: energy of the radiative photon in the nuclear rest frame photonflux: flux factor from PYTHIA (VINT(319)) nrTracks: number of tracks in this event, includes also virtual particles • 4th line: "============================================" • 5th line: now start the track wise information. I: line index, runs from 1 to nrTracks K(I,1): status code KS (1: stable particles 11: particles which decay 55; radiative photon) K(I,2): particle KF code (211: pion, 2112:n, ....) K(I,3): line number of parent particle K(I,4): normally the line number of the first daughter; it is 0 for an undecayed particle or unfragmented parton K(I,5): normally the line number of the last daughter; it is 0 for an undecayed particle or unfragmented parton. P(I,1): px of particle P(I,2): py of particle P(I,3): pz of particle P(I,4): Energy of particle P(I,5): mass of particle V(I,1): x vertex information V(I,2): y vertex information V(I,3): z vertex information • Xth line "=============== Event finished ===============" the information from line 3 to X repeats for each event. ### How to analyze events • create a root tree there are root macros available to convert the output txt-files into root trees. Details how to run the macros can be found [here] ##### MC normalization to normalize your counts to cross section you need two informations • the total number of trials (NGEN(0,3)), it is printed to the screen/logfile if PYTHIA finishes • the total integrated cross section (PARI(1)), the unit is microbarn (10^-6), it is printed to the screen/logfile if PYTHIA finishes ==> count * total integrated cross section /total number of trials to calculate the corresponding luminosity ==> total number of trials/ total integrated cross section the code implemented in PTHIA to calculate radiative corrections is called RADGEN The writeup on it can be found here [hep-ph/9906408] The following steps have been done to implement it in PYTHIA: • change the subroutine pygaga.f so it calls radgen after you have thrown y and Q2 • get the true y and Q2 from radgen and the radiated photon • Pythia will continue to now generate an event based on this y and Q2 • Pythia still operates under accept reject, the extra weigt from the radiative corrections is absorbed in the flux factor	2022-12-07T22:56:37	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5286293625831604, "perplexity": 12236.490714664975}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711221.94/warc/CC-MAIN-20221207221727-20221208011727-00852.warc.gz"}
https://mooseframework.inl.gov/source/kernels/KKSCHBulk.html	# KKSCHBulk KKS model kernel for the Bulk Cahn-Hilliard term. This operates on the concentration 'c' as the non-linear variable Non-split KKS Cahn-Hilliard bulk kernel, which is not fully implemented**. The non-linear variable for this Kernel is the concentration . ### Residual In the residual routine we need to calculate the term . We exploit the KKS identity and arbitrarily use the a-phase instead. The gradient can be calculated through the chain rule (note that is potentially a function of many variables). (1) With being the vector of all arguments to this simplifies to (2) using as a shorthand for the term (and represented in the code as the array _second_derivatives[i]). We do have access to the gradients of through MOOSE (stored in _grad\_args[i]). ### Jacobian The calculation of the Jacobian involves the derivative of the Residual term w.r.t. the individual coefficients of all parameters of . Here can stand for any variable . (3) In the code is given by jvar for the off diagonal case, and (not or !) in the on diagonal case. #### Off-diagonal Let's focus on off diagonal first. Here is zero, if jvar is not equal . Allowing us to remove the sum over and replace it with the single non-zero summand (4) In the first term in the square brackets the derivative is only non-zero if is jvar. We can therefore pull this term out of the sum. (5) With the rules for derivatives we get (6) where is _j in the code. #### On-diagonal For the on diagonal terms we look at the derivative w.r.t. the components of the non-linear variable of this kernel. Note, that is only indirectly a function of . We assume the dependence is given through . The chain rule will thus yield terms of this form (7) which is given as equation (23) in KKS. Following the off-diagonal derivation we get (8) #### On-diagonal second approach Let's get back to the original residual with . Then (9) ## Input Parameters • variableThe name of the variable that this Kernel operates on C++ Type:NonlinearVariableName Options: Description:The name of the variable that this Kernel operates on • cbphase concentration corresponding to the non-linear variable of this kernel C++ Type:std::vector Options: Description:phase concentration corresponding to the non-linear variable of this kernel • caphase concentration corresponding to the non-linear variable of this kernel C++ Type:std::vector Options: Description:phase concentration corresponding to the non-linear variable of this kernel • fa_nameBase name of the free energy function F (f_name in the corresponding derivative function material) C++ Type:MaterialPropertyName Options: Description:Base name of the free energy function F (f_name in the corresponding derivative function material) • fb_nameBase name of the free energy function F (f_name in the corresponding derivative function material) C++ Type:MaterialPropertyName Options: Description:Base name of the free energy function F (f_name in the corresponding derivative function material) ### Required Parameters • mob_nameMThe mobility used with the kernel Default:M C++ Type:MaterialPropertyName Options: Description:The mobility used with the kernel • argsVector of arguments of the mobility C++ Type:std::vector Options: Description:Vector of arguments of the mobility • args_aVector of additional arguments to Fa C++ Type:std::vector Options: Description:Vector of additional arguments to Fa • h_namehBase name for the switching function h(eta) Default:h C++ Type:MaterialPropertyName Options: Description:Base name for the switching function h(eta) • displacementsThe displacements C++ Type:std::vector Options: Description:The displacements • blockThe list of block ids (SubdomainID) that this object will be applied C++ Type:std::vector Options: Description:The list of block ids (SubdomainID) that this object will be applied ### Optional Parameters • enableTrueSet the enabled status of the MooseObject. Default:True C++ Type:bool Options: Description:Set the enabled status of the MooseObject. • save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.) C++ Type:std::vector Options: Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.) • use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used. Default:False C++ Type:bool Options: Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used. • control_tagsAdds user-defined labels for accessing object parameters via control logic. C++ Type:std::vector Options: Description:Adds user-defined labels for accessing object parameters via control logic. • seed0The seed for the master random number generator Default:0 C++ Type:unsigned int Options: Description:The seed for the master random number generator • diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.) C++ Type:std::vector Options: Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.) • implicitTrueDetermines whether this object is calculated using an implicit or explicit form Default:True C++ Type:bool Options: Description:Determines whether this object is calculated using an implicit or explicit form • vector_tagsnontimeThe tag for the vectors this Kernel should fill Default:nontime C++ Type:MultiMooseEnum Options:nontime time Description:The tag for the vectors this Kernel should fill • extra_vector_tagsThe extra tags for the vectors this Kernel should fill C++ Type:std::vector Options: Description:The extra tags for the vectors this Kernel should fill • matrix_tagssystemThe tag for the matrices this Kernel should fill Default:system C++ Type:MultiMooseEnum Options:nontime system Description:The tag for the matrices this Kernel should fill • extra_matrix_tagsThe extra tags for the matrices this Kernel should fill C++ Type:std::vector Options: Description:The extra tags for the matrices this Kernel should fill	2019-04-21T15:01:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.37134209275245667, "perplexity": 3687.4758334776843}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578531984.10/warc/CC-MAIN-20190421140100-20190421162100-00165.warc.gz"}
http://www.martin-ueding.de/projects/git-changelog/de.html	Dieser Inhalt ist nicht in deutsch verfügbar. # git-changelog License (Code): GPLv2 CC-BY git, Python 3 For my jscribble project, I use git. The human readable changes are stored in the annotated tags itself. So I have a tag called v1.5.3 which contains the text that you can read in the changelog. That way, the information is not spread out in the git repository (the microscopic changes) and the changelog file (the macroscopic changes) but combined in the git repository. Each tag description is parsed, which strips all the irrelevant git information (the commit id, the whole patch, time and author) as well as the GnuPG signature and generates a clean changelog. The generated changelog looks like this: v1.5.3 * Create extensive manual page. - Fix drawing dots (broken since v1.5.2). - Allow movements with extra mouse buttons (enable in config). - Add config option to disable eraser. It will only use the tags that are in your current branch. If you have two branches for two versions of your program, like v2-series and v3-series, you do not want the versions that start with a 3 to show up in your other changelog. In case you do want them all, there is an --all option. And if you want more control, you can specify a regular expression with the --filter option. Latest release: git-changelog_1.6.tar.gz git clone git://github.com/martin-ueding/git-changelog.git git clone http://chaos.stw-bonn.de/users/mu/git/git-changelog.git	2013-05-23T17:28:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22660936415195465, "perplexity": 5760.801761272812}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368703635016/warc/CC-MAIN-20130516112715-00085-ip-10-60-113-184.ec2.internal.warc.gz"}
https://www.nist.gov/publications/temperature-extrapolation-henrys-law-constants-and-isosteric-heat-adsorption	An official website of the United States government Official websites use .gov A .gov website belongs to an official government organization in the United States. Secure .gov websites use HTTPS A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites. # Temperature Extrapolation of Henry's Law Constants and the Isosteric Heat of Adsorption Published ### Author(s) Daniel Siderius, Harold Hatch, Vincent K. Shen ### Abstract Computational screening of adsorbent materials often uses the Henry's law constant ($\KH$) (at a particular temperature) as a first discriminator metric due to its relative ease of calculation. The isosteric heat of adsorption in the limit of zero pressure ($\qstinf$) is often calculated along with the Henry's law constant, and both properties are informative metrics of adsorbent material performance at low pressure conditions. In this article, we introduce a method for extrapolating $\KH$ as a function of temperature, using series-expansion coefficients that are easily computed at the same time as $\KH$ itself; the extrapolation function also yields $\qstinf$. The extrapolation is highly accurate over a wide range of temperatures when the basis temperature is sufficiently high, for a wide range of adsorbent materials and adsorbate gases. Various results suggest that the extrapolation is accurate when the extrapolation range in inverse-temperature space is limited to $\left\|\beta - \beta_0\right\| < 0.5$mol/kJ. Application of the extrapolation to a large set of materials is shown to be successful provided that $\KH$ is not extremely large and/or the extrapolation coefficients converge satisfactorily. The extrapolation is also able to predict $\qstinf$ for a system that shows an unusually large temperature dependence. The work provides a robust method for predicting $\KH$ and $\qstinf$ over a wide range of industrially relevant temperatures with minimal effort beyond that necessary to compute those properties at a single temperature, which facilitates the addition of application temperature to computational screening exercises. Citation Journal of Physical Chemistry B Volume 126 Issue 40	2023-02-04T22:13:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4628327786922455, "perplexity": 1422.3313269312875}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500154.33/warc/CC-MAIN-20230204205328-20230204235328-00055.warc.gz"}
https://zbmath.org/authors/?q=ai%3Acianchi.andrea	# zbMATH — the first resource for mathematics ## Cianchi, Andrea Compute Distance To: Author ID: cianchi.andrea Published as: Cianchi, A.; Cianchi, Andrea External Links: Wikidata · ORCID Documents Indexed: 128 Publications since 1989 all top 5 #### Co-Authors 42 single-authored 17 Pick, Luboš 16 Maz’ya, Vladimir Gilelevich 13 Alberico, Angela 11 Fusco, Nicola 9 Slavíková, Lenka 6 Ferone, Adele 4 Breit, Dominic 4 Sbordone, Carlo 3 Carozza, Menita 3 Diening, Lars 3 Schwarzacher, Sebastian 3 Trombetti, Cristina 2 Barletta, Giuseppina 2 Cavaliere, Paola 2 Edmunds, David Eric 2 Ferone, Vincenzo 2 Kerman, Ron 2 Kuusi, Tuomo 2 Lutwak, Erwin 2 Maggi, Francesco 2 Musil, Vít 2 Nitsch, Carlo 2 Pratelli, Aldo 2 Randolfi, Monia 2 Yang, Deane 2 Zhang, Gaoyong 1 Alberico, Teresa 1 Alvino, Angelo 1 Černý, Robert 1 Chlebicka, Iwona 1 Chlebík, Miroslav 1 Esposito, Luca 1 Esteban, Maria J. 1 Gurka, Petr 1 Hencl, Stanislav 1 Ioku, Norisuke 1 Kawohl, Bernd 1 Mercaldo, Anna 1 Opic, Bohumír 1 Salani, Paolo 1 Schianchi, Rosanna 1 Stroffolini, Bianca 1 Zatorska-Goldstein, Anna all top 5 #### Serials 7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Indiana University Mathematics Journal 5 Journal of Functional Analysis 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Advances in Mathematics 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Archive for Rational Mechanics and Analysis 3 Journal of Mathematical Analysis and Applications 3 Journal für die Reine und Angewandte Mathematik 3 Transactions of the American Mathematical Society 3 The Journal of Geometric Analysis 3 Communications in Partial Differential Equations 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Calculus of Variations and Partial Differential Equations 3 Communications on Pure and Applied Analysis 2 Applicable Analysis 2 Journal d’Analyse Mathématique 2 Arkiv för Matematik 2 American Journal of Mathematics 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Journal of Differential Equations 2 Journal of the London Mathematical Society. Second Series 2 Mathematische Annalen 2 Mathematische Nachrichten 2 Ricerche di Matematica 2 SIAM Journal on Mathematical Analysis 2 Bollettino della Unione Matemàtica Italiana. Serie VII. B 2 Potential Analysis 2 Annales Academiae Scientiarum Fennicae. Mathematica 2 Journal of the European Mathematical Society (JEMS) 2 Advances in Calculus of Variations 1 IEEE Transactions on Information Theory 1 Studia Mathematica 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Annales de l’Institut Fourier 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Applied Mathematics and Optimization 1 Bulletin of the London Mathematical Society 1 Duke Mathematical Journal 1 Journal of Differential Geometry 1 Manuscripta Mathematica 1 Le Matematiche 1 Mathematische Zeitschrift 1 Pacific Journal of Mathematics 1 The Quarterly Journal of Mathematics. Oxford Second Series 1 Revista Matemática Iberoamericana 1 Forum Mathematicum 1 Differential and Integral Equations 1 Bulletin des Sciences Mathématiques 1 The Journal of Fourier Analysis and Applications 1 Bollettino della Unione Matematica Italiana. Serie VIII. Sezione B. Articoli di Ricerca Matematica 1 Annals of Mathematics. Second Series 1 Communications in Contemporary Mathematics 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Oberwolfach Reports 1 Bollettino dell’Unione Matematica Italiana. Series IX 1 Nonlinear Analysis. Theory, Methods & Applications 1 Journal of Elliptic and Parabolic Equations all top 5 #### Fields 86 Functional analysis (46-XX) 46 Partial differential equations (35-XX) 28 Real functions (26-XX) 13 Calculus of variations and optimal control; optimization (49-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 6 Measure and integration (28-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Convex and discrete geometry (52-XX) 4 Operator theory (47-XX) 4 Differential geometry (53-XX) 2 Potential theory (31-XX) 1 General and overarching topics; collections (00-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Ordinary differential equations (34-XX) 1 Difference and functional equations (39-XX) 1 Numerical analysis (65-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Information and communication theory, circuits (94-XX) #### Citations contained in zbMATH Open 106 Publications have been cited 1,684 times in 892 Documents Cited by Year A sharp embedding theorem for Orlicz-Sobolev spaces. Zbl 0860.46022 Cianchi, Andrea 1996 Affine Moser-Trudinger and Morrey-Sobolev inequalities. Zbl 1202.26029 Cianchi, Andrea; Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong 2009 Global Lipschitz regularity for a class of quasilinear elliptic equations. Zbl 1220.35065 2011 Global boundedness of the gradient for a class of nonlinear elliptic systems. Zbl 1298.35070 2014 Overdetermined anisotropic elliptic problems. Zbl 1179.35107 Cianchi, Andrea; Salani, Paolo 2009 Sobolev embeddings into BMO, VMO, and $$L_{\infty}$$. Zbl 1035.46502 Cianchi, Andrea; Pick, Luboš 1998 The sharp Sobolev inequality in quantitative form. Zbl 1185.46025 Cianchi, A.; Fusco, N.; Maggi, F.; Pratelli, A. 2009 Optimal Orlicz-Sobolev embeddings. Zbl 1061.46031 Cianchi, Andrea 2004 On the isoperimetric deficit in Gauss space. Zbl 1219.28005 Cianchi, A.; Fusco, N.; Maggi, F.; Pratelli, A. 2011 Boundedness of solutions to variational problems under general growth conditions. Zbl 0892.35048 Cianchi, Andrea 1997 Gradient regularity via rearrangements for $$p$$-Laplacian type elliptic boundary value problems. Zbl 1288.35128 2014 Strong and weak type inequalities for some classical operators in Orlicz spaces. Zbl 0940.46015 Cianchi, Andrea 1999 Functions of bounded variation and rearrangements. Zbl 1028.49035 Cianchi, Andrea; Fusco, Nicola 2002 A fully anisotropic Sobolev inequality. Zbl 0966.46017 Cianchi, Andrea 2000 The perimeter inequality under Steiner symmetrization: cases of equality. Zbl 1087.28003 Chlebík, Miroslav; Cianchi, Andrea; Fusco, Nicola 2005 Moser–Trudinger inequalities without boundary conditions and isoperimetric problems. Zbl 1097.46016 Cianchi, Andrea 2005 Continuity properties of functions from Orlicz-Sobolev spaces and embedding theorems. Zbl 0877.46023 Cianchi, Andrea 1996 Concentration-compactness principles for Moser-Trudinger inequalities: new results and proofs. Zbl 1272.46023 Černý, Robert; Cianchi, Andrea; Hencl, Stanislav 2013 Symmetrization in anisotropic elliptic problems. Zbl 1219.35028 Cianchi, Andrea 2007 Local boundedness of minimizers of anisotropic functionals. Zbl 0984.49019 Cianchi, Andrea 2000 Gradient regularity for minimizers under general growth conditions. Zbl 0913.49024 Cianchi, Andrea; Fusco, Nicola 1999 Steiner symmetric extremals in Pólya-Szegő-type inequalities. Zbl 1110.46021 Cianchi, Andrea; Fusco, Nicola 2006 Hardy inequalities in Orlicz spaces. Zbl 0920.46021 Cianchi, Andrea 1999 Symmetrization and second-order Sobolev inequalities. Zbl 1223.46033 Cianchi, Andrea 2004 Moser–Trudinger trace inequalities. Zbl 1138.46020 Cianchi, Andrea 2008 Maximizing the $$L^ \infty{}$$ norm of the gradient of solutions to the Poisson equation. Zbl 0780.35009 Cianchi, Andrea 1992 On relative isoperimetric inequalities in the plane. Zbl 0674.49030 Cianchi, Andrea 1989 Some results in the theory of Orlicz spaces and applications to variational problems. Zbl 0965.46017 Cianchi, Andrea 1999 Higher-order Sobolev embeddings and isoperimetric inequalities. Zbl 1334.46027 Cianchi, Andrea; Pick, Luboš; Slavíková, Lenka 2015 Korn type inequalities in Orlicz spaces. Zbl 1312.46037 Cianchi, Andrea 2014 Well-posed elliptic Neumann problems involving irregular data and domains. Zbl 1200.35105 Alvino, Angelo; Cianchi, Andrea; Maz’ya, Vladimir G.; Mercaldo, Anna 2010 Global gradient estimates in elliptic problems under minimal data and domain regularity. Zbl 1325.35027 2015 Orlicz-Sobolev boundary trace embeddings. Zbl 1208.46028 Cianchi, Andrea 2010 Hardy inequalities with non-standard remainder terms. Zbl 1153.26310 2008 Quasilinear elliptic problems with general growth and merely integrable, or measure, data. Zbl 1373.35113 2017 Nonlinear potentials, local solutions to elliptic equations and rearrangements. Zbl 1235.31009 Cianchi, Andrea 2011 A quantitative Pólya-Szegő principle. Zbl 1175.46021 Cianchi, Andrea; Esposito, Luca; Fusco, Nicola; Trombetti, Cristina 2008 A quantitative Sobolev inequality in BV. Zbl 1110.46020 Cianchi, Andrea 2006 Optimal Gaussian Sobolev embeddings. Zbl 1203.46019 Cianchi, Andrea; Pick, Luboš 2009 Higher-order Sobolev and Poincaré inequalities in Orlicz spaces. Zbl 1120.46015 Cianchi, Andrea 2006 Differentiability properties of Orlicz-Sobolev functions. Zbl 1119.46030 Alberico, Angela; Cianchi, Andrea 2005 A sharp form of Poincaré type inequalities on balls and spheres. Zbl 0707.53034 Cianchi, Andrea 1989 Dirichlet problems for fully anisotropic elliptic equations. Zbl 1388.35043 Barletta, Giuseppina; Cianchi, Andrea 2017 Comparison estimates in anisotropic variational problems. Zbl 1357.49137 Alberico, Angela; Cianchi, Andrea 2008 Sharp Morrey–Sobolev inequalities and the distance from extremals. Zbl 1153.46019 Cianchi, Andrea 2008 A sharp rearrangement inequality for the fractional maximal operator. Zbl 0968.42014 Cianchi, A.; Kerman, R.; Opic, B.; Pick, L. 2000 On weighted Poincaré inequalities. Zbl 0858.26009 Cianchi, Andrea; Edmunds, David E.; Gurka, Petr 1996 Second-order two-sided estimates in nonlinear elliptic problems. Zbl 1398.35078 2018 Second-order derivatives and rearrangements. Zbl 1017.46023 Cianchi, Andrea 2000 Pointwise Calderón-Zygmund gradient estimates for the $$p$$-Laplace system. Zbl 1390.35101 Breit, Dominic; Cianchi, Andrea; Diening, Lars; Kuusi, Tuomo; Schwarzacher, Sebastian 2018 The $$p$$-Laplace system with right-hand side in divergence form: inner and up to the boundary pointwise estimates. Zbl 1370.35064 Breit, D.; Cianchi, A.; Diening, L.; Kuusi, T.; Schwarzacher, S. 2017 Neumann problems and isocapacitary inequalities. Zbl 1146.35041 2008 An optimal interpolation theorem of Marcinkiewicz type in Orlicz spaces. Zbl 0913.46028 Cianchi, Andrea 1998 Optimal Sobolev trace embeddings. Zbl 1360.46027 Cianchi, Andrea; Pick, Luboš 2016 Sobolev embeddings into spaces of Campanato, Morrey, and Hölder type. Zbl 1031.46039 Cianchi, Andrea; Pick, Luboš 2003 Continuity properties of solutions to the $$p$$-Laplace system. Zbl 1378.35145 Alberico, Angela; Cianchi, Andrea; Sbordone, Carlo 2017 Elliptic equations on manifolds and isoperimetric inequalities. Zbl 0709.58037 Cianchi, Andrea 1990 On the modulus of continuity of weakly differentiable functions. Zbl 1268.46026 Cianchi, Andrea; Randolfi, Monia 2011 On some aspects of the theory of Orlicz-Sobolev spaces. Zbl 1194.46042 Cianchi, Andrea 2010 Boundary trace inequalities and rearrangements. Zbl 1169.46013 Cianchi, Andrea; Kerman, Ron; Pick, Luboš 2008 Negative Orlicz-Sobolev norms and strongly nonlinear systems in fluid mechanics. Zbl 1337.46024 Breit, Dominic; Cianchi, Andrea 2015 A sharp trace inequality for functions of bounded variation in the ball. Zbl 1294.46030 Cianchi, Andrea 2012 Trace-free Korn inequalities in Orlicz spaces. Zbl 1380.46028 Breit, D.; Cianchi, A.; Diening, L. 2017 Gradient regularity for quasilinear elliptic Dirichlet problems in the plane. Zbl 1353.35164 Alberico, Angela; Cianchi, Andrea; Sbordone, Carlo 2016 Bounds for eigenfunctions of the Laplacian on noncompact Riemannian manifolds. Zbl 1280.58018 2013 Best remainder norms in Sobolev-Hardy inequalities. Zbl 1177.46021 2009 Minimal rearrangements, strict convexity and critical points. Zbl 1104.46016 Cianchi, Andrea; Fusco, Nicola 2006 Interpolation of operators and the Sobolev embedding theorem on Orlicz spaces. Zbl 1011.46025 Cianchi, Andrea 1998 An extension of Hedberg’s convolution inequality and applications. Zbl 0914.42014 Cianchi, Andrea; Stroffolini, Bianca 1998 Fully anisotropic elliptic problems with minimally integrable data. Zbl 1428.35124 Alberico, Angela; Chlebicka, Iwona; Cianchi, Andrea; Zatorska-Goldstein, Anna 2019 Balls minimize trace constants in BV. Zbl 1373.46025 Cianchi, Andrea; Ferone, Vincenzo; Nitsch, Carlo; Trombetti, Cristina 2017 Classical and approximate Taylor expansions of weakly differentiable functions. Zbl 1309.46013 Cavaliere, Paola; Cianchi, Andrea 2014 Optimal summability of solutions to nonlinear elliptic problems. Zbl 1387.35282 Alberico, Angela; Cianchi, Andrea 2007 Optimal domain spaces in Orlicz-Sobolev embeddings. Zbl 1440.46028 Cianchi, Andrea; Musil, Vit 2019 Sharp Sobolev type embeddings on the entire Euclidean space. Zbl 1405.46024 Alberico, Angela; Cianchi, Andrea; Pick, Luboš; Slavíková, Lenka 2018 Smooth approximation of Orlicz-Sobolev maps between manifolds. Zbl 1362.46037 Carozza, Menita; Cianchi, Andrea 2016 A unified approach to Cramér-Rao inequalities. Zbl 1364.94228 Cianchi, Andrea; Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong 2014 An optimal endpoint trace embedding. Zbl 1208.46029 Cianchi, Andrea; Pick, Luboš 2010 Dirichlet integrals and Steiner asymmetry. Zbl 1124.46017 Cianchi, Andrea; Fusco, Nicola 2006 On symmetric functionals of the gradient having symmetric equidistributed minimizers. Zbl 1126.46020 2006 Sobolev inequalities in arbitrary domains. Zbl 1346.46022 2016 On the modulus of continuity of solutions to the $$n$$-Laplace equation. Zbl 1378.35112 Alberico, Angela; Cianchi, Andrea; Sbordone, Carlo 2015 On the discreteness of the spectrum of the Laplacian on noncompact Riemannian manifolds. Zbl 1269.58011 2011 Quantitative Sobolev and Hardy inequalities, and related symmetrization principles. Zbl 1179.26054 Cianchi, Andrea 2009 Orlicz-Sobolev algebras. Zbl 1157.46309 Cianchi, Andrea 2008 Borderline sharp estimates for solutions to Neumann problems. Zbl 1225.35075 Alberico, Angela; Cianchi, Andrea 2007 Strict monotonicity of functionals under Steiner symmetrization. Zbl 1114.49040 Cianchi, Andrea; Fusco, Nicola 2004 Optimal second-order regularity for the $$p$$-Laplace system. Zbl 1437.35404 2019 Potential estimates for the $$p$$-Laplace system with data in divergence form. Zbl 1395.35051 Cianchi, A.; Schwarzacher, S. 2018 Quasilinear elliptic equations on noncompact Riemannian manifolds. Zbl 1382.35110 Barletta, Giuseppina; Cianchi, Andrea; Maz’ya, Vladimir 2017 Canceling effects in higher-order Hardy-Sobolev inequalities. Zbl 1377.46024 Cianchi, Andrea; Ioku, Norisuke 2017 Boundedness of solutions to the Schrödinger equation under Neumann boundary conditions. Zbl 1259.35072 2012 Fractional integrals and $$A_p$$-weights: a sharp estimate. Zbl 1180.26001 Alberico, Teresa; Cianchi, Andrea; Sbordone, Carlo 2009 A strengthened version of the Hardy-Littlewood inequality. Zbl 1155.26017 2008 Rearrangements of functions in Besov spaces. Zbl 1022.46021 Cianchi, Andrea 2001 On fractional integration in weighted Lorentz spaces. Zbl 0998.26009 Cianchi, Andrea; Edmunds, David E. 1997 On the $$L^ q$$ norm of functions having equidistributed gradients. Zbl 0884.49011 Cianchi, Andrea 1996 Breaking of symmetry in Poisson equation. Zbl 0833.35030 Cianchi, Andrea 1994 On the limit as $$s\rightarrow 0^+$$ of fractional Orlicz-Sobolev spaces. Zbl 07296359 Alberico, Angela; Cianchi, Andrea; Pick, Luboš; Slavíková, Lenka 2020 Second-order regularity for parabolic $$p$$-Laplace problems. Zbl 1439.35204 2020 On the limit as $$s\rightarrow 0^+$$ of fractional Orlicz-Sobolev spaces. Zbl 07296359 Alberico, Angela; Cianchi, Andrea; Pick, Luboš; Slavíková, Lenka 2020 Second-order regularity for parabolic $$p$$-Laplace problems. Zbl 1439.35204 2020 Sobolev embeddings in Orlicz and Lorentz spaces with measures. Zbl 1450.46019 Cianchi, Andrea; Pick, Luboš; Slavíková, Lenka 2020 Sobolev embeddings, rearrangement-invariant spaces and Frostman measures. Zbl 1440.46030 Cianchi, Andrea; Pick, Luboš; Slavíková, Lenka 2020 Fully anisotropic elliptic problems with minimally integrable data. Zbl 1428.35124 Alberico, Angela; Chlebicka, Iwona; Cianchi, Andrea; Zatorska-Goldstein, Anna 2019 Optimal domain spaces in Orlicz-Sobolev embeddings. Zbl 1440.46028 Cianchi, Andrea; Musil, Vit 2019 Optimal second-order regularity for the $$p$$-Laplace system. Zbl 1437.35404 2019 Second-order two-sided estimates in nonlinear elliptic problems. Zbl 1398.35078 2018 Pointwise Calderón-Zygmund gradient estimates for the $$p$$-Laplace system. Zbl 1390.35101 Breit, Dominic; Cianchi, Andrea; Diening, Lars; Kuusi, Tuomo; Schwarzacher, Sebastian 2018 Sharp Sobolev type embeddings on the entire Euclidean space. Zbl 1405.46024 Alberico, Angela; Cianchi, Andrea; Pick, Luboš; Slavíková, Lenka 2018 Potential estimates for the $$p$$-Laplace system with data in divergence form. Zbl 1395.35051 Cianchi, A.; Schwarzacher, S. 2018 On the continuity of weakly monotone functions. Zbl 1410.46017 Carozza, Menita; Cianchi, Andrea 2018 Quasilinear elliptic problems with general growth and merely integrable, or measure, data. Zbl 1373.35113 2017 Dirichlet problems for fully anisotropic elliptic equations. Zbl 1388.35043 Barletta, Giuseppina; Cianchi, Andrea 2017 The $$p$$-Laplace system with right-hand side in divergence form: inner and up to the boundary pointwise estimates. Zbl 1370.35064 Breit, D.; Cianchi, A.; Diening, L.; Kuusi, T.; Schwarzacher, S. 2017 Continuity properties of solutions to the $$p$$-Laplace system. Zbl 1378.35145 Alberico, Angela; Cianchi, Andrea; Sbordone, Carlo 2017 Trace-free Korn inequalities in Orlicz spaces. Zbl 1380.46028 Breit, D.; Cianchi, A.; Diening, L. 2017 Balls minimize trace constants in BV. Zbl 1373.46025 Cianchi, Andrea; Ferone, Vincenzo; Nitsch, Carlo; Trombetti, Cristina 2017 Quasilinear elliptic equations on noncompact Riemannian manifolds. Zbl 1382.35110 Barletta, Giuseppina; Cianchi, Andrea; Maz’ya, Vladimir 2017 Canceling effects in higher-order Hardy-Sobolev inequalities. Zbl 1377.46024 Cianchi, Andrea; Ioku, Norisuke 2017 Optimal Sobolev trace embeddings. Zbl 1360.46027 Cianchi, Andrea; Pick, Luboš 2016 Gradient regularity for quasilinear elliptic Dirichlet problems in the plane. Zbl 1353.35164 Alberico, Angela; Cianchi, Andrea; Sbordone, Carlo 2016 Smooth approximation of Orlicz-Sobolev maps between manifolds. Zbl 1362.46037 Carozza, Menita; Cianchi, Andrea 2016 Sobolev inequalities in arbitrary domains. Zbl 1346.46022 2016 Higher-order Sobolev embeddings and isoperimetric inequalities. Zbl 1334.46027 Cianchi, Andrea; Pick, Luboš; Slavíková, Lenka 2015 Global gradient estimates in elliptic problems under minimal data and domain regularity. Zbl 1325.35027 2015 Negative Orlicz-Sobolev norms and strongly nonlinear systems in fluid mechanics. Zbl 1337.46024 Breit, Dominic; Cianchi, Andrea 2015 On the modulus of continuity of solutions to the $$n$$-Laplace equation. Zbl 1378.35112 Alberico, Angela; Cianchi, Andrea; Sbordone, Carlo 2015 Global boundedness of the gradient for a class of nonlinear elliptic systems. Zbl 1298.35070 2014 Gradient regularity via rearrangements for $$p$$-Laplacian type elliptic boundary value problems. Zbl 1288.35128 2014 Korn type inequalities in Orlicz spaces. Zbl 1312.46037 Cianchi, Andrea 2014 Classical and approximate Taylor expansions of weakly differentiable functions. Zbl 1309.46013 Cavaliere, Paola; Cianchi, Andrea 2014 A unified approach to Cramér-Rao inequalities. Zbl 1364.94228 Cianchi, Andrea; Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong 2014 Concentration-compactness principles for Moser-Trudinger inequalities: new results and proofs. Zbl 1272.46023 Černý, Robert; Cianchi, Andrea; Hencl, Stanislav 2013 Bounds for eigenfunctions of the Laplacian on noncompact Riemannian manifolds. Zbl 1280.58018 2013 A sharp trace inequality for functions of bounded variation in the ball. Zbl 1294.46030 Cianchi, Andrea 2012 Boundedness of solutions to the Schrödinger equation under Neumann boundary conditions. Zbl 1259.35072 2012 Improving sharp Sobolev type inequalities by optimal remainder gradient norms. Zbl 1276.46023 2012 Differentiability properties of functions from higher-order Orlicz-Sobolev spaces. Zbl 1244.46015 Cianchi, Andrea; Randolfi, Monia 2012 Global Lipschitz regularity for a class of quasilinear elliptic equations. Zbl 1220.35065 2011 On the isoperimetric deficit in Gauss space. Zbl 1219.28005 Cianchi, A.; Fusco, N.; Maggi, F.; Pratelli, A. 2011 Nonlinear potentials, local solutions to elliptic equations and rearrangements. Zbl 1235.31009 Cianchi, Andrea 2011 On the modulus of continuity of weakly differentiable functions. Zbl 1268.46026 Cianchi, Andrea; Randolfi, Monia 2011 On the discreteness of the spectrum of the Laplacian on noncompact Riemannian manifolds. Zbl 1269.58011 2011 Well-posed elliptic Neumann problems involving irregular data and domains. Zbl 1200.35105 Alvino, Angelo; Cianchi, Andrea; Maz’ya, Vladimir G.; Mercaldo, Anna 2010 Orlicz-Sobolev boundary trace embeddings. Zbl 1208.46028 Cianchi, Andrea 2010 On some aspects of the theory of Orlicz-Sobolev spaces. Zbl 1194.46042 Cianchi, Andrea 2010 An optimal endpoint trace embedding. Zbl 1208.46029 Cianchi, Andrea; Pick, Luboš 2010 Affine Moser-Trudinger and Morrey-Sobolev inequalities. Zbl 1202.26029 Cianchi, Andrea; Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong 2009 Overdetermined anisotropic elliptic problems. Zbl 1179.35107 Cianchi, Andrea; Salani, Paolo 2009 The sharp Sobolev inequality in quantitative form. Zbl 1185.46025 Cianchi, A.; Fusco, N.; Maggi, F.; Pratelli, A. 2009 Optimal Gaussian Sobolev embeddings. Zbl 1203.46019 Cianchi, Andrea; Pick, Luboš 2009 Best remainder norms in Sobolev-Hardy inequalities. Zbl 1177.46021 2009 Quantitative Sobolev and Hardy inequalities, and related symmetrization principles. Zbl 1179.26054 Cianchi, Andrea 2009 Fractional integrals and $$A_p$$-weights: a sharp estimate. Zbl 1180.26001 Alberico, Teresa; Cianchi, Andrea; Sbordone, Carlo 2009 Moser–Trudinger trace inequalities. Zbl 1138.46020 Cianchi, Andrea 2008 Hardy inequalities with non-standard remainder terms. Zbl 1153.26310 2008 A quantitative Pólya-Szegő principle. Zbl 1175.46021 Cianchi, Andrea; Esposito, Luca; Fusco, Nicola; Trombetti, Cristina 2008 Comparison estimates in anisotropic variational problems. Zbl 1357.49137 Alberico, Angela; Cianchi, Andrea 2008 Sharp Morrey–Sobolev inequalities and the distance from extremals. Zbl 1153.46019 Cianchi, Andrea 2008 Neumann problems and isocapacitary inequalities. Zbl 1146.35041 2008 Boundary trace inequalities and rearrangements. Zbl 1169.46013 Cianchi, Andrea; Kerman, Ron; Pick, Luboš 2008 Orlicz-Sobolev algebras. Zbl 1157.46309 Cianchi, Andrea 2008 A strengthened version of the Hardy-Littlewood inequality. Zbl 1155.26017 2008 Symmetrization in anisotropic elliptic problems. Zbl 1219.35028 Cianchi, Andrea 2007 Optimal summability of solutions to nonlinear elliptic problems. Zbl 1387.35282 Alberico, Angela; Cianchi, Andrea 2007 Borderline sharp estimates for solutions to Neumann problems. Zbl 1225.35075 Alberico, Angela; Cianchi, Andrea 2007 Steiner symmetric extremals in Pólya-Szegő-type inequalities. Zbl 1110.46021 Cianchi, Andrea; Fusco, Nicola 2006 A quantitative Sobolev inequality in BV. Zbl 1110.46020 Cianchi, Andrea 2006 Higher-order Sobolev and Poincaré inequalities in Orlicz spaces. Zbl 1120.46015 Cianchi, Andrea 2006 Minimal rearrangements, strict convexity and critical points. Zbl 1104.46016 Cianchi, Andrea; Fusco, Nicola 2006 Dirichlet integrals and Steiner asymmetry. Zbl 1124.46017 Cianchi, Andrea; Fusco, Nicola 2006 On symmetric functionals of the gradient having symmetric equidistributed minimizers. Zbl 1126.46020 2006 The perimeter inequality under Steiner symmetrization: cases of equality. Zbl 1087.28003 Chlebík, Miroslav; Cianchi, Andrea; Fusco, Nicola 2005 Moser–Trudinger inequalities without boundary conditions and isoperimetric problems. Zbl 1097.46016 Cianchi, Andrea 2005 Differentiability properties of Orlicz-Sobolev functions. Zbl 1119.46030 Alberico, Angela; Cianchi, Andrea 2005 Optimal Orlicz-Sobolev embeddings. Zbl 1061.46031 Cianchi, Andrea 2004 Symmetrization and second-order Sobolev inequalities. Zbl 1223.46033 Cianchi, Andrea 2004 Strict monotonicity of functionals under Steiner symmetrization. Zbl 1114.49040 Cianchi, Andrea; Fusco, Nicola 2004 Sobolev embeddings into spaces of Campanato, Morrey, and Hölder type. Zbl 1031.46039 Cianchi, Andrea; Pick, Luboš 2003 Functions of bounded variation and rearrangements. Zbl 1028.49035 Cianchi, Andrea; Fusco, Nicola 2002 Rearrangements of functions in Besov spaces. Zbl 1022.46021 Cianchi, Andrea 2001 A fully anisotropic Sobolev inequality. Zbl 0966.46017 Cianchi, Andrea 2000 Local boundedness of minimizers of anisotropic functionals. Zbl 0984.49019 Cianchi, Andrea 2000 A sharp rearrangement inequality for the fractional maximal operator. Zbl 0968.42014 Cianchi, A.; Kerman, R.; Opic, B.; Pick, L. 2000 Second-order derivatives and rearrangements. Zbl 1017.46023 Cianchi, Andrea 2000 Strong and weak type inequalities for some classical operators in Orlicz spaces. Zbl 0940.46015 Cianchi, Andrea 1999 Gradient regularity for minimizers under general growth conditions. Zbl 0913.49024 Cianchi, Andrea; Fusco, Nicola 1999 Hardy inequalities in Orlicz spaces. Zbl 0920.46021 Cianchi, Andrea 1999 Some results in the theory of Orlicz spaces and applications to variational problems. Zbl 0965.46017 Cianchi, Andrea 1999 Sobolev embeddings into BMO, VMO, and $$L_{\infty}$$. Zbl 1035.46502 Cianchi, Andrea; Pick, Luboš 1998 An optimal interpolation theorem of Marcinkiewicz type in Orlicz spaces. Zbl 0913.46028 Cianchi, Andrea 1998 Interpolation of operators and the Sobolev embedding theorem on Orlicz spaces. Zbl 1011.46025 Cianchi, Andrea 1998 An extension of Hedberg’s convolution inequality and applications. Zbl 0914.42014 Cianchi, Andrea; Stroffolini, Bianca 1998 Boundedness of solutions to variational problems under general growth conditions. Zbl 0892.35048 Cianchi, Andrea 1997 On fractional integration in weighted Lorentz spaces. Zbl 0998.26009 Cianchi, Andrea; Edmunds, David E. 1997 A sharp embedding theorem for Orlicz-Sobolev spaces. Zbl 0860.46022 Cianchi, Andrea 1996 Continuity properties of functions from Orlicz-Sobolev spaces and embedding theorems. Zbl 0877.46023 Cianchi, Andrea 1996 On weighted Poincaré inequalities. Zbl 0858.26009 Cianchi, Andrea; Edmunds, David E.; Gurka, Petr 1996 On the $$L^ q$$ norm of functions having equidistributed gradients. Zbl 0884.49011 Cianchi, Andrea 1996 ...and 6 more Documents all top 5 #### Cited by 850 Authors 73 Cianchi, Andrea 28 Mingione, Giuseppe 25 Pick, Luboš 22 Yao, Fengping 19 Alberico, Angela 17 Fusco, Nicola 17 Maz’ya, Vladimir Gilelevich 15 Guliyev, Vagif Sabir 13 Kuusi, Tuomo 12 Deringoz, Fatih 12 Lu, Guozhen 12 Nguyễn Văn Hoàng 12 Shimomura, Tetsu 12 Trombetti, Cristina 12 Yang, Deane 12 Zhang, Gaoyong 11 Byun, Sun-Sig 11 Černý, Robert 11 Mercaldo, Anna 10 Diening, Lars 10 Lutwak, Erwin 10 Maggi, Francesco 9 Chlebicka, Iwona 9 Feo, Filomena 9 Ferone, Adele 9 Leonetti, Francesco 9 Slavíková, Lenka 8 Böröczky, Karoly jun. 8 Ciraolo, Giulio 8 Esposito, Luca 8 Figalli, Alessio 8 Gogatishvili, Amiran 8 Mizuta, Yoshihiro 8 Pratelli, Aldo 8 Zhou, Shulin 7 Breit, Dominic 7 Colesanti, Andrea 7 Di Blasio, Giuseppina 7 Do Ó, João M. Bezerra 7 Nitsch, Carlo 7 Ohno, Takao 7 Pączka, Dariusz 7 Passarelli di Napoli, Antonia 7 Ruf, Bernhard 7 Stroffolini, Bianca 7 Tarsi, Cristina 7 Wang, Lihe 7 Xiao, Jie 7 Yang, Dachun 7 Zhu, Guangxian 6 Brock, Friedemann 6 Carozza, Menita 6 Edmunds, David Eric 6 Ferone, Vincenzo 6 Giannetti, Flavia 6 Haberl, Christoph 6 Hasanov, Sabir G. 6 Ioku, Norisuke 6 Jiang, Renjin 6 Kałamajska, Agnieszka 6 Musil, Vít 6 Sbordone, Carlo 6 Schwarzacher, Sebastian 6 Volpicelli, Roberta 6 Yang, Sibei 6 Zhou, Jiazu 5 Baroni, Paolo 5 Della Pietra, Francesco 5 Fiorenza, Alberto 5 Gavitone, Nunzia 5 Gol’dman, Mikhail L’vovich 5 Kerman, Ron 5 Lam, Nguyen 5 Maksymiuk, Jakub 5 Masmoudi, Nader 5 Sani, Federica 5 Verde, Anna 5 Zhu, Baocheng 4 Alvino, Angelo 4 Barchiesi, Marco 4 Betta, Maria Francesca 4 Bianchi, Gabriele 4 Cagnetti, Filippo 4 Cassani, Daniele 4 Chen, Lu 4 Chiacchio, Francesco 4 di Castro, Agnese 4 Dolbeault, Jean 4 Duzaar, Frank 4 Fan, Xianling 4 Fontana, Luigi 4 Granucci, Tiziano 4 Huang, Qingzhong 4 Hurri-Syrjānen, Ritva 4 Jia, Huilian 4 Ludwig, Monika 4 Martín, Joaquim 4 Migórski, Stanisław 4 Morpurgo, Carlo 4 Nakai, Eiichi ...and 750 more Authors all top 5 #### Cited in 177 Serials 77 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 65 Journal of Mathematical Analysis and Applications 49 Calculus of Variations and Partial Differential Equations 45 Journal of Functional Analysis 43 Journal of Differential Equations 36 Advances in Mathematics 22 Annali di Matematica Pura ed Applicata. Serie Quarta 19 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 17 Archive for Rational Mechanics and Analysis 17 Journal de Mathématiques Pures et Appliquées. Neuvième Série 17 Potential Analysis 16 Proceedings of the American Mathematical Society 16 The Journal of Geometric Analysis 15 Communications in Contemporary Mathematics 14 Manuscripta Mathematica 14 Advances in Applied Mathematics 12 Mathematische Annalen 12 Mathematische Nachrichten 11 Transactions of the American Mathematical Society 11 NoDEA. Nonlinear Differential Equations and Applications 11 Journal of the European Mathematical Society (JEMS) 10 Journal of Inequalities and Applications 8 Communications in Partial Differential Equations 8 Nonlinear Analysis. Real World Applications 7 Archiv der Mathematik 7 Revista Matemática Complutense 7 Advances in Calculus of Variations 6 Forum Mathematicum 6 Communications on Pure and Applied Analysis 5 Arkiv för Matematik 5 Revista Matemática Iberoamericana 5 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 5 Discrete and Continuous Dynamical Systems 5 Positivity 5 Advanced Nonlinear Studies 5 Mediterranean Journal of Mathematics 5 Complex Variables and Elliptic Equations 5 Discrete and Continuous Dynamical Systems. Series S 5 Science China. Mathematics 4 Communications in Mathematical Physics 4 Mathematical Methods in the Applied Sciences 4 Czechoslovak Mathematical Journal 4 Journal für die Reine und Angewandte Mathematik 4 Ricerche di Matematica 4 Zeitschrift für Analysis und ihre Anwendungen 4 Doklady Mathematics 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Journal of Function Spaces 4 Journal of Elliptic and Parabolic Equations 3 Applicable Analysis 3 Rocky Mountain Journal of Mathematics 3 Studia Mathematica 3 Ukrainian Mathematical Journal 3 Tohoku Mathematical Journal. Second Series 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 SIAM Journal on Mathematical Analysis 3 Indagationes Mathematicae. New Series 3 Journal of Mathematical Sciences (New York) 3 St. Petersburg Mathematical Journal 3 Bulletin des Sciences Mathématiques 3 Annales Academiae Scientiarum Fennicae. Mathematica 3 Central European Journal of Mathematics 3 Journal of Fixed Point Theory and Applications 3 Bulletin of Mathematical Sciences 3 Advances in Nonlinear Analysis 2 Computers & Mathematics with Applications 2 Communications on Pure and Applied Mathematics 2 Israel Journal of Mathematics 2 Journal d’Analyse Mathématique 2 Nonlinearity 2 Annales de l’Institut Fourier 2 The Annals of Probability 2 Canadian Mathematical Bulletin 2 Duke Mathematical Journal 2 Indiana University Mathematics Journal 2 Inventiones Mathematicae 2 Mathematische Zeitschrift 2 Mathematika 2 Monatshefte für Mathematik 2 Numerische Mathematik 2 Siberian Mathematical Journal 2 Journal of the American Mathematical Society 2 International Journal of Mathematics 2 Geometric and Functional Analysis. GAFA 2 The Journal of Fourier Analysis and Applications 2 Abstract and Applied Analysis 2 Taiwanese Journal of Mathematics 2 Mathematical Inequalities & Applications 2 Portugaliae Mathematica. Nova Série 2 Analysis and Applications (Singapore) 2 Proceedings of the Steklov Institute of Mathematics 2 Journal of Mathematical Inequalities 2 Analysis and Mathematical Physics 2 Nonlinear Analysis. Theory, Methods & Applications 1 Analysis Mathematica 1 Journal of Statistical Physics 1 Mathematical Notes 1 Russian Mathematical Surveys 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik ...and 77 more Serials all top 5 #### Cited in 42 Fields 457 Partial differential equations (35-XX) 355 Functional analysis (46-XX) 166 Real functions (26-XX) 123 Calculus of variations and optimal control; optimization (49-XX) 94 Convex and discrete geometry (52-XX) 52 Harmonic analysis on Euclidean spaces (42-XX) 40 Operator theory (47-XX) 38 Global analysis, analysis on manifolds (58-XX) 37 Differential geometry (53-XX) 35 Potential theory (31-XX) 26 Measure and integration (28-XX) 20 Probability theory and stochastic processes (60-XX) 19 Fluid mechanics (76-XX) 12 Mechanics of deformable solids (74-XX) 9 Functions of a complex variable (30-XX) 9 Numerical analysis (65-XX) 7 Difference and functional equations (39-XX) 5 History and biography (01-XX) 5 Ordinary differential equations (34-XX) 5 Biology and other natural sciences (92-XX) 4 Geometry (51-XX) 4 Statistics (62-XX) 3 Combinatorics (05-XX) 3 Dynamical systems and ergodic theory (37-XX) 2 General and overarching topics; collections (00-XX) 2 Topological groups, Lie groups (22-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Abstract harmonic analysis (43-XX) 2 Integral equations (45-XX) 2 Computer science (68-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Information and communication theory, circuits (94-XX) 1 Mathematical logic and foundations (03-XX) 1 Number theory (11-XX) 1 Group theory and generalizations (20-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Optics, electromagnetic theory (78-XX) 1 Systems theory; control (93-XX) #### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2021-05-08T08:07:36	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5537925362586975, "perplexity": 7468.800544673394}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988850.21/warc/CC-MAIN-20210508061546-20210508091546-00308.warc.gz"}
https://par.nsf.gov/biblio/10060329-analysis-conformational-properties-amine-ligands-gold-water-interface-qm-mm-qm-mm-simulations	Analysis of the conformational properties of amine ligands at the gold/water interface with QM, MM and QM/MM simulations We describe a strategy of integrating quantum mechanical (QM), hybrid quantum mechanical/molecular mechanical (QM/MM) and MM simulations to analyze the physical properties of a solid/water interface. This protocol involves using a correlated ab initio (CCSD(T)) method to first calibrate Density Functional Theory (DFT) as the QM approach, which is then used in QM/MM simulations to compute relevant free energy quantities at the solid/water interface using a mean-field approximation of Yang et al. that decouples QM and MM thermal fluctuations; gas-phase QM/MM and periodic DFT calculations are used to determine the proper QM size in the QM/MM simulations. Finally, the QM/MM free energy results are compared with those obtained from MM simulations to directly calibrate the force field model for the solid/water interface. This protocol is illustrated by examining the orientations of an alkyl amine ligand at the gold/water interface, since the ligand conformation is expected to impact the chemical properties ( e.g. , charge) of the solid surface. DFT/MM and MM simulations using the INTERFACE force field lead to consistent results, suggesting that the effective gold/ligand interactions can be adequately described by a van der Waals model, while electrostatic and induction effects are largely quenched by solvation. The observed differences more » Authors: ; ; ; ; ; ; Award ID(s): Publication Date: NSF-PAR ID: 10060329 Journal Name: Physical Chemistry Chemical Physics Volume: 20 Issue: 5 Page Range or eLocation-ID: 3349 to 3362 ISSN: 1463-9076	2023-02-05T10:57:06	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8186495900154114, "perplexity": 3486.3444663402884}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500251.38/warc/CC-MAIN-20230205094841-20230205124841-00068.warc.gz"}
https://www.mcs.anl.gov/research/projects/otc/InteriorPoint/abstracts/Andersen-Ye-2.html	## A computational study of the homogeneous algorithm for large-scale convex optimization. ### Erling D. Andersen and Yinyu Ye. Recently the authors have proposed a homogeneous and self-dual algorithm for solving the monotone complementarity problem (MCP) \cite{ANDERSEN:95:A}. The algorithm is a single phase interior-point type method, it nevertheless either yields an approximate optimal solution or detects possible infeasibility of the problem. In this paper we specialize the algorithm to solution of general smooth convex optimization problems that also possess nonlinear equality constraints and free variables. We discuss an implementation of the algorithm for large-scale sparse convex optimization. Moreover, we present computational results for solving quadratically constrained quadratic programming and geometric programming problems, where some of the problems contain more than 100000 constraints and variables. The results indicate that the proposed algorithm is also practically efficient. Contact:[email protected] Publications from Department of Management no. 3/1996, Odense University, Denmark.	2021-09-27T04:39:12	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.810388445854187, "perplexity": 620.3870368921376}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780058263.20/warc/CC-MAIN-20210927030035-20210927060035-00442.warc.gz"}
https://www.usgs.gov/media/images/figure-4-estimated-annual-yields-total-phosphorus-nine-us	# Figure 4 - Estimated Annual Yields of Total Phosphorus at the Nine U.S ### Detailed Description Figure 4 - Estimated Annual Yields of Total Phosphorus at the Nine U.S. Geological Survey River Input Monitoring Stations Public Domain.	2022-06-28T22:07:05	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8028761744499207, "perplexity": 14890.509084702897}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103617931.31/warc/CC-MAIN-20220628203615-20220628233615-00296.warc.gz"}
http://kldns.net/error-propagation/standard-error-propagation-equation.html	## Repair Standard Error Propagation Equation Tutorial Home > Error Propagation > Standard Error Propagation Equation # Standard Error Propagation Equation ## Contents Example: If an object is realeased from rest and is in free fall, and if you measure the velocity of this object at some point to be v = - 3.8+-0.3 Example: Example: Analytical chemists tend to remember these common error propagation results, as they encounter them frequently during repetitive measurements. Physical chemists tend to remember the one general formula The system returned: (22) Invalid argument The remote host or network may be down. These instruments each have different variability in their measurements. his comment is here Second, when the underlying values are correlated across a population, the uncertainties in the group averages will be correlated.[1] Contents 1 Linear combinations 2 Non-linear combinations 2.1 Simplification 2.2 Example 2.3 In this case, expressions for more complicated functions can be derived by combining simpler functions. Then σ f 2 ≈ b 2 σ a 2 + a 2 σ b 2 + 2 a b σ a b {\displaystyle \sigma _{f}^{2}\approx b^{2}\sigma _{a}^{2}+a^{2}\sigma _{b}^{2}+2ab\,\sigma _{ab}} or ERROR PROPAGATION 1. Measurement of Physical Properties The value of a physical property often depends on one or more measured quantities Example: Volume of a cylinder 2. Systematic Errors A ## Error Propagation Formula If we know the uncertainty of the radius to be 5%, the uncertainty is defined as (dx/x)=(∆x/x)= 5% = 0.05. Calculus for Biology and Medicine; 3rd Ed. We know the value of uncertainty for∆r/r to be 5%, or 0.05. This is the most general expression for the propagation of error from one set of variables onto another. Contributors http://www.itl.nist.gov/div898/handb...ion5/mpc55.htm Jarred Caldwell (UC Davis), Alex Vahidsafa (UC Davis) Back to top Significant Digits Significant Figures Recommended articles There are no recommended articles. For example, repeated multiplication, assuming no correlation gives, f = A B C ; ( σ f f ) 2 ≈ ( σ A A ) 2 + ( σ B It can be written that $$x$$ is a function of these variables: $x=f(a,b,c) \tag{1}$ Because each measurement has an uncertainty about its mean, it can be written that the uncertainty of Error Propagation Excel p.2. It is important to note that this formula is based on the linear characteristics of the gradient of f {\displaystyle f} and therefore it is a good estimation for the standard Generated Sun, 30 Oct 2016 12:00:12 GMT by s_fl369 (squid/3.5.20) f = ∑ i n a i x i : f = a x {\displaystyle f=\sum _ σ 4^ σ 3a_ σ 2x_ σ 1:f=\mathrm σ 0 \,} σ f 2 ISSN0022-4316. Multivariate error analysis: a handbook of error propagation and calculation in many-parameter systems. Error Propagation Calculus Thus, the expected uncertainty in V is 39 cm3. 4. Purpose of Error Propagation Quantifies precision of results Example: V = 1131 39 cm3 Identifies principle source However, if the variables are correlated rather than independent, the cross term may not cancel out. First, the measurement errors may be correlated. ## Error Propagation Calculator Uncertainty analysis 2.5.5. http://lectureonline.cl.msu.edu/~mmp/labs/error/e2.htm Retrieved 13 February 2013. Error Propagation Formula In this case, expressions for more complicated functions can be derived by combining simpler functions. Error Propagation Physics Engineering and Instrumentation, Vol. 70C, No.4, pp. 263-273. John Wiley & Sons. this content We will treat each case separately: Addition of measured quantities If you have measured values for the quantities X, Y, and Z, with uncertainties dX, dY, and dZ, and your final Your cache administrator is webmaster. Berkeley Seismology Laboratory. Error Propagation Chemistry doi:10.2307/2281592. Disadvantages of Propagation of Error Approach Inan ideal case, the propagation of error estimate above will not differ from the estimate made directly from the measurements. Further reading Bevington, Philip R.; Robinson, D. weblink Authority control GND: 4479158-6 Retrieved from "https://en.wikipedia.org/w/index.php?title=Propagation_of_uncertainty&oldid=742325047" Categories: Algebra of random variablesNumerical analysisStatistical approximationsUncertainty of numbersStatistical deviation and dispersionHidden categories: Wikipedia articles needing page number citations from October 2012Wikipedia articles needing Introduction Every measurement has an air of uncertainty about it, and not all uncertainties are equal. Error Propagation Definition f k = ∑ i n A k i x i or f = A x {\displaystyle f_ ρ 5=\sum _ ρ 4^ ρ 3A_ ρ 2x_ ρ 1{\text{ or }}\mathrm In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. ## Eq.(39)-(40). For example, the 68% confidence limits for a one-dimensional variable belonging to a normal distribution are ± one standard deviation from the value, that is, there is approximately a 68% probability Since f0 is a constant it does not contribute to the error on f. JCGM 102: Evaluation of Measurement Data - Supplement 2 to the "Guide to the Expression of Uncertainty in Measurement" - Extension to Any Number of Output Quantities (PDF) (Technical report). Error Propagation Average If the uncertainties are correlated then covariance must be taken into account. Structural and Multidisciplinary Optimization. 37 (3): 239–253. H.; Chen, W. (2009). "A comparative study of uncertainty propagation methods for black-box-type problems". When the variables are the values of experimental measurements they have uncertainties due to measurement limitations (e.g., instrument precision) which propagate to the combination of variables in the function. check over here Example: Suppose we have measured the starting position as x1 = 9.3+-0.2 m and the finishing position as x2 = 14.4+-0.3 m. Function Variance Standard Deviation f = a A {\displaystyle f=aA\,} σ f 2 = a 2 σ A 2 {\displaystyle \sigma _{f}^{2}=a^{2}\sigma _{A}^{2}} σ f = \| a \| σ A The propagation of error formula for $$Y = f(X, Z, \ldots \, )$$ a function of one or more variables with measurements, $$(X, Z, \ldots \, )$$ SOLUTION To actually use this percentage to calculate unknown uncertainties of other variables, we must first define what uncertainty is. The exact covariance of two ratios with a pair of different poles p 1 {\displaystyle p_{1}} and p 2 {\displaystyle p_{2}} is similarly available.[10] The case of the inverse of a The equation for molar absorptivity is ε = A/(lc). Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. Propagation of uncertainty From Wikipedia, the free encyclopedia Jump to: navigation, search For the propagation of uncertainty through time, see Chaos theory §Sensitivity to initial conditions. The derivative of f(x) with respect to x is d f d x = 1 1 + x 2 . {\displaystyle {\frac {df}{dx}}={\frac {1}{1+x^{2}}}.} Therefore, our propagated uncertainty is σ f Joint Committee for Guides in Metrology (2011). Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply.	2017-10-23T15:29:10	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8403632044792175, "perplexity": 1905.3957581910547}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187826114.69/warc/CC-MAIN-20171023145244-20171023165244-00436.warc.gz"}
https://par.nsf.gov/biblio/10010140-charged-particle-multiplicity-pseudorapidity-distributions-measured-phobos-detector-au+au-cu+cu-d+au-p+p-collisions-ultrarelativistic-energies	Charged-particle multiplicity and pseudorapidity distributions measured with the PHOBOS detector in $Au+Au$ , $Cu+Cu$ , $d+Au$ , and $p+p$ collisions at ultrarelativistic energies Authors: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more » Publication Date: NSF-PAR ID: 10010140 Journal Name: Physical Review C Volume: 83 Issue: 2 ISSN: 0556-2813 Publisher: American Physical Society	2022-10-07T13:11:00	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 25, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9587358832359314, "perplexity": 11831.243576228082}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030338073.68/warc/CC-MAIN-20221007112411-20221007142411-00766.warc.gz"}
https://issues.cosmos.esa.int/socciwiki/pages/diffpagesbyversion.action?pageId=57546436&selectedPageVersions=14&selectedPageVersions=13	# Page History ## Key • This line was removed. • Formatting was changed. ... Issue Affects Version Status PDS is changing its LID convention for instruments. This will require a change from • urn:esa:psa:context:instrument:frend.tgo to • urn:esa:psa:context:instrument:tgo.frend Coordination is required to make this update as it has an impact on ingestion and the PSA database. Coordination between all missions and instruments is required. 1.x, 2.xIn analysis The lid for the EAICD is incorrect and needs to be rectified with the lid contained in the products1.xIn analysis ExoMars namespace and instrument contexts are not yet registered in the PDS system, therefore the validator by default will not work. Workarounds for the moment are adding the missing items in file validate-1.23.1/resources/registered_context_products.json or running the validator skipping the check on context (--skip-context-validation)-- The lids of calibrated products are currently under revision and will be changed to respect the format <instrument_acronym>_[<processing_level>]_[<type>]_[<subunit>]_<descriptor> 1.xIn analysis NASA validator tool (https://nasa-pds.github.io/validate/) resolves the https PSA protocols with the latest Java version. If validate does not resolve the dictionaries, please consider updating your Java version-- ...	2021-11-28T09:10:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20424385368824005, "perplexity": 6697.443737203044}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358480.10/warc/CC-MAIN-20211128073830-20211128103830-00105.warc.gz"}
https://par.nsf.gov/biblio/10198846-g2sat-learning-generate-sat-formulas	G2SAT: Learning to Generate SAT Formulas The Boolean Satisfiability (SAT) problem is the canonical NP-complete problem and is fundamental to computer science, with a wide array of applications in planning, verification, and theorem proving. Developing and evaluating practical SAT solvers relies on extensive empirical testing on a set of real-world benchmark formulas. However, the availability of such real-world SAT formulas is limited. While these benchmark formulas can be augmented with synthetically generated ones, existing approaches for doing so are heavily hand-crafted and fail to simultaneously capture a wide range of characteristics exhibited by real-world SAT instances. In this work, we present G2SAT, the first deep generative framework that learns to generate SAT formulas from a given set of input formulas. Our key insight is that SAT formulas can be transformed into latent bipartite graph representations which we model using a specialized deep generative neural network. We show that G2SAT can generate SAT formulas that closely resemble given real-world SAT instances, as measured by both graph metrics and SAT solver behavior. Further, we show that our synthetic SAT formulas could be used to improve SAT solver performance on real-world benchmarks, which opens up new opportunities for the continued development of SAT solvers and a deeper understanding of their performance. Authors: ; ; ; ; Award ID(s): Publication Date: NSF-PAR ID: 10198846 Journal Name: Advances in neural information processing systems ISSN: 1049-5258 4. The design of cyber-physical systems (CPSs) requires methods and tools that can efficiently reason about the interaction between discrete models, e.g., representing the behaviors of cyber'' components, and continuous models of physical processes. Boolean methods such as satisfiability (SAT) solving are successful in tackling large combinatorial search problems for the design and verification of hardware and software components. On the other hand, problems in control, communications, signal processing, and machine learning often rely on convex programming as a powerful solution engine. However, despite their strengths, neither approach would work in isolation for CPSs. In this paper, we present a newmore »	2021-11-28T21:10:21	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5177443027496338, "perplexity": 898.5276706647495}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358591.95/warc/CC-MAIN-20211128194436-20211128224436-00326.warc.gz"}
https://par.nsf.gov/biblio/10380229	Accelerated thermal reaction kinetics by indirect microwave heating of a microwave-transparent substrate Macroscopically homogeneous mixtures of p -nitroanisole ( p NA) and mesitylene (MES) can be selectively heated using microwave (MW) energy. The p NA solutes agglomerate into distinct phase domains on the attoliter-scale (1 aL = 10 −18 L), and these agglomerates can be MW-heated selectively to temperatures that far exceed the boiling point of the surrounding MES solvent. Here, a 1 : 20 mixture of p NA : MES is used as a mixed solvent for aryl Claisen rearrangement of allyl naphthyl ether (ANE). ANE itself does not heat effectively in the MW, but selective MW heating of p NA allows for transfer of thermal energy to ANE to accelerate rearrangement kinetics above what would be expected based on Arrhenius kinetics and the measured bulk solution temperature. This focused study builds on prior work and highlights 1 : 20 p NA : MES as a mixed solvent system to consider for strategically exploiting MW-specific thermal effects. Authors: ; ; Award ID(s): Publication Date: NSF-PAR ID: 10380229 Journal Name: Physical Chemistry Chemical Physics Volume: 24 Issue: 5 Page Range or eLocation-ID: 2794 to 2799 ISSN: 1463-9076 Thin film evaporation is a widely-used thermal management solution for micro/nano-devices with high energy densities. Local measurements of the evaporation rate at a liquid-vapor interface, however, are limited. We present a continuous profile of the evaporation heat transfer coefficient ($$h_{\text {evap}}$$${h}_{\text{evap}}$) in the submicron thin film region of a water meniscus obtained through local measurements interpreted by a machine learned surrogate of the physical system. Frequency domain thermoreflectance (FDTR), a non-contact laser-based method with micrometer lateral resolution, is used to induce and measure the meniscus evaporation. A neural network is then trained using finite element simulations to extract the$$h_{\text {evap}}$$${h}_{\text{evap}}$profile from the FDTR data. For a substrate superheat of 20 K, the maximum$$h_{\text {evap}}$$${h}_{\text{evap}}$is$$1.0_{-0.3}^{+0.5}$$$1.{0}_{-0.3}^{+0.5}$ MW/$$\text {m}^2$$${\text{m}}^{2}$-K at a film thickness of$$15_{-3}^{+29}$$${15}_{-3}^{+29}$ nm. This ultrahigh$$h_{\text {evap}}$$${h}_{\text{evap}}$value is two orders of magnitude larger than the heat transfer coefficient for single-phase forced convection or evaporation from a bulk liquid. Under the assumption of constant wall temperature, our profiles of$$h_{\text {evap}}$$${h}_{\text{evap}}$and meniscus thickness suggest that 62% of the heat transfer comes from the region lying 0.1–1 μm from the meniscus edge, whereas just 29% comes from the next 100 μm.	2023-03-24T15:41:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 8, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5708509683609009, "perplexity": 4261.99395789403}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945287.43/warc/CC-MAIN-20230324144746-20230324174746-00154.warc.gz"}
https://www.usgs.gov/media/images/dead-tree-and-lava	Huge ahu and dead ohia tree in small kipuka surrounded by Kohola flow. An ahu is a pile of rocks; most ahu are less than 1 meter high. This one is 2 meters high and serves as a marker along a land boundary. This ahu has been a landmark for years; it is now endangered as the surrounding Kohola flow inflates and nears it.	2021-09-21T21:47:02	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3453376889228821, "perplexity": 6640.423355006995}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057227.73/warc/CC-MAIN-20210921191451-20210921221451-00458.warc.gz"}
https://www.rba.gov.au/publications/rdp/2021/2021-08/why-does-unemployment-reduce-spending.html	# RDP 2021-08: Job Loss, Subjective Expectations and Household Spending 6. Why Does Unemployment Reduce Spending? Next, we identify heterogeneity across households in the spending response to unemployment. This heterogeneity allows us to explore further the mechanisms through which job loss affects spending.[17] We also further explore the role of worker beliefs in determining the size of the effect of job loss on spending.[18] We focus on weekly food spending and test various violations of the PIH which might explain the unemployment effect found in Section 5: • Liquidity constraints: if the effect is due to liquidity constraints then we should find stronger spending responses to unemployment for those individuals that are estimated to be liquidity constrained (or ‘hand-to-mouth’), and we should see no effect until unemployment occurs. • Myopia: if individuals are short-sighted then we should see no spending response until actual unemployment occurs, and the effect should be stronger for households that reportedly do not plan ahead in terms of their saving and spending decisions. • Precautionary saving: if households expect to remain unemployed for longer, they may reduce their expenditure in unemployment by more in order to smooth consumption over the unemployment spell. We explore these forms of heterogeneity through the same event study framework as before, but we now run separate sub-sample regressions for different types of households and/or different unemployment events: $ln( foo d ijt )= α ij + γ jtk + δ jk U ijt−k + ε ijtk , ∀k∈{ −2,−1,...,3 } ∀j∈{ 0,1 }$ where the model specification is as before, but we now include an indicator for whether the household head is, for example, hand-to-mouth (j = 1) and compare to the case in which the household head is not hand-to-mouth (j = 0) in in the year before unemployment based on 2 different regressions. We again also estimate the model with the log of total spending as the dependent variable for comparison.[19] To test for liquidity constraints, we identify households that are liquidity constrained based on the framework developed by Kaplan, Violante and Weidner (2014). Under this approach, households may be sensitive to shocks to current income despite relatively high levels of wealth (because many households hold wealth in relatively illiquid assets, such as housing and superannuation).[20] For this, we estimate the model separately for liquidity-constrained households and all other households. We find that liquidity-constrained households reduce spending by more than other households in response to unemployment (Figure 13). Interestingly, liquidity-constrained households also reduce spending in the year before unemployment. This is consistent with liquidity constraints being an important part of the story. It also highlights that even asset-rich households may experience large consumption losses due to illiquid wealth. Households that are not liquidity constrained also reduce spending in response to unemployment. We follow the same sub-sampling approach to test whether myopic households are more sensitive to unemployment in their spending response. We measure myopia based on responses to a specific question about the time frame in which each household plans saving and spending decisions. A household is considered myopic if the most important time frame is one year or less. On this metric, we find no difference between the spending responses at the onset of unemployment for myopic households compared to forward-looking households (Figures 14 and 15). We also test whether, during unemployment, the consumption response varies by how long individuals expect to remain unemployed. To do this, we follow the same approach but split household heads into low (high) expectations of regaining work based on whether their expected probability of regaining work in the year ahead is below (above) 75 per cent (which is the mean response). We find larger consumption losses for unemployed workers that do not expect to regain employment within the year relative to those that do (Figures 16 and 17). This is consistent with these households smoothing consumption through a period of unemployment. However, these differences are not statistically significant. ## Footnotes We find other sources of heterogeneity in the spending response to job loss, including personal characteristics such as age and income. The effect of job loss on spending varies with age. Specifically, it appears to be a quadratic function of age, with households where the head is aged 45 to 54 most sensitive to unemployment. Two factors may drive this relationship. First, younger households have more time over which to smooth the earnings losses from unemployment. Thus the PIH would imply that they respond less to earnings losses. Second, older households are less likely to be liquidity constrained, and as a result more able to smooth the effect of unemployment. The effect of job loss on spending also varies with the level of household income. Low-income households experience the largest reductions in spending. This is consistent with low-income households being more liquidity constrained. However, even high-income households reduce spending in response to job loss. [17] We also tested whether job loss expectations affect spending in the modelling framework of Stephens (2004). We found similar results in that there is no evidence that anticipated job losses affect spending. We also tested all the spending regressions with a Poisson fixed effects model instead of a log linear model and the results were unchanged. [18] As the hand-to-mouth variable is constructed using variables only available in the wealth module, and total expenditure is only available for a small subset of the sample, we are unable to estimate the total expenditure response to unemployment by hand-to-mouth status. [19] Under the Kaplan et al (2014) framework, households are considered ‘hand-to-mouth’ if their fortnightly income is greater than or equal to their current liquid net wealth. [20]	2022-08-10T23:58:03	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5754992365837097, "perplexity": 2441.0750196867857}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571222.74/warc/CC-MAIN-20220810222056-20220811012056-00558.warc.gz"}
https://phys.libretexts.org/TextBooks_and_TextMaps/University_Physics/Book%3A_University_Physics_(OpenStax)/Map%3A_University_Physics_II_-_Thermodynamics%2C_Electricity%2C_and_Magnetism_(OpenStax)/7%3A_Electric_Potential/7.0%3A_Prelude_to_Electric_Potential	$$\require{cancel}$$ # 7.0: Prelude to Electric Potential • Page ID 11548 • In Electric Charges and Fields, we just scratched the surface (or at least rubbed it) of electrical phenomena. Two terms commonly used to describe electricity are its energy and voltage, which we show in this chapter is directly related to the potential energy in a system. We know, for example, that great amounts of electrical energy can be stored in batteries, are transmitted cross-country via currents through power lines, and may jump from clouds to explode the sap of trees. In a similar manner, at the molecular level, ions cross cell membranes and transfer information. Figure $$\PageIndex{1}$$: The energy released in a lightning strike is an excellent illustration of the vast quantities of energy that may be stored and released by an electric potential difference. In this chapter, we calculate just how much energy can be released in a lightning strike and how this varies with the height of the clouds from the ground. (credit: Anthony Quintano) We also know about voltages associated with electricity. Batteries are typically a few volts, the outlets in your home frequently produce 120 volts, and power lines can be as high as hundreds of thousands of volts. But energy and voltage are not the same thing. A motorcycle battery, for example, is small and would not be very successful in replacing a much larger car battery, yet each has the same voltage. In this chapter, we examine the relationship between voltage and electrical energy, and begin to explore some of the many applications of electricity. ## Contributors • Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).	2018-09-25T01:51:48	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.46546465158462524, "perplexity": 662.3108242685926}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267160853.60/warc/CC-MAIN-20180925004528-20180925024928-00014.warc.gz"}
https://par.nsf.gov/biblio/10312310	Finding High-redshift Galaxies with JWST Abstract One of the primary goals for the upcoming James Webb Space Telescope is to observe the first galaxies. Predictions for planned and proposed surveys have typically focused on average galaxy counts, assuming a random distribution of galaxies across the observed field. The first and most-massive galaxies, however, are expected to be tightly clustered, an effect known as cosmic variance. We show that cosmic variance is likely to be the dominant contribution to uncertainty for high-redshift mass and luminosity functions, and that median high-redshift and high-mass galaxy counts for planned observations lie significantly below average counts. Several different strategies are considered for improving our understanding of the first galaxies, including adding depth, area, and independent pointings. Adding independent pointings is shown to be the most efficient both for discovering the single highest-redshift galaxy and also for constraining mass and luminosity functions. Authors: ; ; Award ID(s): Publication Date: NSF-PAR ID: 10312310 Journal Name: The Astrophysical Journal Volume: 923 Issue: 1 ISSN: 0004-637X We post-process galaxies in the IllustrisTNG simulations with skirt radiative transfer calculations to make predictions for the rest-frame near-infrared (NIR) and far-infrared (FIR) properties of galaxies at z ≥ 4. The rest-frame K- and z-band galaxy luminosity functions from TNG are overall consistent with observations, despite ${\sim}0.5\, \mathrm{dex}$ underprediction at z = 4 for MK ≲ −25 and Mz ≲ −24. Predictions for the JWST MIRI observed galaxy luminosity functions and number counts are given. Based on theoretical estimations, we show that the next-generation survey conducted by JWST can detect 500 (30) galaxies in F1000W in a survey area of $500\, {\rm arcmin}^{2}$ at z = 6 (z = 8). As opposed to the consistency in the UV, optical, and NIR, we find that TNG, combined with our dust modelling choices, significantly underpredicts the abundance of most dust-obscured and thus most luminous FIR galaxies. As a result, the obscured cosmic star formation rate density (SFRD) and the SFRD contributed by optical/NIR dark objects are underpredicted. The discrepancies discovered here could provide new constraints on the sub-grid feedback models, or the dust contents, of simulations. Meanwhile, although the TNG predicted dust temperature and its relations with IR luminosity and redshiftmore »	2022-12-08T23:01:14	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6293821334838867, "perplexity": 3751.7979851169366}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711368.1/warc/CC-MAIN-20221208215156-20221209005156-00650.warc.gz"}
https://par.nsf.gov/biblio/10188106-approximating-back-propagation-biologically-plausible-local-learning-rule-spiking-neural-networks	Approximating Back-propagation for a Biologically Plausible Local Learning Rule in Spiking Neural Networks Asynchronous event-driven computation and communication using spikes facilitate the realization of spiking neural networks (SNN) to be massively parallel, extremely energy efficient and highly robust on specialized neuromorphic hardware. However, the lack of a unified robust learning algorithm limits the SNN to shallow networks with low accuracies. Artificial neural networks (ANN), however, have the backpropagation algorithm which can utilize gradient descent to train networks which are locally robust universal function approximators. But backpropagation algorithm is neither biologically plausible nor neuromorphic implementation friendly because it requires: 1) separate backward and forward passes, 2) differentiable neurons, 3) high-precision propagated errors, 4) coherent copy of weight matrices at feedforward weights and the backward pass, and 5) non-local weight update. Thus, we propose an approximation of the backpropagation algorithm completely with spiking neurons and extend it to a local weight update rule which resembles a biologically plausible learning rule spike-timing-dependent plasticity (STDP). This will enable error propagation through spiking neurons for a more biologically plausible and neuromorphic implementation friendly backpropagation algorithm for SNNs. We test the proposed algorithm on various traditional and non-traditional benchmarks with competitive results. Authors: ; ; ; Award ID(s): Publication Date: NSF-PAR ID: 10188106 Journal Name: International Conference on Neuromorphic Systems Page Range or eLocation-ID: 1 to 8 2. We use a recently developed synchronous Spiking Neural Network (SNN) model to study the problem of learning hierarchically-structured concepts. We introduce an abstract data model that describes simple hierarchical concepts. We define a feed-forward layered SNN model, with learning modeled using Oja’s local learning rule, a well known biologically-plausible rule for adjusting synapse weights. We define what it means for such a network to recognize hierarchical concepts; our notion of recognition is robust, in that it tolerates a bounded amount of noise. Then, we present a learning algorithm by which a layered network may learn to recognize hierarchical concepts according to our robust definition. We analyze correctness and performance rigorously; the amount of time required to learn each concept, after learning all of the sub-concepts, is approximately O ( 1ηk(max log(k) + 1ε) + b log(k)), where k is the number of sub-concepts per concept, max is the maximum hierarchical depth, η is the learning rate, ε describes the amount of uncertainty allowed in robust recognition, and b describes the amount of weight decrease for "irrelevant" edges. An interesting feature of this algorithm is that it allows the network to learn sub-concepts in a highly interleaved manner. This algorithm assumesmore »	2023-03-22T03:42:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6962710022926331, "perplexity": 2338.7868102043144}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943749.68/warc/CC-MAIN-20230322020215-20230322050215-00414.warc.gz"}
https://theory.fnal.gov/theoretical-physics-seminar/tps-archive/	## Theoretical Physics Seminars Archive ### Current year Jan-Aug 2016 Raw date Event date Title Speakers Host Summary Links 20160901 Sept. 1, 2016 New Physics Searches at DUNE Kevin Kelly, Northwestern U. pubs 20160908 Sept. 8, 2016 The Minimal SUSY B-L Model: Simultaneous Wilson Lines and String Thresholds Burt Ovrut, University of Pennsylvania Chris H. pubs 20160922 Sept. 22, 2016 Relaxion from particle production Gustavo Marques-Tavares, Boston U. Jack pubs 20160929 Sept. 29, 2016 Little Conformal Symmetry Rachel Houtz, UC Davis Seyda pubs 20161006 Oct. 6, 2016 Higgs Relaxation Leptogenesis Lauren Pearce, Minnesota U. Seyda 20161013 Oct. 13, 2016 Dark matter annihilation via dark bound state formation Haipeng An, Caltech Paddy pubs 20161018 Oct. 18, 2016 Leaving Plato's Cave: Beyond the Simplest Models of Dark Matter and Flavor Symmetry Alexander Natale, KIAS, Seoul Kiel pubs 20161020 Oct. 20, 2016 Resummation for Differential Distributions Vincent Theeuwes, SUNY Buffalo John pubs 20161027 Oct. 27, 2016 New physics in Supernovae and IceCube Flavor Ratios Vedran Brdar, MITP, Mainz U. Paddy inSPIRE Slides 20161103 Nov. 3, 2016 Towards Realistic Simulation of t-channel Single Top-Quark Production Hua Xing Zhu, MIT Ye inSPIRE 20161110 Nov. 10, 2016 Gravitational Waves as a New Probe of Dark Matter Bhupal Dev, Washington University St. Louis Zhen Abstract: A dark matter (DM) halo intervening along the line of sight of a gravitational wave (GW) signal could induce a change in the speed of GW. We show that this change of speed is observable with the current LIGO sensitivity for a class of self-interacting ultralight DM models, where the DM particles could form... More » inSPIRE 20161115 Nov. 15, 2016 Higgs Effective Field Theories - Systematics and Applications Claudius Krause, University of Munich; Note day and location: Tuesday, WH3NW Marcela 20161117 Nov. 17, 2016 Secluded Neutrinos: From the Early Universe to IceCube Ian Shoemaker, University of South Dakota Pilar HEPNAMES 20161124 Nov. 24, 2016 Happy Thanksgiving! No seminar 20161201 Dec. 1, 2016 The String Soundscape at Gravitational Wave Detectors Isabel Garcia-Garcia, University of Oxford Kiel 20161215 Dec. 15, 2016 INT Workshop on Neutrino-Nucleus Interactions Minerba Betancourt, Fermilab; Andreas Kronfeld, Fermilab Andreas Workshop website Note location: One West Andreas's slides Minerba's slides 20170112 Jan. 12, 2017 The Fate of Axion Stars Hong Zhang, Ohio State U Inspires profile 20170119 Jan. 19, 2017 It's not just the Higgs Sally Dawson, BNL Paddy InSPIREs Profile 20170126 Jan. 26, 2017 Being flat with no symmetry Yue Zhao, University of Michigan Paddy Inspire profile 20170202 Feb. 2, 2017 Exploring the Higgs-top coupling at the LHC Dorival Gonçalves, Pittsburgh U. Pedro Inspires profile Slides 20170209 Feb. 9, 2017 Extraction of the triple Higgs coupling at e+e- colliders using EFT Michael Peskin, SLAC Paddy InSPIRE profile 20170216 Feb. 16, 2017 Hindered M1 Radiative Decay of Υ(2S) and ηb(2S) from Lattice NRQCD Ciaran Hughes, Fermilab (local) Inspire profile 20170223 Feb. 23, 2017 Flavor Gauge Models Below the Fermi Scale (and why neutrinos matter!) Pedro Machado, Fermilab (local) Inspires profile 20170302 March 2, 2017 Neutrino-nucleus Interactions Noemi Rocco, IFIC Valencia Andreas inSPIREs profile Slides 20170309 March 9, 2017 The Trouble with the Lattice Axial Charge Huey-Wen Lin, Michigan State U. Ciaran inSPIRE profile 20170314 March 14, 2017 Relaxed inflation Lorenzo Ubaldi, Tel Aviv University Roni InSPIRE profile 20170316 March 16, 2017 Few-hadron electroweak reactions from lattice QCD Raúl Briceño, Jefferson Lab Ciaran inSPIRE profile Slides 20170323 March 23, 2017 Double Scalar Production at LHC and Beyond Ian Lewis, University of Delaware Zhen The simplest extension of the Standard Model is to add a gauge singlet scalar: the singlet extended Standard Model. Although simple, this model is quite well-motivated and has an interesting phenomenology. Of particular interest is that this model can provide a mechanism for the strong first order phase transition necessary for electroweak baryogenesis. In this... More » InSPIRE profile 20170330 March 30, 2017 Conformal QED3 and the ε expansion Emmanuel Stamou, University of Chicago Pilar The theory of Quantum Electrodynamics in three dimensions (QED3) has received considerable attention due to its applications in condensed matter physics and due to its similarities with stongly coupled QCD-like theories in four dimensions. QED3 is strongly coupled at energies close to the gauge coupling that in this case is dimensionful. Whereas for a large... More » inSPIRE profile 20170406 April 6, 2017 Effective theories for point sources Cliff Burgess, McMaster/PI Paddy Nature comes to us with many hierarchies of scale, and science progresses because we do not need to understand them all at once. Effective theories exploit this fact to isolate what is important at any scale. This talk summarizes how effective theories work for applications to the ordinary and relativistic quantum mechanics of a particle... More » InSPIRE profile Slides 20170411 April 11, 2017 CERN ν-Physics Summary Seyda Ipek, Fermilab Local Inspires Profile 20170413 April 13, 2017 Hadron resonances in coupled-channel scattering from lattice QCD Jozef Dudek, College of William and Mary Ciaran InSPIRE profile Slides 20170420 April 20, 2017 The Vev Flip-Flop: Dark Matter Decay between Weak Scale Phase Transitions Michael Baker, JGU Mainz Stefan InSPIRE profile 20170427 April 27, 2017 Lepton Universality Violation in B decays Ben Grinstein, UC San Diego Ciaran InSPIRE profile 20170502 May 2, 2017 A New Era of Seesaw Phenomenology for a New Era of Colliders Richard Ruiz, IPPP, Durham; (NB: Tuesday, WH7XO) Pilar inSPIRE profile 20170504 May 4, 2017 Transplanckian Cosmic Strings Patrick Draper, U. Mass, Amherst Paddy InSPIRE profile 20170511 May 11, 2017 Neutrinoless double beta decay from lattice QCD Amy Nicholson, UC Berkeley Ciaran inSPIRE profile 20170518 May 18, 2017 Collider Probes of Axion-Like Particles Andrea Thamm, JGU Mainz Stefan Inspires Profile 20170522 May 22, 2017 D* Polarization as a probe to distinguish new physics in B → Dτν Uma Sankar, Indian Institute of Technology Bombay Marcela BaBar, Belle and LHCb have all measured the parameters R(D) and R(D) to be in excess of the Standard Model predictions. Freytsis et al (arXiv:1506.08896) have obtained the coupling strengths of various New Physics operators which can explain this excess. In this work (arXiv:1606.03164), we look at the angular observables which can distinguish between these different solutions. We find that... More » 20170523 May 23, 2017 LHC constraints on mesons from Stealth Dark Matter Bryan Ostdiek, University of Oregon Kiel Inspires Profile 20170525 May 25, 2017 Instability of Lightest Visible Superpartner Points to Hidden Sector Dark Matter Sebastian Ellis, University of Michigan Kiel Inspires Profile 20170601 June 1, 2017 Minimal Seesaw Model: Testable Leptogenesis & CP violation Jacobo Lopez-Pavon, CERN Pilar inSPIRE profile 20170602 June 2, 2017 Lattice QCD predictions of π and K electromagnetic form factors at large Q2 for Jefferson Lab experiments Christine Davies, University of Glasgow Ciaran Inspires Profile Slides 20170615 June 15, 2017 Leptogenesis via Weinberg operator Ye-Ling Zhou, Durham University Pilar Inspires Profile 20170620 June 20, 2017 New directions for LHC boosted object searches Jack Collins, University of Maryland Hadronic boosted object discrimination has been reaching experimental maturity in the last few years especially for the discrimination of boosted Standard Model W’s, Z’s, and H’s against QCD jets, and there is now a wide range of searches utilizing these techniques with great success. In this talk I will discuss a range of topologies that... More » InSPIRE profile Slides 20170622 June 22, 2017 The B -> D() tau nu anomalies: facts and/or fictions Zoltan Ligeti, LBNL InSPIRE profile 20170706 July 6, 2017 Solar neutrinos as a probe of Neutrino-Dark Matter interactions Francesco Capozzi, Ohio State Pilar InSPIRE profile 20170711 July 11, 2017 Axion-photon transition (radiation) caused by dielectric interfaces in a magnetic field: QFT approach Ara Ioannisyan, Yerevan Physics Institute, Armenia Axion-photon transition/conversion at dielectric interfaces, immersed in a near-homogeneous magnetic field, is the basis for the dielectric haloscope method to search for axion dark matter. In analogy to transition radiation, this process is possible because the photon wave function is modified by the dielectric layers (“Garibian wave function”) and is no longer an eigenstate of... More » InSPIRE profile 20170712 July 12, 2017 Impact of the magnetic field in EoS, the structure and velocities of the Quark Stars Aurora Perez Martinez, Havana, ICIMAF Marcela We analyze the impact of anisotropic EoS, due to the presence of a magnetic field, in the structure equations of magnetized quark stars. We assume a cylindrical metric and an anisotropic energy momentum tensor for the source. We found that there is a maximum magnetic field that a quark star can sustain, closely related to... More » Inspires 20170713 July 13, 2017 Lepton flavor universality violation in rare B decays Wolfgang Altmannshofer, Cincinnati U. Ciaran Inspires Profile 20170720 July 20, 2017 New opportunities for old observables at LHC Marc Riembau, DESY Interpreting LHC data requires a few assumptions, even from an Effective Field Theory approach. I will put a question mark on a few on them and study their effects: considering triple Higgs coupling in single Higgs observables gives a complementarity between single and double Higgs; adding anomalous fermion-vector boson couplings in diboson data ends up... More » InSPIRE profile 20170727 July 27, 2017 Toward partial compositeness on the lattice: Lattice results from a candidate SU(4) gauge theory William Jay, Colorado Uni. Ciaran In this seminar, I’ll discuss recent results from lattice simulation of a candidate model of physics beyond the Standard Model. In systems of interest, the Higgs arises as a Goldstone boson of a new strongly coupled sector in the UV, while the top quark obtains its large mass through the mechanism of partial compositeness. This... More » Inspires Profile Slides 20170810 Aug. 10, 2017 Re-examining Lepton Flavor Violation in the Littlest Higgs Model with T-Parity Roberto Vega-Morales, University of Granada Kiel Inspires Profile 20170817 Aug. 17, 2017 New physics searches with the TeV neutrinos Carlos A Arguelles Delgado, MIT Pilar Inspires Profile Slides 20170831 Aug. 31, 2017 Flavoured Dark Matter in Dark Minimal Flavour Violation Simon Kast, KIT Roni We study simplified models of flavoured dark matter in the framework of Dark Minimal Flavour Violation. In this setup the coupling of the dark matter flavour triplet to SM quark triplets constitutes the only new source of flavour and CP violation. The parameter space of the model is restricted by LHC searches with missing energy... More » Inspires Profile 20170907 Sept. 7, 2017 Light Composite Scalars from Lattice Gauge Theory Beyond QCD Ethan Neil, Colorado Uni. Ciaran Inspires Profile Slides 20170914 Sept. 14, 2017 Electric dipole moment using lattice QCD with the gradient flow Andrea Shindler, Michigan State U. Ciaran Inspires Profile 20170921 Sept. 21, 2017 Baryogenesis from Oscillations of Charmed or Beautiful Baryons Ann Nelson, Washington U., Seattle Paddy Inspires 20170928 Sept. 28, 2017 Light Z' coupled to "poorly" conserved currents Maxim Pospelov, Perimeter Institute Ciaran Inspires Profile 20171012 Oct. 12, 2017 Continuum Top Partners Sal Lombardo, Cornell The LHC has put the naturalness paradigm under pressure since one generally expects new colored resonances at the TeV scale to address the hierarchy problem. There exists another possibility, however. New dynamics responsible for furnishing a pseudo-goldstone composite Higgs may have a gapped continuum of colored excitations, in which case the top partners and vector... More » inSPIRE profile 20171017 Oct. 17, 2017 BSM physics searches in the IceCube neutrino telescope Jordi Salvado, Barcelona Stefan inSPIRE profile 20171019 Oct. 19, 2017 The hadronic light-by-light contribution to the muon anomalous magnetic moment from lattice QCD Thomas Blum, Connecticut U. Ciaran Inspires Slides 20171020 Oct. 20, 2017 Special JC: Lattice quantum gravity and asymptotic safety Jack Laiho, Syracuse U. Ciaran Inspires Slides 20171026 Oct. 26, 2017 Modern Machine Learning with Jet Images for High Energy Physics Ben Nachman, Berkeley InSPIRE profile 20171030 Oct. 30, 2017 New Physics with Neutrino Physics Pedro Machado, Fermilab inSPIRE profile 20171102 Nov. 2, 2017 Voronoi Tessellations and Machine Learning in Phase Space Jamie Gainer, Hawaii Kiel InSPIRE profile 20171109 Nov. 9, 2017 Singularities: Long time behavior of their Quantum Noise and holographic Complexity Eliezer Rabinovici, Hebrew University Various properties of some space like singularities in string theory will be discussed in the AdS/CFT holographic framework. Attempts to apply the diagnostic tools such as the study of long time correlations and complexity, to these singularities, will be described. InSPIRE profile 20171116 Nov. 16, 2017 Quantum Monte Carlo predictions for electron- and neutrino-nucleus scattering Alessandro Lovato, Argonne Ciaran Inspires 20171123 Nov. 23, 2017 Happy Thanksgiving 20171128 Nov. 28, 2017 The half-life of a free neutron from Lattice QCD Jason Chang, LBNL Ciaran The axial coupling of the nucleon, $g_A$, is a fundamental property of neutrons and protons. The long-range nuclear force between nucleons and the $\beta$-decay rate of a free neutron both depend on $g_A^2$. This coupling therefore underpins all of low-energy nuclear physics, controlling, for example, the primordial composition of the universe. While the value of... More » Inspires 20171130 Nov. 30, 2017 Deep Learning Seminar 20171205 Dec. 5, 2017 Respect the ELDER Dark Matter & Go Beyond the Direct-Detection Limit with Quilonovae and Neutron Star Mergers Yu-Dai Tsai, Cornell Kiel We present a novel dark matter (DM) candidate, Elastically Decoupling Relic (ELDER), in which the DM current-day abundance is dominantly determined via the elastic decoupling between standard model particles and DM, rather than a usual DM freeze-out. ELDER has a distinctive thermal history and new phenomenological implications in comparison to the CDM/WIMP scenarios. It provides... More » InSPIRE profile 20171212 Dec. 12, 2017 Report on CERN’s Physics Beyond Colliders Annual Workshop Chris Quigg, Fermilab Stefan 20171214 Dec. 14, 2017 Constraining extended Higgs sectors at the LHC and beyond Tania Robens, MSU inSPIRE profile 20180111 Jan. 11, 2018 A new way to determine alpha_s using the QCD gradient flow Tobias Neumann, Fermilab & IIT Ciaran 20180118 Jan. 18, 2018 Searching for beauty-fully bound tetraquarks using lattice Non-relativistic QCD Ciaran Hughes, Fermilab Ciaran Slides 20180125 Jan. 25, 2018 Loop induced inflationary non-Gaussianites that give rise to enhanced galaxy bias at small wave-vectors Mark Wise, Caltech Paddy/Stefan 20180201 Feb. 1, 2018 Three ways to weigh a quark Andrew Lytle, University of Glasgow Ciaran Recent years have seen order of magnitude improvement in knowledge of quark mass parameters — these advances have been due largely to theoretical and computational advances in lattice QCD simulations. Present day calculations are able to obtain percent-level uncertainties; reducing these even further will be important for precision Higgs studies and BSM searches. I will... More » Slides 20180208 Feb. 8, 2018 Displaced Vertices from Folded Supersymmetry Gabriela Lima Lichtenstein, Sao Paulo Ciaran Inspires Slides 20180215 Feb. 15, 2018 (Rel)-axions and SM hierarchies Diego Redigolo, Weizmann Kiel I will discuss two scenarios which connects the strong CP problem to other hierarchies of the Standard Models. In the “axiflavon”, solving the flavor problem with a global abelian flavor symmetry naturally leads to an axion that solves the strong CP problem and constitutes a viable Dark Matter candidate. In the less tuned window for Dark Matter... More » 20180222 Feb. 22, 2018 Effective theory approach to neutrinoless double beta decay Vincenzo Cirigliano, Los Alamos Pedro Inspires Slides 20180301 March 1, 2018 Quark Masses Andreas Kronfeld, Fermilab Ciaran Slides 20180306 March 6, 2018 Heavy quarks flavored scalar dark matter with a vector-like fermion portal Peiwen Wu, KIAS Kiel The absence of confirmed signal in dark matter (DM) direct detection (DD) may suggest weak interaction strengths between DM and the abundant constituents inside nucleon, i.e. gluons and valence light quarks. In this work we consider a real scalar dark matter $S$ interacting only with $SU(2)_L$ singlet Up-type quarks $U_i=u_R,c_R,t_R$ via a vector-like fermion $\psi$.... More » 20180308 March 8, 2018 Anderson localisation in theory space Dave Sutherland, UCSB Kiel 20180315 March 15, 2018 Quantum Information and Quantum Gravity Ning Bao, UC Berkeley Kiel 20180322 March 22, 2018 New Developments in Axion Cosmology Josh Eby, Weizmann Ciaran Slides 20180329 March 29, 2018 Astrophysical signals of axion dark matter Ben Safdi, Michigan Kiel 20180403 April 3, 2018 The quest for dark sectors Claudia Frugiuele, Weizmann Roni Dark sectors are ubiquitous in physics beyond the Standard Model (SM), and may play a role in explaining many of the long-standing problems of the SM such as the existence of dark matter or the electroweak hierarchy problem. By definition, dark sectors are not charged under any of the known forces. Discovering their possible existence... More » 20180412 April 12, 2018 The road from QCD to nuclear double-beta decays Zohreh Davoudi, University of Maryland Ciaran Neutrinoless double-beta decay, as a lepton-number violating process, has been the focus of numerous experimental and theoretical investigations in recent years. While it proves that neutrinos are Majorana particles once observed, the underlying new physics responsible for this process can only be constrained if the theoretical predictions of the rate are substantially refined. This talk... More » Inspires Slides 20180419 April 19, 2018 Electromagnetic Interactions of Neutrinos Baha Balantekin, Univ. of Wisconsin, Madison Stefan 20180501 May 1, 2018 Soft photons, gravitons, and their quantum information content Dan Carney, Maryland Kiel When a particle is accelerated, as in a scattering event, it will radiate gravitons and, if electrically charged, photons. The infrared tail of the spectrum of this radiation has a divergence: an arbitrarily small amount of total energy is divided into an arbitrarily large number of radiated bosons. Each of these in turn carries a... More » 20180510 May 10, 2018 New insights into the quark and gluon structure of hadrons and nuclei from lattice QCD Phiala Shanahan, William & Mary Ciaran Inspires 20180517 May 17, 2018 Towards double differential Higgs production at N3LO Falko Dulat, SLAC With the discovery of the Higgs boson, the LHC has entered an era of precision Higgs physics. The precision determination of the properties of the Higgs boson provides an excellent window into potential new physics. High precision predictions for Higgs boson observables are therefore essential for the future LHC Higgs physics program. This requires highly... More » 20180531 May 31, 2018 Neutrino trident production at near detectors Matheus Hostert, IPPP Durham Jessica Neutrino trident scattering is the production of a charged lepton pair in the coulomb field of a nucleus. It is a rare but observable process expected to occur at near detectors of neutrino oscillation experiments. In this talk, I will revisit the calculation of the trident scattering rate, addressing certain inconsistencies in the literature and presenting revised... More » Inspires 20180614 June 14, 2018 EW Baryogenesis through varying Yukawas in Composite Higgs models Sebastian Bruggisser, DESY Stefan Varying Yukawas open new possibilities for electroweak baryogenesis. In this talk I will start by introducing varying Yukawas as a source of CP-violation and explain how baryogenesis can be successful in this framework. I will then present a realization of this paradigm in Composite Higgs models with partial compositeness. Composite Higgs models are, apart from... More » 20180621 June 21, 2018 Quantum information in quantum gravity: localization, transfer, and black hole evolution Steven Giddings, UCSB Kiel 20180628 June 28, 2018 Characterizing nonhermiticity of calorimetric neutrino detectors Shirley Li, SLAC Pedro Inspires Slides 20180713 July 13, 2018 Automated calculation of two-loop soft functions in SCET Rudi Rahn, Bern University Claudius Perturbative calculations for many collider observables suffer from large logarithmic corrections associated with soft emissions or radiation collinear to beam or jet directions. Resummation using SCET techniques is based on factorisation theorems, and requires the calculation of jet, soft and beam functions to some perturbative accuracy. This task has up to now mainly been achieved... More » InSpire profile 20180719 July 19, 2018 Black Holes and Massive Gravitons (postponed to later date!) Rachel Rosen, Columbia Dan Hooper 20180809 Aug. 9, 2018 Searching Beyond the Standard Model with Light and Gravitational Waves Masha Baryakhtar, Perimeter Institute Dan Hooper 20180830 Aug. 30, 2018 The Leptonic CP Phases: Dirac and Majorana Shaofeng Ge, Kavli IPMU Stephen Parke 20180911 Sept. 11, 2018 Self-Organized Higgs Criticality Jay Hubisz, Syracuse University Roni Harnik 20180920 Sept. 20, 2018 Subleading Colored Parton Showers Joshua Isaacson, Fermilab 20180927 Sept. 27, 2018 Detecting Dark Blobs Dorota Grabowska, Berkeley Kiel Howe Inspires 20181004 Oct. 4, 2018 Light Cone Physics on the Lattice Christopher Monahan, Institute for Nuclear Theory, Seattle 20181011 Oct. 11, 2018 Hiding Blazars with Decaying Alps Edoardo Vitagliano, Max Planck Institute for Physics 20181018 Oct. 18, 2018 ε'/ε beyond the Standard Model Jason Aebischer, Technical University Munich Claudius Krause 20181025 Oct. 25, 2018 Zero-Range Effective Field Theory for Resonant Wino Dark Matter Evan Johnson, Ohio State University 20181101 Nov. 1, 2018 From clockwork to colliders Dipan Sengupta, Michigan State University 20181106 Nov. 6, 2018 Angular distributions in electroweak pion production off nucleons Joanna Sobczyk, IFIC University of Valencia Noemi Rocco 20181108 Nov. 8, 2018 Using machine learning to unlock Gaia’s full potential to determine the dark matter halo Bryan Ostdiek, Oregon University 20181115 Nov. 15, 2018 Muon-proton scattering and the proton radius puzzle Gil Paz, Wayne State University 20181129 Nov. 29, 2018 Light Exotic Higgs Bosons at the LHC Keping Xie, Southern Methodist University Josh Isaacson 20181206 Dec. 6, 2018 Phenomenology of Fermion Production During Inflation Lauren Pearce, University of Illinois 20181213 Dec. 13, 2018 Lattice gauge theory with cold atoms? Yannick Meurice, University of Iowa 20190122 Jan. 22, 2019 Neutrino Oscillation in Particle Physics Ivan Martinez-Soler, Northwestern/Fermilab 20190124 Jan. 24, 2019 Composite BSM physics on the lattice William Jay, Fermilab 20190131 Jan. 31, 2019 Dynamic Dark Matter Production: Finite Temperature Effects in the Early Universe Michael Baker, University of Zurich Jessica Turner 20190205 Feb. 5, 2019 Multiparticle States in Lattice QCD and Prospects for Neutrino Physics Aaron Meyer, BNL Andreas slides inSPIRE 20190207 Feb. 7, 2019 Predicting the neutron lifetime from the Standard Model Chia Cheng Chang, iTHEMS - LBNL Andreas slides inSPIRE 20190212 Feb. 12, 2019 Astrophysical Imaging with Information Field Theory Julia Stadler, Durham University Jessica Turner 20190214 Feb. 14, 2019 Nucleon structure and the proton radius from lattice QCD Jeremy Green, DESY Zeuthen Andreas slides inSPIRE 20190219 Feb. 19, 2019 Leading Hadronic Contribution to the g − 2 of the Muon: A Give-And-Take Between Theory and Experiment Marina Marinković, Trinity College Dublin Andreas slides inSPIRE 20190221 Feb. 21, 2019 Dark halos around neutron stars and gravitational waves Ann Nelson, University of Washington Josh Isaacson 20190226 Feb. 26, 2019 QCD for the Intensity Frontier Michael Wagman, MIT Andreas slides inSPIRE 20190228 Feb. 28, 2019 Calculating with Entanglement: nuclear and particle physics on quantum devices Natalie Klco, University of Washington Josh Isaacson 20190305 March 5, 2019 Chiral Gauge Theories for Dark Sector Construction Kevin Kelly, Fermilab 20190307 March 7, 2019 Towards x-dependent hadron structure for flavor physics Christopher Monahan, University of Washington Andreas slides inSPIRE 20190312 March 12, 2019 LHC phenomenology of Supersymmetric “Unparticles” Christina Gao, Fermilab 20190314 March 14, 2019 Toward a precise definition of branches in a many-body wavefunction Jess Riedel, Perimeter Institute Pedro Machado 20190319 March 19, 2019 Observable signatures of dark photons from supernovae Gustavo Marques Tavares, University of Maryland Nikita Blinov 20190320 March 20, 2019 Precision Physics for Sky Surveys Mikhail Solon, Caltech Richard Hill 20190321 March 21, 2019 Quantum Memories of de Sitter and Phenomenology Gia Dvali, LMU / NYU 20190328 March 28, 2019 Quantum Monte Carlo calculations of neutrino-nucleus interactions Saori Pastore, Washington University, St. Louis Pedro Machado 20190404 April 4, 2019 Minimal Fundamental Partial Compositeness Anders Thomsen, University of Southern Denmark Jessica Turner 20190411 April 11, 2019 Composite Higgs Models at the LHC and beyond Da Liu, Argonne Jessica Turner 20190418 April 18, 2019 Lepton-Nucleus scattering within many-body approaches Noemi Rocco, Argonne/Fermilab 20190425 April 25, 2019 Neutrinos at the frontier of Cosmology and Particle Physics Yuber Perez Gozalez, Northwestern University/Fermilab 20190502 May 2, 2019 Cosmology with Sub-MeV Thermal Relics Nikita Blinov, Fermilab 20190508 May 8, 2019 Softened Goldstone-symmetry breaking Simone Blasi, Max Planck Institute for Physics Pedro Machado 20190516 May 16, 2019 Top Quark Physics at the Precision Frontier Workshop 20190523 May 23, 2019 Signature of supersymmetry and Lμ-Lτ gauge boson at Belle-II Sourov Roy, Indian Association for the Cultivation of Science Bogdan Dobrescu 20190530 May 30, 2019 Disorder at the LHC Matt Low, Fermilab 20190606 June 6, 2019 Fun with Top Spin Kaoru Hagiwara, KEK 20190711 July 11, 2019 Sector Showers for Hadron Collisions - Creating Unique Shower Histories Christian Preuss, Monash University 20190725 July 25, 2019 Strong coupling constant and heavy quark masses from lattice QCD Johannes Weber, Michigan State U. Andreas InSPIRE profile 20190801 Aug. 1, 2019 Coherent Showers In Resonance Decays Using VINCIA Helen Brooks, Monash University Jessica Turner 20190808 Aug. 8, 2019 New-physics interpretation of b->c tau nu data and a novel solution to the little hierarchy problem Ulrich Nierste, Karlsruhe Inst. of Technology Josh Isaacson 20190815 Aug. 15, 2019 Automated label flow using Prony's method for lattice spectroscopy Kimmy Cushman, Yale Josh Isaacson 20190822 Aug. 22, 2019 Sterile Neutrinos with Altered Dispersion Relations as an Explanation for the MiniBooNE, LSND, Gallium and Reactor Anomalies Heinrich Paes, TU Dortmund Pedro Machado slides 20190829 Aug. 29, 2019 New detection prospects for primordial black hole dark matter Nicholas Orlofsky, University of Wisconsin-Madison Christina Gao 20190905 Sept. 5, 2019 Neutrino Oscillation Theory Peter Denton, BNL Stephen Parke 20190912 Sept. 12, 2019 The electroweak effective field theory from on-shell amplitudes Gauthier Durieux, Technion Roni Harnik 20190919 Sept. 19, 2019 B-physics anomalies Sokratis Trifinopoulos, Zurich University Pedro Machado 20190926 Sept. 26, 2019 Heavy Dynamical Axions Rachel Houtz, Universidad Autonoma de Madrid Christina Gao Slides 20191001 Oct. 1, 2019 Probing the Higgs Portal with the SBN Program Ahmed Ismail, Oklahoma State University Pedro Machado 20191017 Oct. 17, 2019 Simplified U(1) lattice gauge theory on quantum computers and simulators Randy Lewis, York University Ciaran Hughes 20191022 Oct. 22, 2019 On the symmetries and the spectrum of a TeV-scale composite sector Michele Frigerio, Univ. of Montpellier Pedro Machado 20191024 Oct. 24, 2019 Generating QCD Corrected Multi-Jet Events at Hadron Colliders using Innovative Phase Space Sampling Methods Terrance Figy, Wichita State University Jessica Turner 20191031 Oct. 31, 2019 Exploring new physics in the early Universe with gravitational waves Jonathan Kozaczuk, Univ. of Mass. Amherst Jessica Turner 20191105 Nov. 5, 2019 SU(2) gauge theory on digital quantum computers Jesse Stryker, University of Washington Hank Lamm 20191107 Nov. 7, 2019 Paul Mackenzie at Fermilab Andreas Kronfeld, Fermilab in connection with Lattice QCD at Fermilab: Celebrating the Career of Paul Mackenzie inSPIRE profile 20191114 Nov. 14, 2019 Exploring the dark universe through molecules and nuclei Harikrishnan Ramani, UC Berkeley & LBL, Berkeley Nikita Blinov 20191121 Nov. 21, 2019 Primordial Non-Gaussianity as a probe of (ultra high-energy) gauge theories Soubhik Kumar, University of Maryland Christina Gao 20191205 Dec. 5, 2019 N3LO predictions for the decay of the Higgs boson to bottom quarks Roberto Mondini, University at Buffalo Josh Isaacson 20191212 Dec. 12, 2019 Learning from Dark Monopoles Christopher Verhaaren, University of California-Davis Christina Gao 20191219 Dec. 19, 2019 Quantum Computing for Neutrino-nucleus Scattering with NISQ devices Andy Li, Fermilab Josh Isaacson 20200109 Jan. 9, 2020 Neutron's Dark Secret Bartosz Fornal, University of Utah Pedro Machado 20200116 Jan. 16, 2020 Quantum Computers for Quantum Field Theory Henry Lamm, Fermilab Pedro 20200130 Jan. 30, 2020 Optimal Control for the Quantum Simulation of Nuclear Dynamics Kyle Wendt, LLNL Pedro 20200206 Feb. 6, 2020 CP violating Yukawas - interplay of baryogenesis, EDM and Higgs physics Elina Fuchs, Fermilab/U. Chicago Pedro 20200218 Feb. 18, 2020 Baryogenesis from B mesons Huangyu Xiao, University of Washington Pedro Machado 20200220 Feb. 20, 2020 Hiding multiple portals in plain sight: dark sectors at neutrino and kaon experiments Matheus Hostert, University of Minnesota Christina Gao 20200225 Feb. 25, 2020 Loops and trees in generic EFTs Ying-Ying Li, Fermilab Pedro 20200227 Feb. 27, 2020 New Approaches to Anomaly Detection at the LHC and Beyond David Shih, Rutgers University Pedro Machado 20200305 March 5, 2020 Weaker than weak physics at the intensity frontier Ryan Plestid, U. Kentucky The advent of precision neutrino physics has resulted in detector technology (easily) capable of observing upwards of 10^5 charged current scattering events in the lifetime of an experiment. This naturally motivates a theoretical program targeting sub-G_F physics at the intensity frontier. In this talk I will discuss some examples of how large-scale neutrino detectors can... More » Slides pubs 20200312 March 12, 2020 Relaxion searches at future colliders Matthias Schlaffer, U Chicago Pedro Machado 20200319 March 19, 2020 Gauge extensions of the SM: Neutrinos, dark matter and the LHC [zoom] Alexis Plascencia, Case Western Reserve University Jessica Turner Slides Slides 20200326 March 26, 2020 On Asymmetry Observables In b → cτν [zoom] Pouya Asadi, MIT Pedro Machado slides 20200402 April 2, 2020 ONLINE ONLY: Looking for New Physics in the low energy experiments Jia Liu, U. Chicago Christina Gao Slides 20200409 April 9, 2020 ONLINE ONLY: Toward analog quantum simulation of lattice gauge theories with trapped ions Zohreh Davoudi, U. Maryland Pedro Machado Slides 20200416 April 16, 2020 ONLINE ONLY: QCD dynamics from hadrons and nuclei to the energy frontier Tim Hobbs, Southern Methodist University Slides 20200423 April 23, 2020 Physics beyond the standard model from Higgs Parity Keisuke Harigaya, Institute for Advanced Study Christina Gao 20200430 April 30, 2020 Axion Production and Detection with Superconducting RF Cavities Ryan Janish, Berkeley Roni Slides 20200507 May 7, 2020 Hadronic Vacuum Polarization in (g-2)μ from Lattice QCD Kalman Szabo, Wuppertal Andreas 20200514 May 14, 2020 The Short-Baseline Neutrino Anomalies Joachim Kopp, U. Mainz and CERN Pedro Machado While over the past two decades a largely consistent picture of neutrino oscillations has emerged, a few unexplained anomalies put a serious dent in this framework. After introducing the LSND, MiniBooNE, and reactor anomalies, we will first discuss attempts to explain the latter two within the Standard Model. In the second part of the talk,... More » video 20200521 May 21, 2020 LIGO/Virgo Black Holes from a First Order QCD Phase Transition Hooman Davoudiasl, BNL Pedro Machado video 20200528 May 28, 2020 Multi-loop Scattering Amplitudes for the HL-LHC, presenting the Caravel Framework Fernando Febres Cordero, Florida State University Pedro Machado slides video 20200604 June 4, 2020 Spin-2 KK Mode Scattering in the Truncated RS1 Dennis Foren, Michigan State U. Joshua Isaacson The Randall-Sundrum model with two branes (RS1) is a gravitational theory on five-dimensional spacetime. Because its fifth dimension is compactified, the theory manifests as a four-dimensional theory at low energies, where it describes interactions among a Kaluza-Klein spectrum that contains a 4D graviton, massless radion, and infinitely many massive spin-2 states. These massive spin-2 states pose... More » video 20200611 June 11, 2020 Quantum Simulation of Gauge Theories Scott Lawrence, U. of Maryland Pedro video 20200618 June 18, 2020 A testable hidden sector model for Dark Matter and neutrino masses Julia Gehrlein, BNL Christina Gao We consider a minimal extension of the Standard Model with a hidden sector charged under a dark local U(1)’ gauge group, accounting simultaneously for light neutrino masses and the observed Dark Matter relic abundance. The model contains two copies of right-handed neutrinos which give rise to light neutrino-masses via an extended seesaw mechanism. The presence... More » video 20200625 June 25, 2020 No seminar (Neutrino 2020) 20200702 July 2, 2020 No seminar (Neutrino 2020) 20200709 July 9, 2020 A New Probe of the Nature of the B Physics Anomalies Stefan Schacht, Cornell Claudius Krause fermilab-schacht slides video 20200716 July 16, 2020 A Swampland Tour, From Photon Masses to Axion Physics Matthew Reece, Harvard Matt Low slides video 20200723 July 23, 2020 Strong First-Order Electroweak Phase Transitions, Models and Probes Peisi Huang, Univ. of Nebraska-Lincoln Ying-Ying Li video slides 20200730 July 30, 2020 Circumventing the sign problem with complex Langevin in lattice field theory Casey Berger, Boston University Will Jay video slides 20200813 Aug. 13, 2020 Higgs-confinement phase transitions with fundamental representation matter Aleksey Cherman, University of Minnesota Will Jay 20200820 Aug. 20, 2020 Prospects for the Detection of Solar Neutrinos in DARWIN via Elastic Electron Scattering (Please note time: 10:00am) Shayne Reichard, Zurich U. Pedro video slides 20200827 Aug. 27, 2020 Unravelling the richness of dark sector by FASERnu (Please note time: 10:00am) Yasaman Farzan, IPM Pedro Machado FASER\nu is a newly proposed experiment which will take data in run III of the LHC during 2021-2023. It will be located in front of the FASER detector, 480~m away from the ATLAS interaction point in the forward direction. Its main goal is to detect neutrinos of all flavors produced at the interaction point with... More » video slides 20200903 Sept. 3, 2020 Ensemble generation for lattice QFT using machine learning Tej Kanwar, MIT Will Jay Monte Carlo sampling is a powerful approach to computing observables in quantum field theories regularized on a discrete spacetime lattice (LQFT), which is necessary for example to study the non-perturbative behavior of QCD in the low-energy regime. The cost of drawing independent samples is a major bottleneck in such studies. I discuss recent work demonstrating... More » video slides 20200910 Sept. 10, 2020 Advances in nucleon-nucleon scattering Amy Nicholson, University of North Carolina Will Jay video 20200917 Sept. 17, 2020 x-dependent hadron structure from lattice QCD Raza Sufian, JLab Will video 20200924 Sept. 24, 2020 Sequential Discontinuities of Scattering Amplitudes Hofie Sigridar Hannesdottir, Harvard Nikita Scattering amplitudes are essential ingredients in theoretical predictions for collider experiments. In some cases, symmetries and other constraints can fix amplitudes completely, and hence conventional Feynman diagram computations are circumvented. The traditional cutting rules relate discontinuities across branch cuts of amplitudes to cuts through the corresponding Feynman diagrams. Here we probe the analytic structure further... More » video slides 20201001 Oct. 1, 2020 Neutrino oscillations as constraints on Effective Field Theory Zahra Tabrizi, Virginia Tech Pedro video slides 20201008 Oct. 8, 2020 Fractional Quantum Hall effect in a relativistic field theory Srimoyee Sen, Iowa State Pedro slides 20201015 Oct. 15, 2020 Cosmological phase transition of composite Higgs confinement and the fifth dimension Majid Ekhterachian, Maryland U. Will video slides 20201022 Oct. 22, 2020 Novel (Quantum) Computational Methods for Quantum Field Theories (Please note the time: 10:30am) Michael Spannowsky, Durham U. Yingying 20201029 Oct. 29, 2020 Collapse of vacuum bubbles in quantum devices Junyu Liu, Caltech Yingying 20201105 Nov. 5, 2020 Precision Neutrino Oscillations: Exploring Possibilities and Important Considerations Rebekah Pestes, Virginia Tech Pedro Machado video 20201112 Nov. 12, 2020 Progress on gluon gravitational form factors on the lattice Daniel Hackett, MIT video 20201119 Nov. 19, 2020 The Hydrogen Mixing Portal as a Novel Mechanism for Colder Baryons in 21 cm Cosmology Seth Koren, University of Chicago Ying-Ying Li video slides 20201126 Nov. 26, 2020 Thanksgiving Day 20201203 Dec. 3, 2020 Rethinking the origin of neutrino masses: the role of gravity Lena Funcke, Perimeter Pedro Machado video slides 20201210 Dec. 10, 2020 A Holographic Realization of Partially Composite Neutrinos Abhish Dev, University of Maryland Pedro Machado 20201217 Dec. 17, 2020 A Futuristic Look at Neutrino Telescopes: Sources, Decay, Non-Unitarity and Extra Dimensions Ningqiang Song, Queen's University Pedro Machado video slides 20201224 Dec. 24, 2020 Christmas Eve 20201231 Dec. 31, 2020 New Year's Eve 20210114 Jan. 14, 2021 Towards quantum simulating non-Abelian lattice gauge theories Indrakshi Raychowdhury, University of Maryland Ying-Ying Li video 20210119 Jan. 19, 2021 Simulating Quantum Field Theories with Quantum Circuits (PLEASE NOTE TIME & DATE: Tuesday at 10:00am) Ananda Roy, Technical University Munich Roni Investigation of strongly interacting quantum field theories (QFTs) remains one of the outstanding challenges of modern physics. Quantum simulation has the potential to be a crucial technique towards solving this problem. In this talk, I will describe analog quantum simulators for strongly interacting QFTs using mesoscopic quantum electronic circuit lattices. The tunable, robust and dispersive... More » video slides 20210121 Jan. 21, 2021 Newtonian binding from lattice quantum gravity Judah Unmuth, FNAL We study the propagators of a scalar field coupled to a lattice regularization of gravity in the limit there is no back-reaction from the matter. We extract the renormalized mass, and binding energy between scalar particles and attempt to recover the known, non-relativistic, tree-level calculation in the infinite-volume, continuum limit for the scaling of the... More » video 20210128 Jan. 28, 2021 Pushed from the Precipice: Lattice Field Theory for Quantum Computers Hank Lamm, FNAL Roni Harnik Over the past five decades, Euclidean lattice field theory has matured into a broad program capable of making precise QCD predictions. While its success is undeniable, certain problems in real time and at finite density elude it due to sign problems. Early on, Feynman pointed out that many of these problems are naturally solvable on... More » video slides 20210211 Feb. 11, 2021 Muon g-2 Experiments as Dark Matter Detectors Ryan Janish, FNAL We propose extending the search for dark matter (DM) by considering muon spin targets. An ultralight DM background may apply an oscillating torque to muon spins, resulting in novel precession trajectories. A time-resolved analysis of muon precession data from the upcoming Fermilab and J-PARC g-2 experiments and future frozen spin EDM measurements are sensitive to... More » video slides 20210218 Feb. 18, 2021 Discovering the Dark Universe Asher Berlin, New York U. Roni Harnik Although it is known to provide the gravitational scaffolding of our universe, the existence of dark matter is a mystery that cannot be explained by our current understanding of fundamental particle physics. Recent years have seen a growing interest in applying developing technologies to enable qualitatively new ways to look for types of dark matter... More » slides video 20210225 Feb. 25, 2021 Gravitational Waves as a Probe of New Physics: from LIGO to NANOGrav Vedran Brdar, FNAL/Northwestern U. In the first part of the talk I will discuss gravitational wave signature arising from first order phase transition in two different models featuring neutrino mass generation through type-I seesaw mechanism. The expected gravitational wave spectra from these models will be confronted with sensitivities of ground-based detectors such as LIGO as well as several future... More » video 20210304 March 4, 2021 An unambiguous test of positivity at lepton colliders Jiayin Gu, U. Mainz Ying-Ying The diphoton channel at lepton colliders, e+e- (mu+mu-) -> gamma gamma, has a remarkable feature that the leading new physics contribution comes only from dimension-eight operators. This contribution is subject to a set of positivity bounds, derived from fundamental principles of Quantum Field Theory, such as unitarity, locality, analyticity and Lorentz invariance. These positivity bounds are thus... More » video 20210311 March 11, 2021 Searching for hidden sectors: new experiments and theory Robert Lasenby, Stanford U. Roni Harnik The problems of dark matter, quantum gravity and the early universe show that physics beyond the Standard Model must be out there, but its nature remains a mystery. In this seminar, I will describe new experimental and theoretical ideas to expand our search for new physics. I’ll talk about how searches for dark matter candidates,... More » slides video 20210318 March 18, 2021 Quantum sensing for dark relics Harikrishnan Ramani, Stanford U. Roni Harnik Direct detection is notoriously hard for a plethora of dark matter models and models of dark relics due to their inability to impart enough energy to the direct detection target. Detecting these dark relics with energy deficit involves tackling the twin challenges of a target that can convert small amounts of dark matter kinetic energy... More » slides video 20210325 March 25, 2021 Higgs boson pair production at NNLO in QCD with finite top quark mass effects Florian Herren, FNAL Higgs boson pair production is the most promising process for testing the scalar potential of the SM beyond the quadratic term. The next-to-leading order QCD corrections for this gluon-fusion process are large and the dependence on the renormalization scheme of the top quark mass are sizeable. In this seminar I will discuss the current... More » video slides 20210401 April 1, 2021 Exciting Prospects for Detecting Late-Time Neutrinos from Core-Collapse Supernovae Shirley Li, FNAL The importance of detecting neutrinos from a Milky Way core-collapse supernova is well known. An under-studied phase is proto-neutron star cooling. With the high statistics expected for present and near-future detectors, it should be possible to obtain detailed neutrino signals from before the start of the cooling phase to very late times. We present the... More » slides 20210408 April 8, 2021 Higgs alignment and the top quark Kenneth Lane, Boston U. There is a surprising connection between the top quark and Higgs alignment in Gildener-Weinberg multi-Higgs-doublet models. Were it not for the top quark and its large mass, the coupling of the 125 GeV Higgs boson H to gauge bosons and fermions would be indistinguishable from those of the Standard Model Higgs. The top quark’s coupling... More » video slides 20210415 April 15, 2021 Continuous Renormalization Group on the Lattice Andrea Carosso, University of Colorado The traditional method of performing renormalization group (RG) transformations for spin systems is by spin-blocking, where the block spins are local averages of the original spins, and they live on a lattice with fewer sites than the original lattice. As such, this transformation is inherently discrete. By contrast, over the last decade a new technique known as... More » slides video 20210422 April 22, 2021 B-physics anomalies: a road to new physics? Olcyr Sumensari, Orsay Pedro Even though the LHC searches did not unveil the new physics particles so far, observations made at LHCb and the B-factories point towards lepton flavor universality violation in both tree-level and loop-induced B-meson semileptonic decays. After a review of the status of these anomalies, I will discuss general implications that can be derived by using... More » slides video 20210429 April 29, 2021 Nucleon Mass and Charges with Lattice Quantum Chromodynamics Yin Lin, Fermilab/University of Chicago Will Jay Theoretical understandings of the neutrino-nucleus cross sections are critical for constraining neutrino parameters in future neutrino oscillation experiments such as DUNE and Hyper-K. For neutrino energies at around 1 GeV, uncertainties in the nucleon axial form factor, which parameterizes the weak response of a neutron or proton as a function of the four momentum transfer,... More » slides video 20210506 May 6, 2021 Precision calculation of the $x$-dependence of PDFs from lattice QCD Yong Zhao, ANL Will Jay video slides 20210513 May 13, 2021 Hint of SUSY in Flavor Anomalies? Bhupal Dev, Washington U at St. Louis Pedro The recent results from the Fermilab muon g-2 experiment have caused quite a stir in the community. At the same time, there are persisting hints of lepton flavor universality violation in some rare B-meson decays. Taken at face value, if these anomalies are interpreted as of beyond the Standard Model (BSM) origin, it is conceivable... More » video slides 20210520 May 20, 2021 Probing the Standard Model with flavor physics: an exclusive determination of $\|V_{cb}\|$ from the $B\to D^\ast\ell\nu$ semileptonic decay at non-zero recoil Alex Vaquero, Utah U. Will Jay A very rich place to look for phenomena to challenge our current understanding of physics is the flavor sector of the Standard Model (SM). In particular, the $V_{cb}$ matrix element of the CKM matrix is the subject of a long standing tension, depending on whether it is determined using inclusive or exclusive methods. On top... More » slides video 20210527 May 27, 2021 Graded Hilbert spaces and quantum distillation in QFT Mithat Unsal, North Carolina State U. I construct various generalizations of partition function in non-supersymmetric theories, including few fairly close to QCD, that do not undergo a phase transition upon circle compactification. This is similar to what happens in supersymmetric index calculations but there it is guaranteed by supersymmetry, and Bose-Fermi grading of Hilbert space. In manifestly non-supersymmetric theories in QM,... More » slides video 20210603 June 3, 2021 Electroweak symmetry in the early universe Yikun Wang, U. Chicago Behavior of the electroweak symmetry and the Higgs thermal history have intriguing implications for matter antimatter asymmetry creation and early universe physics. In this talk, I will present two beyond the Standard Model scenarios resulted in two different early universe paths of the electroweak symmetry. Electroweak phase transition from an electroweak symmetric phase to the... More » video 20210610 June 10, 2021 A lattice QCD calculation of the hadronic light-by-light contribution to the magnetic moment of the muon Harvey Meyer, University of Mainz Will Jay I present a recent calculation of the hadronic light-by-light scattering contribution to the muon g−2 from the up, down, and strange-quark sector directly using lattice QCD. I first describe the methodology based on coordinate-space methods and a pilot calculation at the SU(3)-flavour symmetric point with a pseudoscalar mass of about 420 MeV. The final result... More » slides video 20210617 June 17, 2021 On-shell amplitudes for Dark Matter Camila Machado, DESY Pedro On-shell methods have been shown to be a powerful tool to compute higher-point and loop amplitudes. However, most of the time we hear about the applications for renormalizable theories. In this talk, I will give an introduction to spinors and to (massless/massive) amplitudes and show that we can indeed apply these methods for general effective field... More » slides video 20210624 June 24, 2021 NLO mixed QCD-electroweak corrections to Higgs boson production at the LHC Marco Bonetti, Aachen U. The study of the Higgs boson properties is one of the main tasks of contemporary high-energy physics. At the LHC, gluon fusion is the main production channel of Higgs bosons, and mixed QCD-electroweak corrections represent one of the main sources of theoretical uncertainty for such process, known until few years ago only at leading order... More » slides video 20210701 July 1, 2021 Probing New Physics with Double Beta Decays Lukas Graf, MPIK-Heidelberg Pedro The observation of neutrinoless double beta decay would have far-reaching consequences for particle physics. Most prominently, it would give a hint on the origin of neutrino masses and on the scale at which they are generated. We will discuss the effective description of non-standard mechanisms triggering neutrinoless double beta decay and the implications of their... More » slides video 20210708 July 8, 2021 NLO di-boson production by gluon fusion, in the high-energy limit Josh Davies, Sussex U. In this talk I will discuss computations of NLO virtual corrections to four-point gluon-fusion processes; in particular the production of HH, ZH and ZZ. Recently these processes have been computed numerically, but they are not known analytically. I will discuss how one can perform an expansion of these amplitudes in the high-energy limit, and improve the resulting series through the... More » slides video 20210715 July 15, 2021 Maximal Entanglement in a Quantum Computer (PLEASE NOTE TIME: 1:30PM) Alba Cervera Lierta, University of Toronto Hank Nature is such that Maximal Entangled states exist”. This conjecture is based on the fact that we not only observe maximal entanglement in several physical processes but also we are able to verify that local realism can not describe quantum mechanics. We go a step further and suggest the possibility that maximal entanglement plays a... More » slides video 20210722 July 22, 2021 Effective Field Theory and the Geometry of Electroweak Symmetry Breaking Nathaniel Craig, UC-Santa Barbara There are two canonical approaches to treating the Standard Model as an effective field theory: the Standard Model EFT (SMEFT), respecting the full electroweak gauge symmetry, and the Higgs EFT (HEFT), respecting only electromagnetism. Of these, SMEFT has become the predominant framework for interpreting LHC Higgs data and exploring the systematics of effective field theory.... More » slides video 20210729 July 29, 2021 The Conformal Frontier David Poland, Yale From critical phenomena to quantum gravity, conformal field theories describe the universal scale-invariant structures that lie at the heart of theoretical physics. The conformal bootstrap is the powerful idea, dating back to the 70’s, that one can use fundamental consistency conditions to constrain, solve, and map out the space of conformal field theories. In this... More » video slides 20210805 Aug. 5, 2021 Gravitating vortices in an AdS$_3$ and Minkowski background Ariel Edery, Bishop's University Vortices are non-singular field configurations in $2+1$ dimensions that have finite energy. They have usually been studied in a fixed Minkowski spacetime i.e. without gravity. In this work, we embed vortices in gravity. We find numerically static vortex solutions where the scalar and gauge fields have a non-singular profile under Einstein gravity in an AdS$_3$ background.... More » video slides 20210819 Aug. 19, 2021 Discovering the new physics of (g−2)μ at colliders Rodolfo Capdevilla, Perimeter The Fermilab Muon g−2 collaboration has recently released its first measurement of (g−2)μ. This result is consistent with previous Brookhaven measurements and together they yield a statistically significant 4.2σ discrepancy with the Standard Model prediction. BSM solutions to (g−2)μ feature light weakly coupled neutral particles (Singlet Scenarios) or heavy strongly coupled charged particles (Electroweak Scenarios). In recent investigations,... More » video slides 20210826 Aug. 26, 2021 Toward first-principles calculation of the shear viscosity - classical and quantum approaches Yukari Yamauchi, Maryland U. Hydrodynamics successfully describes low-energy modes of a wide class of theories including QCD in the strongly-coupled regime. Some of the low energy constants in the hydrodynamic description of QCD, such as shear viscosity, are difficult to obtain from first principles on a classical computer due to the sign problem. One long-standing way to address sign... More » video slides 20210902 Sept. 2, 2021 Entanglement in collective neutrino oscillations: quantum simulations and tensor networks Alessandro Roggero, University of Trento In extreme astrophysical phenomena like supernova explosions, the large neutrino density can lead to collective flavor oscillations driven by neutrino-neutrino interactions. These phenomena can greatly modify flavor transport in these environments with potentially important consequences for both the explosion mechanism and nucleosynthesis in the ejected material. Even simple models of neutrino-neutrino interactions lead to a... More » 20210909 Sept. 9, 2021 Gravitational Waves from Cosmological First Order Phase Transitions: Recent Theoretical and Experimental Developments. Huaike Guo, Oklahoma U. 20210923 Sept. 23, 2021 Bubble-Of-Nothing Decay of the de Sitter Universe Benjamin Lillard, UIUC If our apparently four-dimensional spacetime is endowed with compact extra dimensions, our universe may not be entirely stable. It can decay, by the spontaneous nucleation of a “bubble of nothing”: a gravitational instanton that induces a catastrophic annihilation of spacetime. In this talk we discuss the connection between the bubble of nothing and an analogous Coleman-De... More » 20210930 Sept. 30, 2021 Matter-Antimatter Asymmetry in Neutral Kaons Zachary Polonsky, U. Cincinnati The parameter $\epsilon_K$ is an important measure of the imbalance between matter and antimatter in the neutral kaon ($K^0$ and $\bar{K}^0$) system. In particular, $\epsilon_K$ provides a sensitive probe of new physics and plays a critical role in the global fit of the Cabibbo-Kobayashi-Maskawa matrix. As one of the first discovered sources of $CP$ violation,... More » 20211007 Oct. 7, 2021 Dark Photon bounds in the dark EFT Enrico Bertuzzo, University of São Paulo Pedro Dark photons are among the simplest extensions of the Standard Model (SM): a renormalizable kinetic mixing with the ordinary photons generates a coupling between the dark photon and the SM electromagnetic current. Such coupling can be used to probe the parameter space of the model, resulting in severe bounds. In this talk, I will discuss... More » 20211014 Oct. 14, 2021 Neutrino interactions from the cosmos Ivan Esteban, Ohio State U. Do neutrinos have sizable self interactions? They might. As laboratory constraints are weak, strong effects can change our picture of astrophysical and cosmological environments. In this talk, I will explore the rich physics introduced by neutrino self-interactions throughout the Universe. I will discuss how a multidisciplinary approach, ranging from precision cosmology to neutrino telescopes, is... More » 20211021 Oct. 21, 2021 New backgrounds and new ideas for sub-GeV dark matter direct detection Peizhi Du, Stony Brook Probing sub-GeV dark matter requires designing low threshold detectors and understanding backgrounds. In this talk I will address these two issues. First, we point out several unexplored low-energy backgrounds in sub-GeV dark matter searches, which arise from high-energy particles of cosmic or radioactive origin that interact with detector materials. In this talk, I will focus... More » 20211028 Oct. 28, 2021 Reinterpretation of the Weak Mixing Angle Measurement from Atomic Parity Violation Francesca Dordei, INFN Cagliari In this talk, I will present the first measurement of the neutron skin of cesium and iodine using electroweak probes, namely coherent elastic neutrino-nucleus scattering and atomic parity violation. This measurement, differently from hadronic probes, is model-independent and suggests a preference for nuclear models which predict large neutron skin values. Moreover, it permits to perform... More » 20211104 Nov. 4, 2021 Flavor-specific Neutrino self-interaction in Cosmology Subhajit Ghosh, University of Notre Dame Neutrino self-interaction has been proposed as a solution to the Hubble tension, a discrepancy between the measured values of the Hubble constant from CMB and low-redshift data. However, flavor-universal neutrino self-interaction is highly constrained by BBN and laboratory experiments such as K-meson and tau decay, double-neutrino beta decay etc. In this talk, I will discuss... More » 20211111 Nov. 11, 2021 The NASDUCK collaboration: using quantum magnetometers to look for ultralight dark matter Itay Bloch, Tel Aviv U. When DM bosons have an ultra-light mass, they can act as a classical, coherent field. In many cases, and specifically in some ALP models, this field has magnetic properties, and it can therefore be measured by quantum magnetometers. The Noble and Alkali Spin Detectors for Ultralight Coherent darK matter (NASDUCK) collaboration, was formed last year... More » 20211118 Nov. 18, 2021 Axion Archaeology -- Echos from Ancient Supernova Remnants Chen Sun, Tel Aviv U. Stimulated decays of axion dark matter, triggered by a source in the sky, could produce a photon flux along the continuation of the line of sight, pointing backward to the source. The strength of this so-called axion “echo” signal depends on the entire history of the source and could still be strong from sources that... More » 20211125 Nov. 25, 2021 No seminar: Thanksgiving 20211202 Dec. 2, 2021 Lepton flavor violation and other indirect searches for New Physics Alexey Petrov, Michigan U./Wayne State	2021-12-01T12:55:42	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4636283218860626, "perplexity": 5625.966095904653}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964360803.0/warc/CC-MAIN-20211201113241-20211201143241-00015.warc.gz"}
http://www.scstatehouse.gov/sess118_2009-2010/sj10/20100120.htm	South Carolina General Assembly 118th Session, 2009-2010 Journal of the Senate Wednesday, January 20, 2010 (Statewide Session) Indicates Matter Stricken Indicates New Matter The Senate assembled at 11:00 A.M., the hour to which it stood adjourned, and was called to order by the PRESIDENT. A quorum being present, the proceedings were opened with a devotion by the Chaplain as follows: In the Book of Exodus we read: "But Moses said to the Lord, 'O my Lord, I have never been eloquent ... I am slow of speech and slow of tongue.' " (Exodus 4:10) Let us pray: Holy God, we do recall how insecure Moses felt before his confrontations with Pharaoh. Yet, with Your promises of assistance, Moses did become an advocate for righteousness and justice. In a similar manner, O Lord, allow the members of this Senate also to draw strength from You as they labor faithfully to bless all of the women and men and children of this State. Likewise, be with the Honorable Mark Sanford this evening as he addresses both the House and Senate. Together may all of these leaders speak well and effectively, and may their decisions and actions ultimately "speak" even louder. This we pray in Your blessed name, dear Lord. Amen. The PRESIDENT called for Petitions, Memorials, Presentments of Grand Juries and such like papers. Doctor of the Day Senator JACKSON introduced Dr. Thomas Rowland of Columbia, S.C., Doctor of the Day. Leave of Absence Rescinded At 11:05 A.M., the leave of absence granted to Senator S. MARTIN from 11:00 A.M. until 1:30 P.M. today was rescinded. Expression of Personal Interest Senator SHEHEEN rose for an Expression of Personal Interest. S. 151 (Word version) Sen. Fair S. 1032 (Word version) Sen. Verdin The following co-sponsor was removed from the respective Bill: S. 1031 (Word version) Sen. McGill On motion of Senator McCONNELL, the Senate agreed that, when the Senate recedes from business today, it stand in recess until 6:45 P.M., for the sole purpose of attending the Joint Assembly; and, further, that, at the conclusion of the Joint Assembly, the Senate would stand adjourned. On motion of Senator McCONNELL, with unanimous consent, the Senate agreed to go into Executive Session prior to recess. INTRODUCTION OF BILLS AND RESOLUTIONS The following were introduced: S. 1065 (Word version) -- Senators Hayes, Malloy, Lourie, Thomas, Sheheen, Fair and Anderson: A BILL TO AMEND SECTION 37-3-501, AS AMENDED, OF THE 1976 CODE, RELATING TO THE DEFINITION OF SUPERVISED LOAN, TO PROVIDE THAT CERTAIN CLOSED-END CREDIT TRANSACTIONS ARE NOT SUPERVISED LOANS; AND TO AMEND SECTION 37-3-503, RELATING TO A LICENSE TO MAKE SUPERVISED LOANS, TO PROVIDE THAT CERTAIN LICENSED DEFERRED PRESENTMENT PROVIDERS MAY NOT CONDUCT THE BUSINESS OF MAKING SUPERVISED LOANS, TO PROVIDE PENALTIES, AND TO PROVIDE NECESSARY DEFINITIONS. l:\s-res\rwh\004defp.kmm.rwh.docx Senator HAYES spoke on the Bill. Read the first time and referred to the Committee on Banking and Insurance. S. 1066 (Word version) -- Senator O'Dell: A BILL TO AMEND CHAPTER 6, TITLE 12 OF THE 1976 CODE, BY ADDING SECTION 12-6-3595 TO PROVIDE A TAX CREDIT EQUAL TO ONE HUNDRED PERCENT OF AN AMOUNT CONTRIBUTED TO THE SOUTH CAROLINA EXISTING MANUFACTURERS' RETENTION AND GROWTH FUND, TO PROVIDE THAT THE CREDIT MAY NOT EXCEED FIVE HUNDRED THOUSAND DOLLARS FOR A SINGLE TAXPAYER AND NOT TO EXCEED AN AGGREGATE OF FOUR MILLION DOLLARS FOR EACH TAX YEAR, AND TO PROVIDE THE PROCESS AND REQUIREMENTS FOR CLAIMING THE CREDIT. l:\s-financ\drafting\who\001manu.dag.who.docx Read the first time and referred to the Committee on Finance. S. 1067 (Word version) -- Senators Peeler and Hayes: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 58-5-267 SO AS TO REQUIRE AS PART OF THE FILING OF A PROPOSED NEW OR REVISED RATE SCHEDULE FOR WATER OR SEWER SERVICE PROVIDED BY A PRIVATELY OWNED PUBLIC UTILITY, THAT THE UTILITY SHALL MAKE CERTAIN INDEPENDENTLY PREPARED AND AUDITED FINANCIAL STATEMENTS REGARDING INDIVIDUAL AND SEPARABLE OPERATING ENTITIES OF THE UTILITY. l:\council\bills\dka\3822dw10.docx Read the first time and referred to the Committee on Judiciary. S. 1068 (Word version) -- Senator Rose: A BILL TO AMEND CHAPTER 35, TITLE 58 OF THE 1976 CODE, RELATING TO UNDERGROUND UTILITIES, TO INCLUDE THE WORD "SAFETY" IN THE ACT NAME, TO DEFINE TERMS USED IN THE ACT, TO PROVIDE SAFETY REGULATIONS FOR THE USE AND MAINTENANCE OF UNDERGROUND FACILITIES, TO PROVIDE FOR FACILITY NOTIFICATION REQUIREMENTS PRIOR TO EXCAVATION, TO REQUIRE FACILITY OPERATORS TO FORM AND OPERATE A NOTIFICATION CENTER, TO PROVIDE FOR REQUIRED ACTIONS ON THE PART OF THE NOTIFICATION CENTER AFTER THE CENTER HAS RECEIVED NOTIFICATION, TO PROVIDE THAT OPERATORS MUST FOLLOW CERTAIN SOUTH CAROLINA DEPARTMENT OF TRANSPORTATION POLICIES, TO PROVIDE PROCEDURES FOR NEW UTILITY INSTALLATIONS, TO PROVIDE RESTRICTIONS ON CERTAIN TYPES OF EXCAVATION EQUIPMENT, TO PROVIDE FOR ACTIONS THAT MUST BE TAKEN BY AN OPERATOR IN THE EVENT OF DAMAGE TO A FACILITY, TO PROVIDE PROCEDURES FOR DESIGN LOCATE REQUESTS, TO CREATE THE SOUTH CAROLINA UNDERGROUND UTILITY SAFETY AND DAMAGE PREVENTION BOARD AND TO PROVIDE FOR THE DUTIES AND POWERS OF THE BOARD, TO PROVIDE COMPLAINT PROCEDURES, TO PROVIDE FOR THE RECOVERY OF DAMAGES DUE TO VIOLATIONS OF THE ACT, AND TO PROVIDE EXCEPTIONS. l:\s-res\mtr\056util.mrh.mtr.docx Read the first time and referred to the Committee on Judiciary. S. 1069 (Word version) -- Senators Jackson, Ford, Williams, Pinckney, Bryant, Anderson and Matthews: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 22-2-45 SO AS TO ALLOW THE APPROPRIATE LEGISLATIVE DELEGATION TO DESIGNATE THE CHIEF MAGISTRATE FOR ADMINISTRATIVE PURPOSES FOR THAT COUNTY IF THE DELEGATION CHOOSES TO EXERCISE THIS OPTION; AND TO AMEND SECTION 22-8-10, RELATING TO DEFINITIONS FOR PURPOSES OF MAGISTRATES' COMPENSATION, SO AS TO REVISE THE DEFINITION OF THE TERM "CHIEF MAGISTRATE" ACCORDINGLY. l:\council\bills\ms\7494ahb10.docx Read the first time and referred to the Committee on Judiciary. S. 1070 (Word version) -- Senator Hayes: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING PART VII TO ARTICLE 5, TITLE 62 SO AS TO ENACT THE "UNIFORM ADULT GUARDIANSHIP AND PROTECTIVE PROCEEDINGS JURISDICTION ACT", TO DEFINE NECESSARY TERMS, PROVIDE A UNIFORM PROCEDURE FOR JURISDICTION OVER ADULT GUARDIANSHIPS, CONSERVATORSHIPS, AND OTHER PROTECTIVE PROCEEDINGS TO ENSURE ONLY ONE STATE HAS JURISDICTION AT A GIVEN TIME. l:\council\bills\ms\7492ahb10.docx Read the first time and referred to the Committee on Judiciary. S. 1071 (Word version) -- Senator Alexander: A BILL TO AMEND SECTION 40-2-20 OF THE 1976 CODE, RELATING TO PUBLIC ACCOUNTANTS, TO INCLUDE ENGAGEMENTS PERFORMED IN ACCORDANCE WITH INTERNATIONAL ACCOUNTING BOARD STANDARDS WITHIN THE MEANING OF "ATTEST"; TO AMEND SECTION 40-2-250, RELATING TO LICENSE RENEWALS, TO REQUIRE ANNUAL APPLICATION RENEWALS BY FEBRUARY FIRST; TO AMEND SECTION 40-2-255, RELATING TO OUT-OF-STATE REGISTRANTS, TO REQUIRE RENEWAL APPLICATIONS TO BE FILED BIENNIALLY; AND TO AMEND CHAPTER 20, TITLE 40, RELATING TO LICENSE RENEWAL OF ACCOUNTING PRACTITIONERS, BY ADDING SECTION 40-2-565 TO SET FORTH RENEWAL AND REINSTATEMENT PROVISIONS. l:\s-gen\drafting\tca\012acco.jd.tca.docx Read the first time and referred to the Committee on Labor, Commerce and Industry. S. 1072 (Word version) -- Senator Elliott: A CONCURRENT RESOLUTION TO DESIGNATE JUNE 12, 2010, AS ANNUAL NATIONAL MARINA DAY IN SOUTH CAROLINA IN ORDER TO HONOR SOUTH CAROLINA'S MARINAS FOR THEIR CONTRIBUTIONS TO THE COMMUNITY AND MAKE CITIZENS, POLICYMAKERS, AND EMPLOYEES MORE AWARE OF THE OVERALL CONTRIBUTIONS OF MARINAS TO THEIR WELL-BEING, AND TO REQUEST THAT OUR STATE JOIN HANDS WITH OTHER STATES AND THOUSANDS OF WATERFRONT COMMUNITIES ACROSS THE UNITED STATES IN CELEBRATING THIS DAY. l:\council\bills\rm\1025sd10.docx Senator ELLIOTT spoke on the Resolution. On motion of Senator ELLIOTT, with unanimous consent, the Concurrent Resolution was adopted and ordered sent to the House. H. 4290 (Word version) -- Rep. Kirsh: A CONCURRENT RESOLUTION TO INVITE THE NATIONAL COMMANDER OF THE AMERICAN LEGION, THE HONORABLE CLARENCE HILL, TO ADDRESS THE GENERAL ASSEMBLY IN JOINT SESSION IN THE CHAMBER OF THE SOUTH CAROLINA HOUSE OF REPRESENTATIVES AT 12:30 P.M. ON TUESDAY, FEBRUARY 23, 2010. The Concurrent Resolution was introduced and referred to the Committee on Invitations. H. 4303 (Word version) -- Reps. Bingham, Battle, Merrill, J. H. Neal, Ott, M. A. Pitts, Rice, A. D. Young, Sandifer, Cobb-Hunter, Bedingfield, Nanney, G. R. Smith, Hamilton, Stringer, Wylie, Horne, Harrell, Lowe, Ballentine and Clemmons: A JOINT RESOLUTION TO IMPOSE CERTAIN ENFORCEMENT REQUIREMENTS ON THE SOUTH CAROLINA EMPLOYMENT SECURITY COMMISSION RELATED TO DISQUALIFICATION PARAMETERS FOR UNEMPLOYMENT BENEFITS, TO REQUIRE THE COMMISSION TO INSTITUTE CERTAIN ADMINISTRATIVE MEASURES, AND TO PROVIDE THIS JOINT RESOLUTION EXPIRES ON JULY 1, 2011, AMONG OTHER THINGS. Read the first time and referred to the Committee on Labor, Commerce and Industry. H. 4361 (Word version) -- Reps. Sellers, Scott, Erickson, Govan, G. A. Brown, Mitchell, Allison, Parker, Forrester, Kelly, Limehouse, Sottile, Gilliard, Hutto, Stavrinakis, A. D. Young, Horne, Clemmons, T. R. Young, King, Norman, Kirsh, Wylie, Stringer, Chalk, Brantley, J. R. Smith, D. C. Smith, Stewart, Parks and Dillard: A CONCURRENT RESOLUTION TO EXPRESS SINCERE SYMPATHY FOR THE PEOPLE OF HAITI IN THE DEVASTATION AND LOSS OF LIFE FROM THE RECENT CATASTROPHIC EARTHQUAKE THERE, AND TO SEEK ENCOURAGEMENT FROM ALL SOUTH CAROLINIANS TO ASSIST IN THE RESCUE AND REBUILDING OF THAT NATION. The Concurrent Resolution was adopted, ordered returned to the House. REPORTS OF STANDING COMMITTEES Senator LEATHERMAN from the Committee on Finance submitted a favorable report on: S. 728 (Word version) -- Senators Hayes and Fair: A BILL TO AMEND SECTION 12-65-30, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE ENTITLEMENT TO TAX CREDITS UNDER THE TEXTILES COMMUNITIES REVITALIZATION ACT, SO AS TO FURTHER PROVIDE FOR THE APPLICABILITY OF SPECIFIC REQUIREMENTS FOR TEXTILE MILL SITES ACQUIRED BEFORE AND AFTER 2007, TO REVISE THE ALLOWABLE AMOUNT OF THE CREDITS IN CERTAIN INSTANCES, TO PROVIDE THAT THE TAX CREDITS ALLOWED INCLUDE CREDITS AGAINST INSURANCE PREMIUM TAXES, TO MAKE A TECHNICAL CORRECTION, AND TO FURTHER PROVIDE FOR THE MANNER IN WHICH THESE CREDITS ARE VESTED IN A TAXPAYER AND MAY BE ALLOCATED TO PARTNERS OR MEMBERS; BY ADDING SECTION 12-65-50 SO AS TO PROVIDE TRANSITION RULES APPLICABLE TO SPECIFIC MILL SITES; AND BY ADDING SECTION 12-65-60 SO AS TO FURTHER PROVIDE FOR THE ELIGIBILITY CERTIFICATION PROCESS. Ordered for consideration tomorrow. Senator LEATHERMAN from the Committee on Finance submitted a favorable with amendment report on: S. 910 (Word version) -- Senator Land: A BILL TO AMEND SECTION 6-21-185 OF THE 1976 CODE, RELATING TO A SPECIAL PURPOSE DISTRICT MORTGAGE TO SECURE CERTAIN BONDS OR LOANS, TO REMOVE LIMITATIONS FROM THE AUTHORITY OF SUCH DISTRICT TO MORTGAGE ITS PROPERTY UNDER THE REVENUE BOND ACT FOR UTILITIES; TO ADD SECTION 6-17-95 TO AUTHORIZE A SPECIAL PURPOSE DISTRICT PROVIDING HOSPITAL, NURSING HOME, OR CARE FACILITIES TO BORROW MONEY IN A MANNER THAT IS CONSISTENT WITH SECTION 44-7-60; TO ADD SECTION 6-11-101 TO CLARIFY THE POWERS OF HOSPITAL DISTRICTS. Ordered for consideration tomorrow. Senator LEATHERMAN from the Committee on Finance submitted a favorable report on: S. 1034 (Word version) -- Senator Leatherman: A JOINT RESOLUTION TO EXTEND THE DATE BY WHICH THE TAXATION REALIGNMENT COMMISSION MUST PREPARE AND DELIVER ITS REPORT AND RECOMMENDATION UNTIL NOVEMBER 15, 2010. Ordered for consideration tomorrow. HOUSE CONCURRENCES S. 1060 (Word version) -- Senator Scott: A CONCURRENT RESOLUTION TO COMMEND WOMEN HONORING VALOR FOR THEIR WORK TO RECOGNIZE AND CELEBRATE AMERICA'S LIVING RECIPIENTS OF THE MEDAL OF HONOR. Returned with concurrence. S. 1062 (Word version) -- Senators Campsen, Cleary and Grooms: A CONCURRENT RESOLUTION TO CONGRATULATE LUCY BECKHAM, PRINCIPAL OF WANDO HIGH SCHOOL IN CHARLESTON, UPON RECEIVING THE 2010 METLIFE SECONDARY SCHOOL PRINCIPAL OF THE YEAR AWARD BY THE NATIONAL ASSOCIATION OF SECONDARY SCHOOL PRINCIPALS. Returned with concurrence. THE SENATE PROCEEDED TO A CALL OF THE UNCONTESTED LOCAL AND STATEWIDE CALENDAR. The following Bill was read the third time and ordered sent to the House of Representatives: S. 929 (Word version) -- Senators L. Martin and Elliott: A BILL TO AMEND SECTION 41-1-10 OF THE 1976 CODE, RELATING TO POSTING NOTICES CONCERNING THE EMPLOYMENT OF ADULTS AND CHILDREN IN PLACES OF EMPLOYMENT, TO DELETE THE PROVISION REQUIRING NOTICE TO BE POSTED IN EVERY ROOM WHERE FIVE OR MORE PERSONS ARE EMPLOYED; TO AMEND SECTION 41-3-10, RELATING TO THE DIVISION OF LABOR WITHIN THE DEPARTMENT OF LABOR, LICENSING AND REGULATION AND TO THE APPOINTMENT AND DUTIES OF THE DIRECTOR OF THE DEPARTMENT, TO DELETE THE PROVISION ESTABLISHING THE DIVISION OF LABOR; TO AMEND SECTION 41-3-40, RELATING TO THE DIRECTOR OF THE DEPARTMENT OF LABOR, LICENSING AND REGULATION, TO DELETE THE REFERENCE TO REGULATIONS PERTAINING TO THE DIVISION OF LABOR; TO AMEND SECTIONS 41-3-50, 41-3-60, 41-3-100, AND 41-3-120, ALL RELATING TO VARIOUS DUTIES OF THE DIRECTOR OF THE DEPARTMENT OF LABOR, LICENSING AND REGULATION, TO MAKE TECHNICAL CORRECTIONS; AND TO REPEAL SECTIONS 41-1-40, 41-1-50, 41-3-80, 41-15-10, AND 41-15-50; ARTICLE 5, CHAPTER 3, TITLE 41; CHAPTER 21, TITLE 41; AND CHAPTER 23, TITLE 41, ALL RELATING TO VARIOUS OBSOLETE PROVISIONS PERTAINING TO THE DEPARTMENT OF LABOR, LICENSING AND REGULATION. Senator L. MARTIN explained the Bill. S. 929--Recorded Vote Senator RYBERG desired to be recorded as voting in favor of the third reading of the Bill. MINORITY REPORT REMOVED S. 391 (Word version) -- Senators Ryberg, McConnell, Verdin, Bryant, Cleary, Campsen, Shoopman, Campbell, Rose and Davis: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 41-29-300 SO AS CREATE THE WORKFORCE DEPARTMENT APPELLATE PANEL WITHIN THE DEPARTMENT OF WORKFORCE, TO PROVIDE FOR THE FILLING OF A VACANCY, TO REQUIRE THE PRESENT MEMBERS OF THE SOUTH CAROLINA EMPLOYMENT SECURITY COMMISSION MUST CONSTITUTE THE INITIAL MEMBERSHIP OF THE NEW PANEL, TO PROVIDE THE PANEL SHALL DISSOLVE WHEN THE MEMBERS' TERMS EXPIRE IN 2012, AND TO PROVIDE RELATED APPELLATE PROCEDURES. (ABBREVIATED TITLE) Senator LEVENTIS asked unanimous consent to remove the minority report on the Bill. There was no objection and the minority report was removed from the Bill and the proper notation was made. THE CALL OF THE UNCONTESTED CALENDAR HAVING BEEN COMPLETED, THE SENATE PROCEEDED TO THE MOTION PERIOD. MOTION FOR SPECIAL ORDER FAILED H. 3418 (Word version) -- Reps. Harrell, Simrill, Crawford, Huggins, Bedingfield, Merrill, G.R. Smith, Erickson, Ballentine, Brady, Chalk, Daning, Delleney, Frye, Gambrell, Hamilton, Harrison, Hearn, Herbkersman, Loftis, Long, Lucas, Nanney, Pinson, Rice, G.M. Smith, Spires, Stringer, Thompson, Viers, Willis, Wylie, T.R. Young, Clemmons, Owens, Parker, Toole, M.A. Pitts, Lowe, Bingham, Umphlett, Sandifer and Edge: A BILL TO AMEND SECTION 7-13-710, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE PRESENTATION OF A PERSON'S PROOF OF HIS RIGHT TO VOTE, SO AS TO REQUIRE THE ELECTOR TO PRODUCE A VALID PHOTO IDENTIFICATION CARD AT THE TIME OF COSTING HIS BALLOT, TO REQUIRE A POLL MANAGER TO COMPARE THE PHOTOGRAPH ON THE REQUIRED IDENTIFICATION WITH THE PERSON PRESENTING HIMSELF TO VOTE AND VERIFY THAT THE PHOTOGRAPH IS THAT OF THE PERSON SEEKING TO VOTE. Senator L. MARTIN moved to make the bill a Special Order. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 26; Nays 17 AYES Alexander Bright Bryant Campbell Campsen Cleary Courson Cromer Davis Fair Grooms Hayes Knotts Leatherman Martin, L. Martin, S. Massey McConnell Mulvaney O'Dell Peeler Rose Ryberg Shoopman Thomas Verdin Total--26 NAYS Anderson Coleman Elliott Ford Hutto Jackson Land Leventis Lourie Malloy Matthews McGill Nicholson Pinckney Scott Setzler Sheheen Total--17 Having failed to receive the necessary vote, the motion to make the Bill a Special Order failed. MOTION FOR SPECIAL ORDER FAILED S. 391 (Word version) -- Senators Ryberg, McConnell, Verdin, Bryant, Cleary, Campsen, Shoopman, Campbell, Rose and Davis: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 41-29-300 SO AS CREATE THE WORKFORCE DEPARTMENT APPELLATE PANEL WITHIN THE DEPARTMENT OF WORKFORCE, TO PROVIDE FOR THE FILLING OF A VACANCY, TO REQUIRE THE PRESENT MEMBERS OF THE SOUTH CAROLINA EMPLOYMENT SECURITY COMMISSION MUST CONSTITUTE THE INITIAL MEMBERSHIP OF THE NEW PANEL, TO PROVIDE THE PANEL SHALL DISSOLVE WHEN THE MEMBERS' TERMS EXPIRE IN 2012, AND TO PROVIDE RELATED APPELLATE PROCEDURES; BY ADDING SECTION 41-29-310 SO AS TO TRANSFER THE WORKFORCE INVESTMENT ACT PROGRAM FROM THE DEPARTMENT OF COMMERCE TO THE DEPARTMENT OF WORKFORCE; TO AMEND SECTION 1-30-10, AS AMENDED, RELATING TO DEPARTMENTS WITHIN THE EXECUTIVE BRANCH OF STATE GOVERNMENT, SO AS TO CREATE THE SOUTH CAROLINA DEPARTMENT OF WORKFORCE WITHIN THE EXECUTIVE BRANCH; TO AMEND SECTION 41-29-10, RELATING TO THE EMPLOYMENT SECURITY COMMISSION, SO AS TO PROVIDE THAT CERTAIN CHAPTERS WITHIN TITLE 41 MUST BE ADMINISTERED BY THE DEPARTMENT OF WORKFORCE AND TO DELETE REFERENCES TO THE EMPLOYMENT SECURITY COMMISSION; TO AMEND SECTION 41-29-20, RELATING TO THE CHAIRMAN, QUORUM, AND FILLING OF A VACANCY ON THE EMPLOYMENT SECURITY COMMISSION, SO AS TO DELETE THE EXISTING LANGUAGE AND TO PROVIDE THE DEPARTMENT OF WORKFORCE MUST BE MANAGED AND OPERATED BY A DIRECTOR APPOINTED BY THE GOVERNOR WITH THE ADVICE AND CONSENT OF THE SENATE, AND THAT THE DIRECTOR IS SUBJECT TO REMOVAL BY THE GOVERNOR AT HIS DISCRETION BY EXECUTIVE ORDER; TO AMEND SECTION 41-29-30, RELATING TO THE APPOINTMENT OF A SECRETARY OF THE EMPLOYMENT SECURITY COMMISSION, SO AS TO DELETE THE EXISTING LANGUAGE AND PROVIDE THE DIRECTOR OF THE DEPARTMENT OF WORKFORCE OR HIS DESIGNEE MUST RECEIVE ANNUAL COMPENSATION AS PROVIDED BY THE GENERAL ASSEMBLY AND OFFICIAL EXPENSES AS PROVIDED BY LAW FOR EXECUTING THE DUTIES AND FUNCTIONS OF THE DEPARTMENT; TO AMEND SECTION 8-17-370, AS AMENDED, RELATING TO EXEMPTIONS FROM THE STATE EMPLOYEE GRIEVANCE PROCESS, SO AS TO INCLUDE EMPLOYEES OF THE DEPARTMENT OF WORKFORCE AMONG THOSE EXEMPTED; TO AMEND SECTIONS 41-27-10, 41-27-30, 41-27-150, 41-27-160, 41-27-190, 41-27-210, AS AMENDED, 41-27-230, 41-27-235, AS AMENDED, 41-27-260, AS AMENDED, 41-27-360, 41-27-370, AS AMENDED, 41-27-380, 41-27-390, 41-27-510, 41-27-550, 41-27-560, 41-27-570, 41-27-580, 41-27-600, 41-27-610, 41-27-620, 41-27-630, 41-27-670, 41-29-40, 41-29-50, 41-29-60, 41-29-70, 41-29-80, 41-29-90, 41-29-100, 41-29-110, 41-29-120, AS AMENDED, 41-29-130, 41-29-140, 41-29-150, 41-29-170, AS AMENDED, 41-29-180, 41-29-190, 41-29-200, 41-29-210, 41-29-220, 41-29-230, 41-29-240, 41-29-250, 41-29-270, 41-29-280, 41-29-290, 41-33-10, 41-33-20, 41-33-30, 41-33-40, 41-33-45, 41-33-80, AS AMENDED, 41-33-90, 41-33-100, 41-33-110, 41-33-120, 41-33-130, 41-33-170, 41-33-180, 41-33-190, 41-33-200, 41-33-210, 41-33-430, 41-33-460, 41-33-470, 41-33-610, 41-33-710, 41-35-10, 41-35-30, 41-35-100, 41-35-110, AS AMENDED, 41-35-115, AS AMENDED, 41-35-120, AS AMENDED, 41-35-125, 41-35-126, 41-35-130, AS AMENDED, 41-35-140, 41-35-330, 41-35-340, 41-35-410, 41-35-420, AS AMENDED, 41-35-450, 41-35-610, 41-35-630, 41-35-640, AS AMENDED, 41-35-670, 41-35-680, AS AMENDED, 41-35-690, 41-35-700, 41-35-710, AS AMENDED, 41-35-720, 41-35-730, 41-35-740, 41-35-750, AS AMENDED, 41-37-20, 41-37-30, 41-39-30, 41-39-40, 41-41-20, AS AMENDED, 41-41-40, AS AMENDED, 41-41-50, 41-42-10, 41-42-20, 41-42-30, AND 41-42-40, ALL RELATING TO VARIOUS DEPARTMENT PROVISIONS, SO AS TO CONFORM THEM TO THE REPLACEMENT OF THE EMPLOYMENT SECURITY COMMISSION WITH THE DEPARTMENT OF WORKFORCE; AND TO REPEAL SECTION 41-29-260 RELATING TO THE ABILITY OF COMMISSIONERS OF THE EMPLOYMENT SECURITY COMMISSION TO FILE OPINIONS OR OFFICIAL MINUTES. Senator SETZLER moved that the Bill be made a Special Order. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 18; Nays 23 AYES Anderson Coleman Elliott Ford Hutto Jackson Land Leventis Lourie Malloy Matthews McGill Nicholson Pinckney Ryberg Scott Setzler Sheheen Total--18 NAYS Alexander Bright Bryant Campbell Campsen Cleary Courson Cromer Davis Fair Grooms Hayes Knotts Martin, L. Martin, S. Massey McConnell Mulvaney Peeler Rose Shoopman Thomas Verdin Total--23 Having failed to receive the necessary vote, the motion to make the Bill a Special Order failed. On motion of Senator L. MARTIN, the Senate agreed to dispense with the Motion Period. HAVING DISPENSED WITH THE MOTION PERIOD, THE SENATE PROCEEDED TO A CONSIDERATION OF BILLS AND RESOLUTIONS RETURNED FROM THE HOUSE. CARRIED OVER S. 202 (Word version) -- Senator Thomas: A BILL TO AMEND SECTION 38-1-20, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO DEFINITIONS USED IN TITLE 38 RELATING TO THE DEPARTMENT OF INSURANCE, SO AS TO AMEND THE DEFINITION OF "ADMITTED ASSETS" TO INCLUDE THOSE ON THE INSURER'S MOST RECENT STATUTORY FINANCIAL STATEMENT FILED WITH THE DEPARTMENT OF INSURANCE PURSUANT TO THE PROVISIONS OF SECTION 38-13-80 INSTEAD OF THOSE ADMITTED UNDER THE PROVISIONS OF SECTION 38-11-100; TO AMEND SECTION 38-9-10, RELATING TO CAPITAL AND SURPLUS REQUIRED OF STOCK INSURERS, SO AS TO CHANGE THE MARKETABLE SECURITIES THAT MAY BE REQUIRED BY THE DIRECTOR OF INSURANCE; TO AMEND SECTION 38-9-20, RELATING TO THE SURPLUS REQUIRED OF MUTUAL INSURERS, SO AS TO CHANGE THE MARKETABLE SECURITIES WHICH MAY BE REQUIRED BY THE DIRECTOR OF INSURANCE; TO AMEND SECTION 38-9-210, RELATING TO THE REDUCTION FROM LIABILITY FOR THE REINSURANCE CEDED BY A DOMESTIC INSURER, SO AS TO CHANGE THE SECURITIES LISTED THAT QUALIFY AS SECURITY; TO AMEND SECTION 38-10-40, RELATING TO THE PROTECTED CELL ASSETS OF A PROTECTED CELL, SO AS TO CHANGE A CODE REFERENCE; TO AMEND SECTION 38-33-130, RELATING TO THE SECURITY DEPOSIT OF A HEALTH MAINTENANCE ORGANIZATION, SO AS TO DELETE THE REQUIREMENT THAT A HEALTH MAINTENANCE ORGANIZATION SHALL ISSUE A CONVERSION POLICY TO AN ENROLLEE UPON THE TERMINATION OF THE ORGANIZATION; AND TO AMEND SECTION 38-55-80, RELATING TO LOANS TO DIRECTORS OR OFFICERS BY AN INSURER, SO AS TO CHANGE A CODE REFERENCE. The Bill was returned from the House with amendments. On motion of Senator THOMAS, the Bill was carried over. THE SENATE PROCEEDED TO THE SPECIAL ORDERS. AMENDMENT PROPOSED, CARRIED OVER BILL REMAINS IN THE STATUS OF SPECIAL ORDER H. 3272 (Word version) -- Reps. Cooper, Merrill, Erickson, Herbkersman, Chalk, Duncan, Long, Sottile, Daning, Lowe, Bowen, Harrison, Horne, A.D. Young, Limehouse, R.L. Brown, Clemmons, Edge and Wylie: A BILL TO AMEND SECTION 12-37-3140, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO DETERMINING THE FAIR MARKET VALUE OF REAL PROPERTY FOR PURPOSES OF THE SOUTH CAROLINA REAL PROPERTY VALUATION REFORM ACT, SO AS TO POSTPONE THE IMPLEMENTATION OF THE TRANSFER VALUE OF A PARCEL OF REAL PROPERTY UNIMPROVED SINCE THE LAST COUNTYWIDE REASSESSMENT PROGRAM UNTIL THE TIME OF IMPLEMENTATION OF THE NEXT COUNTYWIDE REASSESSMENT PROGRAM AND TO REQUIRE THE FIFTEEN PERCENT LIMIT ON INCREASES IN VALUE TO BE CALCULATED SEPARATELY ON LAND AND IMPROVEMENTS; TO AMEND SECTION 12-37-3150, AS AMENDED, RELATING TO THE TIME AN ASSESSABLE TRANSFER OF INTEREST OCCURS, SO AS TO REVISE THE PENALTY FOR FAILURE TO PROVIDE NOTICE OR FAILURE TO PROVIDE ACCURATE NOTICE TO THE ASSESSING AUTHORITY OF BUSINESS ENTITY TRANSFERS; TO AMEND SECTION 12-43-220, AS AMENDED, RELATING TO THE CLASSIFICATION AND VALUATION OF PROPERTY FOR PURPOSES OF THE PROPERTY TAX, SO AS TO PROVIDE RESIDENTIAL REAL PROPERTY HELD IN TRUST DOES NOT QUALIFY AS A LEGAL RESIDENCE UNLESS A NAMED INDIVIDUAL BENEFICIARY UNDER THE TRUST OCCUPIES THE RESIDENCE AS THAT NAMED BENEFICIARY'S LEGAL RESIDENCE AND THAT INDIVIDUAL BENEFICIARY'S NAME APPEARS ON THE DEED TO THE RESIDENCE AND REQUIRE SOCIAL SECURITY NUMBERS OF APPLICANTS FOR THE LEGAL RESIDENCE ASSESSMENT RATIO; AND TO AMEND SECTION 40-60-35, RELATING TO CONTINUING EDUCATION REQUIREMENTS FOR ASSESSORS, SO AS TO REVISE THE REQUIREMENT. The Senate proceeded to a consideration of the Bill, the question being the adoption of the amendment proposed by the Committee on Finance. PRESIDENT Pro Tempore PRESIDES At 11:44 A.M., Senator McCONNELL assumed the Chair. Amendment No. P-2A Senators ALEXANDER and HAYES proposed the following Amendment No. P-2A (3272FIN005): Amend the committee amendment, as and if amended, by striking all after the enacting words and inserting: / SECTION 1. A. Article 25, Chapter 37, Title 12 of the 1976 Code is amended by adding: "Section 12-37-3135. (A)(1) When a parcel of real property and improvements thereon subject to the six percent assessment ratio provided pursuant to Section 12-43-220(e) and which is currently subject to property tax undergoes an assessable transfer of interest after property tax year 2009, there is allowed an exemption of an amount of the increase in fair market value of that parcel as determined in the assessor's appraisal at the time of the assessable transfer of interest over the fair market value of the parcel as previously carried on the books of the property tax assessor equal to the percentages provided pursuant to item (2) of this subsection. The fair market value to which the cap on increases in fair market value imposed pursuant to Section 12-37-3140(B) applies is the fair market value as it may be reduced by the exemption allowed by this section. The exemption allowed by this section applies at the time the value as determined by an assessable transfer of interest first applies. (2)(a) Property tax year of assessable Amount of increase transfer of interest of fair market value exempted 2010 100 percent 2011 60 percent After 2011 20 percent (b) If countywide reassessment values are implemented for the year in which the assessable transfer of interest occurs, the fair market value to which the exemption applies is the fair market value of the parcel as determined in that reassessment and as that value may be limited pursuant to Section 12-37-3140(B). (B) The exemption allowed by this section continues to apply until the parcel next undergoes an assessable transfer of interest. However, the parcel remains subject to changes in value as determined in a periodic countywide appraisal and equalization program and the limit on the increases in such values pursuant to Section 12-37-3140(B). If a parcel undergoes a subsequent assessable transfer of interest, the owner of the parcel may claim any exemption remaining allowed by this section. (C) The exemption allowed by this section does not apply to the fair market value of additions or improvements made to the parcel not previously subject to property tax." B. Section 12-37-3140(A)(1)(b) of the 1976 Code, as last amended by Act 57 of 2007, is further amended to read: "(b) subject to any exemption allowed pursuant to Section 12-37-3135, December thirty-first of the year in which an assessable transfer of interest has occurred;" SECTION 2. A. Section 12-37-3150(B) of the 1976 Code, as last amended by Act 57 of 2007, is further amended to read: "(B) An assessable transfer of interest does not include: (1) transfers not subject to federal income tax in the following circumstances: (a) 1033 (Conversions-Fire and Insurance Proceeds to Rebuild); (b) 1041 (Transfers of Property Between Spouses or Incident to Divorce); (c) 351 (Transfer to a Corporation Controlled by Transferor); (d) 355 (Distribution by a Controlled Corporation); (e) 368 (Corporate Reorganizations); or (f) 721 (Nonrecognition of Gain or Loss on a Contribution to a Partnership). Number references in the above subitems are to sections of the Internal Revenue Code of 1986, as defined in Section 12-6-40; (2) a transfer of that portion of property subject to a life estate or life lease retained by the transferor, until expiration or termination of the life estate or life lease; (3) a transfer through foreclosure or forfeiture of a recorded instrument or through deed or conveyance in lieu of a foreclosure or forfeiture, until the redemption period has expired; (4) a transfer by redemption by the person to whom taxes are assessed of property previously sold for delinquent taxes; (5) a conveyance to a trust if the settlor or the settlor's spouse, or both, convey the property to the trust and the sole present beneficiary of the trust is the settlor or the settlor's spouse, or both; (6) a transfer for security or an assignment or discharge of a security interest; (7) a transfer of real property or other ownership interests among members of an affiliated group. As used in this item, 'affiliated group' is as defined in Section 1504 of the Internal Revenue Code as defined in Section 12-6-40. Upon request of the applicable property tax assessor, a corporation shall furnish proof within forty-five days that a transfer meets the requirements of this item. A corporation that fails to comply with this request is subject to a civil penalty as provided in Section 12-37-3160(B); (8) a transfer of real property or other ownership interests among corporations, partnerships, limited liability companies, limited liability partnerships, or other legal entities if the entities involved are commonly controlled. Upon request by the applicable property tax assessor, a corporation, partnership, limited liability company, limited liability partnership, or other legal entity shall furnish proof within forty-five days that a transfer meets the requirements of this item. A corporation, partnership, limited liability company, limited liability partnership, or other legal entity that fails to comply with this request is subject to a civil penalty as provided in Section 12-37-3160(B); or (9) a transfer of an interest in a timeshare unit by deed or lease; or (10)(a) a conveyance by deed, distribution under a will, or by intestate succession to a lineal descendent of the grantor or decedent; (b) a conveyance to a trust and the sole present beneficiary or beneficiaries of the trust are lineal descendents of the settlor. (11) a transfer of an undivided, fractional ownership interest in real estate in a single transaction or as a part of a series of related transactions, if the ownership interest or interests conveyed, or otherwise transferred, in the single transaction or series of related transactions within a twenty-five year period, is not more than fifty percent of the entire fee simple title to the real estate; (12) a transfer to a single member limited liability company, not taxed separately as a corporation, by its single member or a transfer from a single member limited liability company, not taxed separately as a corporation, to its single member, as provided in Section 12-2-25(B)(1); (13) a conveyance, assignment, release or modification of an easement, including but not limited to: (a) a conservation easement, as defined in Chapter 8 of Title 27; (b) a utility easement; or (c) an easement for ingress, egress, or regress; (14) a transfer or renunciation by deed, release, or agreement of a claim of interest in real property for the purpose of quieting and confirming title to real property in the name of one or more of the existing owners of the real property or for the purpose of confirming or establishing the location of an uncertain or disputed boundary line; or (15) the execution or recording of a deed to real property for the purpose of creating or terminating a joint tenancy with rights of survivorship, provided the grantors and grantees are the same." B. Section 12-37-3150(A)(8) of the 1976 Code is amended to read: "(8) a transfer of an ownership interest in a single transaction or as a part of a series of related transactions within a twenty-five year period in a corporation, partnership, sole proprietorship, limited liability company, limited liability partnership, or other legal entity if the ownership interest conveyed is more than fifty percent of the corporation, partnership, sole proprietorship, limited liability company, limited liability partnership, or other legal entity. This provision does not apply to transfers that are not subject to federal income tax, as provided in subsection (B)(1), including, but not limited to, transfers of interests to spouses. The corporation, partnership, sole proprietorship, limited liability company, limited liability partnership, or other legal entity shall notify the applicable property tax assessor on a form provided by the Department of Revenue not more than forty-five days after a conveyance of an ownership interest that constitutes an assessable transfer of interest or transfer of ownership under this item;" C. This section applies for real property transfers after 2009. SECTION 3. Section 6-1-320(A), as last amended by Act 116 of 2007 of the 1976 Code, is further amended to read: "(A)(1) Notwithstanding Section 12-37-251(E), a local governing body may increase the millage rate imposed for general operating purposes above the rate imposed for such purposes for the preceding tax year only to the extent of the increase in the average of the twelve monthly consumer price indices for the most recent twelve-month period consisting of January through December of the preceding calendar year, plus, beginning in 2007, the percentage increase in the previous year in the population of the entity as determined by the Office of Research and Statistics of the State Budget and Control Board. If the average of the twelve monthly consumer price indices experiences a negative percentage, the average is deemed to be zero. If an entity experiences a reduction in population, the percentage change in population is deemed to be zero. However, in the year in which a reassessment program is implemented, the rollback millage, as calculated pursuant to Section 12-37-251(E), must be used in lieu of the previous year's millage rate. (2) There may be added to the operating millage increase allowed pursuant to item (1) of this section any such increase, allowed but not previously imposed, for the three property tax years preceding the year to which the current limit applies." SECTION 4. A. Section 12-37-251(E) of the 1976 Code is amended to read: "(E) Rollback millage is calculated by dividing the prior year property tax revenues taxes levied as adjusted by abatements, additions, and nulla bona returns by the adjusted total assessed value applicable in the year the values derived from a countywide equalization and reassessment program are implemented. This amount of assessed value must be adjusted by deducting assessments added for property or improvements not previously taxed, for new construction, and for renovation of existing structures, and assessments attributable to increases in value due to an assessable transfer of interest." B. This section takes effect for rollback millage calculated for property tax years beginning after 2009. SECTION 5. (A) There is created the Index of Taxpaying Ability Study Committee. The committee shall be composed of eight members, all appointed pursuant to subsection (B). The committee shall examine the index of taxpaying ability and its relationship to Education Finance Act resources available to the individual school districts in support of the education foundation program required by the State. The committee shall also examine the manner in which the index is calculated and the impact of this act and other property tax measures on the calculation. (B) The committee shall be composed of: (1) four members appointed by the President Pro Tempore of the Senate; and (2) four members appointed by the Speaker of the House of Representatives. (C) No later than January 1, 2011, the committee shall prepare and deliver a report and recommendation to the Chairman of the Senate Finance Committee, the Chairman of the House Ways and Means Committee, the Chairman of the Senate Education Committee, and the Chairman of House Education and Public Works Committee. (D) Members of the study committee shall serve without compensation for per diem, mileage, and subsistence. SECTION 6. Except where otherwise provided, this act takes effect upon approval by the Governor. / Renumber sections to conform. Amend title to conform. Senator ALEXANDER explained the amendment. PRESIDENT PRESIDES At 12:47 P.M., the PRESIDENT assumed the Chair. Senator ALEXANDER explained the amendment. With Senator ALEXANDER retaining the floor, Senator LARRY MARTIN asked unanimous consent to make a motion to carry over the Bill. There was no objection and the Bill was carried over in the status of Special Order, with Senator ALEXANDER retaining the floor. Senator DAVIS asked unanimous consent to make a motion to take up S. 517 for immediate consideration. There was no objection. AMENDMENT PROPOSED, CARRIED OVER S. 517 (Word version) -- Senators Davis, Bright, Shoopman, Ryberg, Bryant, Mulvaney, Fair, Peeler, Rose, Campsen and S. Martin: A JOINT RESOLUTION TO PROVIDE THAT THE GENERAL ASSEMBLY SHALL NOT AUTHORIZE A STATE AGENCY, DEPARTMENT, OR ENTITY TO INCREASE OR IMPLEMENT A FEE, PENALTY, OR FINE IN THE STATE GENERAL APPROPRIATIONS ACT OR OTHER ACTS SUPPLEMENTAL TO THAT ACT; TO PROVIDE THAT ANY INCREASE OR IMPLEMENTATION OF A FEE OR FINE MAY ONLY BE AUTHORIZED BY AN ACT SEPARATE FROM AN APPROPRIATIONS ACT; TO PROVIDE THAT NO STATE AGENCY, DEPARTMENT, OR ENTITY MAY INCREASE OR IMPLEMENT BY REGULATION OR ADMINISTRATIVE ACTION A FEE, PENALTY, OR FINE; AND TO PROVIDE EXCEPTIONS FOR INTERNAL CHARGES BETWEEN STATE AGENCIES AND FOR FEES, INCLUDING TUITION, IMPOSED BY SCHOOLS AND COLLEGES ON STUDENTS; AND TO PROVIDE FOR THE EXPIRATION OF THIS JOINT RESOLUTION JULY 1, 2010, UNLESS REAUTHORIZED BY LAW. The Senate proceeded to a consideration of the Bill, the question being the third reading of the Resolution. Senator DAVIS explained the Resolution. Amendment No. 1 Senator LEVENTIS proposed the following Amendment No. 1 (517FIN006): Amend the joint resolution, as and if amended, by adding an appropriately numbered SECTION to read: / SECTION ___. (A) There is established the Other Funds Study Committee to review, study, and make recommendations concerning agency earmarked and restricted fund accounts to include a review of all sources of other fund revenue retained and expended for agency operations. (B) The study committee must be composed of ten members. Notwithstanding Section 8-13-770, the committee shall be composed of: (1) five members of the Senate appointed by the Chairman of the Senate Finance Committee; and (2) five members of the House of Representative appointed by the Chairman of the House Ways and Means Committee. (C) The study committee shall make a preliminary report of its findings and recommendations to the General Assembly no later than January 15, 2011, at which time the study committee must be abolished. The study committee may make recommendations it considers appropriate including, but not limited to, licensing and regulation of debt collection and recovery agencies. / Renumber sections to conform. Amend title to conform. Senator DAVIS explained the amendment. Senator LEVENTIS explained the amendment. On motion of Senator McCONNELL, with unanimous consent, the Resolution was carried over. EXECUTIVE SESSION On motion of Senator McCONNELL, with unanimous consent, the Senate agreed to go into Executive Session and, upon lifting of the veil of secrecy, stand in recess. On motion of Senator McCONNELL, the seal of secrecy was removed and the Senate stood in recess. RECESS At 1:30 P.M., on motion of Senator McCONNELL, the Senate receded from business until 6:45 P.M. NIGHT SESSION The Senate reassembled at 6:45 P.M. and was called to order by the PRESIDENT. Committee to Escort The PRESIDENT appointed Senators JACKSON, KNOTTS, PEELER, CAMPBELL and McGILL to escort the Honorable Marshall Clement (Mark) Sanford, Governor of South Carolina, and members of his party to the House of Representatives for the Joint Assembly. RECESS At 6:55 P.M., on motion of Senator McCONNELL, the Senate receded from business for the purpose of attending the Joint Assembly. JOINT ASSEMBLY At 7:00 P.M., the Senate appeared in the Hall of the House. The PRESIDENT of the Senate called the Joint Assembly to order and announced that it had convened under the terms of H. 4289, a Concurrent Resolution adopted by both Houses. The Honorable Marshall Clement (Mark) Sanford and members of his party were escorted to the rostrum by Senators JACKSON, KNOTTS, PEELER, CAMPBELL and McGILL and Representatives G. Brown, Stringer, A.D. Young, T.R. Young and Gilliard. The PRESIDENT of the Senate introduced the Honorable Mark C. Sanford, Governor of the State of South Carolina. The Governor addressed the Joint Assembly as follows: 2010 State of the State Address Governor Mark Sanford Mr. Speaker, Mr. PRESIDENT, Ladies and Gentlemen of the General Assembly, Constitutional Officers and my fellow South Carolinians: It's an honor to be with you tonight to deliver my view on the state of our State, but as I've done in the past, I'd first ask that we pay tribute to the South Carolinians who died fighting in the Middle East and Afghanistan over the last year. Their deaths are a reminder to every one of us how short and fragile life can be - and beg of us the larger question of what are we doing to both honor their sacrifice, and to live the gift of life each of us has been granted? Their service is also a reminder to all of us, particularly in these trying economic times, of how important it is that we look for ways to serve others. There are little things that we can do here that can make a big difference. For instance, as one of their initiatives this year Seacoast Church decided to make a difference with a community in Kenya where one of the biggest obstacles to life comes in what we take for granted - clean water. Each member of the congregation was given a bottle of what looked to be dirty water and the challenge to empty it and refill it with coins saved by simply forgoing soft drinks or coffee and instead drinking water over the couple of weeks leading up to Christmas. Fifty cents here and seventy-five cents there doesn't seem a big service or sacrifice, but cumulatively enabled the church to provide five water purification machines through Water Missions International in Charleston that will give 15,000 people clean drinking water. Or take more locally what Wayne Fields and his team at the Oliver Gospel Mission are doing in the lives of homeless men just a couple of blocks from where we are now. If every person in this State volunteered one day a month at institutions like this, it would dwarf anything that government might do in the way of social service. So here in the New Year let's all recognize that many families across our State and nation are indeed hurting in these economic times - that there is a lot of need out there - in some cases unimaginable levels of need as we see the tragedy of Haiti unfolding - and it all begs one question. Can we follow these soldiers' examples in looking for ways to serve? In fact, under the category of service from men and women in this Chamber, Representative Ted Pitts is bound for Afghanistan. His wife, Christina - and father Ed - are here and I'd ask you not only offer a round of applause for his service to our country, but that you match it with a prayer for his safety. Finally, the fact that each of the soldiers I alluded to earlier died in service to their country is again a reminder that freedom isn't free. This year's list of heroes is as follows: Private First Class Jason Watson Staff Sergeant Ralph Futrell Corporal Ryan McGhee Specialist Abraham Wheeler III Lance Corporal Christopher Fowlkes Specialist Demetrius Void Specialist Gary Gooch, Jr. Private First Class Geoffrey Whitsitt While on the topic of thanking I have historically asked a state worker, someone in the private sector, and often times the First Lady - to stand while we thanked them for their different efforts. Tonight, for one last time, let me continue that tradition. First, I'd like to recognize a state worker who is representative of so many who do their work without recognition. Barry Franco works at Trident Tech down in North Charleston and will train workers to take on roles at the new Boeing plant. Will you join me in thanking him for that important work - and for representing those who work in state government? We've also been joined tonight by Maxine White. She is an artist in the Upstate and a reminder of the creative talents and the innovative spirit found in the private sector. She reminds me of the ways in which every one of us can make a difference in South Carolina if we so choose. We don't have to wait for a government program - we can just do it - as she does, and so will you please join me in welcoming her as well? Never losing the taxpayers' perspective, let me underscore that the savings Jenny created at the Lace House, the Waring House, and the Mansion, is a reminder of how every one of us tied to government can follow the lead of working South Carolinians in being creative in finding ways to do more with less. Doing more with less is what families across our State are doing everyday - and those of us who work in government should find ways to honor these daily decisions being made by the people who pay for government. So with all that being said - the State of our State is that we have both enormous challenges and opportunities before us. Our economic challenges for instance are in some ways historic in nature, but with every great challenge in life comes an opportunity. The opportunity in this moment is that many changes are possible in tough economic times that would not be possible in good times. Few people, few companies, few states and few nations change until they have to. We have an environment for change we have never had in the last seven years I have been with you. Some things are going to change by virtue of the world economy whether we like them or not, and in much of this, the question will be whether or not we make the change - or change simply happens to us. For the sake of future generations I think it's important we be as deliberate as possible in making changes I believe will accrue to the people of this State. I ask for the people of South Carolina to make loud, but respectful, noise for change. And I need to be a better messenger because if the people push for these changes, and we're not too tone deaf in hearing, they will happen - if the people don't, they won't. As the people need to do their part, we need to do ours. Not only in my conversations with the public, but in my work with you, I need to be a humble messenger, and take joy in the fact that our Maker can use imperfect people in all walks of life. This very imperfection underscores the importance of both the grace of God and the grace of others. Though at times we may try to cover it or forget it, the imperfections of any of us underscore the degree to which we really are of the people, and by the people - and my simple hope this year is that we be for the people in the results we produce. So it is with that spirit that I hope we can come together. It doesn't mean we won't have our differences. We always will as we come from differing political ideologies, parties, parts of this State and more, but we can bridge them by committing to work alongside each other to make meaningful changes in this legislative session. Toward that end, this year we decided to narrow our focus to that which we believed was specific, measurable and achievable in this term. I still have strong opinions on the need to do something about unfunded liabilities at the state level, on the need for school choice, on capping higher education costs and more, but this final year we want to suggest just a few things in the hope this focus by you, me and the people more greatly insures their passage. Accordingly, could we make this the year that we add just a couple of tools to the tool kit of economic development and jobs, that we put in place spending limits so that we avoid otherwise inevitable harm to both those who pay for government and those served by it - and finally could we make just three changes to the structure of our government that will pay tremendous dividends over time in both the efficiency and the effectiveness of South Carolina state government? Boeing's announcement this fall was indeed great news for the 3800 permanent jobs, 2000 construction jobs - and supplier and support jobs that will come with it. It is the single largest economic development announcement in the history of the State - and it has been named the economic deal of the year in the country. It is again an example of the success that can come our way when we work together - as so many at all levels of government, and the private sector, worked collaboratively on this project. But as great as those efforts were, if our soil conditions for the germination of the business that they would plant here in South Carolina were not better than other choices available to them, they wouldn't have come here. It's a reminder of how every one of us need to work to improve the business soil conditions of this State each year, and the item most immediately before us on this front is long overdue reform to the Employment Security Commission. This change is the tool we could add this year to the tool kit of job growth in South Carolina. The Employment Security Commission is yet another separate island of government in South Carolina, and it in some ways seemed accountable to no one as their trust fund was bled from a positive of $500 million to a negative of$800 million. If nothing is done here, taxes will go up on every small, mid-sized, and large business in our State - and I believe that tax increases would hurt job creation in South Carolina. I am joined in that belief by Kenny Bingham and Greg Ryberg - and I thank both of them for leading the charge this year on ESC Reform. Separate islands of government are not only bad for the taxpayer and harmful to the business soil conditions of our State - they also in this case hurt those searching for a job. By linking the Employment Security Commission to the efforts of the Department of Commerce in the creation of a Department of Workforce, the ESC would move from in too many ways simply processing claims for those unemployed to more actively coordinating with the Department of Commerce and others to connect those seeking jobs with job opportunities. We continue to believe that there are other things we could do to improve the economy like raising our lowest-in-the-nation cigarette tax and swapping this with an equal dollar cut to the corporate income tax. The net effect of the change we have proposed here is that South Carolina's ranking on the state business tax climate index would move from 25th to the 6th most competitive state in the country - and changes like this would produce jobs. But regardless of these merits, in picking just one legislative change that would maximize economic prospects this year - it is ESC reform, and I ask for its passage. Concurrent with these legislative efforts, I am committed to working with each of you, those spearheading local economic development efforts - and the Department of Commerce - to maximize every possibility in recruiting jobs and investment to our State. The success that came in Boeing's landing in Charleston is a reminder of how South Carolina can win in these economic development contests. Secondly, can we make this the year we get off the spending and budget roller coaster? To do so, we ask that the General Assembly enact spending limits. In fairness, measures aimed in this direction have passed the House several times, and once looked to come close in the Senate. Senator McConnell has committed to constitutional change as the most lasting way to make this concrete, and I applaud those efforts. I would ask for your passage of a Bill that limits government's growth to population plus inflation, and then allocates everything beyond this to first paying down our state's huge unfunded liabilities - which now amount to more than $20 billion - and when this is done, to then either set money aside for a rainy day or return it to the taxpayer. The importance of addressing spending and our unfunded liabilities can't be underscored enough. It is the reason I got into politics, and I realize my convictions on these things can get old, but history has consistently shown how governments spend their way into oblivion - and pain for the people they supposedly represent. As a starting point I would simply ask you look at what we proposed in our budget in addressing unfunded liabilities. On spending limits, if your political persuasion is from the right, then they make sense for the way that they protect the taxpayer in the good times. They help to avoid money going into wants and wishes rather than core needs - as when an additional$1.5 billion comes into our state government as it did just three years ago. If your political persuasion is from the left, spending limits make sense for the way that they avoid us cutting past muscle and right into bone when times aren't so good. Financial restraint is in many ways impossible without them, because as I've said repeatedly this fall at Rotary Club talks across the State, it's as if over the last seven years' worth of budgets we've been having parallel universe conversations, much like that described in the book, Men Are from Mars, Women Are from Venus. On the one hand I was over here pointing out that our spending was in no way sustainable. I pointed that out in each of the previous States of the State and literally a thousand other places as well. Just last year, I noted I didn't have a crystal ball on economic trends; I simply heard from a lot of South Carolinians on common sense principles that they believed ought to apply to government. Trees don't grow to the sky, winter follows summer, and economies go through cycles - these things represent thinking that has been around for a very long time. Unfortunately as a nation, and as a state government, this idea had been forgotten by too many for too long. The unsustainable debt march we were on has now come to an end, and so as a nation, and again by extension as a state, we will face a tremendous de-leveraging. I said then, and still believe, there is no way to avoid this reality. In last year's State of the State I said that anybody who said that this economic slowdown would be short-lived was missing what I was hearing across the State - and that I believed that anyone who suggested that things wouldn't get a whole lot worse before they got better had missed how high the forest of debt and spending had indeed grown over these 20 years. Unfortunately, I've been proven right - but in fairness to every one of you as legislators that was not the decision most immediately before you as each budget year approached. I say this because the reality that we all know of any dollar that comes into the political system is not whether or not it will be spent, but where it will be spent. Whether the spending of that dollar was sustainable or not becomes a purely intellectual exercise for you at budget time when the question before each one of you was at that point, "Do I fight for my district - and some of that money coming to the people that I serve - or do I simply let others spend it?" I don't begrudge any one of you for doing that which you were elected to do in trying to watch out for the people of your district, and so if we do nothing we will be left at the impasse that we have found ourselves at for seven years. This means future governors - if they choose to try and hold the line on spending will simply burn bridges and large amounts of political capital with less than commensurate results - or they may punt on the issue as many have done with consequential results to the taxpayer. Doing nothing will leave every one of you in the less than ideal position of voting for spending that you know is unsustainable as the only way of getting a portion of that money back to your district and the people you represent. Doing nothing would perpetuate the peaks and valleys approach to government spending that we have seen for far too long. Doing nothing locks in a spending track that can almost guarantee future tax increases. People are hurting in our State, and they rightly expect action to be taken. But what we do in addressing the jobs and spending issues is very important for the way unsustainable spending can bring even greater harm to the economy and job prospects. Spending money we don't have will never be the key to economic prosperity - this is true of bailouts from Washington just as it is true of our own approach to spending in this State. So we have a second opportunity in these trying economic times - and that is to pass spending limits. I don't know when it will ever happen if it doesn't happen in this kind of budget year - and so I join thousands across our State in asking that you pass meaningful and real spending limits this year. While on this topic of spending there is one other thing we need to do - make our voices heard in Washington. Everyone well knows my opinions on the fallacy of stimulus money - and my belief that lasting jobs and economic growth can never come from a government bailout. I won't restate my beliefs on how damaging those efforts are to future generations, the American dollar and the long term viability of the American and South Carolina economies. But there is a new threat to each one of us, the dollar and the financial stability of this country as debts are spiraling in Washington. So-called healthcare reform will bring immediate damages to our State and nation, as for instance in South Carolina alone it would expand South Carolina Medicaid roles by over 500,000 people - costing our state's taxpayers more than $1 billion over the next ten years. It would also mean Medicaid would grow to almost 40 percent of the state budget in five years, and in so doing effectively place about one-third of the state's population on Medicaid. All this means is that unless people across this State really make their voices heard, significant cuts to other parts of state government - or substantial raises in taxes - are coming our way. If you take but one pearl from this talk it is that now is the time to make your voice heard - whether in correcting the path Washington is now on, or in bettering our State. Finally, in this last year of office I backed away from some of our more ambitious proposals in changing our government structure - and by extension the way things are done in Columbia - and instead we're just asking for three changes that we, again, believe will be specific, measurable and achievable in moving us toward a more balanced - and thereby more efficient and effective state government. It is important to remember that government in South Carolina costs about 140 percent of the national average. Our governmental structure leads in mighty ways to this cost and this is something that hurts business and job prospects - as well as the taxpayer. Three things that we believe would move us in a different direction are a Department of Administration, having the Governor and Lt. Governor run together on a ticket and allowing the people to decide whether a host of constitutional officers should be elected or appointed. Last year, a Department of Administration bill passed the House unanimously before stalling in the Senate. Its premise is that we don't need to continue to be the only state in the country that does not allow its Governor to administer the laws administered by the other 49 Governors in the United States. You would not be giving this power to me; I'm gone in 11 months - but for the sake of good government please give this power to whomever follows me, whether they are Republican or Democrat - male or female - please give them the tools by which they may succeed or fail, and then hold them accountable. Two, put the Governor and Lt. Governor together as a team. To me it makes no sense to have a governor elected by the people, and yet have his first check on delivering promises made by, not the legislative or judicial branches of government - but the Lieutenant Governor, who in our State could be of opposite political persuasion and party. Would it make any sense to have the President and Vice President in Washington elected with opposing agendas and wanting to go in opposition directions? I don't believe it would, and I respectfully ask we make this change. Finally, can we let the people of South Carolina decide on whether a host of constitutional officers should be appointed rather than elected. We are for instance the only state in the country where the Adjutant General is elected. We are not asking that any of you take a position for or against change in any of these changes, just that you let the people of South Carolina decide. We are asking you do what was done at the time of the lottery when many in this chamber said they were against a lottery - but felt it was such an important issue that they would vote to allow the people to decide. If this reasoning can be good enough for a lottery, can it be good enough for the taxpayers chance to make decisions on our constitutional framework? This is the case particularly in South Carolina when that framework was handed to us in the 1800's based on fears of black men in politics that are wrong and long outdated. These truths on the need for change have been recognized by Democrats like Anton Gunn or Vincent Sheheen along with Republicans like Garry Smith or Tom Young - and I think it is vital we all do something this year about these truths. So these are our simple requests for this legislative term. I ask for your work in their passage, and hope that you will call on me as I am committed to doing anything in your respective districts that might help toward that end. I am tempted to end here, but as this is my last State of the State let me add a few other words of thanks, as together we have effected some changes over these last seven years that have made, and will continue to make, a difference in people's lives. In fact when I ran for this office eight years ago, I pledged to work to make South Carolina a better place to call home. While this work is never done, and never complete in today's global competition for jobs, capital and way of life, we have made changes in each of the areas talked about in that now distant campaign. We talked about the need to improve the chance for a job, the chance to better what we brought home in building a life or a family, how even a job was key to using one's talents, and therefore how important it was that we do things each year to make our business climate more competitive. That's why I thank you for passing the first cut to the marginal income tax rate in South Carolina's history. As a result of this change,$292 million has already stayed in the hands of small business people that would have gone to government. It has made a difference in how many of those small businesses could add a job to their payroll - or even survive in these economic times. I thank you for passing the largest recurring tax cut in South Carolina history. Already $260 million has stayed in the hands of taxpayers and for the difference this will make in their lives - I again thank you. I thank you for passing the first tort reform bill of its kind. That bill took us off the list of "judicial hell holes" and is the kind of change instrumental to bettering our state's business climate and the prospect of jobs. I thank you for passing our state's first reform to the workers' compensation system. A change like that one is also just the kind of thing that a business from afar looking at South Carolina takes into consideration. And I thank you for passing things like the small business healthcare bill. The byproduct of these changes is in part evident in the record setting more than$4 billion in capital investment brought to our State last year, which followed the year before in record setting investment. It is borne in the more than $19 billion invested in our State over the last seven years, or the 64,000 more people working today than in 2003. These job numbers are not where we would like them to be, but it is important to remember that we rank 14th in the nation in employment growth - and 9th in labor force growth - which means a lot of people are voting with their feet in leaving the Northeast or Upper Midwest and coming to South Carolina to seek opportunity. It is evident in the decision of companies like Boeing, Google, Starbucks or Adidas to put down roots in South Carolina. It is evident in the expansions of companies like BMW, GE Aviation or Husqvarna. It is evident in the efforts of unsung heroes out working to grow and sustain small business like Southern Aluminum in Clinton, JVS Roofing in Simpsonville, or Elliott Sawmilling in Estill. We talked about changing the way Columbia works, and once again we haven't reached the promised land on where we would like to end, but we have made real changes and for your efforts I thank you. For too long too many votes were never recorded in these chambers and there can be no accountability without transparency. Thank you for what all of you did to change this. We now have on-line transparency to allow a taxpayer to see more directly how their money is spent in state government. We ended the Competitive Grants program. We ended pass-throughs and bobtailing - and I thank you here too. When even the Ethics Committee said it couldn't be done back in 2005, we found a way to begin on-line disclosure so that citizens could better see where money was coming from and going to in campaigns. We passed campaign finance reform. It had been vetoed twice during the previous administration, and its passage ended the Wild West practice that had prevailed in South Carolina that allowed unlimited and undisclosed amounts to go to a political party or caucus. Thank you for passing steps toward improving governmental structure that in turn yields better results. The Department of Transportation had not been changed since 1919, and changes there mean more money will go to the place where congestion and need exist rather than to the places of few cars but greater political power. You know the DMV story and its impact in people's lives. We only have so much time here on earth and you can spend it doing something you love or instead wait in a DMV line. The change you made has meant that wait times have on average gone from 66 minutes to 16. That kind of time matters, and so accordingly I'd thank the staff at DMV that has been remarkable in the way they have embraced and fostered change. We talked about improving quality of life. For me and so many others this is in part measured in the look and feel of this State, and that is why I am particularly proud of the fact that more land has been set aside during this governorship than any other in state history. These 153,000 acres will pay dividends economically in attracting and retaining people in our State, and in giving them a glimpse of the splendor that keeps so many of us here. Quality of life begins with life itself, and so I want to thank each of you for your work in passing DUI reforms. Over the course of this administration fatalities due to drinking and driving have decreased by about one-third, and this means over 100 people each year continue in this gift called life. That would not have been the case without these changes. Did you know we passed one of the toughest immigration reform bills in the country? It was based on the simple notion that if you are going to have rules we all ought to play by those rules, and has made a real difference for families across this State. If you live on, or near, the coast, some would define quality of life as being able to get insurance for your home. The Coastal Insurance Bill protected taxpayers in the Midlands and Upstate from paying the bill for storm damages as is now the case in the state government-run Florida program. Just as when we walk into Walmart they never give us the exact price we would love - we still get a better price than if there was no competition. This bill has allowed the private sector and the marketplace to work. We talked about improving education. As a result of all that back and forth on this administration's core belief that parents ought to have every opportunity to decide what school works best for their child - for a choice - more have been offered. We now have virtual schools and classrooms that allow someone in rural South Carolina to be taught by an expert in a different corner of the State. We passed a statewide charter school bill that was the first of its kind in the nation. I don't believe we would have gotten that bill through - or other choices that now come in education - without the larger debate on full-scale choice in education. Whether in the additional$2.7 billion that has gone to education above and beyond the level of funding that came at this administration's start in 2003 - or with the Education and Economic Development Act that offered a tech-prep choice to students - or in physical fitness programs offered as a result of the South Carolina Health and Fitness Act - or even in outright full choice in education now offered in early childhood education, I know that a long list of people deserve credit for work here that is making a difference in the minds of students across our State. Finally, I said I'd watch out for the taxpayer. I have always believed that money was a close proxy for freedom - and freedom at the end of the day is what the American political system was designed to perpetuate. It is economic freedom that unleashes the very initiative that drives our economy. It is freedom that empowers us to strive toward our respective dreams that individually define what "the pursuit of happiness" means to each one of us. Yet when you spend a third, or half, your year working just to pay taxes, you are, in essence, indentured to government part of that time. And we ought to always get to the heart of what drives taxes - what we spend in government. As mentioned earlier, this conviction is to the core. At times I wasn't as diplomatic as I should have been in expressing my thoughts on this - but the good news is that as a result of all that fussing and fighting - the taxpayer was recognized at the table of our government in ways that would have not been the case. Though the pigs are still remembered, what is forgotten about that chapter was the way we faced a $155 million unconstitutional deficit. We set precedent back then for the next 100 years on the sanctity of our balanced budget in this State - and for your work I thank you. Did you know we are the second state in the nation to offer Health Savings Accounts for all state workers and retirees, and with this health and budget initiative millions will be saved? Did you know those changes we instituted at the front end of this administration with Corrections producing their own eggs and growing their own corn for grits, Commerce selling jets, PRT consolidating programs - millions more have been saved - and will continue to be saved? Did you know$110 million has been saved with the proviso you put into the budget with the preferred drug list, or that we have saved \$1.8 billion over the last six years with our first in the nation Community Long-Term Care Program? I could go down a lot of "did you knows" on taxpayer savings, but I'll spare you that laundry list of savings, and simply thank you for your part in all those little, and at times unseen, efforts to save the taxpayer money. I have always believed in the notion that the ultimate measure of government was found in what it spends - and that all too often it spends at a rate that surpasses the taxpayer's ability to keep up with it. All those conversations, and even consternations, have been worthwhile for the way they served to force people in government to follow the lead of the people paying for government in looking for ways to do more with less. Lest the length of this talk of mine lead you to the conclusion that I will ask for legislative change beyond the three things I mentioned, I will call it quits. But I will leave you with two parting thoughts. The first is from our family minister Greg Surratt. In the prayer service before my second inaugural he encouraged me to live by Micah 6:8 which simply asks that we love mercy, do justice and walk humbly. I never got that charge quite right over the following four years, I don't know that I ever will - but I do know that I will be trying and would pass his charge to each of you who bear the pressures and responsibilities of elected leadership. Under the category of life beyond politics, I'd ask you to focus on the things that matter most. Many of you are far ahead of me on this journey, but I heard a story a few months ago that has helped me in refocusing - and in the hope it might help you too, I offer it. In early December I was at the grand opening of Red Ventures in Lancaster, where I ended up in an amazing conversation with its CEO, Ric Elias, who had found himself in seat 1A of the plane that went down in the Hudson River. The plane lifted off from LaGuardia, and a short time after takeoff the captain came on mentioning a bird strike and matter-of-factly said that they would have to be heading back to the airport to re-land. Ric's position was interesting because he sat cattycorner to the flight attendant and saw no fear in her eyes as the captain said what he said. Another couple minutes go by and the captain comes back on announcing just three words, "prepare for impact." At that point, he could see the absolute sheer horror in the flight attendant's eyes as she knew what that meant. They were fully loaded with fuel and you don't put down a jet of that size on a street in Queens, Brooklyn or Manhattan. Ric did the mental calculation and figured he would be dying in about 40 to 45 seconds and his whole life went rolling by. He said though he had previously had the natural fears of death, he was not afraid of death as it was so near. What he did think about was the time he had wasted - the time he had spent arguing about petty things, about things that didn't matter with people who did, the times he had let little things get to him. He said it was the most amazing process of letting go of all these things in those 45 seconds. In essence, he died to himself and to those previous aggravations in the short window of time that he had left on earth. But he didn't die, and he now likened life to playing on bonus time in a video game - that he shouldn't be here, but he was, and therefore he was going to fully live each day. In profoundly positive ways he would try and make a difference in the lives of those around him and the world at large. He would invest in things that truly matter - those things that you can't see, you can't touch, you can't feel - but are the things that will have lasting value. I don't know if I will ever see Ric again, but I do know I'll be trying to follow his lead. As we work together over the next 11 months and as we go different ways after that, I hope you will too. If we all strive in this direction I suspect it will make a difference in bringing all of us - Republicans and Democrats, as representatives from the Coast, Midlands, and Upstate - as South Carolinians - together to better the lives of people in our State. That's my prayer. Thank you and good night. The purpose of the Joint Assembly having been accomplished, the PRESIDENT declared it adjourned, whereupon the Senate returned to its Chamber and was called to order by the PRESIDENT. On motion of Senator PEELER, with unanimous consent, the Senate stood adjourned out of respect to the memory of Mr. Mose Louis "Butch" Manini, Jr. of Columbia, S.C., beloved father of Ms. Lisa Manini Sox, Senate Republican Caucus Director. Mr. Manini was the owner/operator of Columbia Granite Company until 1976 and later joined the S. C. 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https://www.usgs.gov/center-news/photo-and-video-chronology-k-lauea-november-3-1997	# Photo and Video Chronology - Kīlauea - November 3, 1997 Release Date: Kilauea Volcano's east rift zone eruption continues in a regular pattern, with most lava traveling through tubes from the vent area to the coast [Eruption updates are posted approximately every two weeks. More frequent updates will accompany drastic changes in activity or increased threat to residential areas.] For readers familiar with events of the past few months, recent changes include these: • The vent inside Puu Oo discharges lava almost constantly. The lava flows eastward about 200 m and disappears through a hole in the crater floor, 60 m below the east crater rim. • At night, a spectacular orange glow emanates from Puu Oo. The glow comes from incandescent lava that streams across the crater. We've received reports of the glow from as far away as Papaikou, a town on Hawaii's Hamakua (northeastern) coast, 45 km north of the volcano. • Lava from the south shield travels in tubes to the coast, an in-tube distance of about 10 km. Travel time for a particle of melt is probably about 3 hours from vent to ocean. Eruption rate is generally 500,000-600,000 cubic meters per day. Lava occasionally escapes from the tube to form new surface flows, but no breakouts have occurred in the past two weeks. • Ocean entries remain situated at Wahaula and East Kamokuna, which are the distal ends of the tube system. • Sulfur dioxide gas emission from vents in the Puu Oo area remains high, about 5,000 tons per day. • For Big Island residents and tourists, symposia on Vog and Laze (volcanic fog and lava haze) will be held on November 8 (Hilo) and November 22 (Kona). Details are listed at the end of this report. The 55th episode of Kilauea's 14.5-year-long east rift zone eruption continues. This episode, which began February 24, 1997, was characterized in its early months by shifting vent locations on the west and southwest flanks of Puu Oo cone and by rapid enlargement of the episode 50-55 lava shield. The flow field expanded slowly until, in July, lava reached the sea. The supply of lava to these flows became restricted to tubes, and surface flow activity diminished greatly. During the last thirteen weeks, eruptive activity has been concentrated at two main vents: a vent on the Puu Oo crater floor and the "south shield," a lava shield about 300 m south of the Puu Oo cone. The most obvious of these has been the "crater vent," which began as a spatter cone on the Puu Oo crater floor. In September, however, the spatter cone subsided into its own throat, leaving a pit. The pit is about 40 m in diameter, and from this cauldron, lava froths and sloshes. This vent is the source of glow seen in the night sky from many vantage points on the east slope of Kilauea volcano. Lava issuing from the crater vent flows eastward a short distance into Puu Oo crater and drains through holes in the crater floor. Overflows occur when the subvolcanic drainage becomes clogged, which last occurred on October 18-19. The overflowing lava never travels far but has been visible throughout much of east Hawaii. The other main vent is the south shield, source of the flows entering the ocean at the Wahaula and Kamokuna sites near the eastern boundary of Hawaii Volcanoes National Park. The flows are encased within lava tubes for most of their length and are visible only through skylights in the roof of the tube. The tubes discharge their lava at the shoreline. The hot lava, about 1,150 degrees Celsius when it reaches the ocean, generates thick plumes of steam upon contact with seawater. The new lava builds benches beyond the former seacliffs. Small explosions periodically disrupt the rapidly chilling lava and throw it onto the bench, constructing low nearshore (littoral) cones. These small explosions pose a minor threat for visitors. A far greater threat exists, however; these benches can collapse into the sea without warning, triggering large steam explosions that hurl dense rock and molten spatter tens of meters inland. No one should venture onto the benches, no matter how stable the new land may appear. Eruption-viewing opportunities change constantly, so those readers planning a visit to the volcano should contact Hawaii Volcanoes National Park for the most current eruption information (808-985-6000). Big Island residents and tourists who wish to learn more about vog and its effects on health, agriculture, equipment, and air quality are invited to attend one of two Vog and Laze Symposia, to be presented by the Center for the Study of Active Volcanoes. The first symposium will be held November 8 at the University of Hawaii at Hilo Campus Center, Room 306-307; the second will be held in Kona on November 22 at the Kona Surf Hotel in the Kamehameha Ballroom. Both symposia begin at 9 a.m., with presentations by scientists and medical professionals who will discuss the composition of vog and laze and its impact on the community. An informal discussion and resource booths will also be featured. These admission-free symposia are sponsored by a grant from the Federal Emergency Management Agency. For additional information call (808)-974-7631 (Hilo, Hawai`i).	2019-11-21T19:09:17	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17154289782047272, "perplexity": 7655.142080356171}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670948.64/warc/CC-MAIN-20191121180800-20191121204800-00424.warc.gz"}
https://zims-en.kiwix.campusafrica.gos.orange.com/wikipedia_en_all_nopic/A/Comparison_of_topologies	# Comparison of topologies In topology and related areas of mathematics, the set of all possible topologies on a given set forms a partially ordered set. This order relation can be used for comparison of the topologies. ## Definition A topology on a set may be defined as the collection of subsets which are considered to be "open". An alternative definition is that it is the collection of subsets which are considered "closed". These two ways of defining the topology are essentially equivalent because the complement of an open set is closed and vice versa. In the following, it doesn't matter which definition is used. Let τ1 and τ2 be two topologies on a set X such that τ1 is contained in τ2: ${\displaystyle \tau _{1}\subseteq \tau _{2}}$ . That is, every element of τ1 is also an element of τ2. Then the topology τ1 is said to be a coarser (weaker or smaller) topology than τ2, and τ2 is said to be a finer (stronger or larger) topology than τ1. [nb 1] If additionally ${\displaystyle \tau _{1}\neq \tau _{2}}$ we say τ1 is strictly coarser than τ2 and τ2 is strictly finer than τ1.[1] The binary relation ⊆ defines a partial ordering relation on the set of all possible topologies on X. ## Examples The finest topology on X is the discrete topology; this topology makes all subsets open. The coarsest topology on X is the trivial topology; this topology only admits the empty set and the whole space as open sets. In function spaces and spaces of measures there are often a number of possible topologies. See topologies on the set of operators on a Hilbert space for some intricate relationships. All possible polar topologies on a dual pair are finer than the weak topology and coarser than the strong topology. ## Properties Let τ1 and τ2 be two topologies on a set X. Then the following statements are equivalent: Two immediate corollaries of this statement are • A continuous map f : XY remains continuous if the topology on Y becomes coarser or the topology on X finer. • An open (resp. closed) map f : XY remains open (resp. closed) if the topology on Y becomes finer or the topology on X coarser. One can also compare topologies using neighborhood bases. Let τ1 and τ2 be two topologies on a set X and let Bi(x) be a local base for the topology τi at xX for i = 1,2. Then τ1 ⊆ τ2 if and only if for all xX, each open set U1 in B1(x) contains some open set U2 in B2(x). Intuitively, this makes sense: a finer topology should have smaller neighborhoods. ## Lattice of topologies The set of all topologies on a set X together with the partial ordering relation ⊆ forms a complete lattice that is also closed under arbitrary intersections. That is, any collection of topologies on X have a meet (or infimum) and a join (or supremum). The meet of a collection of topologies is the intersection of those topologies. The join, however, is not generally the union of those topologies (the union of two topologies need not be a topology) but rather the topology generated by the union. Every complete lattice is also a bounded lattice, which is to say that it has a greatest and least element. In the case of topologies, the greatest element is the discrete topology and the least element is the trivial topology. ## Notes 1. There are some authors, especially analysts, who use the terms weak and strong with opposite meaning (Munkres, p. 78). ## See also • Initial topology, the coarsest topology on a set to make a family of mappings from that set continuous • Final topology, the finest topology on a set to make a family of mappings into that set continuous ## References 1. Munkres, James R. (2000). Topology (2nd ed.). Saddle River, NJ: Prentice Hall. pp. 77–78. ISBN 0-13-181629-2. This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.	2021-04-14T05:18:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 2, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7943150401115417, "perplexity": 487.0439021880439}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038076819.36/warc/CC-MAIN-20210414034544-20210414064544-00358.warc.gz"}
https://zbmath.org/authors/?q=orlov.dmitri-o	# zbMATH — the first resource for mathematics ## Orlov, Dmitri O. Compute Distance To: Author ID: orlov.dmitri-o Published as: Orlov, D. O.; Orlov, Dmitri; Orlov, Dmitri O.; Orlov, D.; Orlov, Dmitriĭ O. External Links: MGP · ORCID · Wikidata Documents Indexed: 55 Publications since 1989 all top 5 all top 5 #### Serials 17 Russian Mathematical Surveys 6 Advances in Mathematics 3 Izvestiya: Mathematics 2 Communications in Mathematical Physics 2 Moscow University Mathematics Bulletin 2 Mathematische Annalen 2 Journal of the American Mathematical Society 2 Russian Academy of Sciences. Izvestiya. Mathematics 2 Annals of Mathematics. Second Series 1 Journal of Geometry and Physics 1 Compositio Mathematica 1 Publications Mathématiques 1 Inventiones Mathematicae 1 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika 1 Journal of Algebraic Geometry 1 Journal of Mathematical Sciences (New York) 1 Sbornik: Mathematics 1 Matemática Contemporânea 1 Moscow Mathematical Journal 1 Central European Journal of Mathematics 1 Chebyshevskiĭ Sbornik 1 Proceedings of the Steklov Institute of Mathematics 1 Journal of Noncommutative Geometry all top 5 #### Fields 37 Algebraic geometry (14-XX) 28 Category theory; homological algebra (18-XX) 12 History and biography (01-XX) 8 Quantum theory (81-XX) 7 Associative rings and algebras (16-XX) 4 Differential geometry (53-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Algebraic topology (55-XX) 2 Nonassociative rings and algebras (17-XX) 1 Number theory (11-XX) 1 Commutative algebra (13-XX) 1 $$K$$-theory (19-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Functional analysis (46-XX) 1 Manifolds and cell complexes (57-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) 1 Relativity and gravitational theory (83-XX) #### Citations contained in zbMATH Open 41 Publications have been cited 1,351 times in 901 Documents Cited by Year Triangulated categories of singularities and D-branes in Landau-Ginzburg models. Zbl 1101.81093 Orlov, D. O. 2004 Equivalences of derived categories and $$K3$$ surfaces. Zbl 0938.14019 Orlov, D. O. 1997 Derived categories of coherent sheaves and triangulated categories of singularities. Zbl 1200.18007 Orlov, Dmitri 2009 Reconstruction of a variety from the derived category and groups of autoequivalences. Zbl 0994.18007 Bondal, Alexey; Orlov, Dmitri 2001 Uniqueness of enhancement for triangulated categories. Zbl 1197.14014 Lunts, Valery A.; Orlov, Dmitri O. 2010 An exact sequence for $$K^M_/2$$ with applications to quadratic forms. Zbl 1124.14017 Orlov, D.; Vishik, A.; Voevodsky, V. 2007 Derived categories of coherent sheaves. Zbl 0996.18007 Bondal, A.; Orlov, D. 2002 Mirror symmetry for weighted projective planes and their noncommutative deformations. Zbl 1175.14030 Auroux, Denis; Katzarkov, Ludmil; Orlov, Dmitri 2008 Projective bundles, monoidal transformations, and derived categories of coherent sheaves. Zbl 0798.14007 Orlov, D. O. 1992 Mirror symmetry for Del Pezzo surfaces: Vanishing cycles and coherent sheaves. Zbl 1110.14033 Auroux, Denis; Katzarkov, Ludmil; Orlov, Dmitri 2006 Noncommutative instantons and twistor transform. Zbl 0989.81127 Kapustin, Anton; Kuznetsov, Alexander; Orlov, Dmitri 2001 Remarks on A-branes, mirror symmetry, and the Fukaya category. Zbl 1029.81058 Kapustin, Anton; Orlov, Dmitri 2003 Triangulated categories of singularities and equivalences between Landau-Ginzburg models. Zbl 1161.14301 Orlov, D. O. 2006 Smooth and proper noncommutative schemes and gluing of dg categories. Zbl 1368.14031 Orlov, Dmitri 2016 Derived categories of coherent sheaves on abelian varieties and equivalences between them. Zbl 1031.18007 Orlov, D. O. 2002 Formal completions and idempotent completions of triangulated categories of singularities. Zbl 1216.18012 Orlov, Dmitri 2011 Vertex algebras, mirror symmetry, and D-branes: the case of complex tori. Zbl 1051.17017 Kapustin, Anton; Orlov, Dmitri 2003 Exceptional sheaves on del Pezzo surfaces. Zbl 0842.14009 Kuleshov, S. A.; Orlov, D. O. 1994 Matrix factorizations for nonaffine LG-models. Zbl 1243.81178 Orlov, Dmitri 2012 Homological mirror symmetry for punctured spheres. Zbl 1276.53089 Abouzaid, Mohammed; Auroux, Denis; Efimov, Alexander I.; Katzarkov, Ludmil; Orlov, Dmitri 2013 Geometric phantom categories. Zbl 1285.14018 Gorchinskiy, Sergey; Orlov, Dmitri 2013 Derived categories of coherent sheaves and motives. Zbl 1146.18302 Orlov, D. O. 2005 Derived categories of coherent sheaves and equivalences between them. Zbl 1118.14021 Orlov, D. O. 2003 Homological mirror symmetry for manifolds of general type. Zbl 1200.53079 Kapustin, Anton; Katzarkov, Ludmil; Orlov, Dmitri; Yotov, Mirroslav 2009 Derived categories of Burniat surfaces and exceptional collections. Zbl 1282.14030 Alexeev, Valery; Orlov, Dmitri 2013 Remarks on generators and dimensions of triangulated categories. Zbl 1197.18004 Orlov, Dmitri 2009 Deformation theory of objects in homotopy and derived categories. I: General theory. Zbl 1180.18006 Efimov, Alexander I.; Lunts, Valery A.; Orlov, Dmitri O. 2009 Mirror symmetry for abelian varieties. Zbl 1014.14020 Golyshev, V.; Lunts, V.; Orlov, D. 2001 Lectures on mirror symmetry, derived categories, and D-branes. Zbl 1074.14036 Kapustin, A. N.; Orlov, D. O. 2004 Geometric realizations of quiver algebras. Zbl 1348.14050 Orlov, Dmitri O. 2015 Does full imply faithful? Zbl 1276.14026 Canonaco, Alberto; Orlov, Dmitri; Stellari, Paolo 2013 Deformation theory of objects in homotopy and derived categories. II: Pro-representability of the deformation functor. Zbl 1197.18003 Efimov, Alexander I.; Lunts, Valery A.; Orlov, Dmitri O. 2010 Deformation theory of objects in homotopy and derived categories. III: Abelian categories. Zbl 1225.18009 Efimov, Alexander I.; Lunts, Valery A.; Orlov, Dmitri O. 2011 Exceptional collection of vector bundles on the manifold $$V_ 5$$. Zbl 0753.14012 Orlov, D. O. 1991 Landau-Ginzburg models, D-branes and mirror symmetry. Zbl 1297.14019 Orlov, Dmitri 2012 An exceptional collection of vector bundles on the threefold $$V_ 5$$. Zbl 0784.14010 Orlov, D. O. 1991 Quasicoherent sheaves in commutative and noncommutative geometry. Zbl 1077.14021 Orlov, D. O. 2003 Derived noncommutative schemes, geometric realizations, and finite dimensional algebras. Zbl 1430.14006 Orlov, Dmitriĭ O. 2018 Gluing of categories and Krull-Schmidt partners. Zbl 1358.18004 Orlov, D. O. 2016 Finite-dimensional DG algebras and their properties. Zbl 07179269 Orlov, D. O. 2019 Finite-dimensional differential graded algebras and their geometric realizations. Zbl 07183750 Orlov, Dmitri 2020 Finite-dimensional differential graded algebras and their geometric realizations. Zbl 07183750 Orlov, Dmitri 2020 Finite-dimensional DG algebras and their properties. Zbl 07179269 Orlov, D. O. 2019 Derived noncommutative schemes, geometric realizations, and finite dimensional algebras. Zbl 1430.14006 Orlov, Dmitriĭ O. 2018 Smooth and proper noncommutative schemes and gluing of dg categories. Zbl 1368.14031 Orlov, Dmitri 2016 Gluing of categories and Krull-Schmidt partners. Zbl 1358.18004 Orlov, D. O. 2016 Geometric realizations of quiver algebras. Zbl 1348.14050 Orlov, Dmitri O. 2015 Homological mirror symmetry for punctured spheres. Zbl 1276.53089 Abouzaid, Mohammed; Auroux, Denis; Efimov, Alexander I.; Katzarkov, Ludmil; Orlov, Dmitri 2013 Geometric phantom categories. Zbl 1285.14018 Gorchinskiy, Sergey; Orlov, Dmitri 2013 Derived categories of Burniat surfaces and exceptional collections. Zbl 1282.14030 Alexeev, Valery; Orlov, Dmitri 2013 Does full imply faithful? Zbl 1276.14026 Canonaco, Alberto; Orlov, Dmitri; Stellari, Paolo 2013 Matrix factorizations for nonaffine LG-models. Zbl 1243.81178 Orlov, Dmitri 2012 Landau-Ginzburg models, D-branes and mirror symmetry. Zbl 1297.14019 Orlov, Dmitri 2012 Formal completions and idempotent completions of triangulated categories of singularities. Zbl 1216.18012 Orlov, Dmitri 2011 Deformation theory of objects in homotopy and derived categories. III: Abelian categories. Zbl 1225.18009 Efimov, Alexander I.; Lunts, Valery A.; Orlov, Dmitri O. 2011 Uniqueness of enhancement for triangulated categories. Zbl 1197.14014 Lunts, Valery A.; Orlov, Dmitri O. 2010 Deformation theory of objects in homotopy and derived categories. II: Pro-representability of the deformation functor. Zbl 1197.18003 Efimov, Alexander I.; Lunts, Valery A.; Orlov, Dmitri O. 2010 Derived categories of coherent sheaves and triangulated categories of singularities. Zbl 1200.18007 Orlov, Dmitri 2009 Homological mirror symmetry for manifolds of general type. Zbl 1200.53079 Kapustin, Anton; Katzarkov, Ludmil; Orlov, Dmitri; Yotov, Mirroslav 2009 Remarks on generators and dimensions of triangulated categories. Zbl 1197.18004 Orlov, Dmitri 2009 Deformation theory of objects in homotopy and derived categories. I: General theory. Zbl 1180.18006 Efimov, Alexander I.; Lunts, Valery A.; Orlov, Dmitri O. 2009 Mirror symmetry for weighted projective planes and their noncommutative deformations. Zbl 1175.14030 Auroux, Denis; Katzarkov, Ludmil; Orlov, Dmitri 2008 An exact sequence for $$K^M_/2$$ with applications to quadratic forms. Zbl 1124.14017 Orlov, D.; Vishik, A.; Voevodsky, V. 2007 Mirror symmetry for Del Pezzo surfaces: Vanishing cycles and coherent sheaves. Zbl 1110.14033 Auroux, Denis; Katzarkov, Ludmil; Orlov, Dmitri 2006 Triangulated categories of singularities and equivalences between Landau-Ginzburg models. Zbl 1161.14301 Orlov, D. O. 2006 Derived categories of coherent sheaves and motives. Zbl 1146.18302 Orlov, D. O. 2005 Triangulated categories of singularities and D-branes in Landau-Ginzburg models. Zbl 1101.81093 Orlov, D. O. 2004 Lectures on mirror symmetry, derived categories, and D-branes. Zbl 1074.14036 Kapustin, A. N.; Orlov, D. O. 2004 Remarks on A-branes, mirror symmetry, and the Fukaya category. Zbl 1029.81058 Kapustin, Anton; Orlov, Dmitri 2003 Vertex algebras, mirror symmetry, and D-branes: the case of complex tori. Zbl 1051.17017 Kapustin, Anton; Orlov, Dmitri 2003 Derived categories of coherent sheaves and equivalences between them. Zbl 1118.14021 Orlov, D. O. 2003 Quasicoherent sheaves in commutative and noncommutative geometry. Zbl 1077.14021 Orlov, D. O. 2003 Derived categories of coherent sheaves. Zbl 0996.18007 Bondal, A.; Orlov, D. 2002 Derived categories of coherent sheaves on abelian varieties and equivalences between them. Zbl 1031.18007 Orlov, D. O. 2002 Reconstruction of a variety from the derived category and groups of autoequivalences. Zbl 0994.18007 Bondal, Alexey; Orlov, Dmitri 2001 Noncommutative instantons and twistor transform. Zbl 0989.81127 Kapustin, Anton; Kuznetsov, Alexander; Orlov, Dmitri 2001 Mirror symmetry for abelian varieties. Zbl 1014.14020 Golyshev, V.; Lunts, V.; Orlov, D. 2001 Equivalences of derived categories and $$K3$$ surfaces. Zbl 0938.14019 Orlov, D. O. 1997 Exceptional sheaves on del Pezzo surfaces. Zbl 0842.14009 Kuleshov, S. A.; Orlov, D. O. 1994 Projective bundles, monoidal transformations, and derived categories of coherent sheaves. Zbl 0798.14007 Orlov, D. O. 1992 Exceptional collection of vector bundles on the manifold $$V_ 5$$. Zbl 0753.14012 Orlov, D. O. 1991 An exceptional collection of vector bundles on the threefold $$V_ 5$$. Zbl 0784.14010 Orlov, D. O. 1991 all top 5 #### Cited by 828 Authors 25 Katzarkov, Ludmil 24 Tabuada, Gonçalo 19 Orlov, Dmitri O. 18 Stellari, Paolo 17 Polishchuk, Alexander Evgen’evich 13 Kuznetsov, Aleksandr Gennad’evich 13 Lunts, Valery A. 12 Ballard, Matthew Robert 12 Chen, Xiaowu 11 Favero, David 11 Ueda, Kazushi 11 Van den Bergh, Michel 9 Bernardara, Marcello 9 Efimov, Alexander I. 9 Lu, Ming 9 Macrì, Emanuele 8 Canonaco, Alberto 8 Fasel, Jean 8 Huybrechts, Daniel 8 Kalck, Martin 8 Lee, Kyoung-Seog 8 Li, Huanhuan 8 Smith, Ivan 8 Sosna, Pawel 7 Harder, Andrew 7 Schnürer, Olaf M. 7 Yoshioka, Kōta 6 Bayer, Arend 6 Bridgeland, Tom 6 Kerr, Gabriel 6 López Martín, Ana Cristina 6 Nadler, David 6 Ploog, David 6 Positselski, Leonid Efimovich 6 Psaroudakis, Chrysostomos 6 Sheridan, Nick 6 Takahashi, Atsushi 6 Zhang, Pu 5 Abouzaid, Mohammed 5 Asok, Aravind 5 Becher, Karim Johannes 5 Hochenegger, Andreas 5 Przhiyalkovskiĭ, Viktor Vladimirovich 5 Stevenson, Greg 5 Takahashi, Ryo 5 Wemyss, Michael 5 Yagita, Nobuaki 5 Zhang, James J. 4 Antieau, Benjamin 4 Aspinwall, Paul S. 4 Auroux, Denis 4 Belmans, Pieter 4 Bergh, Daniel 4 Bocklandt, Raf 4 Bondal, Alexey I. 4 Chen, Xinhong 4 Chiodo, Alessandro 4 Cho, Cheol-Hyun 4 Di, Zhenxing 4 Diemer, Colin 4 Futaki, Masahiro 4 Halpern-Leistner, Daniel 4 Hirano, Yuki 4 Huang, Zhaoyong 4 Iyama, Osamu 4 Kajiura, Hiroshige 4 Kaledin, Dmitry B. 4 Kapustin, Anton 4 Karp, Robert L. 4 Kawamata, Yujiro 4 Liu, Zhong-kui 4 Mináč, Ján 4 Minasian, Ruben 4 Rizzardo, Alice 4 Ruan, Yongbin 4 Sancho de Salas, Fernando 4 Segal, Ed 4 Seidel, Paul 4 Shinder, Evgeny 4 Sibilla, Nicolò 4 Szabo, Richard J. 4 Toda, Yukinobu 4 Toën, Bertrand 4 Uehara, Hokuto 4 Walcher, Johannes 3 Addington, Nicolas M. 3 Ben-Bassat, Oren 3 Ben-Zvi, David 3 Bodzenta, Agnieszka 3 Böhning, Christian 3 Bolognesi, Michele 3 Borisov, Lev A. 3 Buchweitz, Ragnar-Olaf 3 Bullimore, Mathew Richard 3 Chalykh, Oleg A. 3 Chan, Kwokwai 3 Costa, Laura 3 Craw, Alastair 3 Deliu, Dragos 3 Dell’Ambrogio, Ivo ...and 728 more Authors all top 5 #### Cited in 135 Serials 101 Advances in Mathematics 69 Journal of Algebra 32 Communications in Mathematical Physics 31 Journal of Geometry and Physics 30 Compositio Mathematica 29 Transactions of the American Mathematical Society 28 Duke Mathematical Journal 27 Journal of High Energy Physics 26 Proceedings of the American Mathematical Society 26 Selecta Mathematica. New Series 25 Journal of Pure and Applied Algebra 24 Mathematische Zeitschrift 21 Mathematische Annalen 15 Inventiones Mathematicae 14 Journal of Algebraic Geometry 13 Journal of Mathematical Physics 13 Nuclear Physics. B 13 Manuscripta Mathematica 13 Algebras and Representation Theory 10 Journal of the European Mathematical Society (JEMS) 10 Journal of Noncommutative Geometry 8 Annales de l’Institut Fourier 8 Publications Mathématiques 8 Journal of the American Mathematical Society 8 Documenta Mathematica 8 Comptes Rendus. Mathématique. Académie des Sciences, Paris 8 Kyoto Journal of Mathematics 7 Russian Mathematical Surveys 7 International Journal of Mathematics 7 Izvestiya: Mathematics 7 Proceedings of the Steklov Institute of Mathematics 7 European Journal of Mathematics 6 International Journal of Modern Physics A 6 Communications in Algebra 6 Mathematical Proceedings of the Cambridge Philosophical Society 6 Bulletin of the London Mathematical Society 6 Journal of $$K$$-Theory 5 Mathematical Notes 5 Geometry & Topology 5 Science China. Mathematics 4 Letters in Mathematical Physics 4 Journal of the London Mathematical Society. Second Series 4 Journal für die Reine und Angewandte Mathematik 4 Geometric and Functional Analysis. GAFA 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Expositiones Mathematicae 4 Annals of Mathematics. Second Series 4 Central European Journal of Mathematics 4 Journal of the Institute of Mathematics of Jussieu 4 Journal of Algebra and its Applications 4 Forum of Mathematics, Sigma 4 Research in the Mathematical Sciences 3 Archiv der Mathematik 3 Journal of the Mathematical Society of Japan 3 Mathematische Nachrichten 3 Memoirs of the American Mathematical Society 3 Michigan Mathematical Journal 3 Nagoya Mathematical Journal 3 Proceedings of the Edinburgh Mathematical Society. Series II 3 Sugaku Expositions 3 Bulletin of the American Mathematical Society. New Series 3 Applied Categorical Structures 3 Journal of Mathematical Sciences (New York) 3 International Journal of Geometric Methods in Modern Physics 3 Journal of Homotopy and Related Structures 3 Journal of Topology 2 Reviews in Mathematical Physics 2 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Commentarii Mathematici Helvetici 2 Fundamenta Mathematicae 2 Geometriae Dedicata 2 Rendiconti del Seminario Matematico della Università di Padova 2 Bulletin of the Korean Mathematical Society 2 Chinese Annals of Mathematics. Series B 2 Differential Geometry and its Applications 2 Sbornik: Mathematics 2 Acta Mathematica Sinica. English Series 2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 2 Journal of Commutative Algebra 2 Annals of $$K$$-Theory 1 General Relativity and Gravitation 1 Physics Reports 1 Arkiv för Matematik 1 Fortschritte der Physik 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Colloquium Mathematicum 1 Glasgow Mathematical Journal 1 Journal of the Korean Mathematical Society 1 Kodai Mathematical Journal 1 Pacific Journal of Mathematics 1 Proceedings of the London Mathematical Society. Third Series 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Results in Mathematics 1 Tohoku Mathematical Journal. Second Series 1 Tokyo Journal of Mathematics 1 Topology and its Applications 1 Ergodic Theory and Dynamical Systems 1 Boletim da Sociedade Portuguesa de Matemática ...and 35 more Serials all top 5 #### Cited in 34 Fields 623 Algebraic geometry (14-XX) 338 Category theory; homological algebra (18-XX) 194 Associative rings and algebras (16-XX) 140 Differential geometry (53-XX) 108 Quantum theory (81-XX) 71 $$K$$-theory (19-XX) 70 Commutative algebra (13-XX) 47 Several complex variables and analytic spaces (32-XX) 46 Number theory (11-XX) 34 Algebraic topology (55-XX) 30 Manifolds and cell complexes (57-XX) 23 Nonassociative rings and algebras (17-XX) 23 Relativity and gravitational theory (83-XX) 20 Global analysis, analysis on manifolds (58-XX) 19 Group theory and generalizations (20-XX) 17 Field theory and polynomials (12-XX) 10 Partial differential equations (35-XX) 7 Functional analysis (46-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Dynamical systems and ergodic theory (37-XX) 5 History and biography (01-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Convex and discrete geometry (52-XX) 3 Topological groups, Lie groups (22-XX) 2 Combinatorics (05-XX) 1 General and overarching topics; collections (00-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Ordinary differential equations (34-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Mechanics of particles and systems (70-XX) 1 Mathematics education (97-XX) #### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2021-12-05T04:28:30	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.37759432196617126, "perplexity": 5780.402391755888}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363135.71/warc/CC-MAIN-20211205035505-20211205065505-00566.warc.gz"}
https://www.pnnl.gov/news-media/wireless-metering-challenge	June 12, 2017 Web Feature Wireless Metering Challenge Commercial buildings benefit from DOE challenge for market solution to reduce energy use, improve operations Commercial building owners spend more than $120 billion dollars on electricity each year. The average cost per building hovers around$21,500/year—that’s a lot! Building owners can reduce their energy costs by better understanding energy-use profiles via metering system data. Consumption data can be used to identify energy reduction opportunities, improve operations, verify improvements, and assess system performance. However, installing a metering system in an existing building requires expensive hardwiring of communication links, retrofitting, and new software. Such investments can be too significant to be considered cost effective, thus leaving energy optimization and efficiency opportunities unaddressed. To overcome this cost barrier, the DOE's Buildings Technology Office tasked researchers at PNNL with developing and leading the DOE Low-Cost Wireless Metering Challenge. The Challenge set requirements for a low-cost, wireless system that measures electricity use at various locations in a building and communicates data wirelessly to a local collection point. The Challenge winner is a system developed by Meazon. Challenge Issued Specifications and attributes of the desired wireless metering system included: • Low cost meter with a target purchase price less than $100 • Electrical energy measurement units that are easy to use and quick to install • Full compliance with NFPA 70 and UL 61010 • Wireless data communication success rate greater than or equal to 95 percent • Operation independent from existing building internet and intranet networks • All data encrypted using 128-bit or greater Advanced Encryption Standard. Initially, 30 companies indicated interest in the Wireless Metering Challenge. Several firms met basic criteria and approached the cost target. From those, one system—developed by Meazon—met all of the prerequisites. This system was then installed and tested at the General Services Administration’s Headquarters in Washington, D.C. Results The Meazon system exceeded the required communication success rate of 95%, included a meter cost less than$100, and provided data in an easy to use CSV format successfully meeting the Challenge specification. The Wireless Metering Challenge effectively stimulated the market to meet an unmet need for a low-cost system that measures whole building and/or internal loads, eliminates the need for hardwiring in an existing building, and provides communications independently from a building's other networks. This effort builds on years of experience in technology research at PNNL. Key Capabilities Published: June 12, 2017 PNNL Research Team Anne Wagner, Linda Sandahl, Mike Hoffman, Dave Hunt, Jian Zhang, and Michael Richart	2020-09-21T17:59:22	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24828699231147766, "perplexity": 9342.952264752485}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400202007.15/warc/CC-MAIN-20200921175057-20200921205057-00549.warc.gz"}
https://control.com/textbook/pneumatic-instrumentation/advantages-and-disadvantages-of-pneumatic-instruments/	## Chapter 12 - Basics of Pneumatic Instruments The disadvantages of pneumatic instruments are painfully evident to anyone familiar with both pneumatic and electronic instruments. Sensitivity to vibration, changes in temperature, mounting position, and the like affect calibration accuracy to a far greater degree for pneumatic instruments than electronic instruments. Compressed air is an expensive utility – much more expensive per equivalent watt-hour than electricity – making the operational cost of pneumatic instruments far greater than electronic. The installed cost of pneumatic instruments can be quite high as well, given the need for special (stainless steel, copper, or tough plastic) tubes to carry supply air and pneumatic signals to distant locations. The volume of air tubes used to convey pneumatic signals over distances acts as a low-pass filter, naturally damping the instrument’s response and thereby reducing its ability to respond quickly to changing process conditions. Pneumatic instruments cannot be made “smart” like electronic instruments, either. With all these disadvantages, one might wonder why pneumatic instruments are still used at all in modern industry. Part of the answer is legacy. For an industrial facility built decades ago, it makes little sense to replace instruments that still work just fine. The cost of labor to remove old tubing, install new conduit and wires, and configure new (expensive) electronic instruments often is not worth the benefits. However, pneumatic instruments actually enjoy some definite technical advantages which secure their continued use in certain applications even in the 21$$^{st}$$ century. One decided advantage is the intrinsic safety of pneumatic field instruments. Instruments that do not run on electricity cannot generate electrical sparks. This is of utmost importance in “classified” industrial environments where explosive gases, liquids, dusts, and powders exist. Pneumatic instruments are also self-purging. Their continual bleeding of compressed air from vent ports in pneumatic relays and nozzles acts as a natural clean-air purge for the inside of the instrument, preventing the intrusion of dust and vapor from the outside with a slight positive pressure inside the instrument case. It is not uncommon to find a field-mounted pneumatic instrument encrusted with corrosion and filth on the outside, but factory-clean on the inside due to this continual purge of clean air. Pneumatic instruments mounted inside larger enclosures with other devices tend to protect them all by providing a positive-pressure air purge for the entire enclosure. Some pneumatic instruments can also function in high-temperature and high-radiation environments that would damage electronic instruments. Although it is often possible to “harden” electronic field instruments to such harsh conditions, pneumatic instruments are practically immune by nature. An interesting feature of pneumatic instruments is that they may operate on compressed gases other than air. This is an advantage in remote natural gas installations, where the natural gas itself is sometimes used as a source of pneumatic “power” for instruments. So long as there is compressed natural gas in the pipeline to measure and to control, the instruments will operate. No air compressor or electrical power source is needed in these installations. What is needed, however, is good filtering equipment to prevent contaminants in the natural gas (dirt, debris, liquids) from causing problems within the sensitive instrument mechanisms. • Share Published under the terms and conditions of the Creative Commons Attribution 4.0 International Public License	2020-09-29T14:07:36	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5876378417015076, "perplexity": 3409.273004215815}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401643509.96/warc/CC-MAIN-20200929123413-20200929153413-00628.warc.gz"}
https://pokemon.fandom.com/wiki/Individual_Values?diff=prev&oldid=894166	## FANDOM 17,652 Pages Individual Values, or IVs function like a Pokémon's "Genes". They are the traits which are passed down from one generation to the next. Every stat has an IV ranging from 0 to 31 for each stat (HP, ATK, DEF, SPA, SPD, and SPE), and at level 100, their IVs are added to the Pokémon's stats for their total values. For example, a level 100 Tyranitar with no Effort Values and 0 IVs has 310 HP, however if it had 31 IVs, it would have 341 HP. These stats are provided randomly for every Pokémon, caught or bred, and although as insignificant as 31 points may seem, they are required for Ace Trainers to obtain when breeding Pokémon with perfect natures/stats. On some occasions they are even the tipping point in a close matchup. For example, if there was a Terrakion with 0 Attack IV, it will have an attack of 358 at level 100 (with an attack improving nature), while a Terrakion with perfect Attack IVs would have 392 Attack. This small difference can mean the difference between a one-hit kill (not an OHKO) and survival with 1 HP. ## Breeding IVs Fortunately for trainers, Ace Trainers and Pokémon Breeders especially, IVs can be bred to obtain the perfect Pokémon. The process of breeding IVs is as follows, the example displayed below is to breed Nidorans: • The child's IV's are generated randomly, for example: 7/27/31/14/19/2, in HP/ATK/DEF/SPA/SPD/SPE format. • Three stats are inherited from the parents, and are selected in three checks: 1. First check: A random stat (HP/ATK/DEF/SPA/SPD/SPE) is selected from either the Mother or the Father and passed on to the child. 2. Second check: A random stat with the exception of HP (ATK/DEF/SPA/SPD/SPE) is selected from either the Mother or the Father and passed on to the child. 3. Third check: A random stat with the exception of HP and DEF (ATK/SPA/SPD/SPE) is selected from either the Mother or the Father and passed on to the child. This means that HP and DEF are less likely to pass on to the child, however there are ways to make sure the IVs are passed on. Letting either one of the parents hold a Power Item can ensure that the Power Item's respective stat will be passed on to the offspring from the parent that holds it. If the Power Item called Power Weight (doubles all HP EV gained) is held by a parent with a perfect IV of 31 for HP and the first check selects this parent, the child is ensured to have a perfect IV for HP. The other checks, though, will be random, and either luck or patience is required to eventually get the desired stats. Important: Only three stats are inherited per Pokémon, and these can stack. For example, the DEF IV can be inherited from both parents, thus rendering one redundant. ## Checking IVs Beginning in Generation III, there has always been an NPC that allows players to check the IVs of their Pokémon. A list of the locations of the NPCs: • Pokémon HeartGold: The NPC is located in the Battle Tower; he is the NPC that is dressed like a scientist standing closest to the PC on the top right side of the room. He will only give information about one of a Pokémon's IVs each time he is asked, so he should be consulted more than once to learn about all of a Pokémon's stats. • Pokémon Black: The NPC is located in the Battle Subway; he is the closest NPC to the exit. He will give information about a Pokémon's highest IVs. If it has more than one, he will include all of the information in a single consultation according to the following list: • Sum of IV's: • "This Pokémon's potential is decent all around." (0-90) • "This Pokémon's potential is above average overall." (91-120) • "This Pokémon has relatively superior potential overall." (121-150) • "This Pokémon has outstanding potential overall." (150-186) • One IV: • "It's rather decent in that regard." (0-15) • "It's very good in that regard." (16-25) • "It's fantastic in that regard." (26-30) • "It can't be better in that regard." (31) If you wanted to check the IV's yourself the formula is as follows: • The formula for HP is different from the rest of the stats, so here is the formula for HP: • IV=((Stat - Level Value - 10) * 100 / Level Value) - 2 * Base stat - (Math.Floor(EV/4)) • In layman terms: • Individual Value= ((Current Stat Level - Current Level Value - 10) * 100 / Current Level Value) - 2 * Base Stat - (Math.Floor(EV/4)) • Just in case you don't know (Math.Floor(EV/4)) means to take the amount of EVs you have in HP and divide it by 4 and then round down. • The formula you use for the rest of the stats is the same, so here it is: • IV=((Math.Ceiling(Stat/Nature) - 5) * 100 / Level Value) - 2 * Base Stat - (Math.Floor(EV/4)) • In layman terms: • Individual Value= (Math.Ceiling(Current Stat Value/Nature Bonus) * 100 / Current Level Value) - 2 * Base Stat - (Math.Floor(EV/4)) • Just in case you don't know (Math.Floor(EV/4)) means to take the amount of EVs you have in HP and divide it by 4 and then round down. • Just in case you don't know (Math.Ceiling(Current Stat Value/Nature Bonus)) means to take the Current Stat Value and divide it by the bonus you get from the Pokémon's nature and then round up. If the stat gets an increase from the nature you divide the Current Stat Value by 1.1, and if it is a decrease from the nature you divide the Current Stat Value by 0.9. ## Formula The formulae for calculating stats differ. In Generations I and II, the EV is squared root and Nature never exists. EVs are usually denoted in letter σ (Sigma). ### Generation I and II The formulae are known as "Oak's Theorem". It is denoted by the letter ρ (Rho). Hit Points: $\rho_{HP} = \left [ \frac{(B + I) \times 2 + \left [\frac{\sqrt \sigma}{4} \right ] \times \alpha}{100} \right] + \alpha + 10$ Other Stats: $\rho_{other} = \left [ \frac{(B + I) \times 2 + \left [\frac{\sqrt \sigma}{4} \right ] \times \alpha}{100} \right] + 5$ Where: B - Base Stat I - Individual Values σ - Effort Value α - Pokémon's Level Example: Find the total HP stat of a Level 40 Lugia. Substitute: B - 106 I - 6 σ - 50000 α - 40 Since it is HP, the HP version will be used. $\rho_{HP} = \left [ \frac{(B + I) \times 2 + \left [\frac{\sqrt \sigma}{4} \right ] \times \alpha}{100} \right] + \alpha + 10$ Substituting every givens into the formula: $\rho_{HP} = \left [ \frac{(106 + 6) \times 2 + \left [\frac{\sqrt 50000}{4} \right ] \times 40}{100} \right] + 40 + 10$ Doing the order of operations: $\rho_{HP} = \left [ \frac{112 \times 2 + \left [\frac{\sqrt 50000}{4} \right ] \times 40}{100} \right] + 40 + 10$ $\rho_{HP} = \left [ \frac{112 \times 2 + \left [\frac{224}{4} \right ] \times 40}{100} \right] + 40 + 10$ $\rho_{HP} = \left [ \frac{224 + 56 \times 40}{100} \right] + 40 + 10$ $\rho_{HP} = \left [ \frac{224 + 2240}{100} \right] + 40 + 10$ $\rho_{HP} = \left [ \frac{2464}{100} \right] + 40 + 10$ $\rho_{HP} = 24.64 + 40 + 10$ $\rho_{HP} \doteq 74.64$ • Rounding it off to the nearest stat: $\rho_{HP} \doteq 75$ ### Generations III and above The formulae are known as "Birch's Theorem". It is denoted by the letter Γ (Gamma). Hit Points: $\Gamma_{HP} =\left [\frac{\left ( 2 \times B \times I +\left [ \frac{\sigma}{4} \right ]\right ) \times \alpha }{100} \right ] + \alpha + 10$ Other Stats: $\Gamma_{other} =\left (\left [\frac{\left ( 2 \times B \times I +\left [ \frac{\sigma}{4} \right ]\right ) \times \alpha }{100} \right ] + 5\right ) \times \varphi$ B - Base Stat I - Individual Values σ - Effort Value α - Pokémon's Level φ - Nature The constants of Nature (φ) are as follows: • 1.1x increase for the Nature's first stat • 0.9x decrease for the Nature's second stat Example: Find the Defence stat of a Level 40 Accelgor with a Bold nature. Substitute: B - 40 I - 7 σ - 116 α - 51 φ - Bold (+1.1 Def, -0.9 Att) The other stats version will be used. $\Gamma_{other} =\left (\left [\frac{\left ( 2 \times B \times I +\left [ \frac{\sigma}{4} \right ]\right ) \times \alpha }{100} \right ] + 5\right ) \times \varphi$ • For Defence: Substituting every givens into the formula: $\Gamma_{other} =\left (\left [\frac{\left ( 2 \times 40 \times 7 +\left [ \frac{116}{4} \right ]\right ) \times 51}{100} \right ] + 5\right ) \times 1.1$ Doing the order of operations: $\Gamma_{other} =\left (\left [\frac{\left ( 2 \times 40 \times 7 +\left [ \frac{116}{4} \right ]\right ) \times 51}{100} \right ] + 5\right ) \times 1.1$ $\Gamma_{other} =\left (\left [\frac{\left ( 560 +\left [ \frac{116}{4} \right ]\right ) \times 51}{100} \right ] + 5\right ) \times 1.1$ $\Gamma_{other} =\left (\left [\frac{\left ( 560 + 29 \right ) \times 51}{100} \right ] + 5\right ) \times 1.1$ $\Gamma_{other} =\left (\left [\frac{589 \times 51}{100} \right ] + 5\right ) \times 1.1$ $\Gamma_{other} =\left (\left [\frac{30039}{100} \right ] + 5\right ) \times 1.1$ $\Gamma_{other} =300.39 + 5 \times 1.1$ $\Gamma_{other} =300.39 + 5.5$ $\Gamma_{other} \doteq 305.89$ Rounding it off to the nearest stat: $\Gamma_{other} \doteq 306$ Therefore, its defence stat is 306. • For Attack: - Accelgor's base attack is 70, so sigma = 70. Substituting every givens into the formula: $\Gamma_{other} =\left (\left [\frac{\left ( 2 \times 40 \times 7 +\left [ \frac{70}{4} \right ]\right ) \times 51}{100} \right ] + 5\right ) \times 1.1$ Doing the order of operations: $\Gamma_{other} =\left (\left [\frac{\left ( 2 \times 40 \times 7 +\left [ \frac{70}{4} \right ]\right ) \times 51}{100} \right ] + 5\right ) \times 1.1$ $\Gamma_{other} =\left (\left [\frac{\left ( 560 +\left [ \frac{70}{4} \right ]\right ) \times 51}{100} \right ] + 5\right ) \times 0.9$ $\Gamma_{other} =\left (\left [\frac{\left ( 560 + 17.5 \right ) \times 51}{100} \right ] + 5\right ) \times 0.9$ $\Gamma_{other} =\left (\left [\frac{577.5 \times 51}{100} \right ] + 5\right ) \times 0.9$ $\Gamma_{other} =\left (\left [\frac{29452}{100} \right ] + 5\right ) \times 0.9$ $\Gamma_{other} =295 + 5 \times 0.9$ $\Gamma_{other} \doteq 295 + 4.5$ Rounding it off to the nearest stat: $\Gamma_{other} \doteq 300$ Therefore, its attack stat is 300. Community content is available under CC-BY-SA unless otherwise noted.	2020-08-13T15:06:52	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2966148257255554, "perplexity": 3799.7167015610125}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439739046.14/warc/CC-MAIN-20200813132415-20200813162415-00592.warc.gz"}
https://pdglive.lbl.gov/DataBlock.action?node=M003M1&home=MXXX005	#### ${{\mathit f}_{{0}}{(980)}}$ MASS VALUE (MeV) EVTS DOCUMENT ID TECN COMMENT $\bf{ 990 \pm20}$ OUR ESTIMATE • • We do not use the following data for averages, fits, limits, etc. • • $992.0$ ${}^{+8.5}_{-7.5}$ $\pm8.6$ 1 2019 H LHCB ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit D}^{\pm}}{{\mathit X}}$ $989.4$ $\pm1.3$ 424 2015 P BES3 ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$3 ${{\mathit \pi}}$ $989.9$ $\pm0.4$ 706 2012 E BES3 ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}}$3 ${{\mathit \pi}}$ $977$ ${}^{+11}_{-9}$ $\pm1$ 44 2 2009 CLEO 4.17 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}_{{s}}^{-}}{{\mathit D}_{{s}}^{+}}$ + c.c. $982.2$ $\pm1.0$ ${}^{+8.1}_{-8.0}$ 3 2008 A BELL 10.6 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ $976.8$ $\pm0.3$ ${}^{+10.1}_{-0.6}$ 64k 4 2007 KLOE 1.02 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \gamma}}$ $984.7$ $\pm0.4$ ${}^{+2.4}_{-3.7}$ 64k 5 2007 KLOE 1.02 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \gamma}}$ $973$ $\pm3$ $262$ $\pm30$ 6 2007 AK BABR 10.6 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$ $970$ $\pm7$ $54$ $\pm9$ 6 2007 AK BABR 10.6 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \gamma}}$ $953$ $\pm20$ 2.6k 7 2007 CLEO ${{\mathit D}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{+}}$ $985.6$ ${}^{+1.2}_{-1.5}$ ${}^{+1.1}_{-1.6}$ 8 2007 BELL 10.6 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $983.0$ $\pm0.6$ ${}^{+4.0}_{-3.0}$ 9 2006 B KLOE 1.02 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$ $977.3$ $\pm0.9$ ${}^{+3.7}_{-4.3}$ 10 2006 B KLOE 1.02 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$ $950$ $\pm9$ 4286 11 2006 BELL ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $965$ $\pm10$ 12 2005 BES2 ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ , ${{\mathit \phi}}{{\mathit K}^{+}}{{\mathit K}^{-}}$ $1031$ $\pm8$ 13 2003 RVUE $1037$ $\pm31$ 2003 SPEC 40.0 ${{\mathit \pi}^{-}}$ ${}^{}\mathrm {C}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ ${{\mathit K}_L^0}$ X $973$ $\pm1$ 2438 14 2002 D KLOE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \gamma}}$ $977$ $\pm3$ $\pm2$ 848 15 2001 A E791 ${{\mathit D}_{{s}}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{+}}$ $969.8$ $\pm4.5$ 419 16 2000 H SND ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \gamma}}$ $985$ ${}^{+16}_{-12}$ 419 17, 18 2000 H SND ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \gamma}}$ $976$ $\pm5$ $\pm6$ 19 1999 B CMD2 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$ $977$ $\pm3$ $\pm6$ 268 19 1999 C CMD2 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \gamma}}$ $975$ $\pm4$ $\pm6$ 20 1999 C CMD2 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \gamma}}$ $975$ $\pm4$ $\pm6$ 21 1999 C CMD2 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$ , ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \gamma}}$ $985$ $\pm10$ 1999 OMEG 450 ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}_{{s}}}{{\mathit p}_{{f}}}{{\mathit K}^{+}}{{\mathit K}^{-}}$ $982$ $\pm3$ 1999 B OMEG 450 ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}_{{s}}}{{\mathit p}_{{f}}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $982$ $\pm3$ 1999 C OMEG 450 ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}_{{s}}}{{\mathit p}_{{f}}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ $987$ $\pm6$ $\pm6$ 22 1999 D OMEG 450 ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ , ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $989$ $\pm15$ 1999 GAM4 450 ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}}{{\mathit p}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ $991$ $\pm3$ 23 1999 RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$ , ${{\mathit \sigma}}{{\mathit \sigma}}$ $\sim{}\text{ 980}$ 23 1999 RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$ $\sim{}\text{ 993.5}$ 1999 B RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$ $\sim{}\text{ 987}$ 23 1999 C RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$ , ${{\mathit \eta}}{{\mathit \eta}}$ $957$ $\pm6$ 24 1998 Q OPAL ${{\mathit Z}}$ $\rightarrow$ ${{\mathit f}_{{0}}}$ X $960$ $\pm10$ 1998 GAM4 $1015$ $\pm15$ 23 1998 B RVUE Compilation $1008$ 25 1998 RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$ $955$ $\pm10$ 24 1997 GAM2 450 ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}}{{\mathit p}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ $994$ $\pm9$ 26 1997 C OBLX 0.0 ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $993.2$ $\pm6.5$ $\pm6.9$ 27 1996 RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$ $1006$ 1996 RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$ , ${{\mathit K}}{{\mathit \pi}}$ , ${{\mathit \eta}}{{\mathit \pi}}$ $997$ $\pm5$ 3k 28 1995 B GAM2 38 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit n}}$ $960$ $\pm10$ 10k 29 1995 B GAM2 38 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit n}}$ $994$ $\pm5$ 1995 B CBAR $0.0$ ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ 3 ${{\mathit \pi}^{0}}$ $\sim{}\text{ 996}$ 30 1995 D CBAR 0.0 ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ , ${{\mathit \pi}^{0}}{{\mathit \eta}}{{\mathit \eta}}$ , ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \eta}}$ $987$ $\pm6$ 31 1995 RVUE $1015$ 1995 RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$ $983$ 32 1994 RVUE ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \eta}}$2 ${{\mathit \pi}^{0}}$ $973$ $\pm2$ 33 1994 RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit K}}{{\overline{\mathit K}}}$ $988$ 34 1994 B RVUE $988$ $\pm10$ 35 1993 RVUE ${{\mathit \pi}}$ ${{\mathit \pi}}$ ${{\mathit K}}$ ${{\overline{\mathit K}}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit \pi}}$( ${{\mathit K}}{{\overline{\mathit K}}}$), ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit \pi}}{{\mathit \pi}}$( ${{\mathit K}}{{\overline{\mathit K}}}$), ${{\mathit D}_{{s}}}$ $\rightarrow$ ${{\mathit \pi}}$( ${{\mathit \pi}}{{\mathit \pi}}$) $971.1$ $\pm4.0$ 24 1991 EHS 400 ${{\mathit p}}{{\mathit p}}$ $979$ $\pm4$ 36 1991 OMEG 300 ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}}{{\mathit p}}{{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit p}}{{\mathit p}}{{\mathit K}}{{\overline{\mathit K}}}$ $956$ $\pm12$ 1990 SFM ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}}{{\mathit p}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $959.4$ $\pm6.5$ 24 1989 DM2 ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \omega}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $978$ $\pm9$ 24 1986 B HRS ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ X $985.0$ ${}^{+9.0}_{-39.0}$ 1982 B MPS 23 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit n}}$2 ${{\mathit K}_S^0}$ $974$ $\pm4$ 36 1981 MRK2 ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ X $975$ 37 1980 RVUE $986$ $\pm10$ 36 1978 HBC 0.7 ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ $969$ $\pm5$ 36 1977 ASPK 2$-$2.4 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit n}}$ , ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit n}}$ $987$ $\pm7$ 36 1973 CNTR ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit n}}$ MM $1012$ $\pm6$ 38 1973 ASPK 17 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit n}}$ $1007$ $\pm20$ 38 1973 ASPK 17 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit n}}$ $997$ $\pm6$ 38 1973 HBC 7 ${{\mathit \pi}^{+}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit p}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ 1 From the ${{\mathit D}^{\pm}}$ $\rightarrow$ ${{\mathit K}^{\pm}}{{\mathit K}^{+}}{{\mathit K}^{-}}$ Dalitz plot fit with the Triple-M amplitude in the multimeson model of AOUDE 2018 . 2 Using a relativistic Breit-Wigner function and taking into account the finite ${{\mathit D}_{{s}}}$ mass. 3 Breit-Wigner mass. Using finite width corrections according to FLATTE 1976 and ACHASOV 2005 , and the ratio $\mathit g_{ {{\mathit f}_{{0}}} {{\mathit K}} {{\mathit K}} }/\mathit g_{ {{\mathit f}_{{0}}} {{\mathit \pi}} {{\mathit \pi}} }$ = 0. 4 In the kaon-loop fit. 5 In the no-structure fit. 6 Systematic errors not estimated. 7 FLATTE 1976 parameterization. g$_{ {{\mathit f}_{{0}}} {{\mathit \pi}} {{\mathit \pi}} }$ = $329$ $\pm96$ MeV/c${}^{2}$ assuming g$_{ {{\mathit f}_{{0}}} {{\mathit K}} {{\overline{\mathit K}}} }$/g$_{ {{\mathit f}_{{0}}} {{\mathit \pi}} {{\mathit \pi}} }$=2. 8 Breit-Wigner mass. Using finite width corrections according to FLATTE 1976 and ACHASOV 2005 , and the ratio $\mathit g_{ {{\mathit f}_{{0}}} {{\mathit K}} {{\mathit K}} }/\mathit g_{ {{\mathit f}_{{0}}} {{\mathit \pi}} {{\mathit \pi}} }$ = $4.21$ $\pm0.25$ $\pm0.21$ from ABLIKIM 2005 . 9 In the kaon-loop fit following formalism of ACHASOV 1989 . 10 In the no-structure fit assuming a direct coupling of ${{\mathit \phi}}$ to ${{\mathit f}_{{0}}}{{\mathit \gamma}}$ . 11 FLATTE 1976 parameterization. Supersedes GARMASH 2005 . 12 FLATTE 1976 parameterization, $\mathit g_{ {{\mathit f}_{{0}}} {{\mathit K}} {{\overline{\mathit K}}} }/\mathit g_{ {{\mathit f}_{{0}}} {{\mathit \pi}} {{\mathit \pi}} }$ = $4.21$ $\pm0.25$ $\pm0.21$. 13 K-matrix pole from combined analysis of ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit n}}$ , ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}}{{\overline{\mathit K}}}{{\mathit n}}$ , ${{\mathit \pi}^{+}}$ ${{\mathit \pi}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ , ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ , ${{\mathit \pi}^{0}}{{\mathit \eta}}{{\mathit \eta}}$ , ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \eta}}$ , ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ , ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{0}}$ , ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{0}}$ , ${{\mathit K}^{+}}{{\mathit K}_S^0}$ ${{\mathit \pi}^{-}}$ at rest, ${{\overline{\mathit p}}}$ ${{\mathit n}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$ , ${{\mathit K}_S^0}$ ${{\mathit K}^{-}}{{\mathit \pi}^{0}}$ , ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{-}}$ at rest. 14 From the negative interference with the ${{\mathit f}_{{0}}{(500)}}$ meson of AITALA 2001B using the ACHASOV 1989 parameterization for the ${{\mathit f}_{{0}}{(980)}}$ , a Breit-Wigner for the ${{\mathit f}_{{0}}{(500)}}$, and ACHASOV 2001F for the ${{\mathit \rho}}{{\mathit \pi}}$ contribution. 15 Coupled-channel Breit-Wigner, couplings $\mathit g_{{{\mathit \pi}}}=0.09$ $\pm0.01$ $\pm0.01$, $\mathit g_{{{\mathit K}}}=0.02$ $\pm0.04$ $\pm0.03$. 16 Supersedes ACHASOV 1998I. Using the model of ACHASOV 1989 . 17 Supersedes ACHASOV 1998I. 18 In the narrow resonance'' approximation. 19 Assuming $\Gamma\mathrm {({{\mathit f}_{{0}}})}$= 40 MeV. 20 From a narrow pole fit taking into account ${{\mathit f}_{{0}}{(980)}}$ and ${{\mathit f}_{{0}}{(1200)}}$ intermediate mechanisms. 21 From the combined fit of the photon spectra in the reactions ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$ , ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \gamma}}$ . 22 Supersedes BARBERIS 1999 and BARBERIS 1999B 23 T-matrix pole. 24 From invariant mass fit. 25 On sheet II in a 2 pole solution. The other pole is found on sheet$~$III at (1039$−93\mathit i$) MeV. 26 On sheet II in a 2 pole solution. The other pole is found on sheet III at (963-29i) MeV. 27 Reanalysis of data from HYAMS 1973 , GRAYER 1974 , SRINIVASAN 1975 , and ROSSELET 1977 using the interfering amplitude method. 28 At high $\vert {{\mathit t}}\vert$. 29 At low $\vert {{\mathit t}}\vert$. 30 On sheet II in a 4-pole solution, the other poles are found on sheet$~$III at (953$−55\mathit i$) MeV and on sheet$~$IV at (938$−35\mathit i$) MeV. 31 Combined fit of ALDE 1995B, ANISOVICH 1994 , AMSLER 1994D. 32 On sheet II in a 2 pole solution. The other pole is found on sheet$~$III at (996$-103\mathit i$) MeV. 33 From sheet II pole position. 34 On sheet II in a 2 pole solution. The other pole is found on sheet$~$III at (797$-185\mathit i$) MeV and can be interpreted as a shadow pole. 35 On sheet II in a 2 pole solution. The other pole is found on sheet$~$III at (978$-28\mathit i$) MeV. 36 From coupled channel analysis. 37 Coupled channel analysis with finite width corrections. 38 Included in AGUILAR-BENITEZ 1978 fit. References: AAIJ 2019H JHEP 1904 063 Dalitz plot analysis of the $D^+\to K^-K^+K^+$ decay ABLIKIM 2015P PR D92 012007 Observation of the Isospin-Violating Decay ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit \pi}^{0}}{{\mathit f}_{{0}}{(980)}}$ ABLIKIM 2012E PRL 108 182001 First Observation of ${{\mathit \eta}{(1405)}}$ Decays into ${{\mathit f}_{{0}}{(980)}}{{\mathit \pi}^{0}}$ ECKLUND 2009 PR D80 052009 Study of the Semileptonic Decay ${{\mathit D}_{{s}}^{+}}$ $\rightarrow$ ${{\mathit f}_{{0}}{(980)}}{{\mathit e}^{+}}{{\mathit \nu}}$ and Implications for ${{\mathit B}_{{s}}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit f}_{{0}}}$ UEHARA 2008A PR D78 052004 High-Statistics Measurement of Neutral-Pion Pair Production in Two-Photon Collisions AMBROSINO 2007 EPJ C49 473 Dalitz Plot Analysis of ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \gamma}}$ Events at $\sqrt {s }$ $\simeq{}$ $\mathit M_{{{\mathit \phi}}}$ with the KLOE Detector AUBERT 2007AK PR D76 012008 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ , ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ and ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit K}^{+}}{{\mathit K}^{-}}$ Cross Sections Measured with Initial-State Radiation BONVICINI 2007 PR D76 012001 Dalitz Plot Analysis of the ${{\mathit D}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{+}}$ Decay MORI 2007 PR D75 051101 High Statistics Study of the Resonance in ${{\mathit \gamma}}$ ${{\mathit \gamma}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Production AMBROSINO 2006B PL B634 148 Study of the Decay ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit \gamma}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$ with the KLOE Detector GARMASH 2006 PRL 96 251803 Evidence for Large Direct $\mathit CP$ Violation in ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit \rho}{(770)}^{0}}{{\mathit K}^{\pm}}$ from Analysis of Three-Body Charmless ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit K}^{\pm}}{{\mathit \pi}^{\pm}}{{\mathit \pi}^{\pm}}$ Decays ABLIKIM 2005 PL B607 243 Resonances in ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \phi}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ and ${{\mathit \phi}}{{\mathit K}^{+}}{{\mathit K}^{-}}$ ANISOVICH 2003 EPJ A16 229 K Matrix Analysis of the ($\mathit IJ{}^{PC}$ = 00${}^{++}$)-wave in the Mass Region below 1900 MeV TIKHOMIROV 2003 PAN 66 828 Resonances in the ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ ${{\mathit K}_L^0}$ System Produced in Collisions of Negative Pions with a Carbon Target at a Momentum of 40 GeV ALOISIO 2002D PL B537 21 Study of the Decay ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \gamma}}$ with the KLOE Detector AITALA 2001A PRL 86 765 Study of the ${{\mathit D}_{{s}}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{+}}$ Decay Measurement of ${{\mathit f}_{{0}}}$ Masses and Widths ACHASOV 2000H PL B485 349 The ${{\mathit \phi}{(1020)}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \gamma}}$ Decay AKHMETSHIN 1999C PL B462 380 Study of the ${{\mathit \phi}}$ Decays into ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \gamma}}$ and ${{\mathit \eta}}{{\mathit \pi}^{0}}{{\mathit \gamma}}$ Final States AKHMETSHIN 1999B PL B462 371 First Observation of the ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$ Decay BARBERIS 1999B PL B453 316 A Partial Wave Analysis of the Centrally Produced ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ System in ${{\mathit p}}{{\mathit p}}$ Interactions at 450 ${\mathrm {GeV/}}\mathit c$ BARBERIS 1999 PL B453 305 A Partial Wave Analysis of the Centrally Produced ${{\mathit K}^{+}}{{\mathit K}^{-}}$ and ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ Systems in ${{\mathit p}}{{\mathit p}}$ Interactions at 450 ${\mathrm {GeV/}}\mathit c$ and New Information on the Spin of the ${{\mathit f}_{{J}}{(1710)}}$ BARBERIS 1999C PL B453 325 A Partial Wave Analysis of the Centrally Produced ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ System in ${{\mathit p}}{{\mathit p}}$ Interactions at 450 ${\mathrm {GeV/}}\mathit c$ BARBERIS 1999D PL B462 462 A Coupled Channel Analysis of the Centrally Produced ${{\mathit K}^{+}}{{\mathit K}^{-}}$ and ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Final States in ${{\mathit p}}{{\mathit p}}$ Interactions at 450 ${\mathrm {GeV/}}\mathit c$ BELLAZZINI 1999 PL B467 296 A Partial Wave Analysis of the Centrally Produced ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ System in ${{\mathit p}}{{\mathit p}}$ Interactions at 450 ${\mathrm {GeV/}}\mathit c$ KAMINSKI 1999 EPJ C9 141 Scalar Mesons and Multichannel Amplitudes OLLER 1999 PR D60 099906 (erratum) Meson-Meson Interaction in a Nonperturbative Chiral Approach OLLER 1999B NP A652 407 (erratum) Chiral Symmetry Amplitudes in the S-wave Isoscalar and Isovector Channels and the ${{\mathit \sigma}}$, ${{\mathit f}_{{0}}{(980)}}$, ${{\mathit a}_{{0}}{(980)}}$ Scalar Mesons OLLER 1999C PR D60 074023 N/D Description of Two Meson Amplitudes and Chiral Symmetry ACKERSTAFF 1998Q EPJ C4 19 Production of ${{\mathit f}_{{0}}{(980)}}$, ${{\mathit f}_{{2}}{(1270)}}$ and ${{\mathit \phi}{(1020)}}$ in Hadronic ${{\mathit Z}^{0}}$ Decay ALDE 1998 EPJ A3 361 Study of the ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ System with the GAMS-4000 Spectrometer at 100 ${\mathrm {GeV/}}\mathit c$ Also PAN 62 405 Investigation of the ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ System at a Primary Momentum of 100 ${\mathrm {GeV/}}\mathit c$ by using the GAMS-4000 Spectrometer ANISOVICH 1998B SPU 41 419 The Lightest Scalar Glueball LOCHER 1998 EPJ C4 317 Structure of ${{\mathit f}_{{0}}{(980)}}$ from a Coupled Channel Analysis of S-wave ${{\mathit \pi}}{{\mathit \pi}}$ Scattering ALDE 1997 PL B397 350 Study of the ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ System in ${{\mathit p}}{{\mathit p}}$ Central Collisions at 450 ${\mathrm {GeV/}}\mathit c$ BERTIN 1997C PL B408 476 Spin Parity Analysis of the Final State ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ from ${{\overline{\mathit p}}}{{\mathit p}}$ Annihilation at Rest in Hydrogen Targets at Three Densities ISHIDA 1996 PTP 95 745 An Analysis of ${{\mathit \pi}}{{\mathit \pi}}$ Scattering Phase Shift and Existence of ${{\mathit \sigma}{(555)}}$ Particle TORNQVIST 1996 PRL 76 1575 Resurrection of the ${{\mathit \sigma}}$ Meson ALDE 1995B ZPHY C66 375 Study of the ${{\mathit f}_{{0}}{(995)}}$ Resonance in the ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ Decay Channel AMSLER 1995B PL B342 433 High Statistical Study of ${{\mathit f}_{{0}}{(1500)}}$ Decay into ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ AMSLER 1995D PL B355 425 Coupled Channel Analysis of ${{\overline{\mathit p}}}{{\mathit p}}$ Annihilation into ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$, ${{\mathit \pi}^{0}}{{\mathit \eta}}{{\mathit \eta}}$ and ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \eta}}$ ANISOVICH 1995 PL B355 363 Two Resonance Structure of the ($\mathit I(\mathit J{}^{PC}) = 0(0{}^{++})$) ${{\mathit \pi}}{{\mathit \pi}}$ Amplitude in Mass Region around 1 GeV JANSSEN 1995 PR D52 2690 On the Structure of the Scalar Mesons ${{\mathit f}_{{0}}{(975)}}$ and ${{\mathit a}_{{0}}{(980)}}$ BUGG 1994 PR D50 4412 Coupled Channel Analysis of Data on ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ 3 ${{\mathit \pi}^{0}}$ , ${{\mathit \eta}}{{\mathit \eta}}{{\mathit \pi}^{0}}$, and ${{\mathit \eta}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ at Rest, with the N/D Method KAMINSKI 1994 PR D50 3145 Relativistic Effects in the Scalar Meson Dynamics ZOU 1994B PR D50 591 Remarks on $\mathit I = 0$ $\mathit J{}^{PC} = 0{}^{++}$ States: $\sigma /\epsilon$ and ${{\mathit f}_{{0}}{(975)}}$ MORGAN 1993 PR D48 1185 New Data on the ${{\mathit K}}{{\overline{\mathit K}}}$ Threshold Region and the Nature of the ${{\mathit f}_{{0}}{(S)}}$ Also NC A Conf. Suppl. Issues in Light Hadron Spectroscopy AGUILAR-BENITEZ 1991 ZPHY C50 405 Inclusive Particle Production in 400 ${\mathrm {GeV/}}\mathit c$ ${{\mathit p}}{{\mathit p}}$ Interactions ARMSTRONG 1991 ZPHY C51 351 Study of the Centrally Produced ${{\mathit \pi}}{{\mathit \pi}}$ and ${{\mathit K}}{{\overline{\mathit K}}}$ Systems at 85 and 300 ${\mathrm {GeV/}}\mathit c$ BREAKSTONE 1990 ZPHY C48 569 The Reaction pomeron pomeron $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ and an Unusual Production Mechanism for the ${{\mathit f}_{{2}}{(1270)}}$ AUGUSTIN 1989 NP B320 1 Study of the ${{\mathit J / \psi}}$ Decay into Five Pions ABACHI 1986B PRL 57 1990 Observation of Tensor and Scalar Mesons Produced in ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Annihilation at 29 GeV ETKIN 1982B PR D25 1786 Amplitude Analysis of the ${{\mathit K}_S^0}{{\mathit K}_S^0}$ System Produced in the Reaction ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ ${{\mathit n}}$ at 23 ${\mathrm {GeV/}}\mathit c$ GIDAL 1981 PL 107B 153 Observation of ${{\mathit S}^{}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ in ${{\mathit \psi}}$ Decay ACHASOV 1980 SJNP 32 566 Nature of Scalar Resonances AGUILAR-BENITEZ 1978 NP B140 73 Study of a ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ Plus Threshold Enhancement Observed in the Final States ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}_S^0}$ Pions at 700 to 760 ${\mathrm {MeV}}/\mathit c$ LEEPER 1977 PR D16 2054 A Study of the Reactions ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit n}}$ and ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit n}}$ at 1.98 and 2.41 ${\mathrm {GeV/}}\mathit c$ BINNIE 1973 PRL 31 1534 Direct Evidence for the ${{\mathit S}^{}}$ Meson near the ${{\mathit K}}{{\overline{\mathit K}}}$ Threshold GRAYER 1973 Tallahassee Coupled Channel Analysis in the ${{\mathit K}}{{\overline{\mathit K}}}$ Threshold Region HYAMS 1973 NP B64 134 ${{\mathit \pi}}{{\mathit \pi}}$ Phase Shift Analysis from 600 to 1900 MeV PROTOPOPESCU 1973 PR D7 1279 ${{\mathit \pi}}{{\mathit \pi}}$ Partial Wave Analysis from Reactions ${{\mathit \pi}^{+}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \Delta}^{++}}$ and ${{\mathit \pi}^{+}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \Delta}^{++}}$ at 7.1 ${\mathrm {GeV/}}\mathit c$	2022-09-29T20:55:39	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8240457773208618, "perplexity": 2584.163008766422}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335365.63/warc/CC-MAIN-20220929194230-20220929224230-00531.warc.gz"}
http://webarchive.nationalarchives.gov.uk/20110809091832/http:/www.teachingandlearningresources.org.uk/node/29890	This snapshot, taken on 10/08/2011 , shows web content acquired for preservation by The National Archives. External links, forms and search may not work in archived websites and contact details are likely to be out of date. The UK Government Web Archive does not use cookies but some may be left in your browser from archived websites. # Questions Use this set of questions to test your knowledge on proportion, ratio and graphs. ## Exercise 1. Which of these number pairs are in proportion and which are not? Convince a friend. 1. (12, 3), (20, 4) 2. (6, 48), (21, 168) 3. (5, 15), (10, 20) 4. (28, 7), (96, 24), (16, 4) 2. A photograph is 150 mm by 100 mm. Which of the following gives the dimensions of an accurate enlargement of the photograph? 1. 450 mm by 350 mm 2. 375 mm by 250 mm What is the scale factor of the enlargement (i.e. the constant of proportionality)? 3. In each of these examples the relationship between y and x is linear; that is, as x changes, y changes at a constant rate. In each case, state the rate of change and determine whether y is proportional to x. 1. x y 1 2 3 4 5 … 6 10 14 18 22 … 2. x y 1 2 3 4 5 … 0.2 0.4 0.6 0.8 1 … 3. x y 1 2 3 4 5 … 12 10 8 6 4 … 4. x y 5 10 15 20 25 … 8 16 24 32 40 … Plot graphs for each of these relationships and relate the features of your graphs to what you have discovered. For each of the examples, can you find an equation connecting y and x? 4. Which of the following situations are examples of direct proportion and which are not? 1. Cost of purchasing a given quantity of tomatoes at £1.38 per kilogram. 2. Distance travelled on a bicycle in a given time, at a steady speed of 15 mph. 3. Number of dollars you can purchase for your money, at the rate of \$1.45 for every pound sterling, together with a flat rate commission of £5 per transaction. 4. Table of distances in miles converted roughly into kilometres. 1. No, because $\frac{12}{3}=4$ and $\frac{20}{4}=5$ 2. Yes, because $\frac{6}{48}=\frac{21}{168}=\frac{1}{8}$ 3. No, because $\frac{5}{15}=\frac{1}{3}$ and $\frac{10}{20}=\frac{1}{2}$ 4. Yes, because $\frac{28}{7}=\frac{96}{24}=\frac{16}{4}=4$ 1. No, because $\frac{450}{150}=3$ and $\frac{350}{100}=3.5$ 2. Yes, because $\frac{375}{150}=\frac{250}{100}=2.5$ Scale factor of enlargement is 2.5 1. $m=4$ (y changes by 4 for every 1 of x). Not a proportion, because $\frac{6}{1}=6$, $\frac{10}{2}=5$, etc. 2. $m=0.2$. A proportion, because $\frac{0.2}{1}=\frac{0.4}{2}=\dots =0.2$ 3. $m=-2$. Not a proportion, because $\frac{12}{1}=12$, $\frac{10}{2}=5$, etc. 4. $m=\frac{8}{5}$ (y changes by 8 for every 5 of x, or by $\frac{8}{5}$ for every 1 of x). A proportion, because $\frac{8}{5}=\frac{16}{10}=\dots =1.6$ • Equations are 1. $y=4x+2$ 2. $y=0.2x$ 3. $y=14-2x$ 4. $y=\frac{8x}{5}$ 1. Yes – cost of tomatoes is proportional to quantity purchased. 2. Yes – distance travelled is proportional to the time on the journey. 3. No – because of the fixed charge of £5 (but it is a linear relationship). 4. Yes – distance in kilometres is proportional to distance in miles.	2013-05-19T03:29:03	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 24, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7192308902740479, "perplexity": 839.941167050824}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368696383218/warc/CC-MAIN-20130516092623-00053-ip-10-60-113-184.ec2.internal.warc.gz"}
https://mooseframework.inl.gov/python/TestHarness.html	# TestHarness The TestHarness is the Python code behind the run_tests script in MOOSE and every MOOSE-based application. It is responsible for finding tests and running them. Here we describe how to use the run_tests script and how to create your own tests. The ideas behind testing are described over the in the MOOSE Test System documentation. ## run_tests run_tests is a small Python script that can be found in every MOOSE-based application and in the framework itself (under moose/test). The run_tests script will find tests and run them with your compiled binary for your app. ### Basic Usage To run the tests for any application, make sure the executable is built (generally by running make see the Build System) and then do: ./run_tests -j 8 There are many options for run_tests, but the -j option shown above is by far the most widely used. It tells the run_tests script how many processors to utilize on your local machine for running tests concurrently. Put the correct number there (instead of 8). The script will then go find and run your tests and display the results. ### More Options To see more options for run_tests you can invoke it with -h. There are many options to look through, but some of the important ones are: • --failed-tests: Runs the tests that just failed. Note: as long as you keep using the --failed-tests option the set of failed tests will not change. • --n-threads #: Causes the tests to run with # of (OpenMP/Pthread/TBB) threads. • -p #: Causes the tests to run with # MPI processes. Useful for guaranteeing that you get the same result in parallel! • --valgrind: Run all of the tests with the Valgrind utility. Does extensive memory checking to catch segfaults and uninitialized memory errors. • --recover: Run all of the tests in "recovery" mode. This runs the test halfway, stops, then attempts to "recover" it and run until the end. This is very rigorous testing that tests whether everything in your application can work with restart/recover. • --opt (The default) Builds an optimized executable suitable for running calculations. • --dbg An executable meant for use in a debugger (like gdb or lldb). Will be very slow and not meant to be used on large problems • --oprof Not normally used. Can be used for "code profiling": running your code with a utility like oprof, gprof, vtune, etc. • --pro An alias to --oprof • --devel Something in-between opt and dbg. Attempts to be faster but also does some more run-time checks (asserts and mooseAsserts) ## testroot The testroot file is a small configuration file that is formatted like a MOOSE input file. It is read by the run_tests script. It should be placed in the root of your application directory (i.e. right next to where the binary is). Some things you can set in that file are: • app_name: A unique, short name for your application. • allow_warnings: true by default, set this to false to make all warnings from running tests be _errors_ instead. • allow_override and allow_unused: true by default if set to false then syntax errors in your test input files will be treated as errors. The one thing we do not recommend is enforcing that the use of deprecated code should be treated like an error. That is entirely too rigid of a requirement and impedes the normal flow of development. Instead, developers should periodically run their tests with --error-deprecated to see if any of their tests are using deprecated code / parameters and then fix them up at that point. The MOOSE team is not responsible for fixing deprecated code. ## Influential Environment Variables #### PYTHONPATH PYTHONPATH instructs python to include the designated paths while attempting to import python modules. While normally not needing to be set, sometimes it is necessary. For example, when testing the TestHarness (unittests). Another use-case, is when a developer wants to utilize the moosedocs system for creating moose documentation (the website you are using right now). In either case, when you need to modify PYTHONPATH for MOOSE related development, you will almost always want to point it at moose/python. PYTHONPATH functions just as PATH does (semi-colon separate list of paths, for which items contained within paths on the left, are found before items contained within paths on the right). #### METHOD Set the METHOD environment variable to one of the following to control which type of application binary to use: Variable NameArgumentUsage METHODoptTestHarness will use the binary built with optimizations while running tests: your_appname-opt (the default) METHODdbgTestHarness will use the binary built with debugging symbols while running tests: your_appname-dbg METHODoprofTestHarness will use the binary built with code profiling while running tests: your_appname-oprof METHODproAn alias for oprof METHODdevelSomething in-between opt and dbg note The methods described here can also be controlled via command line arguments. See "More Options" above. #### MOOSE_TERM_FORMAT Set MOOSE_TERM_FORMAT to any or all of the following, as well as in a particular order and case (restricted) to control where, what, and how the TestHarness prints that specific item: Variable NameArgumentUsage MOOSE_TERM_FORMATcPrint caveats MOOSE_TERM_FORMATjPrint justification filler MOOSE_TERM_FORMATpPrint pre-formated status (10 character buffer fill) MOOSE_TERM_FORMATsPrint status MOOSE_TERM_FORMATn-NPrint test name MOOSE_TERM_FORMATtPrint test completion time Example, if we set MOOSE_TERM_FORMAT to tpNsc, we would print the time, pre-fromatted status, test name (converted to upper-case), long naming status, and then the caveats. In that order: MOOSE_TERM_FORMAT=tpNsc ./run_tests --re=simple_diffusion.test -p4 -t [0.144s] OK KERNELS/SIMPLE_DIFFUSION.TEST [OVERSIZED] Caveats with the... caveats of MOOSE_TERM_FORMAT; When caveats are requested to be printed last, the TestHarness will allow the entire caveat to print, regardless of MOOSE_TERM_COLS (see below). #### MOOSE_TERM_COLS Set MOOSE_TERM_COLS to a positive integer, to set the available terminal column count to this amount: Variable NameArgumentUsage MOOSE_TERM_COLS(int)Allow for this many columns when printing output Example, if we set MOOSE_TERM_COLS to 50, we will restrict the default amount of columns the TestHarness normally uses while printing output: MOOSE_TERM_COLS=50 ./run_tests --re=simple_diffusion.test	2019-04-23T12:31:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2656783163547516, "perplexity": 4480.265141046137}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578602767.67/warc/CC-MAIN-20190423114901-20190423140901-00439.warc.gz"}
https://gea.esac.esa.int/archive/documentation/GDR1/Catalogue_consolidation/sec_cu1cva/sec_cu9gat.html	# 7.5 Catalogue statistics and plots ## 7.5.1 Introduction Author(s): Raúl Borrachero and Frédéric Arenou The data fields of the main table of the Gaia Catalogue and a short description of these fields are indicated Table 7.4. A more extensive description of these fields is available where all other tables concerning variability and crossmatch are also described. The TGAS subset has the same content plus two more fields, Hipparcos and Tycho-2_id which are respectively the Hipparcos identifier and the Tycho-2 identifier. A summary of statistics and plots by Gaia analysis Tool (GAT) on these fields for the 1 142 679 769 sources is shown Table 7.5 and following pages.	2022-07-01T14:45:10	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 103, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.469688355922699, "perplexity": 4243.646954406119}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103941562.52/warc/CC-MAIN-20220701125452-20220701155452-00178.warc.gz"}
https://pdglive.lbl.gov/DataBlock.action?node=S047M&home=sumtabB	${{\mathit \Omega}_{{c}}^{0}}$ MASS VALUE (MeV) EVTS DOCUMENT ID TECN COMMENT $\bf{ 2695.2 \pm1.7}$ OUR FIT Error includes scale factor of 1.3. $\bf{ 2695.2 {}^{+1.8}_{-1.6}}$ OUR AVERAGE Error includes scale factor of 1.3. See the ideogram below. $2693.6$ $\pm0.3$ ${}^{+1.8}_{-1.5}$ 725 2009 BELL ${{\mathit \Omega}^{-}}{{\mathit \pi}^{+}}$ in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ $2694.6$ $\pm2.6$ $\pm1.9$ 40 1 2001 CLE2 ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}$ $10.6$ GeV $2699.9$ $\pm1.5$ $\pm2.5$ 42 2 1994 H E687 ${{\mathit \gamma}}{}^{}\mathrm {Be}$, ${{\overline{\mathit E}}}_{\gamma }$= 221 GeV • • We do not use the following data for averages, fits, limits, etc. • • $2705.9$ $\pm3.3$ $\pm2.0$ 10 3 1993 E687 ${{\mathit \gamma}}{}^{}\mathrm {Be}$, ${{\overline{\mathit E}}}_{\gamma }$= 221 GeV $2719.0$ $\pm7.0$ $\pm2.5$ 11 4 1992 H ARG ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}10.6$ GeV $2740$ $\pm20$ 3 1985 B SPEC ${{\mathit \Sigma}^{-}}{}^{}\mathrm {Be}$ 135 ${\mathrm {GeV/}}\mathit c$ 1 CRONIN-HENNESSY 2001 sees $40.4$ $\pm9.0$ events in a sum over five channels. 2 FRABETTI 1994H claims a signal of $42.5$ $\pm8.8$ ${{\mathit \Sigma}^{+}}{{\mathit K}^{-}}{{\mathit K}^{-}}{{\mathit \pi}^{+}}$ events. The background is about 24 events. 3 FRABETTI 1993 claims a signal of $10.3$ $\pm3.9$ ${{\mathit \Omega}^{-}}{{\mathit \pi}^{+}}$ events above a background of $5.8$ events. 4 ALBRECHT 1992H claims a signal of $11.5$ $\pm4.3$ ${{\mathit \Xi}^{-}}{{\mathit K}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{+}}$ events. The background is about 5 events. ${{\mathit \Omega}_{{c}}^{0}}$ mass (MeV) References: SOLOVIEVA 2009 PL B672 1 Study of ${{\mathit \Omega}_{{c}}^{0}}$ and ${{\mathit \Omega}_{{c}}^{*0}}$ Baryons at Belle CRONIN-HENNESSY 2001 PRL 86 3730 Observation of the ${{\mathit \Omega}_{{c}}^{0}}$ Charmed Baryon at CLEO FRABETTI 1994H PL B338 106 Observation and Mass Measurement of ${{\mathit \Omega}_{{c}}^{0}}$ $\rightarrow$ ${{\mathit \Sigma}^{+}}{{\mathit K}^{-}}{{\mathit K}^{-}}{{\mathit \pi}^{+}}$ FRABETTI 1993 PL B300 190 First Evidence of ${{\mathit \Omega}_{{c}}^{0}}$ $\rightarrow$ ${{\mathit \Omega}^{-}}{{\mathit \pi}^{+}}$ ALBRECHT 1992H PL B288 367 Evidence for the Production of the Charmed, Doubly Strange Baryon ${{\mathit \Omega}_{{c}}}$ in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ Annihilation BIAGI 1985B ZPHY C28 175 Properties of the Charmed Strange Baryon ${{\mathit A}^{+}}$ and Evidence for the Charmed Doubly Strange Baryon ${{\mathit T}^{0}}$ at 2.74 ${\mathrm {GeV/}}\mathit c{}^{2}$	2022-10-01T08:31:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7760272026062012, "perplexity": 6010.360315780036}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335573.50/warc/CC-MAIN-20221001070422-20221001100422-00136.warc.gz"}
https://control.com/textbook/instrument-connections/fiber-optics/	# Fiber Optic Data Communication ## Chapter 10 - Instrument Connection and Communication Light has long been used as a long-range signaling medium. While communication by light through open air is still possible using modern technology, it is far more practical in most cases to channel the light signals through a special strand of optically transparent material called an optical fiber. When packaged in a protective sheath, it is known as a fiber optic cable. The transmission of light through a “light pipe” was demonstrated as early as 1842 by Daniel Colladon and Jacques Babinet in Paris, using a running stream of water to guide a beam of light. Many modern houses in the United States are equipped with light-pipes directing natural sunlight into rooms for illumination, without the use of “skylight” ceiling windows. Modern fiber optic cables apply similar optical principles to very small-diameter fibers of transparent material (usually ultra-pure glass), able to convey optical energy and optically-encoded information. ### Fiber optic data communication Simply put, an optical fiber is a “pipe” through which light flows. This is, of course, merely an analogy for how an optical fiber works, but it conveys the basic idea. The interface between a piece of electronic equipment and an optical fiber consists of an optical source (typically an LED or a semiconductor laser) to generate light signals from electrical signals, and an optical detector (typically a photodiode or phototransistor) to generate electrical signals from received light signals. The predominant use of optical fiber in modern industry is as a data communication medium between digital electronic devices, replacing copper-wire signal and network cabling. An illustration showing two digital electronic devices communicating over a pair of optical fibers appears here, each fiber “conducting” pulses of light (representing serial digital data) from an LED source to a photodiode detector: The following photograph shows a serial converter (the black rectangular plastic box with a blue label) used to convert optical data pulses entering and exiting through orange-jacketed optical cables (on the left) into EIA/TIA-232 compliant electrical signals through a DB-9 connector (on the right) and vice-versa, allowing the electronic serial data device on the right-hand side of the photograph to communicate via fiber optic cabling: Note how the two optical fiber ports on the converter body are labeled “R” and “T” for Receive and Transmit, respectively. Serial devices with built-in electronic/optical converters will similarly label their optical ports. For this device, connection to each of the optical fibers is made using an “ST” style connector, with a quarter-turn locking ring holding each one in place (much like the quarter-turn barrel body of a “BNC” style electrical connector). The next photograph shows a pair of optical fibers terminated with ST-style connectors. White plastic caps cover the connector tips, keeping the glass fiber ends protected from dust and abrasion: As a data pathway, optical fiber enjoys certain advantages over electrical cable, including: • Much greater bandwidth (data-carrying capacity), estimated to be in the terahertz range • Much less equivalent signal power loss per unit cable length (less than 1 dB per kilometer compared with 25 dB per kilometer for coaxial cable) • Complete immunity to external “noise” sources • No radiation of energy or data from the cable, thus will not create interference nor be liable to eavesdropping • No electrical conductivity, allowing safe routing of cables near high voltage conductors • Total galvanic isolation (i.e. no electrically conductive connection) between data devices, allowing operation at different electrical potentials • Safe for use in areas with explosive vapors, dust, and/or fibers These advantages deserve some elaboration. The superior bandwidth of fiber-optic cable is so dramatic that the present-day (2015) limitation on data transfer rates for most fiber-optic installations is the electronic devices at each end, and not the optical fiber itself! This, combined with the low inherent power loss of optical fiber, makes it an ideal medium for long-range data communication such as telephone and internet. Thousands of miles of optical fiber cable have been buried in underground trenches, laid down on sea floors, strung as overhead lines, and used as “patch” cables in room-scale applications since the advent of affordable optical cabling in the 1980’s. The “tech boom” of the 1990’s saw an impressive amount of trans-continental and inter-continental optical fiber installation, paving the way for the global expansion of internet services into the 21st century. The limitations of electronics at each end of these long fibers means we have not yet begun to tap their full data-carrying capacity, either. Conveying data in photonic – as opposed to electronic – form means there is absolutely no such thing as capacitive or inductive coupling with external systems as there is with conductive wire cable, which not only means optical fiber communication is immune to external interference but also that the optical signals cannot create interference for any other system. Since optical fibers are customarily manufactured from glass which is electrically non-conductive, it is possible to route optical fibers alongside high-voltage power lines, and also connecting together devices at vastly different electrical potentials from each other, with no risk of bridging those differing potentials. Finally, the low power levels associated with optical fiber signals also makes this technology completely safe in areas where explosive compounds in the atmosphere might otherwise be ignited by faults in electrical communications cable. Optical fibers also suffer from some unique limitations when compared against electrical cable, including: • Need to avoid tight bend radii for optical cables • Connections need to be extremely clean • Specialized tools and skills necessary for installation and maintenance • Expensive testing equipment While electrical “transmission line” signal cables must also avoid sharp bends and other discontinuities caused by cramped installations, this need is especially pronounced for optical fiber (for reasons which will be explained later in this section). Since fiber-to-fiber connections consist of glass pressed against glass, the presence of even microscopic contaminants such as dust particles may damage fiber optic connectors if they aren’t cleaned prior to insertion. Cutting, preparing, and terminating optical fiber cables requires its own set of specialized tools and skills, and is not without unique hazards. Lastly, the test equipment necessary to check the integrity of an optical pathway is similarly specialized and typically quite expensive. ### Fiber optic sensing applications Optical fibers find applications beyond electronic data cable replacement, though, which means they will be a growing presence in the field of industrial instrumentation above and beyond their use as serial data communication cables. Some industrial process transmitters use optical fibers to send and receive light between the transmitter electronics and an optically-based primary sensing element. This may be as simple as a non-contact proximity switch using light to sense the presence of an object within a gap between the two fibers’ ends, or as sophisticated as a chemical analyzer relying on the absorption of specific light wavelengths to detect the presence of a chemical substance in a solution. #### Turbine flowmeter sensing One example of a specialized application for optical fibers is shown in this photograph of a paddlewheel-style liquid flowmeter using a pair of optical fibers to convey light to and from the paddlewheel assembly, where the spinning paddlewheel serves to “chop” the light beam and thereby represent liquid flow rate as a frequency of pulsing light: An end-view of the two optical fibers is shown in the next photograph. When installed as a working system, these two fibers will plug into a flow transmitter device sending a continuous beam of light through one fiber and sensing the pulsed light signal coming back from the paddlewheel through the other fiber: #### Fabry-Perot interferometry temperature measurement Another example of a specialized application for optical fibers is measurement of high temperatures using the Fabry-Perot interferometry method. This technology utilizes a small, thin disk of sapphire as a temperature sensor. The thickness of this disk as well as the speed of light through the sapphire are both temperature-dependent, which means a photon261 of light shot at the face of the disk will reflect off the back face of the disk and return to the source at different times depending on the temperature of the disk. In a Fabry-Perot interferometer instrument, the “optical thickness” of the sapphire disk is measured by sending a continuous beam of white light to the disk and receiving the reflected light from the disk through a single optical fiber, the optical interference resulting from the incident and reflected light beams representing the disk’s temperature. This novel method of temperature measurement shows promise for certain challenging industrial process applications such as high-temperature measurement inside slagging coal gasifiers used to efficiently extract energy and chemical feedstocks from coal: #### Dissolved oxygen measurement Yet another example of a specialized application for optical fibers is the measurement of dissolved oxygen in aqueous solutions using the dynamic luminescence quenching or fluorescence quenching method. This technology uses a thin layer of solid material containing molecules known to fluoresce with red light when exposed to visible light of a shorter wavelength (typically green or blue). Oxygen molecules present in the liquid solution tend to bond with the fluorescing molecules in the sensor and inhibit that fluorescence, thus providing a means of measuring oxygen concentration near the sensor: the less O$$_{2}$$ dissolved in solution, the stronger the fluorescence (i.e. more red light received, for a longer duration); the more O$$_{2}$$, the less fluorescence. Optical fibers convey both the incident (green or blue) and returned (red) light between the wet sensing element and the interpreting electronics. In both the Fabry-Perot interferometry and the fluorescence quenching sensors, the function of the fiber optic cable is to physically separate the sensing element from the sophisticated and fragile electronic transmitter needed to interpret the optical signal as a process variable measurement. #### Arc flash detection There is at least one application where the optical fiber itself is the sensing element: arc flash detection within high-voltage switchgear cabinets. “Arc flash” is the phenomenon of intense heat and light developed at a high-current electrical arc, especially a phase-to-phase arc between electric power conductors where there is little circuit resistance to limit fault current. High-voltage switchgear is constructed in such a way as to extinguish the arc normally developed at the contacts during each “opening” cycle, but certain faults within a piece of switchgear may inhibit this extinguishing function. In such cases the potential for equipment damage and threat to human health and life is severe. If a bare (unjacketed) optical fiber is properly arranged within a piece of switchgear, an arc flash event will inject enough light through the fiber that some of it will be detected at the far end where it meets a light-sensitive receiver. Since the fiber itself is not electrically conductive, there is no risk of conducting a high-voltage arc back to this receiver. The receiver, meanwhile, serves the purpose of commanding any “upstream” switchgear to trip open in the event of a detected arc fault. The early detection of arc flash by optical means rather than the time-delayed detection of the same fault by overcurrent or current-imbalance detection results in much faster clearing of the faulted switchgear from the power grid, both limiting equipment damage and limiting the potential for injury or death. ### Fiber optic cable construction Communication-grade optical fibers are manufactured from fused silica (SiO$$_{2}$$) glass of exceptional purity. A single strand of optical fiber made from this glass called the “core” serves as a waveguide for the light. The core is surrounded by another layer of glass called the “cladding” which has a different index of refraction necessary to “channel” the majority of the optical energy through the core and inhibit “leakage” of optical power from the cable. Additional layers of plastic and other materials around the core/cladding center provide coloring (for fiber identification in multi-fiber cables), protection against abrasion, and tensile strength so the cable will not suffer damage when pulled through conduit. The purpose of building a fiber optic cable with a core and a cladding having different refractive indices (i.e. different speeds of light) is to exploit a phenomenon called total internal reflection, whereby rays of light reflect off the interface between core and cladding to prevent its unintentional escape from the core at any point along the length of the fiber. When light crosses an interface between two materials having different speeds, the light beam will become refracted as a function of those two speeds as described by Snell’s Law: Snell’s Law relates the sine of the incident angle to the sine of the refracted angle as a ratio to each material’s speed of light, the material possessing the greatest speed of light (i.e. the lowest refractive index value) exhibiting the greatest angle as measured from perpendicular to the interface: ${{\sin \theta_1} \over v_1} = {{\sin \theta_2} \over v_2}$ According to Snell’s Law, there will be a critical angle at which the incident light ray will refract to being parallel to the interface. Beyond this critical angle, the light ray ideally reflects off the interface and never enters the second material at all. This is the condition of total internal reflection, and it is what we desire in an optical fiber where the core is the first material and the cladding is the second material: Both the core and cladding of an optical fiber are manufactured from the same base material of ultra-pure fused silica, but “doped” with specific impurities designed to alter the refractive index of each one (raising the refractive index of the core to decrease its optical velocity and lowering the refractive index of the cladding to increase its optical velocity). The diameter of core and cladding vary with the type of optical fiber, but several standard sizes have emerged in the industry, each one specified by the diameter of the core followed by the diameter of the cladding expressed in microns (millionths of a meter). A common optical fiber standard in the United States is 62.5/125 (62.5 micron core diameter, 125 micron cladding diameter), and 50/125 in Europe. Some less common standard core/cladding diameters include 85/125 and 100/140. To give some perspective on the physical size of an optical fiber core, the following photograph shows the end-view of an “ST” style fiber optic connector for a 50/125 micron cable, held by my hand. A green LED light source is shining into the other end of this cable, the tiny green dot visible at the center of the ST connector revealing the diameter of the 50 micron core: Several other layers of material must be placed over the core and cladding to form a rugged optical fiber. A plastic jacket with a typical diameter of 250 microns (0.25 mm) covers the cladding, and provides a base for color-coding the fiber. This three-layer construction of core, cladding, and jacket is known in the industry as Primary Coated Optical Fiber, or PCOF. PCOF is still too fragile for end-user applications, and so another layer of plastic is typically added (900 microns in diameter) to make the fiber Secondary Coated Optical Fiber, or SCOF. When wrapped with fiberglass or Kevlar fibers around the secondary jacket for tensile strength, and a protective PVC plastic outer layer to protect against abrasion, the cable becomes suitable for indoor use. Cables suitable for outdoor, direct burial, and undersea applications usually take the form of groups of PCOF fibers packaged within an extremely rugged encasement with metal strands for tensile strength. Sometimes a gel material helps cushion the fibers from each other within the confines of the cable sheath. ### Multi-mode and single-mode optical fibers In any sort of waveguide – optical, electrical, or even acoustical (sound) – the signal energy may be able to propagate down the waveguide in different orientations. This is true for optical fibers where the core diameter is relatively large compared to the wavelength of the light: there will be many alternative pathways for light to travel along the length of a fiber’s core. Optical fibers with core diameters of 50 microns or more are referred to as multi-mode fibers, because multiple independent pathways, or “modes”, of light are possible within the core’s width. If an optical fiber’s core is manufactured to be small enough, relative to the wavelength of the light used, the fiber will only support one “mode” or pathway down its core. Such fiber is called single-mode. Single-mode fiber cores typically range from 4 to 10 microns in diameter, with 8 micron being typical. The purpose of single-mode optical fiber is to avoid a problem called modal dispersion. When multiple “modes” of light propagate down the length of an optical fiber, they don’t all have the same length. That is to say, some modes actually take a straighter (and more direct) path down the fiber’s core than others. The reason this is a problem is that this phenomenon corrupts the integrity of high-speed (i.e. short-period) pulses. An exaggerated illustration of this problem appears here, showing the relative path lengths of three different light rays, each one entering the fiber core at a slightly different angle. The light ray closest to parallel with the core’s centerline finds the shortest “mode” to the fiber’s end, and arrives in the least amount of time: With different “modes” of light arriving at different times from the same incident pulse, the received light pulse at the exiting end of the fiber will no longer possess a crisp “square-wave” shape. Instead, the pulse will be “smeared” over time, occupying a larger time span. This poses a bandwidth limit on the fiber, as there will be some maximum pulse frequency at which adjacent pulses will begin to merge together and become indistinguishable. The longer the length of optical fiber, the more pronounced this dispersion will be. This problem is most evident in applications where the fiber length is very long (hundreds of miles) and the data rate is very high (hundreds of megahertz). Thus, it is a significant problem for long-distance data trunk cables such as those used for transcontinental and intercontinental internet traffic. Single-mode optical fiber completely averts this problem by eliminating multiple modes within the fiber core. When there is only one mode (pathway) for light to travel, there will be exactly one distance for light to travel from one end of the fiber to the other. Therefore, all portions of the incident light pulse experience the same travel time, and the light pulse arrives at the far end of the cable suffering no modal dispersion: As you can imagine, single-mode fiber is more challenging to splice than multi-mode fiber, as the smaller core diameter provides less room for alignment error. A compromise solution to the problem of modal dispersion in multi-mode fibers is to manufacture the core glass with a graded index of refraction rather than a homogeneous index of refraction. This means the concentration of doping material in the glass varies from the center of the core to the outer diameter of the core where it interfaces with the cladding. The result of this graded dispersion is that modes traveling closest to the core’s centerline will experience a slower speed of light (i.e. greater index of refraction) than modes near the edge of the core, which means the difference in travel time from one mode to the next will be less pronounced than within normal “step-index” fibers. Of course, this also means graded-index optical fiber is more costly to manufacture than step-index optical fiber. ### Fiber optic cable connectors, routing, and safety One of the most popular styles of single-fiber connector is the so-called “ST” style, which uses a quarter-turn locking barrel to secure the connector into its matching socket: Communication patch cables such as the one shown above come in pairs of fibers, one for receiving and one for transmitting. Note how the plastic strain-relief grips between the metal barrel of each connector and each orange-jacketed cable are color-coded (one white, one black) for easy identification at each end of the cable. An older style of connector based on the type used to connect small coaxial cables together is the “SMA” style, which used a threaded barrel to lock each fiber in place. The SMA-style connectors were very secure, but laborious to engage and disengage due to the fine pitch of the barrel’s threads and the subsequent need to turn the barrel multiple rotations (versus one-quarter turn of the barrel for an ST connector). Given that communication patch cables typically have two fibers (one for each direction of data flow), connector styles have emerged to accommodate fiber pairs. One such style is the so-called “SC” connector, with a pair of side-by-side plugs accommodating twin optical fibers. Terminating a bare cable of fibers with individual connectors is a time-consuming process, requiring the technician to unbundle the individual fibers, strip the jacketing off of each one to reveal the core and cladding, cleave each glass fiber to give it a flat end, and finally insert and secure each fiber into its respective connector. Typical fiber connectors use either a “hot-melt” or a chemical epoxy system of attachment, where the glue adheres to the strain-relief fibers of the cable for tensile strength, while the central glass fiber protrudes through a small hole in the center of the connector tip. This protruding glass fiber must be carefully cut and polished to produce a flat end suitable for engagement with another optical fiber aligned to its center. Optical fibers may be spliced mid-way in a cable run, although this practice should be avoided whenever possible. If the fibers are multi-mode, the splicing may be done using “butt” connectors but the power losses may be unacceptable. Alternatively, stripped fibers may be inserted into both ends of a small-diameter tube filled with gel having the same index of refraction as the core glass, to “conduct” light with as little loss as possible from one fiber core to the other. A very good technique often applied to single-mode fiber is that of fusion splicing, where two single-mode fiber ends are literally melted together using an electric arc so that they form one seamless glass fiber. The alignment of fibers prior to fusion is done under the view of a microscope, and often with the aid of a light source on one end and an optical power meter on the other end to give a quantitative measurement of alignment accuracy. When the two fibers are aligned as close as possible, the electric arc is fired to melt the two fibers together, creating a single fiber. Fusion splicing is the method of choice for long-distance runs of single-mode fiber, where low power loss and high integrity of the splice are paramount factors. When laying optical fiber in wire trays, pulling through rigid conduit, or arranging it in connection panels, an important physical consideration is to maintain a minimum bend radius at all points along the fiber’s length. This is important because sharp bends will cause light to “leak” out of the fiber core and into the cladding where it may then escape the cable altogether. A sharp bend in an optical fiber will cause the angle between the light ray and the core/cladding interface to reach the critical point where total internal reflection no longer occurs: The light leakage from an optical fiber may be dramatic if the bend is sharp enough. On an indoor cable, using visible laser light, you can actually see the light “leak” through to the PVC outer coating on the outside of the cable! Junction boxes and connection panels where excess lengths of fiber optic cabling may be coiled will typically provide plastic forms over which those loops of cable may be bent, the radius of that plastic form exceeding the manufacturer’s specification for minimum bend radius. A common way in which the minimum bend radius requirement is violated is when a cable tie is used to anchor a fiber optic cable to some sturdy surface such as a wiretray or a cabinet post. The sharp bend created by the tension of a tightened cable tie on the fiber optic cable will easily exceed the minimum bend radius for that cable, creating light leakage and subsequent performance problems. Therefore, a good installation practice for fiber optic cables is to always leave cable ties loose enough that they do not tightly grip the cable. There are multiple safety concerns when working with optical fibers, both when installing them and when doing maintenance-type work. Installation hazards center around dangers of the glass fiber itself, while maintenance hazards center around the light sources used to “power” the optical fibers. Installation of fiber optic cable requires that individual glass fibers be separated from each other in a multi-fiber cable and each one terminated with a connector, and this requires at some point that the technician strip each fiber down to its glass core and cladding. Both the core and the cladding are extremely small in diameter, and are made of ultra-pure glass. If a piece of core/cladding breaks off the fiber and penetrates the skin, the resulting “sliver” will be nearly invisible due to its exceptional transparency. Its outer surface is also very smooth, making extraction difficult. Unextracted pieces of an optical fiber, if left in the body, can actually migrate through the victim’s flesh and become buried even deeper to the point where they can cause serious health problems. Technicians working with optical fiber typically lay a length of adhesive tape, sticky-side up, on whatever workbench or table they are using to prepare the cable, as a tool to catch any loose fiber ends they cut off. At the conclusion of the job, this length of tape is carefully rolled up and then disposed of in the same manner that “sharps” may be disposed of in a medical environment. Maintenance technicians working with functioning fiber optic systems need to be careful when disconnecting “hot” fibers, due to the intensity of the light used in some systems. This is especially true of long-distance telecommunication fibers using laser sources rather than regular LEDs, which may have power levels reaching a half watt or so. One-half of a watt doesn’t sound like very much power, but when you consider this power level is concentrated over a circular area with a diameter less than 10 microns (for single-mode fiber), the watt-per-square-meter value is actually large enough to cause significant temperature increases wherever the light beam happens to fall. In fact, you can actually damage a fiber-optic connector on such a system by disconnecting the fiber with the fiber “powered”, the laser light being intense enough to burn and pit the aluminum ferrule of the connector! Even standard LED light sources may pose a hazard if a technician directly views the end of the cable with his or her eyes, due to the focused nature of the light beam. The retina of your eye is extremely sensitive to light, and may easily be damaged by viewing such an intensely focused beam coming out of an optical fiber, where the entire LED’s light output is channeled into a core just a fraction of a millimeter in diameter. The optical hazard is even greater when infra-red light sources are used, because there is no visible indication of the light’s presence. A technician won’t even be able to see the light coming out, yet it could still be intense enough to damage their retina(s). Laser-sourced fibers should never be unplugged from the equipment. One should treat a laser-sourced fiber with the same respect as a “live” electrical circuit, and use the same lockout/tagout procedures to ensure personnel safety. In systems using visible light wavelengths, a safe way to view the light coming out the end of an optical fiber is to point the fiber end at a piece of paper and look for the colored dot falling on the paper. The paper’s rough surface scatters the light so that it is no longer a focused beam. The only time it is truly safe to view the end of an optical fiber to check for light is when the light source is something diffuse such as natural sunlight or a flashlight. It is common for technicians to use a flashlight to identify fibers from one end of a multi-fiber cable to the other, one technician shining the flashlight at the end of one fiber while another technician views all the fibers at the other end of the cable to see which one is lit. Some optical communications equipment come equipped with a feature called an Open Fiber Control (OFC) safety system, which turns off all light sources on a channel whenever an interruption of light is detected at the receiver port. Since most duplex (two-way) optical fiber channels consist of two fibers (one for each direction of light), a break in any one fiber will darken one receiver, which then commands the transmitter port on that equipment to darken as well to prevent anyone getting injured from the light. It also completely disrupts communication in that channel, requiring a re-initialization of the channel after the fiber is plugged back in. ### Fiber optic cable testing Optical fibers, like electrical communications cable, may need to be tested to measure certain performance characteristics. Such testing is commonplace for new installations of fiber optic cabling to ensure all installed cable lengths and connectors are functioning properly. Repeated tests over time, compared with the initial installation test, quantifies any degradation of cables or connectors. Another common testing procedure, called acceptance testing, tests the optical cable while it is still on the spool prior to installation. Two basic types of optical fiber tests are presented here: one where the power level of light is measured at the far end of the fiber from a source of known optical power, and another where a pulse of light is sent down a fiber and the light received at the same end of the fiber is analyzed. The former test is simply a measurement of optical power, while the latter test is a sophisticated analysis of light over very brief periods of time (time domain reflectometry). #### Optical power loss testing Perhaps the simplest quantitative test of an optical fiber consists of shining a light source of known optical power at one end of a fiber and monitoring the amount of optical power received at the other end of the fiber. This type of test is typically performed with two pieces of equipment: the source and the power meter. First, the optical power meter and light source are short-coupled together using a pair of patch cables and a single “butt” connector: Once light is received by the optical power meter, the technician presses the “zero” button to set the baseline or reference point for all future power measurements. Although some light will be lost in the two patch cables and connector, this amount of loss will also be present in the final test and so it must be ignored. After “zeroing” the optical power meter, the actual fiber to be tested is connected between the light source and the power meter. Any additional light lost within the tested fiber will register at the power meter as a negative decibel figure: Recall that the definition of a “decibel” is 10 times the common logarithm of the power ratio between output and input for any system: $\hbox{dB} = 10 \log \left( P_{out} \over P_{in} \right)$ Thus, the power loss of $$-0.6$$ dB shown in the illustration represents 87.1% of the optical source power received by the optical power meter. Decibels are very commonly used as an expression of power gain and loss in communication system testing, because dB figures directly add when components are connected in series with each other. For example, if we knew that a certain type of “butt” connector for optical fiber exhibited a typical power loss of $$-1.2$$ dB and that three of these connectors would be used to join a single run of fiber, we would know to expect a total connector loss of $$-3.6$$ dB (i.e. 3 $$\times$$ $$-1.2$$ dB). Excessive optical power losses may be caused by a number of different factors, including: • Poor alignment between fibers in a connector $$\rightarrow$$ Connector flaw causing fibers to be mis-aligned (e.g. angular misalignment) $$\rightarrow$$ Fiber flaw causing mis-alignment in a good connector (e.g. cores not concentric) • Mismatched fiber sizes (e.g. 62.5 micron core sending light into a 50 micron core) • Oil or debris on the end of a connector • Rough (improperly polished) end on one or more fibers • Minimum bend radius violated at any point along the fiber’s length • Cracked fiber core Unfortunately, a power meter test will not indicate what kind of flaw is causing excessive power loss, nor where that flaw might be located. If the cable in question has removable connectors mid-way in its length, the power meter and/or source may be relocated to test portions of the cable to determine which section contributes more to the power loss, but an end-to-end power test cannot pinpoint the location or the type of fault. #### OTDR testing An Optical Time-Domain Reflectometer or OTDR is a sophisticated test instrument used to probe the characteristics of long optical fibers. They work by injecting a very brief pulse of light into one end of a long optical fiber, then monitoring any light received at that same end of the fiber. As the light pulse travels down the length of the fiber, it continuously loses some of its magnitude due to scattering in the glass. Some of this scattered light returns back to the source-end of the fiber, presenting a sort of “continuous echo” of the moving pulse. This continuous echo is analogous to the noise heard from an object moving away from the listener. As the light pulse encounters flaws and other discontinuities in the fiber and/or connectors along its length, the echoed signal changes in magnitude. This received signal is displayed as a time-domain plot on the OTDR viewing screen, and will look something like this: The “trace” shown on the display screen of an OTDR is a plot of the received optical signal strength over time. A large “spike” at the left-hand side of this trace marks the incident pulse of light injected into the optical fiber by the OTDR from the traveling pulse as it propagates down the length of the fiber. All signals after that (to the right of that initial “spike”) represent light received from that same end of the optical fiber. In a completely uniform fiber the resulting “echo” would trace a downward-sloping straight line as the traveling light pulse gradually weakens. In an imperfect fiber, any discontinuities such as splices, connector joints, sharp bends, cracks, etc. will cause the traveling light pulse to lose more photons than usual at the location of the discontinuity: sometimes returning a strong echo back toward the OTDR and other times not. A discontinuity such as a mis-aligned fiber connector will tend to return a strong echo as part of the traveling light pulse reflects off the mis-aligned connector end and returns to the OTDR. A discontinuity such as a mal-formed fusion splice merely scatters a greater-than-normal amount of light out through the fiber’s cladding, in which case there is no echo “pulse” received by the OTDR but rather just a further weakening of the echo signal. The OTDR trace shown in the previous illustration demands further explanation. Shown here is a magnified view of it, complete with numbers to identify each noteworthy event: Legend: 1. Incident pulse output by the OTDR, and injected into the launch fiber 2. Reflection off the face of the near-end connection between the launch fiber and the fiber under test 3. Loss of light due to a non-reflective discontinuity (e.g. sharp bend, splice) 4. Loss of light due to a reflective discontinuity (e.g. mis-aligned connector) 5. Reflection off the face of the far-end connection at the end of the fiber under test 6. The “noise floor” As you can see, an OTDR trace provides much more information about the performance of an optical fiber than a simple power test. Each flaw in the cable or its associated connectors appears as a deviation from the normal downward-sloped line of the trace, the location in time revealing the distance between the OTDR and the flaw. Thus, an OTDR not only indicates the nature of each flaw, and the amount of optical power lost at each flaw, but also the location270 of each flaw along the fiber’s length. One important caveat exists for this distance calculation, and that is the fact that the length of a fiber in a multi-fiber cable will always be somewhat longer than the length of the cable itself, since individual fibers inside a cable are often “wound” in a spiral configuration or otherwise deviating from the straight centerline of the cable. “Loose tube” cables, for example, often exhibit fiber lengths 5% to 10% greater than the physical length of the cable itself. • Share Published under the terms and conditions of the Creative Commons Attribution 4.0 International Public License	2020-02-17T00:44:23	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33072131872177124, "perplexity": 1353.7602600421014}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875141460.64/warc/CC-MAIN-20200217000519-20200217030519-00050.warc.gz"}
https://www.anl.gov/es/fuels	# Argonne National Laboratory .st0{fill:none;} .st1{fill:#007934;} .st2{fill:#0082CA;} .st3{fill:#101E8E;} .st4{fill:#FFFFFF;} .st5{fill:#A22A2E;} .st6{fill:#D9272E;} .st7{fill:#82BC00;} Argonne National Laboratory Energy Systems Division # Fuels Assessing fuel options to displace fossil fuels with bio-derived as well as other domestically sourced alternatives Today, the world meets much of its energy needs by burning fossil fuels such as crude-oil-derived fuels for transportation applications and natural gas for stationary power supply. The overarching goal of Argonne’s research activities in this area is the assessment of fuel options to displace fossil fuels with bio-derived as well as other domestically sourced alternatives. This research has the potential to help diversify our energy supply base while reducing greenhouse gas emissions and criteria pollutants. These research activities also represent a critical part of the ongoing multi-lab effort in the area of fuel/engine co-optimization. Experts at Argonne work closely with industrial partners to evaluate alternative fuel options for a range of internal combustion engine and gas turbine applications. Applications include light-duty and heavy-duty on-road transportation as well as the off-road transportation and the stationary power supply sector. Argonne’s diverse team of experts and state-of-the-art experimental facilities for fundamental fuel kinetics studies as well as engine and vehicle evaluations make Argonne the ideal place to conduct these interdisciplinary research projects. Specialists with backgrounds in engine and combustion system development as well as fuel chemistry collaborate with our leading experts in advanced engine simulations, allowing for a comprehensive assessment of alternative fuels for a range of applications. Related Project ### Fuel Kinetics Investigating the autoignition behavior of transportation-relevant fuels to better understand how these influence combustion in advanced internal combustion engines Related Project ### Fuel Spray Analysis Visualizing the flow inside the engine’s fuel injector nozzle using X-ray beams at the Advanced Photon Source Related Project ### International RCM Workshop A collaborative forum for experimentalists, modelers and theoreticians to work synergistically to better understand low-temperature combustion regimes	2019-09-23T11:38:06	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8175132274627686, "perplexity": 6433.345283025441}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514576355.92/warc/CC-MAIN-20190923105314-20190923131314-00179.warc.gz"}
https://pdglive.lbl.gov/DataBlock.action?node=Q009TPP	# ${{\boldsymbol t}^{\,'}}$(2/3)-quark/hadron mass limits in ${{\boldsymbol p}}{{\overline{\boldsymbol p}}}$ and ${{\boldsymbol p}}{{\boldsymbol p}}$ collisions INSPIRE search VALUE (GeV) CL% DOCUMENT ID TECN COMMENT $\bf{> 1280}$ 95 1 2019 AQ CMS B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit t}}$ ) = 1 $>1370$ 95 2 2019 BW CMS B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit h}}{{\mathit t}}$ ) = 1 $>980$ 95 3 2018 CE ATLS ${}\geq{}2{{\mathit \ell}}$ + $\not E_T$ + ${}\geq{}1{{\mathit b}}$j $> 1010$ 95 4 2018 CL ATLS B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit h}}{{\mathit t}}$ ) = 1 $> 1030$ 95 5, 6 2018 CP ATLS 2,3${{\mathit \ell}}$, singlet model $> 1210$ 95 5, 7 2018 CP ATLS 2,3${{\mathit \ell}}$, doublet model $\bf{> 1310}$ 95 8, 9 2018 CR ATLS singlet ${{\mathit t}^{\,'}}$. ATLAS combination $\bf{> 1370}$ 95 8, 10 2018 CR ATLS ${{\mathit t}^{\,'}}$ in a weak isospin doublet (${{\mathit t}^{\,'}},{{\mathit b}^{\,'}}$). ATLAS combination. $> 1140$ 95 11 2018 BM CMS ${{\mathit W}}{{\mathit b}}$ , ${{\mathit Z}}{{\mathit t}}$ , ${{\mathit h}}{{\mathit t}}$ modes $> 845$ 95 12 2018 Q CMS B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit q}}$ ) = 1 (${{\mathit q}}={{\mathit d}},{{\mathit s}}$) $\bf{> 1295}$ 95 13 2018 W CMS B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit b}}$ ) = 1 $>1160$ 95 14 2017 L ATLS B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit t}}$ ) = 1 $>860$ 95 15 2017 AU CMS $> 770$ 95 16 2015 AR ATLS B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit b}}$ ) = 1 $> 590$ 95 17 2015 BY ATLS ${{\mathit W}}{{\mathit b}}$ , ${{\mathit Z}}{{\mathit t}}$ , ${{\mathit h}}{{\mathit t}}$ modes $> 745$ 95 18 2015 AI CMS B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit h}}{{\mathit t}}$ ) = 1 $> 735$ 95 19 2014 AZ ATLS B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit t}}$ ) = 1 $> 700$ 95 20 2014 A CMS B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit b}}$ ) = 1 $> 706$ 95 20 2014 A CMS B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit t}}$ ) = 1 $> 782$ 95 20 2014 A CMS B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit h}}{{\mathit t}}$ ) = 1 $> 350$ 95 21 2012 BC ATLS B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit q}}$ )=1 (${{\mathit q}}={{\mathit d}},{{\mathit s}},{{\mathit b}}$) $> 420$ 95 22 2012 C ATLS ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit X}}{{\mathit t}}$ (${\mathit m}_{{{\mathit X}}}<$ 140 GeV) $> 685$ 95 23 2012 BH CMS ${\mathit m}_{{{\mathit b}^{\,'}}}$ = ${\mathit m}_{{{\mathit t}^{\,'}}}$ $> 557$ 95 24 2012 P CMS ${{\mathit t}^{\,'}}$ ${{\overline{\mathit t}}^{\,'}}$ $\rightarrow$ ${{\mathit W}^{+}}{{\mathit b}}{{\mathit W}^{-}}{{\overline{\mathit b}}}$ $\rightarrow$ ${{\mathit b}}{{\mathit \ell}^{+}}{{\mathit \nu}}{{\overline{\mathit b}}}{{\mathit \ell}^{-}}{{\overline{\mathit \nu}}}$ • • • We do not use the following data for averages, fits, limits, etc. • • • $> 656$ 95 25 2013 F ATLS B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit b}}$ ) = 1 $> 625$ 95 26 2013 I CMS B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit t}}$ ) = 1 $> 404$ 95 27 2012 AR ATLS B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit b}}$ ) = 1 $> 570$ 95 28 2012 BC CMS ${{\mathit t}^{\,'}}$ ${{\overline{\mathit t}}^{\,'}}$ $\rightarrow$ ${{\mathit W}^{+}}{{\mathit b}}{{\mathit W}^{-}}{{\overline{\mathit b}}}$ $> 400$ 95 29 2011 AH CDF ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit X}}{{\mathit t}}$ (${\mathit m}_{{{\mathit X}}}<$ 70 GeV) $> 358$ 95 30 2011 AL CDF ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit b}}$ $> 340$ 95 30 2011 AL CDF ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit q}}$ (${{\mathit q}}={{\mathit d}},{{\mathit s}},{{\mathit b}}$) $> 360$ 95 31 2011 O CDF ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit X}}{{\mathit t}}$ (${\mathit m}_{{{\mathit X}}}<$ 100 GeV) $> 285$ 95 32 2011 Q D0 ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit q}}$ (${{\mathit q}}={{\mathit d}},{{\mathit s}},{{\mathit b}}$) $> 256$ 95 33, 34 2008 H CDF ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit q}}$ 1 SIRUNYAN 2019AQ based on 35.9 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 13 TeV. Pair production of vector-like ${{\mathit t}^{\,'}}$ is seached for with one ${{\mathit t}^{\,'}}$ decaying into ${{\mathit Z}}{{\mathit t}}$ and the other ${{\mathit t}^{\,'}}$ decaying into ${{\mathit W}}{{\mathit b}}$ , ${{\mathit Z}}{{\mathit t}}$ , ${{\mathit h}}{{\mathit t}}$ . Events with an opposite-sign lepton pair consistent with coming from ${{\mathit Z}}$ and jets are used. Mass limits are obtained for a variety of branching ratios of ${{\mathit t}^{\,'}}$. 2 SIRUNYAN 2019BW based on 35.9 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 13 TeV. The limit is for the pair-produced vector-like ${{\mathit t}^{\,'}}$ using all-hadronic final state. The analysis is made for the ${{\mathit W}}{{\mathit b}}$ , ${{\mathit Z}}{{\mathit t}}$ , ${{\mathit h}}{{\mathit t}}$ modes and mass limits are obtained for a variety of branching ratios. 3 AABOUD 2018CE based on 36.1 fb${}^{-1}$ of proton-proton data taken at $\sqrt {s }$ = 13 TeV. Events including a same-sign lepton pair are used. The limit is for a singlet model, assuming the branching ratios of ${{\mathit t}^{\,'}}$ into ${{\mathit Z}}{{\mathit t}}$ , ${{\mathit W}}{{\mathit b}}$ and ${{\mathit H}}{{\mathit t}}$ as predicted by the model. 4 AABOUD 2018CL based on 36.1 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 13 TeV. The limit is for the pair-produced vector-like ${{\mathit t}^{\,'}}$ using all-hadronic final state. The analysis is also made for the ${{\mathit W}}{{\mathit b}}$ , ${{\mathit Z}}{{\mathit t}}$ , ${{\mathit h}}{{\mathit t}}$ modes and mass limits are obtained for a variety of branching ratios. 5 AABOUD 2018CP based on 36.1 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 13 TeV. Pair and single production of vector-like ${{\mathit t}^{\,'}}$ are seached for with at least one ${{\mathit t}^{\,'}}$ decaying into ${{\mathit Z}}{{\mathit t}}$ . In the case of B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit t}}$ ) = 1, the limit is ${\mathit m}_{{{\mathit t}^{\,'}}}$ $>$ 1340 GeV. 6 The limit is for the singlet model, assuming that the branching ratios into ${{\mathit Z}}{{\mathit t}}$ , ${{\mathit W}}{{\mathit b}}$ , and ${{\mathit H}}{{\mathit t}}$ add up to one. 7 The limit is for the doublet model, assuming that the branching ratios into ${{\mathit Z}}{{\mathit t}}$ , ${{\mathit W}}{{\mathit b}}$ , and ${{\mathit H}}{{\mathit t}}$ add up to one. 8 AABOUD 2018CR based on 36.1 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 13 TeV. A combination of searches for the pair-produced vector-like ${{\mathit t}^{\,'}}$ in various decay channels ( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit b}}$ , ${{\mathit Z}}{{\mathit t}}$ , ${{\mathit h}}{{\mathit t}}$ ). Also a model-independent limit is obtained as ${\mathit m}_{{{\mathit t}^{\,'}}}$ $>$ 1.31 TeV, assuming that the branching ratios into ${{\mathit Z}}{{\mathit t}}$ , ${{\mathit W}}{{\mathit b}}$ and ${{\mathit h}}{{\mathit t}}$ add up to one. 9 The limit is for the singlet ${{\mathit t}^{\,'}}$. 10 The limit is for ${{\mathit t}^{\,'}}$ in a weak isospin doublet (${{\mathit t}^{\,'}},{{\mathit b}^{\,'}}$) and $\vert {{\mathit V}}_{{{\mathit t}^{\,'}}{{\mathit b}}}\vert$ ${}\ll$ $\vert {{\mathit V}}_{{{\mathit t}}{{\mathit b}^{\,'}}}\vert$. 11 SIRUNYAN 2018BM based on 35.9 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 13 TeV. The limit is for the pair-produced vector-like ${{\mathit t}^{\,'}}$. Three channels (single lepton, same-charge 2 leptons, or at least 3 leptons) are considered for various branching fraction combinations. Assuming B( ${{\mathit t}}{{\mathit H}}$ ) = 1, the limit is 1270 GeV and for B( ${{\mathit t}}{{\mathit Z}}$ ) = 1 it is 1300 GeV. 12 SIRUNYAN 2018Q based on 19.7 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 8 TeV. The limit is for the pair-produced vector-like ${{\mathit t}^{\,'}}$ that couple only to light quarks. Constraints for other decay channels ( ${{\mathit Z}}{{\mathit q}}$ and ${{\mathit H}}{{\mathit q}}$ ) are also given in the paper. 13 SIRUNYAN 2018W based on 35.8 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 13 TeV. The limit is for the vector-like ${{\mathit t}^{\,'}}$ pair-produced by strong interaction using lepton-plus-jets mode and assuming that B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit b}}$ ) is 100%. Generally the measurement sets upper limits on the product of the production cross section and branching faction to ${{\mathit W}}{{\mathit b}}$ for any new pair-produced heavy quark decaying to this channel as a narrow resonance. 14 AABOUD 2017L based on 36.1 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 13 TeV. No signal is found in the search for heavy quark pair production that decay into ${{\mathit Z}}{{\mathit t}}$ followed by ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \nu}}{{\mathit \nu}}$ in the events with one lepton, large $\not E_T$, and ${}\geq{}$4 jets. The lower mass limit 0.87 (1.05) TeV is obtained for the singlet (doublet) model with other possible decay modes. 15 SIRUNYAN 2017AU based on 2.3-2.6 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 13 TeV. Limit on pair-produced singlet vector-like ${{\mathit t}^{\,'}}$ using one lepton and several jets. The mass bound is given for a ${{\mathit t}^{\,'}}$ transforming as a singlet under the electroweak symmetry group, assumed to decay through ${{\mathit W}}$, ${{\mathit Z}}$ or Higgs boson (which decays to jets) and to a third generation quark. For a doublet, the limit is $>$830 GeV. Other limits are also given in the paper. 16 AAD 2015AR based on 20.3 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 8 TeV. Used lepton-plus-jets final state. See Fig. 20 for mass limits in the plane of B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit H}}{{\mathit t}}$ ) vs. B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit b}}$ ) from a combination of ${{\mathit t}^{\,'}}$ ${{\overline{\mathit t}}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit b}}{+}$ ${{\mathit X}}$ and ${{\mathit t}^{\,'}}$ ${{\overline{\mathit t}}^{\,'}}$ $\rightarrow$ ${{\mathit H}}{{\mathit t}}{+}$ ${{\mathit X}}$ searches. Any branching ratio scenario is excluded for mass below 715 GeV. 17 AAD 2015BY based on 20.3 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 8 TeV. Limit on pair-produced vector-like ${{\mathit t}^{\,'}}$ assuming the branching fractions to ${{\mathit W}}$, ${{\mathit Z}}$, and ${{\mathit h}}$ modes of the singlet model. Used events containing ${}\geq{}2{{\mathit \ell}}$ + $\not E_T$ + ${}\geq{}$2j (${}\geq{}$1 ${{\mathit b}}$) and including a same-sign lepton pair. 18 KHACHATRYAN 2015AI based on 19.7 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 8 TeV. The search exploits all-hadronic final states by tagging boosted Higgs boson using jet substructure and ${{\mathit b}}$-tagging. 19 Based on 20.3 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 8 TeV. No significant excess over SM expectation is found in the search for pair production or single production of ${{\mathit t}^{\,'}}$ in the events with dilepton from a high $p_T$ ${{\mathit Z}}$ and additional jets (${}\geq{}$ 1 ${{\mathit b}}$-tag). If instead of B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit t}}$ ) = 1 an electroweak singlet with B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit t}}$ ) $\sim{}$ 0.45 is assumed, the limit reduces to 685 GeV. 20 Based on 19.5 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 8TeV. The ${{\mathit t}^{\,'}}$ quark is pair produced and is assumed to decay into three different final states of , , and . The search is carried out using events with at least one isolated lepton. 21 Based on 1.04 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 7 TeV. No signal is found for the search of heavy quark pair production that decay into ${{\mathit W}}$ and a quark in the events with dileptons, large $\not E_T$, and ${}\geq{}$2 jets. 22 Based on 1.04 fb${}^{-1}$ of data in ${{\mathit p}}{{\mathit p}}$ collisions at 7 TeV. AAD 2012C looked for ${{\mathit t}^{\,'}}{{\overline{\mathit t}}^{\,'}}$ production followed by ${{\mathit t}^{\,'}}$ decaying into a top quark and ${{\mathit X}}$, an invisible particle, in a final state with an isolated high-P$_{T}$ lepton, four or more jets, and a large missing transverse energy. No excess over the SM ${{\mathit t}}{{\overline{\mathit t}}}$ production gives the upper limit on ${{\mathit t}^{\,'}}{{\overline{\mathit t}}^{\,'}}$ production cross section as a function of ${\mathit m}_{{{\mathit t}^{\,'}}}$ and ${\mathit m}_{{{\mathit X}}}$. The result is obtained for B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit t}}$ ) = 1. 23 Based on 5 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 7 TeV. CHATRCHYAN 2012BH searched for QCD and EW production of single and pair of degenerate 4'th generation quarks that decay to ${{\mathit W}}{{\mathit b}}$ or ${{\mathit W}}{{\mathit t}}$ . Absence of signal in events with one lepton, same-sign dileptons or tri-leptons gives the bound. With a mass difference of 25 GeV/c${}^{2}$ between ${\mathit m}_{{{\mathit t}^{\,'}}}$ and ${\mathit m}_{{{\mathit b}^{\,'}}}$, the corresponding limit shifts by about $\pm20$ GeV/c${}^{2}$. 24 Based on 5.0 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 7 TeV. CHATRCHYAN 2012P looked for ${{\mathit t}^{\,'}}{{\overline{\mathit t}}^{\,'}}$ production events with two isolated high $p_T$ leptons, large $\not E_T$, and 2 high $p_T$ jets with ${{\mathit b}}$-tag. The absence of signal above the SM background gives the limit for B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit b}}$ ) = 1. 25 Based on 4.7 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 7 TeV. No signal is found for the search of heavy quark pair production that decay into ${{\mathit W}}$ and a ${{\mathit b}}$ quark in the events with a high $p_T$ isolated lepton, large $\not E_T$ and at least 3 jets (${}\geq{}$ 1 ${{\mathit b}}$-tag). Vector-like quark of charge 2/3 with 400 $<$ ${\mathit m}_{{{\mathit t}^{\,'}}}$ $<$ 550 GeV and B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit b}}$ ) $>$ 0.63 is excluded at 95$\%$ CL. 26 Based on 5.0 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 7 TeV. CHATRCHYAN 2013I looked for events with one isolated electron or muon, large $\not E_T$, and at least four jets with large transverse momenta, where one jet is likely to originate from the decay of a bottom quark. 27 Based on 1.04 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 7 TeV. No signal is found in the search for pair produced heavy quarks that decay into ${{\mathit W}}$ boson and a ${{\mathit b}}$ quark in the events with a high $p_T$ isolated lepton, large $\not E_T$ and at least 3 jets (${}\geq{}$1 ${{\mathit b}}$-tag). 28 Based on 5.0 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ data at $\sqrt {s }$ = 7 TeV. CHATRCHYAN 2012BC looked for ${{\mathit t}^{\,'}}{{\overline{\mathit t}}^{\,'}}$ production events with a single isolated high $p_T$ lepton, large $\not E_T$ and at least 4 high $p_T$ jets with a ${{\mathit b}}$-tag. The absence of signal above the SM background gives the limit for B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit W}}{{\mathit b}}$ ) = 1. 29 Based on 5.7 fb${}^{-1}$ of data in ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at 1.96 TeV. AALTONEN 2011AH looked for ${{\mathit t}^{\,'}}{{\overline{\mathit t}}^{\,'}}$ production followed by ${{\mathit t}^{\,'}}$ decaying into a top quark and ${{\mathit X}}$, an invisible particle, in the all hadronic decay mode of ${{\mathit t}}{{\overline{\mathit t}}}$ . No excess over the SM ${{\mathit t}}{{\overline{\mathit t}}}$ production gives the upper limit on ${{\mathit t}^{\,'}}{{\overline{\mathit t}}^{\,'}}$ production cross section as a function of ${\mathit m}_{{{\mathit t}^{\,'}}}$ and ${\mathit m}_{{{\mathit X}}}$. The result is obtained for B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit X}}{{\mathit t}}$ ) = 1. 30 Based on 5.6 fb${}^{-1}$ of data in ppbar collisions at 1.96 TeV. AALTONEN 2011AL looked for ${{\mathit \ell}}$ + ${}\geq{}$4j events and set upper limits on ${\mathit \sigma (}$ ${{\mathit t}^{\,'}}{{\overline{\mathit t}}^{\,'}}{)}$ as functions of ${\mathit m}_{{{\mathit t}^{\,'}}}$. 31 Based on 4.8 fb${}^{-1}$ of data in ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at 1.96 TeV. AALTONEN 2011O looked for ${{\mathit t}^{\,'}}{{\overline{\mathit t}}^{\,'}}$ production signal when ${{\mathit t}^{\,'}}$ decays into a top quark and ${{\mathit X}}$, an invisible particle, in ${{\mathit \ell}}$ + $\not E_T$ + jets channel. No excess over the SM ${{\mathit t}}{{\overline{\mathit t}}}$ production gives the upper limit on ${{\mathit t}^{\,'}}{{\overline{\mathit t}}^{\,'}}$ production cross section as a function of ${\mathit m}_{{{\mathit t}^{\,'}}}$ and ${\mathit m}_{{{\mathit X}}}$. The result is obtained for B( ${{\mathit t}^{\,'}}$ $\rightarrow$ ${{\mathit X}}{{\mathit t}}$ ) = 1. 32 Based on 5.3 fb${}^{-1}$ of data in ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at 1.96 TeV. ABAZOV 2011Q looked for ${{\mathit \ell}}$ + $\not E_T$ + ${}\geq{}$4j events and set upper limits on ${\mathit \sigma (}$ ${{\mathit t}^{\,'}}{{\overline{\mathit t}}^{\,'}}{)}$ as functions of ${\mathit m}_{{{\mathit t}^{\,'}}}$. 33 Searches for pair production of a new heavy top-like quark ${{\mathit t}^{\,'}}$ decaying to a ${{\mathit W}}$ boson and another quark by fitting the observed spectrum of total transverse energy and reconstructed ${{\mathit t}^{\,'}}$ mass in the lepton + jets events. 34 HUANG 2008 reexamined the ${{\mathit t}^{\,'}}$ mass lower bound of 256 GeV obtained in AALTONEN 2008H that assumes B( ${{\mathit b}^{\,'}}$ $\rightarrow$ ${{\mathit q}}{{\mathit Z}}$ ) = 1 for ${{\mathit q}}$ = ${{\mathit u}}$, ${{\mathit c}}$ which does not hold when ${\mathit m}_{{{\mathit b}^{\,'}}}<{\mathit m}_{{{\mathit t}^{\,'}}}−{\mathit m}_{{{\mathit W}}}$ or the mixing sin$^2(\theta _{ {{\mathit b}} {{\mathit t}^{\,'}} })$ is so tiny that the decay occurs outside of the vertex detector. Fig. 1 gives that lower bound on ${\mathit m}_{{{\mathit t}^{\,'}}}$ in the plane of sin$^2(\theta _{ {{\mathit b}} {{\mathit t}^{\,'}} })$ and ${\mathit m}_{{{\mathit b}^{\,'}}}$. References: SIRUNYAN 2019AQ EPJ C79 364 Search for vector-like quarks in events with two oppositely charged leptons and jets in proton-proton collisions at $\sqrt{s} =$ 13 TeV SIRUNYAN 2019BW PR D100 072001 Search for pair production of vectorlike quarks in the fully hadronic final state AABOUD 2018CR PRL 121 211801 Combination of the searches for pair-produced vector-like partners of the third-generation quarks at $\sqrt{s} =$ 13 TeV with the ATLAS detector AABOUD 2018CL PR D98 092005 Search for pair production of heavy vector-like quarks decaying into hadronic final states in $pp$ collisions at $\sqrt{s} = 13$ TeV with the ATLAS detector AABOUD 2018CE JHEP 1812 039 Search for new phenomena in events with same-charge leptons and $b$-jets in $pp$ collisions at $\sqrt{s}= 13$ TeV with the ATLAS detector AABOUD 2018CP PR D98 112010 Search for pair- and single-production of vector-like quarks in final states with at least one $Z$ boson decaying into a pair of electrons or muons in $pp$ collision data collected with the ATLAS detector at $\sqrt{s} = 13$ TeV SIRUNYAN 2018W PL B779 82 Search for pair production of vector-like quarks in the bW$\overline{\mathrm{b}}$W channel from proton-proton collisions at $\sqrt{s} =$ 13 TeV SIRUNYAN 2018BM JHEP 1808 177 Search for vector-like T and B quark pairs in final states with leptons at $\sqrt{s} =$ 13 TeV SIRUNYAN 2018Q PR D97 072008 Search for vectorlike light-flavor quark partners in proton-proton collisions at $\sqrt s$ =8??TeV AABOUD 2017L JHEP 1708 052 Search for Pair Production of Vector-Like Top Quarks in Events with One Lepton, Jets, and Missing Transverse Momentum in $\sqrt {s }$ = 13 TeV ${{\mathit p}}{{\mathit p}}$ Collisions with the ATLAS Detector SIRUNYAN 2017AU JHEP 1711 085 Search for Pair Production of Vector-Like and Quarks in Single-Lepton Final States using Boosted Jet Substructure in Proton-Proton Collisions at $\sqrt {s }$ = 13 TeV JHEP 1510 150 Analysis of Events with ${\mathit {\mathit b}}$-Jets and a Pair of Leptons of the Same Charge in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector JHEP 1508 105 Search for Production of Vector-Like Quark Pairs and of Four Top Quarks in the Lepton-plus-Jets Final State in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector KHACHATRYAN 2015AI JHEP 1506 080 Search for Vector-Like Quarks Decaying to Top Quarks and Higgs Bosons in the All-Hadronic Channel using Jet Substructure JHEP 1411 104 Search for Pair and Single Production of New Heavy Quarks that Decay to a ${{\mathit Z}}$ Boson and a Third-Generation Quark in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector CHATRCHYAN 2014A PL B729 149 Inclusive Search for a Vector-Like t Quark with Charge ${2\over 3}$ in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV PL B718 1284 Search for Pair Production of Heavy Top-Like Quarks Decaying to a High-$p_T$ ${{\mathit W}}$ Boson and a ${\mathit {\mathit b}}$ Quark in the Lepton Plus Jets Final State at $\sqrt {s }$ = 7 TeV with the ATLAS Detector CHATRCHYAN 2013I JHEP 1301 154 Search for Heavy Quarks Decaying into a Top Quark and a ${{\mathit W}}$ or ${{\mathit Z}}$ Boson using Lepton + Jets Events in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV PRL 108 261802 Search for Pair Production of a Heavy Up-Type Quark Decaying to a ${{\mathit W}}$ Boson and a ${\mathit {\mathit b}}$ Quark in the lepton+jets Channel with the ATLAS Detector PRL 108 041805 Search for New Phenomena in ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Events with Large Missing Transverse Momentum in Proton$−$Proton Collisions at $\sqrt {s }$ = 7$~$TeV with the ATLAS Detector PR D86 012007 Search for Pair-Produced Heavy Quarks Decaying to ${{\mathit W}}{\mathit {\mathit q}}$ in the Two-Lepton Channel at $\sqrt {s }$ = 7 TeV with the ATLAS Detector CHATRCHYAN 2012P PL B716 103 Search for Heavy, Top-Like Quark Pair Production in the Dilepton Final State in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV CHATRCHYAN 2012BH PR D86 112003 Combined Search for the Quarks of a Sequential Fourth Generation CHATRCHYAN 2012BC PL B718 307 Search for Pair Produced Fourth-Generation Up-Type Quarks in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV with a Lepton in the Final State AALTONEN 2011AH PRL 107 191803 Search for New ${{\mathit T}^{\,'}}$ Particles in Final States with Large Jet Multiplicities and Missing Transverse Energy in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV AALTONEN 2011AL PRL 107 261801 Search for a Heavy Toplike Quark in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV AALTONEN 2011O PRL 106 191801 Search for Production of Heavy Particles Decaying to Top Quarks and Invisible Particles in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV ABAZOV 2011Q PRL 107 082001 Search for a Fourth Generation Quark in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at = 1.96 TeV AALTONEN 2008H PRL 100 161803 Search for Heavy Toplike Quarks using Lepton Plus Jets Events in 1.96 TeV ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions	2021-03-02T20:33:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9120343923568726, "perplexity": 1738.5554028014074}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": 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http://dlmf.nist.gov/12.11	# §12.11 Zeros ## §12.11(i) Distribution of Real Zeros If then has no real zeros. If , then has no positive real zeros. If , , then has positive real zeros. Lastly, when , (Hermite polynomial case) has zeros and they lie in the interval . For further information on these cases see Dean (1966). If then has no positive real zeros, and if , , then has a zero at . ## §12.11(ii) Asymptotic Expansions of Large Zeros When , has a string of complex zeros that approaches the ray as , and a conjugate string. When the zeros are asymptotically given by and , where is a large positive integer and with and When these zeros are the same as the zeros of the complementary error function ; compare (12.7.5). Numerical calculations in this case show that corresponds to the th zero on the string; compare §7.13(ii). ## §12.11(iii) Asymptotic Expansions for Large Parameter For large negative values of the real zeros of , , , and can be approximated by reversion of the Airy-type asymptotic expansions of §§12.10(vii) and 12.10(viii). For example, let the th real zeros of and , counted in descending order away from the point , be denoted by and , respectively. Then as () , fixed. Here , denoting the th negative zero of the function (see §9.9(i)). The first two coefficients are given by 12.11.5 where is the function inverse to , defined by (12.10.39) (see also (12.10.41)), and 12.11.6 Similarly, for the zeros of we have where , denoting the th negative zero of the function and 12.11.8 For the first zero of we also have where the numerical coefficients have been rounded off. For further information, including associated functions, see Olver (1959).	2013-05-25T16:50:57	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9501156210899353, "perplexity": 1175.1760068700203}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368705976722/warc/CC-MAIN-20130516120616-00038-ip-10-60-113-184.ec2.internal.warc.gz"}
https://par.nsf.gov/biblio/10078464-efficient-statistics-high-dimensions-from-truncated-samples	Efficient Statistics, in High Dimensions, from Truncated Samples We provide an efficient algorithm for the classical problem, going back to Galton, Pearson, and Fisher, of estimating, with arbitrary accuracy the parameters of a multivariate normal distribution from truncated samples. Truncated samples from a d-variate normal N(μ,Σ) means a samples is only revealed if it falls in some subset S⊆Rd; otherwise the samples are hidden and their count in proportion to the revealed samples is also hidden. We show that the mean μ and covariance matrix Σ can be estimated with arbitrary accuracy in polynomial-time, as long as we have oracle access to S, and S has non-trivial measure under the unknown d-variate normal distribution. Additionally we show that without oracle access to S, any non-trivial estimation is impossible. Authors: ; ; ; Award ID(s): Publication Date: NSF-PAR ID: 10078464 Journal Name: Annual Symposium on Foundations of Computer Science ISSN: 0272-5428 3. We provide a computationally and statistically efficient estimator for the classical problem of trun-cated linear regression, where the dependent variabley=wTx+εand its corresponding vector ofcovariatesx∈Rkare only revealed if the dependent variable falls in some subsetS⊆R; otherwisethe existence of the pair(x,y)is hidden. This problem has remained a challenge since the earlyworks of Tobin (1958); Amemiya (1973); Hausman and Wise (1977); Breen et al. (1996), its appli-cations are abundant, and its history dates back even further to the work of Galton, Pearson, Lee,and Fisher Galton (1897); Pearson and Lee (1908); Lee (1914); Fisher (1931). While consistent es-timators of the regression coefficients have been identified, the error rates are not well-understood,especially in high-dimensional settings.Under a “thickness assumption” about the covariance matrix of the covariates in the revealed sample, we provide a computationally efficient estimator for the coefficient vectorwfromnre-vealed samples that attains2errorO(√k/n), recovering the guarantees of least squares in thestandard (untruncated) linear regression setting. Our estimator uses Projected Stochastic Gradi-ent Descent (PSGD) on the negative log-likelihood of the truncated sample, and only needs ora-cle access to the setS, which may otherwise be arbitrary, and in particular may be non-convex.PSGD must be restricted to an appropriately defined convex cone to guarantee that the negativelog-likelihood is stronglymore » 5. Given data drawn from an unknown distribution, D, to what extent is it possible to amplify'' this dataset and faithfully output an even larger set of samples that appear to have been drawn from D? We formalize this question as follows: an (n,m) amplification procedure takes as input n independent draws from an unknown distribution D, and outputs a set of m > n `samples'' which must be indistinguishable from m samples drawn iid from D. We consider this sample amplification problem in two fundamental settings: the case where D is an arbitrary discrete distribution supported on k elements, and the case where D is a d-dimensional Gaussian with unknown mean, and fixed covariance matrix. Perhaps surprisingly, we show a valid amplification procedure exists for both of these settings, even in the regime where the size of the input dataset, n, is significantly less than what would be necessary to learn distribution D to non-trivial accuracy. We also show that our procedures are optimal up to constant factors. Beyond these results, we describe potential applications of sample amplification, and formalize a number of curious directions for future research.	2022-12-03T03:32:10	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7520438432693481, "perplexity": 959.3279920407125}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710918.58/warc/CC-MAIN-20221203011523-20221203041523-00682.warc.gz"}
https://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/goodfit.htm	Dataplot Vol 1 Vol 2 # GOODNESS OF FIT Name: GOODNESS OF FIT Type: Analysis Command Purpose: Perform Anderson-Darling, Kolmogorov-Smirnov, chi-square, or PPCC distributional goodness of fit tests. Description: There are a number of tests for assessing the goodness of fit for a distributional model. Several of these have been incorporated into this command. Specifically, the following goodness of fit methods are supported: 1. Kolmogorov-Smirnov 2. Anderson-Darling 3. Chi-Square 4. PPCC Detailed descriptions of each of these methods is given below in the Notes section. As a general comment, goodness of fit methods are typically based on comparing the cumulative distribution of the data with a theoretical distribution or comparing the quantiles of the data with the a theoretical percent point function. Previous versions of Dataplot supported separate commands (ANDERSON DARLING TEST, KOLMOGOROV SMIRNOV GOODNESS OF FIT TEST, and CHI-SQUARE GOODNESS OF FIT TEST). These separate commands have been replaced with the unified GOODNESS OF FIT command and are no longer available). 1. Dataplot separates the estimation of distribution parameters from the goodness of fit assessment (the old version of the ANDERSON DARLING TEST would generate the maximum likelihood estimates if the user did not specify them). The location and scale parameters are specified generically with the following commands: LET KSLOC = <value> LET KSSCALE = <value> The location and scale parameters default to 0 and 1 if not specified. For distributions with one or more shape parameters, you should enter the values of the shape parameter. For a list of appropriate parameter values, enter 2. For certain methods/distributions, appropriate critical values may be tabulated in published articles. Alternatively, critical values can be generated dynamically. See the Notes section below for each individual method for more information. Dynamically generated critical values are determined by generating 10,000 monte carlo simulations (and therefore computing 10,000 values of the goodness of fit statistic). The value of the goodness of fit statistic for the original data is compared to these monte carlo values to determine critical values and p-values. These dynamically generated critical values should be close to the published values, but they may not match exactly. This is due to the use of different random number generators and seed values. The differences tend to be greatest for small sample sizes. The advantage of using published tables is speed. The advantage of dynamically generated critical values is that a greater number of distributions are supported and there is more flexibility in specifying the alpha for the critical values (published tables are typically limited to a few values of ). 3. If critical values are determined dynamically, there are two distinct cases, • In the first case, we assume that the parameters are known. • In the second case, we assume that the parameters are not known (this is the more common case). This affects how the simulation is performed. In both cases, for a given simulation random numbers are generated using the specified parameters. For the case where the parameters are assumed known, the goodness of fit statistic is computed using the assumed known parameters. For the case where the parameters are assumed unknown, the parameters are estimated from the simulated random numbers first and then the goodness of fit statistic is computed using these fitted parameters. To specify which case is used, enter the command SET GOODNESS OF FIT FULLY SPECIFIED <ON/OFF> where ON means the parameters are assumed known and OFF means the parameters are assumed unknown. When the parameters must be estimated from the data, you can specify the fit method to use with the following command SET GOODNESS OF FIT FIT METHOD <ML/PPCC/DEFAULT> with ML and PPCC denoting maximum likelihood and PPCC methods, respectively. Using DEFAULT will select the fit method based on the goodness of fit criterion selected. For the DEFAULT choice, the Kolmogorov-Smirnov and Anderson-Darling goodness of fit criterion will use maximum likelihood and the PPCC goodness of fit criterion will use PPCC fitting. The chi-square method uses a chi-square approximation to obtain the critical values, so no simulation is required. The ML method will only be supported for distributions for which Dataplot supports maximum likelihood estimation. If maximum likelihood estimation is used, the following command can be used (see Note: section below for details) SET DISTRIBUTIONAL FIT TYPE <method> Syntax 1: <dist> <method> GOODNESS OF FIT <y> <SUBSET/EXCEPT/FOR qualification> where <dist> is one Dataplot's supported distributions; <method> is one of ANDERSON DARLING, KOLMOGOROV SMIRNOV, CHI-SQUARE, or PPCC; <y> is the response variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional. Enter HELP PROBABILITY DISTRIBUTIONS for a list of supported distributions and the name of any required parameters. Syntax 2: <dist> <method> MULTIPLE GOODNESS OF FIT <y1> ... <yk> <SUBSET/EXCEPT/FOR qualification> where <dist> is one Dataplot's supported distributions; <method> is one of ANDERSON DARLING, KOLMOGOROV SMIRNOV, CHI-SQUARE, or PPCC; <y1> ... <yk> is a list of 1 to 30 response variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax will generate the goodness of fit statistic for each variable in the list. Note that the syntax <dist> <method> MULTIPLE GOODNESS OF FIT Y1 TO Y4 is supported. This is equivalent to <dist> <method> MULTIPLE GOODNESS OF FIT Y1 Y2 Y3 Y4 Syntax 3: <dist> <method> REPLICATED GOODNESS OF FIT <y> <x1> ... <xk> <SUBSET/EXCEPT/FOR qualification> where <dist> is one Dataplot's supported distributions; <method> is one of ANDERSON DARLING, KOLMOGOROV SMIRNOV, CHI-SQUARE, or PPCC; <y> is the response variable; <x1> ... <xk> is a list of 1 to 6 group-id variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax peforms a cross-tabulation of ... and performs a goodness of fit test for each unique combination of cross-tabulated values. For example, if X1 has 3 levels and X2 has 2 levels, there will be a total of 6 goodness of fit tests performed. Note that the syntax <dist> <method> REPLICATED GOODNESS OF FIT Y X1 TO X4 is supported. This is equivalent to <dist> <method> REPLICATED GOODNESS OF FIT Y X1 X2 X3 X4 Syntax 4: <dist> CHI-SQUARE GOODNESS OF FIT <y> <x> <SUBSET/EXCEPT/FOR qualification> where <dist> is one Dataplot's supported distributions; <y> is a variable of pre-computed frequencies; <x> is a variable containing the mid-points of the bins; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax is used for the case where you have binned data with equal size bins. Currently, only the chi-square goodness of fit method is supported for grouped data (although this may change in future releases). Syntax 5: <dist> CHI-SQUARE GOODNESS OF FIT <y> <xlow> <xhigh> <SUBSET/EXCEPT/FOR qualification> where <dist> is one Dataplot's supported distributions; <y> is a variable of pre-computed frequencies; <xlow> is a variable containing the lower limits of the bins; <xhigh> is a variable containing the upper limits of the bins; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax is used for the case where you have binned data with unequal size bins. Currently, only the chi-square goodness of fit method is supported for grouped data (although this may change in future releases). Examples: LET GAMMA = 2.5 LET KSLOC = 5 LET KSSCALE = 10 WEIBULL ANDERSON DARLING GOODNESS OF FIT Y WEIBULL KOLMOGOROV SMIRNOV GOODNESS OF FIT Y WEIBULL PPCC GOODNESS OF FIT Y WEIBULL CHI-SQUARE GOODNESS OF FIT Y Note: The Kolmogorov-Smirnov (K-S) test is based on the empirical distribution function (ECDF). Given N data points Y1 Y2 ..., Yn the ECDF is defined as $$E_{N} = n(i)/N$$ where ni is the number of points less than Yi This is a step function that increases by 1/N at the value of each data point. The Kolmogorov-Smirnov goodness of fit test statistic is defined as $$D = \max_{1 \le i \le N}\|F(Y_{i}) - \frac{i} {N}\|$$ where F is the theoretical cumulative distribution of the distribution being tested. We can graph a plot of the empirical distribution function with a cumulative distribution function for a given distribution. The K-S test is based on the maximum distance between these two curves. An example of this plot for a sample of 100 normal random numbers is given here. An attractive feature of this test is that the distribution of the K-S test statistic itself does not depend on the underlying cumulative distribution function being tested. Another advantage is that it is an exact test (the chi-square goodness of fit depends on an adequate sample size for the approximations to be valid). Despite these advantages, the K-S test has several important limitations: 1. It only applies to continuous distributions (there are extensions for discrete distributions, although these are not yet implemented in Dataplot). 2. The K-S test looks for the maximum difference wherever it occurs. That is, it is equally sensitive to differences at the centers and tails of the distribution. Some analysts prefer the Anderson-Darling test since it is designed to be more sensitive in the tails of the distribution. 3. The attractive feature that the critical values do not depend on the underlying distribution only applies if the distribution is fully specified (i.e., the parameters are assumed known). If the SET GOODNESS OF FIT FULLY SPECIFIED OFF command is entered, the K-S test will generate the critical values dynamically. For the fully specified case, you can specify whether to use published critical values (limited to a few specific values of alpha) or determine a more complete distribution via simulation with the command SET KOLMOGOROV SMIRNOV CRITICAL VALUES <TABLE/SIMULATION> There are several formulations for obtaining the tabled critical values in the literature. Dataplot uses the critical values from Chakravart, Laha, and Roy (see Reference: below). Note: The Anderson-Darling test (Stephens, 1974) is used to test if a sample of data comes from a specific distribution. It is a modification of the Kolmogorov-Smirnov (K-S) test and gives more weight to the tails than the K-S test. The K-S test is distribution free in the sense that the critical values do not depend on the specific distribution being tested. The Anderson-Darling test makes use of the specific distribution in calculating critical values. This has the advantage of allowing a more sensitive test and the disadvantage that critical values must be calculated for each distribution. For cases where published tables are not available, critical values can be computed dynamically via simulation. This extends the number of distributions for which the Anderson-Darling test can be used. To specify whether published tables or simulation will be used to generate the critical values, enter the command (if the specified distribution does not support published tables, simulation will automatically be used). SET ANDERSON DARLING CRITICAL VALUES <TABLE/SIMULATION> Currently, Dataplot supports critical values from published tables for the following distributions: 1. normal 2. lognormal 3. exponential 4. Weibull 5. extreme value type 1 (Gumbel) 6. logistic 7. double exponential 8. uniform ((0,1) 9. generalized pareto 10. Cauchy 11. Extreme Value Type 2 (Frechet) Dynamic simulation of critical values for other distributions is available when there is a built-in maximum likelihood estimation procedure available (see the Note section below for the SET DISTRIBUTIONAL FIT TYPE command for a complete list of supported distributions). Note that the uniform (0,1) case can be used for fully specified distributions (i.e., the shape, location, and scale parameters are not estimated from the data). Simply apply the appropriate CDF function to the data (this transforms it to a (0,1) interval) and apply the uniform (0,1) test to the transformed data. The Anderson-Darling test statistic is $$A^{2} = -N - S$$ where $$S = \sum_{i=1}^{N}\frac{(2i - 1)}{N}[\log{F(Y_{i})} + \log{(1 - F(Y_{N+1-i}))}]$$ where F is the cumulative distribution function of interest. Note: The basic idea behind the chi-square goodness of fit test is to divide the range of the data into a number of intervals. Then the number of points that fall into each interval is compared to expected number of points for that interval if the data in fact come from the hypothesized distribution. More formally, the chi-square goodness of fit test statistic can be defined as follows. For the chi-square goodness of fit, the data is divided into k bins and the test statistic is defined as $$\chi^{2} = \sum_{i=1}^{k}(O_{i} - E_{i})^{2}/E_{i}$$ where Oi is the observed frequency for bin i and Ei is the expected frequency for bin i. The expected frequency is calculated by $$E_{i} = F(Y_{u}) - F(Y_{l})$$ where F is the cumulative distribution function for the distribution being tested, Yu is the upper limit for class i, and Yl is the lower limit for class i. This test is sensitive to the choice of bins. There is no optimal choice for the bin width (since the optimal bin width depends on the distribution). Most reasonable choices should produce similar, but not identical, results. This test is most frequently used when the data are received in pre-binned form (for raw data, the Anderson-Darling test is more powerful). However, you can use the chi-square test for raw data (you typically will want to have a reasonably large data set before doing this). For raw data, you can specify the binning with the commands CLASS WIDTH, CLASS LOWER, and CLASS UPPER. The default class width is 0.3 times the sample standard deviation. To specify other default algorithms, enter HELP HISTOGRAM CLASS WIDTH. For the chi-square approximation to be valid, the expected frequency should be at least 5. The chi-square approximation may not be valid for small samples, and if some of the counts are less than five, you may need to combine some bins in the tails. The test statistic follows, approximately, a chi-square distribution with (k - c) degrees of freedom where k is the number of non-empty cells and c = the number of parameters (including location and scale parameters and shape parameters) for the distribution + 1. For example, for a 3-parameter Weibull distribution, c = 4. The primary advantage of the chi square goodnes of fit test is that it is quite general. It can be applied for any distribution, either discrete or continuous, for which the cumulative distribution function can be computed. Dataplot supports the chi-square goodness of fit test for all distributions for which it supports a CDF function. 1. The test is sensitive to how the binning of the data is performed. 2. It requires sufficient sample size so that the minimum expected frequency is five. 3. It is generally not as powerful as other goodness of fit tests such as the Anderson-Darling. Note: The PPCC method is supported for location/scale distributions and for distributions with a single shape parameter. Critical values are generated dynamically via simulation. For more information on the PPCC method, enter HELP PPCC PLOT. Also see the NIST/SEMATACH e-Handbook of Statistical Methods: Note: When the Anderson-Darling and Kolmogorov-Smirnov methods generate critical values dynamically, the maximum likelihood method is used to estimate the distribution parameters from the simulated data. For several distributions, you can choose an alternative estimation method using the command SET DISTRIBUTIONAL FIT TYPE <value> where <value> can be one of the following (since this applies to the Anderson-Darling or Kolmogorov-Smirnov methods, only continuous distributions are listed). ML (or MAXIMUM LIKELIHOOD): use the default maximum likelihood, available for normal, uniform, logistic, double exponential, Cauchy, Gumbel, Slash, 1-para exponential, 2-para exponential, folded normal, 1-para Rayleigh, 2-para Rayleigh, 1-para Maxwell, 2-para Maxwell, 2-para Weibull, 3-para Weibull, 2-para inverted Weibull, 2-para lognormal, 2-para gamma, 2-para inverted gamma, 2-para geom extreme exponential, 2-para fatigue life, 2-para Frechet, 2-para Burr Type 10, 2-para logistic exponential, 2-para Von Mises (location/shape), triangular, Topp and Leone, power, reflected power, generalized Pareto, 2-para alpha, asymmetric Laplace, Pareto, truncated Pareto, 2-para brittle fiber Weibull, 2-para beta, 4-para beta, beta normal, two-sided power, reflected generalized Topp and Leone, normal mixture BC (or BIAS CORRECTED): use the bias corrected maximum likelihood, available for 1-para exponential, 2-para exponential, 2-para Weibull, 2-para inverted Weibull, 2-para Frechet MOMENT: use the moment estimates, available for uniform, Gumbel, 1-para Maxwell, 2-para Maxwell, 2-para gamma, 2-para inverted gamma, 2-para fatigue life, 2-para Beta, 4-para Beta, Pareto, generalized Pareto, MODIFIED MOMENT: use the modified moment estimates, available for the 3-para Weibull, 2-para Rayleigh, 3-para inverted Weibull, Pareto LMOMENT (or L MOMEMNT): use the L-moment estimates, available for generalized Pareto, generalized extreme value, Wakeby, Pearson Type 3, generalized logistic type 5, Kappa PERCENTILE: use Zynakis percentile method for the 3-para Weibull or 3-para inverted Weibull WYCOFF BAIN ENGLEHARDT (or WBE): use Wycoff, Bain, Englehardt percentile method for the 3-para Weibull or 3-para inverted Weibull ELEMENTAL PERCENTILE: use the elemental percentile method, available for the generalized Pareto, generalized extremed value ORDER STATISTIC (or OS): use the order statistic method, available for Cauchy WEIGHTED ORDER STATISTIC (or WOS): use the weighted order statistic method, available for Cauchy Note that the above list gives the distributions for which dynamic critical values can be obtained by simulation when the parameters are assumed unknown for the Anderson-Darling and Kolmogorov-Smirnov methods. If a particular distribution only supports a single method (e.g., several currently only support L-moment estimates), that method will always be used. If you specify a method that is not supported for a given distribution, the default method (usually maximum likelihood) will be used. Also note that a given estimation method for a particular distribution may fail for certain data sets. Since a large number of simulated data sets are generated, this may be an issue for some distributions. The output will return the number of times a failure in the estimation procedure was detected in the simulations. Default: None Synonyms: GOODNESS OF FIT TEST is a synonym for GOODNESS OF FIT GOF is a synonym for GOODNESS OF FIT Related Commands: WILK SHAPIRO TEST = Perform a Wilks-Shapiro test for normality. MAXIMUM LIKELIHOOD = Perform maximum likelihood estimation for several distributions. PROBABILITY PLOT = Generate a probability plot. PPCC PLOT = Generate a PPCC plot. HISTOGRAM = Generates a histogram. RANDOM NUMBERS = Generate random numbers. Reference: Stephens, M. A. (1974), "EDF Statistics for Goodness of Fit and Some Comparisons," Journal of the American Statistical Association, Vol. 69, pp. 730-737. Stephens, M. A. (1976), "Asymptotic Results for Goodness-of-Fit Statistics with Unknown Parameters," Annals of Statistics, Vol. 4, pp. 357-369. Stephens, M. A. (1977), "Goodness of Fit for the Extreme Value Distribution," Biometrika, Vol. 64, pp. 583-588. Stephens, M. A. (1977), "Goodness of Fit with Special Reference to Tests for Exponentiality," Technical Report No. 262, Department of Statistics, Stanford University, Stanford, CA. Stephens, M. A. (1979), "Tests of Fit for the Logistic Distribution Based on the Empirical Distribution Function," Biometrika, Vol. 66, pp. 591-595. "MIL-HDBK-17 Volume 1: Guidelines for Characterization of Structural Materials", Depeartment of Defense, chapter 8. The URL for MIL-HDBK-17 is http://mil-17.udel.edu/. V. Choulakian and M. A. Stephens (2001), "Goodness-of-Fit Tests for the Generalized Pareto Distribution", Technometrics, Vol. 43, No. 4, pp. 478-484. James J. Filliben (1975), "The Probability Plot Correlation Coefficient Test for Normality," Technometrics, Vol. 17, No. 1. Chakravart, Laha, and Roy (1967), "Handbook of Methods of Applied Statistics, Volume I," John Wiley, pp. 392-394. Snedecor and Cochran (1989), "Statistical Methods", Eight Edition, Iowa State, 1989, pp. 76-79. Applications: Distributional Modeling Implementation Date: 2009/10 Program: . Step 1: Read the data . . Following data from Jeffery Fong of the NIST . Applied and Computational Mathematics Division. . This is strength data in ksi units. . 18.830 20.800 21.657 23.030 23.230 24.050 24.321 25.500 25.520 25.800 26.690 26.770 26.780 27.050 27.670 29.900 31.110 33.200 33.730 33.760 33.890 34.760 35.750 35.910 36.980 37.080 37.090 39.580 44.045 45.290 45.381 end of data . . Step 2: Apply goodness of fit tests for Weibull distribution . based on ML estimates . set write decimals 5 3-parameter weibull mle y let ksloc = locml let ksscale = scaleml let gamma = shapeml . . Anderson-Darling . set anderson darling critical values table weibull anderson darling goodness of fit y set anderson darling critical values simulation weibull anderson darling goodness of fit y . . Step 3: Apply goodness of fit tests for normal distribution . normal mle y let ksloc = xmean let ksscale = xsd . set anderson darling critical values table normal anderson darling goodness of fit y set anderson darling critical values simulation normal anderson darling goodness of fit y set kolmogorov smirnov critical values simulation normal kolmogorov smirnov goodness of fit y The following output is generated. ******************************* 3-parameter weibull mle y ***************************** Three-Parameter Weibull (Minimum) Parameter Estimation: Full Sample Case Summary Statistics: Number of Observations: 31 Sample Mean: 30.81141 Sample Standard Deviation: 7.25338 Sample Skewness: 0.39880 Sample Minimum: 18.82999 Sample Maximum: 45.38100 Zanakis Percentile Method: Estimate of Location: 18.65836 Estimate of Scale: 15.10163 Estimate of Shape: 1.86735 Value of Log-Likelihood Function: -104.60286 AIC: 215.20572 AICC: 216.09461 BIC: 219.50768 Wycoff-Bain-Englehardt Percentile Method Estimate of Location: 16.64362 Estimate of Scale: 16.41275 Estimate of Shape: 1.92760 Value of Log-Likelihood Function: -103.63967 AIC: 213.27934 AICC: 214.16823 BIC: 217.58131 Modified Moments: Estimate of Location: 15.60378 Estimate of Scale: 17.17121 Estimate of Shape (Gamma): 2.21477 Standard Error of Location: 0.71154 Standard Error of Scale: 0.52547 Standard Error of Shape: 0.09924 Value of Log-Likelihood Function: -103.56460 AIC: 213.12921 AICC: 214.01810 BIC: 217.43118 Maximum Likelihood: Estimate of Location: 17.64420 Estimate of Scale: 14.83507 Estimate of Shape (Gamma): 1.91358 Value of Log-Likelihood Function: -103.26267 AIC: 212.52535 AICC: 213.41423 BIC: 216.82731 ********************* let ksloc = locml ********************* THE COMPUTED VALUE OF THE CONSTANT KSLOC = 0.1764420E+02 ************************* let ksscale = scaleml ************************* THE COMPUTED VALUE OF THE CONSTANT KSSCALE = 0.1483507E+02 *********************** let gamma = shapeml *********************** THE COMPUTED VALUE OF THE CONSTANT GAMMA = 0.1913580E+01 ******************************* . Anderson-Darling ******************************* ********************************************** set anderson darling critical values table ********************************************** THE FORTRAN COMMON CHARACTER VARIABLE ANDEDARL HAS JUST BEEN SET TO TABL ********************************************** weibull anderson darling goodness of fit y ********************************************** Anderson-Darling Goodness of Fit Test (Critical Values from Published Tables) Response Variable: Y H0: The distribution fits the data Ha: The distribution does not fit the data Distribution: WEIBULL Location Parameter: 17.64420 Scale Parameter: 14.83507 Shape Parameter 1: 1.91358 Summary Statistics: Number of Observations: 31 Sample Minimum: 18.82999 Sample Maximum: 45.38100 Sample Mean: 30.81141 Sample SD: 7.25338 Anderson-Darling Test Statistic Value: 0.33805 Conclusions (Upper 1-Tailed Test) ---------------------------------------------- Alpha CDF Critical Value Conclusion ---------------------------------------------- 10% 90% 0.637 Accept H0 5% 95% 0.757 Accept H0 2.5% 97.5% 0.877 Accept H0 1% 99% 1.038 Accept H0 *************************************************** set anderson darling critical values simulation *************************************************** THE FORTRAN COMMON CHARACTER VARIABLE ANDEDARL HAS JUST BEEN SET TO SIMU ********************************************** weibull anderson darling goodness of fit y ************************************************ Anderson-Darling Goodness of Fit Test (Fully Specified Model) Response Variable: Y H0: The distribution fits the data Ha: The distribution does not fit the data Distribution: WEIBULL Location Parameter: 17.64420 Scale Parameter: 14.83507 Shape Parameter 1: 1.91358 Summary Statistics: Number of Observations: 31 Sample Minimum: 18.82999 Sample Maximum: 45.38100 Sample Mean: 30.81141 Sample SD: 7.25338 Anderson-Darling Test Statistic Value: 0.33805 Number of Monte Carlo Simulations: 10000.00000 CDF Value: 0.09370 P-Value 0.90630 Percent Points of the Reference Distribution ----------------------------------- Percent Point Value ----------------------------------- 0.0 = 0.000 50.0 = 0.772 75.0 = 1.248 90.0 = 1.964 95.0 = 2.579 97.5 = 3.230 99.0 = 4.115 99.5 = 4.814 Conclusions (Upper 1-Tailed Test) ---------------------------------------------- Alpha CDF Critical Value Conclusion ---------------------------------------------- 10% 90% 1.964 Accept H0 5% 95% 2.579 Accept H0 2.5% 97.5% 3.230 Accept H0 1% 99% 4.115 Accept H0 Critical Values Based on 10000 Monte Carlo Simulations ***************** normal mle y **************** Normal Parameter Estimation Summary Statistics: Number of Observations: 31 Sample Minimum: 18.82999 Sample Maximum: 45.38100 Maximum Likelihood: Estimate of Location (Mean): 30.81141 Standard Error of Location: 1.30274 Estimate of Scale (SD): 7.25338 Standard Error of Scale: 0.93640 Log-likelihood: -0.1049126E+03 AIC: 0.2138252E+03 AICc: 0.2142538E+03 BIC: 0.2166932E+03 Confidence Interval for Location Parameter (Normal Approximation) --------------------------------------------- Confidence Lower Upper Coefficient Limit Limit --------------------------------------------- 50.00 29.92196 31.70087 75.00 29.28321 32.33962 90.00 28.60032 33.02251 95.00 28.15085 33.47198 99.00 27.22887 34.39396 99.90 26.06166 35.56117 --------------------------------------------- Confidence Interval for Scale Parameter (Normal Approximation) --------------------------------------------- Confidence Lower Upper Coefficient Limit Limit --------------------------------------------- 50.00 6.73462 8.03002 75.00 6.35897 8.58825 90.00 6.00479 9.23849 95.00 5.79626 9.69540 99.00 5.42284 10.69967 99.90 5.03893 12.08652 --------------------------------------------- ********************* let ksloc = xmean ********************* THE COMPUTED VALUE OF THE CONSTANT KSLOC = 0.3081142E+02 ********************* let ksscale = xsd ********************* THE COMPUTED VALUE OF THE CONSTANT KSSCALE = 0.7253381E+01 ********************************************** set anderson darling critical values table ********************************************** THE FORTRAN COMMON CHARACTER VARIABLE ANDEDARL HAS JUST BEEN SET TO TABL ********************************************* normal anderson darling goodness of fit y ********************************************* Anderson-Darling Goodness of Fit Test (Critical Values from Published Tables) Response Variable: Y H0: The distribution fits the data Ha: The distribution does not fit the data Distribution: NORMAL Location Parameter: 30.81141 Scale Parameter: 7.25338 Summary Statistics: Number of Observations: 31 Sample Minimum: 18.82999 Sample Maximum: 45.38100 Sample Mean: 30.81141 Sample SD: 7.25338 Anderson-Darling Test Statistic Value: 0.53219 Conclusions (Upper 1-Tailed Test) ---------------------------------------------- Alpha CDF Critical Value Conclusion ---------------------------------------------- 10% 90% 0.616 Accept H0 5% 95% 0.735 Accept H0 2.5% 97.5% 0.861 Accept H0 1% 99% 1.020 Accept H0 *************************************************** set anderson darling critical values simulation *************************************************** THE FORTRAN COMMON CHARACTER VARIABLE ANDEDARL HAS JUST BEEN SET TO SIMU ********************************************* normal anderson darling goodness of fit y *********************************************** Anderson-Darling Goodness of Fit Test (Fully Specified Model) Response Variable: Y H0: The distribution fits the data Ha: The distribution does not fit the data Distribution: NORMAL Location Parameter: 30.81141 Scale Parameter: 7.25338 Summary Statistics: Number of Observations: 31 Sample Minimum: 18.82999 Sample Maximum: 45.38100 Sample Mean: 30.81141 Sample SD: 7.25338 Anderson-Darling Test Statistic Value: 0.53219 Number of Monte Carlo Simulations: 10000.00000 CDF Value: 0.29750 P-Value 0.70250 Percent Points of the Reference Distribution ----------------------------------- Percent Point Value ----------------------------------- 0.0 = 0.000 50.0 = 0.764 75.0 = 1.231 90.0 = 1.919 95.0 = 2.478 97.5 = 3.115 99.0 = 3.942 99.5 = 4.535 Conclusions (Upper 1-Tailed Test) ---------------------------------------------- Alpha CDF Critical Value Conclusion ---------------------------------------------- 10% 90% 1.919 Accept H0 5% 95% 2.478 Accept H0 2.5% 97.5% 3.115 Accept H0 1% 99% 3.942 Accept H0 Critical Values Based on 10000 Monte Carlo Simulations ****************************************************** set kolmogorov smirnov critical values simulation ***************************************************** THE FORTRAN COMMON CHARACTER VARIABLE KOLMSMIR HAS JUST BEEN SET TO SIMU *********************************************** normal kolmogorov smirnov goodness of fit y ************************************************* Kolmogorov-Smirnov Goodness of Fit Test Response Variable: Y H0: The distribution fits the data Ha: The distribution does not fit the data Distribution: NORMAL Location Parameter: 30.81141 Scale Parameter: 7.25338 Summary Statistics: Number of Observations: 31 Sample Minimum: 18.82999 Sample Maximum: 45.38100 Sample Mean: 30.81141 Sample SD: 7.25338 Kolmogorov-Smirnov Test Statistic Value: 0.15139 Number of Monte Carlo Simulations: 10000.00000 CDF Value: 0.57660 P-Value 0.42340 (Fully Specified Model) Percent Points of the Reference Distribution ----------------------------------- Percent Point Value ----------------------------------- 0.0 = 0.000 50.0 = 0.143 75.0 = 0.176 90.0 = 0.213 95.0 = 0.236 97.5 = 0.256 99.0 = 0.284 99.5 = 0.305 Conclusions (Upper 1-Tailed Test) ---------------------------------------------- Alpha CDF Critical Value Conclusion ---------------------------------------------- 10% 90% 0.213 Accept H0 5% 95% 0.236 Accept H0 1% 99% 0.284 Accept H0 *Critical Values Based on 10000 Monte Carlo Simulations NIST is an agency of the U.S. Commerce Department. 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https://zbmath.org/authors/?q=rv%3A11302	# zbMATH — the first resource for mathematics ## Gugat, Martin Compute Distance To: Author ID: gugat.martin Published as: Gugat, Martin; Gugat, M. External Links: MGP · ORCID · Wikidata Documents Indexed: 101 Publications since 1992, including 1 Book Reviewing Activity: 32 Reviews all top 5 #### Co-Authors 41 single-authored 24 Leugering, Günter 13 Herty, Michael Matthias 7 Dick, Markus 4 Wintergerst, David 3 Hante, Falk M. 3 Klar, Axel 3 Schleper, Veronika 3 Schultz, Rüdiger 3 Schuster, Michael J. 3 Steffensen, Sonja 3 Zuazua, Enrique 2 Grimm, Volker 2 Keimer, Alexander 2 Martin, Alexander 2 Schmidt, E. J. P. Georg 2 Schmidt, Martin 2 Sirvent, Mathias 2 Tröltzsch, Fredi 2 Ulbrich, Stefan 1 Farshbaf-Shaker, Mohammad Hassan 1 Gerster, Stephan 1 Giesselmann, Jan 1 Heitsch, Holger 1 Henrion, René 1 Hettich, Rainer 1 Hirsch-Dick, Markus 1 Mateos, Mariano 1 Müller, Siegfried 1 Perrollaz, Vincent 1 Pfeiffer, Barbara 1 Rosier, Lionel 1 Schittkowski, Klaus 1 Sigalotti, Mario 1 Sklyar, Grigory Mikhailovitch 1 Sokołowski, Jan 1 Tamasoiu, Simona Oana 1 Trélat, Emmanuel 1 Tucsnak, Marius 1 Weber, Gerhard-Wilhelm 1 Yu, Hui all top 5 #### Serials 9 SIAM Journal on Control and Optimization 6 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 6 Networks and Heterogeneous Media 5 Journal of Optimization Theory and Applications 4 Systems & Control Letters 4 Optimization 3 Mathematical Methods in the Applied Sciences 3 Computational Optimization and Applications 3 Computational and Applied Mathematics 3 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Applicable Analysis 2 Control and Cybernetics 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 IMA Journal of Mathematical Control and Information 2 MCSS. Mathematics of Control, Signals, and Systems 2 Mathematical Programming. Series A. Series B 2 Mathematical Problems in Engineering 2 Mathematical Control and Related Fields 1 International Journal of Control 1 Journal of Mathematical Analysis and Applications 1 Automatica 1 Journal of Computational and Applied Mathematics 1 Management Science 1 Networks 1 SIAM Journal on Numerical Analysis 1 Optimal Control Applications & Methods 1 Chinese Annals of Mathematics. Series B 1 Constructive Approximation 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Numerical Algorithms 1 SIAM Journal on Applied Mathematics 1 Vietnam Journal of Mathematics 1 Optimization Methods & Software 1 Mathematical Methods of Operations Research 1 International Journal of Applied Mathematics and Computer Science 1 Journal of Evolution Equations 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Advanced Modeling and Optimization 1 Numerical Algebra, Control and Optimization 1 Arabian Journal of Mathematics 1 Pure and Applied Functional Analysis 1 SpringerBriefs in Electrical and Computer Engineering all top 5 #### Fields 55 Partial differential equations (35-XX) 49 Systems theory; control (93-XX) 44 Calculus of variations and optimal control; optimization (49-XX) 29 Operations research, mathematical programming (90-XX) 24 Fluid mechanics (76-XX) 12 Numerical analysis (65-XX) 10 Mechanics of deformable solids (74-XX) 2 Approximations and expansions (41-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Combinatorics (05-XX) 1 Operator theory (47-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of particles and systems (70-XX) #### Citations contained in zbMATH Open 89 Publications have been cited 698 times in 354 Documents Cited by Year Existence of classical solutions and feedback stabilization for the flow in gas networks. Zbl 1429.76090 Gugat, Martin; Herty, Michaël 2011 Global boundary controllability of the de St. Venant equations between steady states. Zbl 1032.93030 Gugat, M.; Leugering, G. 2003 Gas flow in fan-shaped networks: classical solutions and feedback stabilization. Zbl 1237.35107 Gugat, Martin; Dick, Markus; Leugering, Günter 2011 Optimal control for traffic flow networks. Zbl 1079.49024 Gugat, M.; Herty, M.; Klar, A.; Leugering, G. 2005 Flow control in gas networks: exact controllability to a given demand. Zbl 1394.76112 Gugat, M.; Herty, M.; Schleper, V. 2011 Global controllability between steady supercritical flows in channel networks. Zbl 1047.93028 Gugat, Martin; Leugering, Günter; Schmidt, E. J. P. Georg 2004 Stationary states in gas networks. Zbl 1332.93154 Gugat, Martin; Hante, Falk M.; Hirsch-Dick, Markus; Leugering, Günter 2015 Classical solutions and feedback stabilization for the gas flow in a sequence of pipes. Zbl 1263.76059 Dick, Markus; Gugat, Martin; Leugering, Günter 2010 Global boundary controllability of the Saint-Venant system for sloped canals with friction. Zbl 1154.76009 Gugat, M.; Leugering, G. 2009 Stars of vibrating strings: switching boundary feedback stabilization. Zbl 1258.93088 Gugat, Martin; Sigalotti, Mario 2010 Optimal Neumann control for the 1D wave equation: finite horizon, infinite horizon, boundary tracking terms and the turnpike property. Zbl 1335.49012 Gugat, Martin; Trélat, Emmanuel; Zuazua, Enrique 2016 $$L^{p}$$-optimal boundary control for the wave equation. Zbl 1083.49017 Gugat, M.; Leugering, G.; Sklyar, G. 2005 Optimal switching boundary control of a string to rest in finite time. Zbl 1242.49008 Gugat, Martin 2008 Analysis of a system of nonlocal conservation laws for multi-commodity flow on networks. Zbl 1335.49011 Gugat, Martin; Keimer, Alexander; Leugering, Günter; Wang, Zhiqiang 2015 Prox-regularization methods for generalized fractional programming. Zbl 0973.90078 Gugat, M. 1998 Boundary feedback stabilization by time delay for one-dimensional wave equations. Zbl 1198.93177 Gugat, Martin 2010 $$L^\infty$$-norm minimal control of the wave equation: on the weakness of the bang-bang principle. Zbl 1133.49006 Gugat, Martin; Leugering, Gunter 2008 $$H^2$$-stabilization of the isothermal Euler equations: a Lyapunov function approach. Zbl 1253.76112 Gugat, Martin; Leugering, Günter; Tamasoiu, Simona 2012 Well-posedness of networked hyperbolic systems of balance laws. Zbl 1356.49004 Gugat, Martin; Herty, Michael; Klar, Axel; Leugering, Günther; Schleper, Veronika 2012 An example for the switching delay feedback stabilization of an infinite dimensional system: the boundary stabilization of a string. Zbl 1216.93084 Gugat, Martin; Tucsnak, Marius 2011 The smoothed-penalty algorithm for state constrained optimal control problems for partial differential equations. Zbl 1201.90186 Gugat, Martin; Herty, Michael 2010 Optimal boundary control and boundary stabilization of hyperbolic systems. Zbl 1328.49001 Gugat, Martin 2015 Boundary feedback stabilization of the telegraph equation: decay rates for vanishing damping term. Zbl 1288.93066 Gugat, Martin 2014 Optimal nodal control of networked hyperbolic systems: evaluation of derivatives. Zbl 1165.49307 Gugat, Martin 2005 Modelling, stabilization, and control of flow in networks of open channels. Zbl 0987.93056 Gugat, Martin; Leugering, Günter; Schittkowski, Klaus; Schmidt, E. J. P. Georg 2001 Controllability of a slowly rotating Timoshenko beam. Zbl 1031.93103 Gugat, Martin 2001 A fast algorithm for a class of generalized fractional programs. Zbl 0881.90113 Gugat, Martin 1996 A strict $$H^1$$-Lyapunov function and feedback stabilization for the isothermal Euler equations with friction. Zbl 1242.76296 Dick, Markus; Gugat, Martin; Leugering, Günter 2011 Approximation of semigroups and related operator functions by resolvent series. Zbl 1222.65052 Grimm, Volker; Gugat, Martin 2010 One-sided derivatives for the value function in convex parametric programming. Zbl 0822.90130 Gugat, M. 1994 Optimal distributed control of the wave equation subject to state constraints. Zbl 1176.35176 Gugat, Martin; Keimer, Alexander; Leugering, Günter 2009 MIP-based instantaneous control of mixed-integer PDE-constrained gas transport problems. Zbl 1391.49040 Gugat, Martin; Leugering, Günter; Martin, Alexander; Schmidt, Martin; Sirvent, Mathias; Wintergerst, David 2018 Neumann boundary feedback stabilization for a nonlinear wave equation: A strict $$H^2$$-Lyapunov function. Zbl 1366.76079 Gugat, Martin; Leugering, Günter; Wang, Ke 2017 Boundary controllability between sub- and supercritical flow. Zbl 1047.35087 Gugat, Martin 2003 Time-delayed boundary feedback stabilization of the isothermal Euler equations with friction. Zbl 1368.76010 Gugat, Martin; Dick, Markus 2011 Penalty techniques for state constrained optimal control problems with the wave equation. Zbl 1202.49037 Gugat, Martin 2010 Boundary feedback stabilization of the Schlögl system. Zbl 1309.93121 Gugat, Martin; Tröltzsch, Fredi 2015 Weber problems with mixed distances and regional demand. Zbl 1146.90464 Gugat, Martin; Pfeiffer, Barbara 2007 Networks of pipelines for gas with nonconstant compressibility factor: stationary states. Zbl 1416.76253 Gugat, Martin; Schultz, Rüdiger; Wintergerst, David 2018 Parametric disjunctive programming: One-sided differentiability of the value function. Zbl 0886.90113 Gugat, M. 1997 The isothermal Euler equations for ideal gas with source term: product solutions, flow reversal and no blow up. Zbl 1372.35224 Gugat, Martin; Ulbrich, Stefan 2017 Solutions of $$L^p$$-norm-minimal control problems for the wave equation. Zbl 1119.90353 Gugat, Martin; Leugering, G. 2002 Optimal boundary feedback stabilization of a string with moving boundary. Zbl 1141.93047 Gugat, Martin 2008 Boundary stabilization of quasilinear hyperbolic systems of balance laws: exponential decay for small source terms. Zbl 1421.35213 Gugat, Martin; Perrollaz, Vincent; Rosier, Lionel 2018 On the turnpike phenomenon for optimal boundary control problems with hyperbolic systems. Zbl 1418.35252 Gugat, Martin; Hante, Falk M. 2019 Regularization of $$L^\infty$$-optimal control problems for distributed parameter systems. Zbl 1015.49020 Gugat, M.; Leugering, G. 2002 Analytic solutions of $$L^{\infty}$$ optimal control problems for the wave equation. Zbl 1012.49025 Gugat, M. 2002 Norm-minimal Neumann boundary control of the wave equation. Zbl 1314.35205 Gugat, Martin 2015 Towards simulation based mixed integer optimization with differential equations. Zbl 1397.90308 Gugat, Martin; Leugering, Günter; Martin, Alexander; Schmidt, Martin; Sirvent, Mathias; Wintergerst, David 2018 Contamination source determination in water distribution networks. Zbl 1260.49005 Gugat, Martin 2012 An algorithm for Chebyshev approximation by rationals with constrained denominators. Zbl 0886.41013 Gugat, M. 1996 Coupling conditions for the transition from supersonic to subsonic fluid states. Zbl 1379.35241 Gugat, Martin; Herty, Michael; Müller, Siegfried 2017 Exact penalization of terminal constraints for optimal control problems. Zbl 1353.49005 Gugat, Martin; Zuazua, Enrique 2016 Optimal boundary control of the wave equation with pointwise control constraints. Zbl 1226.49023 Gugat, Martin; Grimm, Volker 2011 Exponential stabilization of the wave equation by Dirichlet integral feedback. Zbl 1339.35156 Gugat, Martin 2015 Optimal boundary control of a string to rest in finite time with continuous state. Zbl 1092.49020 Gugat, Martin 2006 A note on the approximation of Dirichlet boundary control problems for the wave equation on curved domains. Zbl 1273.49009 Gugat, M.; Sokolowski, J. 2013 Conservation law constrained optimization based upon Front-Tracking. Zbl 1116.65079 Gugat, Martin; Herty, Michaël; Klar, Axel; Leugering, Gunter 2006 Time-parametric control: Uniform convergence of the optimal value functions of discretized problems. Zbl 0951.49032 Gugat, Martin 1999 A Newton method for the computation of time-optimal boundary controls of one-dimensional vibrating systems. Zbl 0953.93042 Gugat, Martin 2000 The Newton differential correction algorithm for rational Chebyshev approximation with constrained denominators. Zbl 0860.65006 Gugat, M. 1996 A parametric view on the Mangasarian-Fromovitz constraint qualification. Zbl 0976.90111 Gugat, Martin 1999 Optimization under functional constraints (semi-infinite programming) and applications. Zbl 0770.90070 Hettich, Rainer; Gugat, Martin 1992 Lavrentiev-prox-regularization for optimal control of PDEs with state constraints. Zbl 1200.65051 Gugat, Martin 2009 Optimal energy control in finite time by varying the length of the string. Zbl 1144.49016 Gugat, Martin 2007 Erratum to: “Flow control in gas networks: exact controllability to a given demand”. Zbl 1464.76183 Gugat, M.; Herty, M.; Schleper, V. 2015 Lipschitz continuity of the value function in mixed-integer optimal control problems. Zbl 1439.49047 Gugat, Martin; Hante, Falk M. 2017 $$L^1$$-optimal boundary control of a string to rest in finite time. Zbl 1108.49017 Gugat, Martin 2006 Stabilization of networked hyperbolic systems with boundary feedback. Zbl 1327.93312 Dick, Markus; Gugat, Martin; Herty, Michael; Leugering, Günter; Steffensen, Sonja; Wang, Ke 2014 On the limits of stabilizability for networks of strings. Zbl 1425.93229 Gugat, Martin; Gerster, Stephan 2019 Lipschitz solutions of initial boundary value problems for balance laws. Zbl 1394.35261 Gugat, Martin; Ulbrich, Stefan 2018 Convex semi-infinite parametric programming: Uniform convergence of the optimal value functions of discretized problems. Zbl 0956.90054 Gugat, M. 1999 Optimal boundary control in flood management. Zbl 1239.49030 Gugat, Martin 2007 Error bounds for infinite systems of convex inequalities without Slater’s condition. Zbl 0997.90090 Gugat, Martin 2000 Computation of lower bounds for spectra via fractional semi-infinite programming. Zbl 0841.65091 Gugat, Martin 1995 Transient flow in gas networks: traveling waves. Zbl 1442.35316 Gugat, Martin; Wintergerst, David 2018 Exact boundary controllability for free traffic flow with Lipschitz continuous state. Zbl 1400.90098 Gugat, Martin 2016 A smoothed penalty iteration for state constrained optimal control problems for partial differential equations. Zbl 1290.90072 Gugat, Martin; Herty, Michael 2013 Stationary gas networks with compressor control and random loads: optimization with probabilistic constraints. Zbl 1427.76234 Gugat, Martin; Schuster, Michael; Weber, Gerhard-Wilhelm 2018 Parametric convex optimization: One-sided derivatives of the value function in singular parameters. Zbl 0961.90114 Gugat, Martin 1998 Corrigendum: One-sided derivatives for the value function in convex parametric programming. Zbl 0864.90113 Gugat, M. 1996 Semi-infinite terminal problems: A Newton type method. Zbl 0916.65066 Gugat, Martin 1998 Lavrentiev prox-regularization methods for optimal control problems with pointwise state constraints. Zbl 1197.49042 Gugat, Martin 2009 Nodal control of conservation laws on networks. Sensitivity calculations for the control of systems of conservation laws with source terms on networks. Zbl 1097.65071 Gugat, Martin 2005 On the relaxation approximation of boundary control of the isothermal Euler equations. Zbl 1253.93110 Dick, M.; Gugat, M.; Herty, M.; Steffensen, S. 2012 Stabilization of the gas flow in star-shaped networks by feedback controls with varying delay. Zbl 1264.93206 Gugat, Martin; Dick, Markus; Leugering, Günter 2013 On the relaxation approximation for $$2\times 2$$ hyperbolic balance laws. Zbl 1407.65105 Gugat, Martin; Herty, Michael; Yu, Hui 2018 Boundary feedback stabilization of the isothermal Euler equations with uncertain boundary data. Zbl 1391.76673 Gugat, Martin; Schultz, Rüdiger 2018 A turnpike result for convex hyperbolic optimal boundary control problems. Zbl 1458.35259 Gugat, Martin 2019 On the turnpike phenomenon for optimal boundary control problems with hyperbolic systems. Zbl 1418.35252 Gugat, Martin; Hante, Falk M. 2019 On the limits of stabilizability for networks of strings. Zbl 1425.93229 Gugat, Martin; Gerster, Stephan 2019 A turnpike result for convex hyperbolic optimal boundary control problems. Zbl 1458.35259 Gugat, Martin 2019 MIP-based instantaneous control of mixed-integer PDE-constrained gas transport problems. Zbl 1391.49040 Gugat, Martin; Leugering, Günter; Martin, Alexander; Schmidt, Martin; Sirvent, Mathias; Wintergerst, David 2018 Networks of pipelines for gas with nonconstant compressibility factor: stationary states. Zbl 1416.76253 Gugat, Martin; Schultz, Rüdiger; Wintergerst, David 2018 Boundary stabilization of quasilinear hyperbolic systems of balance laws: exponential decay for small source terms. Zbl 1421.35213 Gugat, Martin; Perrollaz, Vincent; Rosier, Lionel 2018 Towards simulation based mixed integer optimization with differential equations. Zbl 1397.90308 Gugat, Martin; Leugering, Günter; Martin, Alexander; Schmidt, Martin; Sirvent, Mathias; Wintergerst, David 2018 Lipschitz solutions of initial boundary value problems for balance laws. Zbl 1394.35261 Gugat, Martin; Ulbrich, Stefan 2018 Transient flow in gas networks: traveling waves. Zbl 1442.35316 Gugat, Martin; Wintergerst, David 2018 Stationary gas networks with compressor control and random loads: optimization with probabilistic constraints. Zbl 1427.76234 Gugat, Martin; Schuster, Michael; Weber, Gerhard-Wilhelm 2018 On the relaxation approximation for $$2\times 2$$ hyperbolic balance laws. Zbl 1407.65105 Gugat, Martin; Herty, Michael; Yu, Hui 2018 Boundary feedback stabilization of the isothermal Euler equations with uncertain boundary data. Zbl 1391.76673 Gugat, Martin; Schultz, Rüdiger 2018 Neumann boundary feedback stabilization for a nonlinear wave equation: A strict $$H^2$$-Lyapunov function. Zbl 1366.76079 Gugat, Martin; Leugering, Günter; Wang, Ke 2017 The isothermal Euler equations for ideal gas with source term: product solutions, flow reversal and no blow up. Zbl 1372.35224 Gugat, Martin; Ulbrich, Stefan 2017 Coupling conditions for the transition from supersonic to subsonic fluid states. Zbl 1379.35241 Gugat, Martin; Herty, Michael; Müller, Siegfried 2017 Lipschitz continuity of the value function in mixed-integer optimal control problems. Zbl 1439.49047 Gugat, Martin; Hante, Falk M. 2017 Optimal Neumann control for the 1D wave equation: finite horizon, infinite horizon, boundary tracking terms and the turnpike property. Zbl 1335.49012 Gugat, Martin; Trélat, Emmanuel; Zuazua, Enrique 2016 Exact penalization of terminal constraints for optimal control problems. Zbl 1353.49005 Gugat, Martin; Zuazua, Enrique 2016 Exact boundary controllability for free traffic flow with Lipschitz continuous state. Zbl 1400.90098 Gugat, Martin 2016 Stationary states in gas networks. Zbl 1332.93154 Gugat, Martin; Hante, Falk M.; Hirsch-Dick, Markus; Leugering, Günter 2015 Analysis of a system of nonlocal conservation laws for multi-commodity flow on networks. Zbl 1335.49011 Gugat, Martin; Keimer, Alexander; Leugering, Günter; Wang, Zhiqiang 2015 Optimal boundary control and boundary stabilization of hyperbolic systems. Zbl 1328.49001 Gugat, Martin 2015 Boundary feedback stabilization of the Schlögl system. Zbl 1309.93121 Gugat, Martin; Tröltzsch, Fredi 2015 Norm-minimal Neumann boundary control of the wave equation. Zbl 1314.35205 Gugat, Martin 2015 Exponential stabilization of the wave equation by Dirichlet integral feedback. Zbl 1339.35156 Gugat, Martin 2015 Erratum to: “Flow control in gas networks: exact controllability to a given demand”. Zbl 1464.76183 Gugat, M.; Herty, M.; Schleper, V. 2015 Boundary feedback stabilization of the telegraph equation: decay rates for vanishing damping term. Zbl 1288.93066 Gugat, Martin 2014 Stabilization of networked hyperbolic systems with boundary feedback. Zbl 1327.93312 Dick, Markus; Gugat, Martin; Herty, Michael; Leugering, Günter; Steffensen, Sonja; Wang, Ke 2014 A note on the approximation of Dirichlet boundary control problems for the wave equation on curved domains. Zbl 1273.49009 Gugat, M.; Sokolowski, J. 2013 A smoothed penalty iteration for state constrained optimal control problems for partial differential equations. Zbl 1290.90072 Gugat, Martin; Herty, Michael 2013 Stabilization of the gas flow in star-shaped networks by feedback controls with varying delay. Zbl 1264.93206 Gugat, Martin; Dick, Markus; Leugering, Günter 2013 $$H^2$$-stabilization of the isothermal Euler equations: a Lyapunov function approach. Zbl 1253.76112 Gugat, Martin; Leugering, Günter; Tamasoiu, Simona 2012 Well-posedness of networked hyperbolic systems of balance laws. Zbl 1356.49004 Gugat, Martin; Herty, Michael; Klar, Axel; Leugering, Günther; Schleper, Veronika 2012 Contamination source determination in water distribution networks. Zbl 1260.49005 Gugat, Martin 2012 On the relaxation approximation of boundary control of the isothermal Euler equations. Zbl 1253.93110 Dick, M.; Gugat, M.; Herty, M.; Steffensen, S. 2012 Existence of classical solutions and feedback stabilization for the flow in gas networks. Zbl 1429.76090 Gugat, Martin; Herty, Michaël 2011 Gas flow in fan-shaped networks: classical solutions and feedback stabilization. Zbl 1237.35107 Gugat, Martin; Dick, Markus; Leugering, Günter 2011 Flow control in gas networks: exact controllability to a given demand. Zbl 1394.76112 Gugat, M.; Herty, M.; Schleper, V. 2011 An example for the switching delay feedback stabilization of an infinite dimensional system: the boundary stabilization of a string. Zbl 1216.93084 Gugat, Martin; Tucsnak, Marius 2011 A strict $$H^1$$-Lyapunov function and feedback stabilization for the isothermal Euler equations with friction. Zbl 1242.76296 Dick, Markus; Gugat, Martin; Leugering, Günter 2011 Time-delayed boundary feedback stabilization of the isothermal Euler equations with friction. Zbl 1368.76010 Gugat, Martin; Dick, Markus 2011 Optimal boundary control of the wave equation with pointwise control constraints. Zbl 1226.49023 Gugat, Martin; Grimm, Volker 2011 Classical solutions and feedback stabilization for the gas flow in a sequence of pipes. Zbl 1263.76059 Dick, Markus; Gugat, Martin; Leugering, Günter 2010 Stars of vibrating strings: switching boundary feedback stabilization. Zbl 1258.93088 Gugat, Martin; Sigalotti, Mario 2010 Boundary feedback stabilization by time delay for one-dimensional wave equations. Zbl 1198.93177 Gugat, Martin 2010 The smoothed-penalty algorithm for state constrained optimal control problems for partial differential equations. Zbl 1201.90186 Gugat, Martin; Herty, Michael 2010 Approximation of semigroups and related operator functions by resolvent series. Zbl 1222.65052 Grimm, Volker; Gugat, Martin 2010 Penalty techniques for state constrained optimal control problems with the wave equation. Zbl 1202.49037 Gugat, Martin 2010 Global boundary controllability of the Saint-Venant system for sloped canals with friction. Zbl 1154.76009 Gugat, M.; Leugering, G. 2009 Optimal distributed control of the wave equation subject to state constraints. Zbl 1176.35176 Gugat, Martin; Keimer, Alexander; Leugering, Günter 2009 Lavrentiev-prox-regularization for optimal control of PDEs with state constraints. Zbl 1200.65051 Gugat, Martin 2009 Lavrentiev prox-regularization methods for optimal control problems with pointwise state constraints. Zbl 1197.49042 Gugat, Martin 2009 Optimal switching boundary control of a string to rest in finite time. Zbl 1242.49008 Gugat, Martin 2008 $$L^\infty$$-norm minimal control of the wave equation: on the weakness of the bang-bang principle. Zbl 1133.49006 Gugat, Martin; Leugering, Gunter 2008 Optimal boundary feedback stabilization of a string with moving boundary. Zbl 1141.93047 Gugat, Martin 2008 Weber problems with mixed distances and regional demand. Zbl 1146.90464 Gugat, Martin; Pfeiffer, Barbara 2007 Optimal energy control in finite time by varying the length of the string. Zbl 1144.49016 Gugat, Martin 2007 Optimal boundary control in flood management. Zbl 1239.49030 Gugat, Martin 2007 Optimal boundary control of a string to rest in finite time with continuous state. Zbl 1092.49020 Gugat, Martin 2006 Conservation law constrained optimization based upon Front-Tracking. Zbl 1116.65079 Gugat, Martin; Herty, Michaël; Klar, Axel; Leugering, Gunter 2006 $$L^1$$-optimal boundary control of a string to rest in finite time. Zbl 1108.49017 Gugat, Martin 2006 Optimal control for traffic flow networks. Zbl 1079.49024 Gugat, M.; Herty, M.; Klar, A.; Leugering, G. 2005 $$L^{p}$$-optimal boundary control for the wave equation. Zbl 1083.49017 Gugat, M.; Leugering, G.; Sklyar, G. 2005 Optimal nodal control of networked hyperbolic systems: evaluation of derivatives. Zbl 1165.49307 Gugat, Martin 2005 Nodal control of conservation laws on networks. Sensitivity calculations for the control of systems of conservation laws with source terms on networks. Zbl 1097.65071 Gugat, Martin 2005 Global controllability between steady supercritical flows in channel networks. Zbl 1047.93028 Gugat, Martin; Leugering, Günter; Schmidt, E. J. P. Georg 2004 Global boundary controllability of the de St. Venant equations between steady states. Zbl 1032.93030 Gugat, M.; Leugering, G. 2003 Boundary controllability between sub- and supercritical flow. Zbl 1047.35087 Gugat, Martin 2003 Solutions of $$L^p$$-norm-minimal control problems for the wave equation. Zbl 1119.90353 Gugat, Martin; Leugering, G. 2002 Regularization of $$L^\infty$$-optimal control problems for distributed parameter systems. Zbl 1015.49020 Gugat, M.; Leugering, G. 2002 Analytic solutions of $$L^{\infty}$$ optimal control problems for the wave equation. Zbl 1012.49025 Gugat, M. 2002 Modelling, stabilization, and control of flow in networks of open channels. Zbl 0987.93056 Gugat, Martin; Leugering, Günter; Schittkowski, Klaus; Schmidt, E. J. P. Georg 2001 Controllability of a slowly rotating Timoshenko beam. Zbl 1031.93103 Gugat, Martin 2001 A Newton method for the computation of time-optimal boundary controls of one-dimensional vibrating systems. Zbl 0953.93042 Gugat, Martin 2000 Error bounds for infinite systems of convex inequalities without Slater’s condition. Zbl 0997.90090 Gugat, Martin 2000 Time-parametric control: Uniform convergence of the optimal value functions of discretized problems. Zbl 0951.49032 Gugat, Martin 1999 A parametric view on the Mangasarian-Fromovitz constraint qualification. Zbl 0976.90111 Gugat, Martin 1999 Convex semi-infinite parametric programming: Uniform convergence of the optimal value functions of discretized problems. Zbl 0956.90054 Gugat, M. 1999 Prox-regularization methods for generalized fractional programming. Zbl 0973.90078 Gugat, M. 1998 Parametric convex optimization: One-sided derivatives of the value function in singular parameters. Zbl 0961.90114 Gugat, Martin 1998 Semi-infinite terminal problems: A Newton type method. Zbl 0916.65066 Gugat, Martin 1998 Parametric disjunctive programming: One-sided differentiability of the value function. Zbl 0886.90113 Gugat, M. 1997 A fast algorithm for a class of generalized fractional programs. Zbl 0881.90113 Gugat, Martin 1996 An algorithm for Chebyshev approximation by rationals with constrained denominators. Zbl 0886.41013 Gugat, M. 1996 The Newton differential correction algorithm for rational Chebyshev approximation with constrained denominators. Zbl 0860.65006 Gugat, M. 1996 Corrigendum: One-sided derivatives for the value function in convex parametric programming. Zbl 0864.90113 Gugat, M. 1996 Computation of lower bounds for spectra via fractional semi-infinite programming. Zbl 0841.65091 Gugat, Martin 1995 One-sided derivatives for the value function in convex parametric programming. Zbl 0822.90130 Gugat, M. 1994 Optimization under functional constraints (semi-infinite programming) and applications. Zbl 0770.90070 Hettich, Rainer; Gugat, Martin 1992 all top 5 #### Cited by 441 Authors 55 Gugat, Martin 21 Leugering, Günter 18 Herty, Michael Matthias 12 Keimer, Alexander 10 Roubi, Ahmed 9 Coron, Jean-Michel 9 Göttlich, Simone 9 Hante, Falk M. 9 Prieur, Christophe 8 Kunisch, Karl 8 Schmidt, Martin 7 Pflug, Lukas 6 Li, Tatsien 6 Zuazua, Enrique 5 Bastin, Georges 5 Grüne, Lars 5 Krstić, Miroslav 5 Schewe, Lars 5 Shang, Peipei 4 Bermúdez, Alfredo 4 Boufi, Karima 4 Clason, Christian 4 Grimm, Volker 4 Gu, Qilong 4 Hayat, Amaury 4 Klar, Axel 4 López, Xián 4 Nicaise, Serge 4 Piccoli, Benedetto 4 Pignotti, Cristina 4 Trélat, Emmanuel 4 Vázquez-Cendón, María Elena 4 Xu, Huifu 3 Aamo, Ole Morten 3 Alvarez-Vázquez, Lino Jose 3 Banda, Mapundi Kondwani 3 Bayen, Alexandre M. 3 Chitour, Yacine 3 D’Apice, Ciro 3 Delle Monache, Maria Laura 3 El Haffari, Mostafa 3 Garavello, Mauro 3 Girard, Antoine 3 Goatin, Paola 3 Kmit, Irina 3 Kröner, Axel 3 Manita, Larissa A. 3 Martin, Alexander 3 Martinez, Aurea 3 Mazanti, Guilherme 3 Schaller, Manuel 3 Schiela, Anton 3 Schillen, Peter 3 Schleper, Veronika 3 Schultz, Rüdiger 3 Schuster, Michael J. 3 Sirvent, Mathias 3 Spinola, Michele 3 Steinbach, Marc Christian 3 Sun, Hailin 3 Tröltzsch, Fredi 3 Ulbrich, Stefan 3 Wintergerst, David 3 Xu, Gen-Qi 3 Zelikin, Mikhail Il’ich 3 Zhang, Liguo 3 Zhuang, Kaili 2 Addoune, Smail 2 Barnard, Richard C. 2 Borsche, Raul 2 Boutoulout, Ali 2 Bressan, Alberto 2 Briani, Maya 2 Chang, Ching-Ter 2 Colombo, Rinaldo M. 2 Corli, Andrea 2 Crouzeix, Jean-Pierre 2 El Alami, Abdessamad 2 Elosmani, Mohamed 2 Espejo, Inmaculada 2 Fardigola, Larissa V. 2 Ferland, Jacques A. 2 García-Chan, Néstor 2 Gerdts, Matthias 2 Gerster, Stephan 2 Glass, Olivier 2 Göckler, Tanja 2 Goudiaby, Mouhamadou Samsidy 2 Grossmann, Christian 2 Guglielmi, Roberto 2 Heitsch, Holger 2 Hu, Long 2 Ivanov, Sergei A. 2 Jiang, Bin 2 Jiao, Hongwei 2 Kolb, Oliver 2 Kreiss, Gunilla 2 Lamare, Pierre-Olivier 2 Liu, Qian 2 Liu, Yongchao ...and 341 more Authors all top 5 #### Cited in 108 Serials 20 SIAM Journal on Control and Optimization 18 Automatica 18 Systems & Control Letters 16 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 15 Networks and Heterogeneous Media 14 Journal of Optimization Theory and Applications 11 Optimization 10 Mathematical Methods in the Applied Sciences 9 Journal of Differential Equations 9 Mathematical Control and Related Fields 8 Computational Optimization and Applications 7 Journal of Computational and Applied Mathematics 6 Mathematical Programming. Series A. Series B 6 SIAM Journal on Scientific Computing 5 Journal of Mathematical Analysis and Applications 5 European Journal of Operational Research 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 5 Vietnam Journal of Mathematics 4 International Journal of Control 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Chinese Annals of Mathematics. Series B 4 MCSS. Mathematics of Control, Signals, and Systems 4 Journal of Global Optimization 4 European Journal of Control 4 Mathematical Methods of Operations Research 4 Journal of Hyperbolic Differential Equations 3 Computers & Mathematics with Applications 3 Journal of Computational Physics 3 Journal of Scientific Computing 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 SIAM Journal on Mathematical Analysis 3 Top 3 Mathematical Problems in Engineering 3 International Journal of Applied Mathematics and Computer Science 3 Optimization and Engineering 2 Computers and Fluids 2 Ukrainian Mathematical Journal 2 Applied Mathematics and Computation 2 Applied Mathematics and Optimization 2 Numerical Functional Analysis and Optimization 2 SIAM Journal on Numerical Analysis 2 Optimal Control Applications & Methods 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Computers & Operations Research 2 Journal of Dynamics and Differential Equations 2 SIAM Journal on Optimization 2 Journal of Mathematical Sciences (New York) 2 Discrete and Continuous Dynamical Systems 2 Optimization Methods & Software 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Journal of the European Mathematical Society (JEMS) 2 Journal of Dynamical and Control Systems 2 RAIRO. Operations Research 2 Discrete and Continuous Dynamical Systems. Series B 2 Journal of Applied Mathematics 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Discrete and Continuous Dynamical Systems. Series S 1 Applicable Analysis 1 Journal of Engineering Mathematics 1 Journal of the Franklin Institute 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Mathematics of Computation 1 Chaos, Solitons and Fractals 1 BIT 1 International Journal for Numerical Methods in Engineering 1 Journal of Approximation Theory 1 Mathematics and Computers in Simulation 1 Opsearch 1 Quarterly of Applied Mathematics 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Transactions of the American Mathematical Society 1 Acta Applicandae Mathematicae 1 Constructive Approximation 1 Numerical Methods for Partial Differential Equations 1 Asia-Pacific Journal of Operational Research 1 Mathematical and Computer Modelling 1 Asymptotic Analysis 1 Numerical Algorithms 1 International Journal of Computer Mathematics 1 Pattern Recognition 1 SIAM Journal on Applied Mathematics 1 Journal of Computer and Systems Sciences International 1 Set-Valued Analysis 1 Numerical Linear Algebra with Applications 1 Computational and Applied Mathematics 1 Journal of Inverse and Ill-Posed Problems 1 ETNA. Electronic Transactions on Numerical Analysis 1 NoDEA. Nonlinear Differential Equations and Applications 1 Advances in Computational Mathematics 1 Discrete Dynamics in Nature and Society 1 Nonlinear Analysis. Real World Applications 1 Journal of Evolution Equations 1 Journal of Systems Science and Complexity 1 Journal of Applied Mathematics and Computing 1 SIAM Journal on Applied Dynamical Systems 1 4OR 1 Mathematical Biosciences and Engineering 1 Journal of Industrial and Management Optimization 1 GAMM-Mitteilungen 1 Proceedings of the Steklov Institute of Mathematics ...and 8 more Serials all top 5 #### Cited in 32 Fields 183 Partial differential equations (35-XX) 156 Systems theory; control (93-XX) 114 Operations research, mathematical programming (90-XX) 103 Calculus of variations and optimal control; optimization (49-XX) 59 Numerical analysis (65-XX) 46 Fluid mechanics (76-XX) 12 Mechanics of deformable solids (74-XX) 8 Operator theory (47-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Dynamical systems and ergodic theory (37-XX) 5 Approximations and expansions (41-XX) 4 Ordinary differential equations (34-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Probability theory and stochastic processes (60-XX) 2 Combinatorics (05-XX) 2 Real functions (26-XX) 2 Difference and functional equations (39-XX) 2 Functional analysis (46-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Biology and other natural sciences (92-XX) 1 General and overarching topics; collections (00-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 General topology (54-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Information and communication theory, circuits (94-XX) #### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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https://zbmath.org/authors/?q=ai%3Awest.james-e	# zbMATH — the first resource for mathematics ## West, James E. Compute Distance To: Author ID: west.james-e Published as: West, J.; West, J. E.; West, James; West, James E. Homepage: http://www.math.cornell.edu/m/People/Faculty/westj External Links: MGP · Wikidata Documents Indexed: 48 Publications since 1968, including 1 Book all top 5 #### Co-Authors 21 single-authored 7 Steinberger, Mark 3 Schori, Richard M. 3 Toruńczyk, Henryk 2 Cappell, Sylvain E. 2 Dranishnikov, Alexander Nikolaevich 2 Henderson, David Wilson 2 Shaneson, Julius L. 1 Anderson, Richard D. 1 Berstein, I. 1 Heisey, Richard E. 1 Weinberger, Shmuel 1 Wong, Raymund Y. T. all top 5 #### Serials 6 Bulletin of the American Mathematical Society 5 Proceedings of the American Mathematical Society 4 Transactions of the American Mathematical Society 3 Pacific Journal of Mathematics 2 Compositio Mathematica 2 Topology and its Applications 2 Bulletin of the American Mathematical Society. New Series 2 General Topology and its Applications 1 American Journal of Mathematics 1 Colloquium Mathematicum 1 Memoirs of the American Mathematical Society 1 Topological Methods in Nonlinear Analysis 1 Topology Proceedings 1 Annals of Mathematics. Second Series all top 5 #### Fields 27 Manifolds and cell complexes (57-XX) 17 General topology (54-XX) 8 Algebraic topology (55-XX) 7 Global analysis, analysis on manifolds (58-XX) 2 Group theory and generalizations (20-XX) 1 History and biography (01-XX) #### Citations contained in zbMATH 38 Publications have been cited 275 times in 213 Documents Cited by Year Mapping Hilbert cube manifolds to ANR’s: A solution of a conjecture of Borsuk. Zbl 0375.57013 West, James E. 1977 Infinite products which are Hilbert cubes. Zbl 0198.56001 West, J. E. 1970 Negligible subsets of infinite-dimensional manifolds. Zbl 0185.50803 Anderson, R. D.; Henderson, David W.; West, J. E. 1969 The ambient homeomorphy of an incomplete subspace of infinite-dimensional Hilbert spaces. Zbl 0198.46001 West, James E. 1970 Mapping cylinders of Hilbert cube factors. Zbl 0224.57004 West, James E. 1971 Compact ANR’s have finite type. Zbl 0297.54015 West, James E. 1975 Nonlinear similarity begins in dimension six. Zbl 0686.57025 Cappell, Sylvain E.; Shaneson, Julius L.; Steinberger, Mark; West, James E. 1989 The hyperspace of the closed unit interval is a Hilbert cube. Zbl 0312.54011 Schori, R. M.; West, J. E. 1975 Triangulated infinite-dimensional manifolds. Zbl 0203.25806 Henderson, David W.; West, J. E. 1970 $$2^ \prime$$ is homeomorphic to the Hilbert cube. Zbl 0242.54006 Schori, R.; West, J. E. 1972 Fibrations and bundles with Hilbert cube manifold fibers. Zbl 0689.57013 Toruńczyk, H.; West, J. 1989 Equivariant h-cobordisms and finiteness obstructions. Zbl 0572.57021 Steinberger, Mark; West, James 1985 On compacta that intersect unstably in Euclidean space. Zbl 0791.54048 Dranishnikov, A. N.; West, J. 1992 Products of complexes and Frechet spaces which are manifolds. Zbl 0236.57005 West, James E. 1972 The diffeomorphic excision of closed local compacta from infinite- dimensional Hilbert manifolds. Zbl 0181.51303 West, James E. 1969 The ranges of $$K$$-theoretic invariants for nonsimple graph algebras. Zbl 1350.46042 Eilers, Søren; Katsura, Takeshi; Tomforde, Mark; West, James 2016 Compact group actions that raise dimension to infinity. Zbl 0883.55002 Dranishnikov, A. N.; West, J. E. 1997 Approximation by equivariant homeomorphisms. I. Zbl 0643.57019 Steinberger, Mark; West, James 1987 Based free compact Lie group actions on Hilbert cubes. Zbl 0401.57029 Berstein, I.; West, J. E. 1978 Induced involutions on Hilbert cube hyperspaces. Zbl 0391.54004 West, J. E. 1976 The classification of nonlinear similarities over $$Z_{2^ r}$$. Zbl 0697.57018 Cappell, Sylvain E.; Shaneson, Julius L.; Steinberger, Mark; Weinberger, Shmuel; West, James E. 1990 Orbit spaces of the hyperspace of a graph which are Hilbert cubes. Zbl 0675.57017 Heisey, R. E.; West, J. E. 1988 Covering homotopy properties of maps between C.W. complexes or ANR’s. Zbl 0557.55011 Steinberger, Mark; West, James 1984 Hyperspaces of graphs are Hilbert cubes. Zbl 0292.54009 Schori, R. M.; West, J. E. 1974 The subcontinua of a dendron form a Hilbert cube factor. Zbl 0279.54018 West, James E. 1973 Fixed-point sets of Transformation groups on infinite-product spaces. Zbl 0175.41703 West, J. E. 1969 A Hilbert space limit for the iterated hyperspace functor. Zbl 0541.54016 Toruńczyk, H.; West, J. 1983 Based-free actions of finite groups on Hilbert cubes with absolute retract orbit spaces are conjugate. Zbl 0469.57028 West, J. E.; Wong, R. Y.-T. 1979 Approximating homotopies by isotopies in Frechet manifolds. Zbl 0187.45205 West, J. E. 1969 Extending certain transformation group actions in separable, infinite- dimensional Frechet spaces and the Hilbert cube. Zbl 0184.26703 West, J. E. 1968 Three questions on special homeomorphisms on subgroups of $$\mathbb R$$ and $${\mathbb R}^{\infty}$$. Zbl 1400.54043 Buzyakova, Raushan; West, James 2018 Absolute retract involutions of Hilbert cubes: fixed point sets of infinite codimension. Zbl 1392.57015 West, James 2018 Equivariant handles in finite group actions. Zbl 0613.57023 Steinberger, Mark; West, James 1987 The fine structure of $$S^ 1/S^ 1$$; a Q-manifold hyperspace localization of the integers. Zbl 0469.57012 Torunczyk, H.; West, J. E. 1980 Mapping cylinders of Hilbert cube factors. II: The relative case. Zbl 0299.57002 West, James E. 1975 Sums of Hilbert cube factors. Zbl 0297.57007 West, James E. 1974 Identifying Hilbert cubes: general methods and their application to hyperspaces by Schori and West. Zbl 0312.54010 West, J. E. 1972 Factoring the Hilbert cube. Zbl 0191.21903 West, James E. 1970 Three questions on special homeomorphisms on subgroups of $$\mathbb R$$ and $${\mathbb R}^{\infty}$$. Zbl 1400.54043 Buzyakova, Raushan; West, James 2018 Absolute retract involutions of Hilbert cubes: fixed point sets of infinite codimension. Zbl 1392.57015 West, James 2018 The ranges of $$K$$-theoretic invariants for nonsimple graph algebras. Zbl 1350.46042 Eilers, Søren; Katsura, Takeshi; Tomforde, Mark; West, James 2016 Compact group actions that raise dimension to infinity. Zbl 0883.55002 Dranishnikov, A. N.; West, J. E. 1997 On compacta that intersect unstably in Euclidean space. Zbl 0791.54048 Dranishnikov, A. N.; West, J. 1992 The classification of nonlinear similarities over $$Z_{2^ r}$$. Zbl 0697.57018 Cappell, Sylvain E.; Shaneson, Julius L.; Steinberger, Mark; Weinberger, Shmuel; West, James E. 1990 Nonlinear similarity begins in dimension six. Zbl 0686.57025 Cappell, Sylvain E.; Shaneson, Julius L.; Steinberger, Mark; West, James E. 1989 Fibrations and bundles with Hilbert cube manifold fibers. Zbl 0689.57013 Toruńczyk, H.; West, J. 1989 Orbit spaces of the hyperspace of a graph which are Hilbert cubes. Zbl 0675.57017 Heisey, R. E.; West, J. E. 1988 Approximation by equivariant homeomorphisms. I. Zbl 0643.57019 Steinberger, Mark; West, James 1987 Equivariant handles in finite group actions. Zbl 0613.57023 Steinberger, Mark; West, James 1987 Equivariant h-cobordisms and finiteness obstructions. Zbl 0572.57021 Steinberger, Mark; West, James 1985 Covering homotopy properties of maps between C.W. complexes or ANR’s. Zbl 0557.55011 Steinberger, Mark; West, James 1984 A Hilbert space limit for the iterated hyperspace functor. Zbl 0541.54016 Toruńczyk, H.; West, J. 1983 The fine structure of $$S^ 1/S^ 1$$; a Q-manifold hyperspace localization of the integers. Zbl 0469.57012 Torunczyk, H.; West, J. E. 1980 Based-free actions of finite groups on Hilbert cubes with absolute retract orbit spaces are conjugate. Zbl 0469.57028 West, J. E.; Wong, R. Y.-T. 1979 Based free compact Lie group actions on Hilbert cubes. Zbl 0401.57029 Berstein, I.; West, J. E. 1978 Mapping Hilbert cube manifolds to ANR’s: A solution of a conjecture of Borsuk. Zbl 0375.57013 West, James E. 1977 Induced involutions on Hilbert cube hyperspaces. Zbl 0391.54004 West, J. E. 1976 Compact ANR’s have finite type. Zbl 0297.54015 West, James E. 1975 The hyperspace of the closed unit interval is a Hilbert cube. Zbl 0312.54011 Schori, R. M.; West, J. E. 1975 Mapping cylinders of Hilbert cube factors. II: The relative case. Zbl 0299.57002 West, James E. 1975 Hyperspaces of graphs are Hilbert cubes. Zbl 0292.54009 Schori, R. M.; West, J. E. 1974 Sums of Hilbert cube factors. Zbl 0297.57007 West, James E. 1974 The subcontinua of a dendron form a Hilbert cube factor. Zbl 0279.54018 West, James E. 1973 $$2^ \prime$$ is homeomorphic to the Hilbert cube. Zbl 0242.54006 Schori, R.; West, J. E. 1972 Products of complexes and Frechet spaces which are manifolds. Zbl 0236.57005 West, James E. 1972 Identifying Hilbert cubes: general methods and their application to hyperspaces by Schori and West. Zbl 0312.54010 West, J. E. 1972 Mapping cylinders of Hilbert cube factors. Zbl 0224.57004 West, James E. 1971 Infinite products which are Hilbert cubes. Zbl 0198.56001 West, J. E. 1970 The ambient homeomorphy of an incomplete subspace of infinite-dimensional Hilbert spaces. Zbl 0198.46001 West, James E. 1970 Triangulated infinite-dimensional manifolds. Zbl 0203.25806 Henderson, David W.; West, J. E. 1970 Factoring the Hilbert cube. Zbl 0191.21903 West, James E. 1970 Negligible subsets of infinite-dimensional manifolds. Zbl 0185.50803 Anderson, R. D.; Henderson, David W.; West, J. E. 1969 The diffeomorphic excision of closed local compacta from infinite- dimensional Hilbert manifolds. Zbl 0181.51303 West, James E. 1969 Fixed-point sets of Transformation groups on infinite-product spaces. Zbl 0175.41703 West, J. E. 1969 Approximating homotopies by isotopies in Frechet manifolds. Zbl 0187.45205 West, J. E. 1969 Extending certain transformation group actions in separable, infinite- dimensional Frechet spaces and the Hilbert cube. Zbl 0184.26703 West, J. E. 1968 all top 5 #### Cited by 203 Authors 11 Chapman, Thomas Ashland 10 Antonyan, Sergey A. 10 Repovš, Dušan D. 8 Geoghegan, Ross 8 West, James E. 7 Schori, Richard M. 6 Sakai, Katsuro 6 van Mill, Jan 6 Wong, Raymond Y. T. 5 Dobrowolski, Tadeusz 5 Dranishnikov, Alexander Nikolaevich 5 Henderson, David Wilson 5 Zarichnyi, Michael Mikhailovich 4 Anderson, Richard D. 4 Dijkstra, Jan J. 4 Guilbault, Craig R. 4 Kołodziejczyk, Danuta 4 Sanjurjo, José M. R. 3 Antonyan, Natella 3 Azagra, Daniel 3 Bazylevych, Lidiya 3 Curtis, Douglas W. 3 Hastings, Harold M. 3 Hegenbarth, Friedrich 3 Mogilski, Jerzy 3 Rybalkina, Tetiana 3 Siebenmann, Laurence C. 3 Steinberger, Mark 3 Wong, Raymund Y. T. 2 Andres, Jan 2 Belegradek, Igor 2 Bentmann, Rasmus 2 Bryant, John Logan 2 Chigogidze, A. Ch. 2 Chigogidze, Alex 2 Dydak, Jerzy 2 Edwards, David A. 2 Farrell, F. Thomas 2 Fedorchuk, Vitaly Vitalievich 2 García-Bravo, Miguel 2 Giraldo, Antonio 2 Hambleton, Ian 2 Hughes, C. Bruce 2 Karimov, Umed H. 2 Katsura, Takeshi 2 Koshino, Katsuhisa 2 Kroonenberg, Nelly 2 Lacher, R. C. 2 Levin, Michael Y. 2 Moran, Molly A. 2 Moron, Manuel Alonso 2 Prassidis, Stratos 2 Ranicki, Andrew A. 2 Ruiz del Portal, Francisco Romero 2 Ruiz, Efren 2 Sánchez-Gabites, Jaime J. 2 Sergeĭchuk, Volodymyr Vasyl’ovych 2 Sergeichuk, Vladimir Vasil’evich 2 Sternfeld, Yaki 2 Summerhill, R. Richard 2 Tomforde, Mark 2 Vo Thanh Liem 2 Walsh, John J. 2 Weinberger, Shmuel 1 Abrams, Gene D. 1 Ageev, Sergei M. 1 Akin, Ethan 1 Amarasinghe, Ashwini 1 Aranda Pino, Gonzalo 1 Arklint, Sara E. 1 Artamonov, Dmitry V. 1 Auslander, Joseph 1 Ayala, Victor 1 Baik, Hyungryul 1 Ball, Billy Joe 1 Banakh, Taras Onufrievich 1 Bazilevich, L. Ë. 1 Berger, Arno 1 Bogatyĭ, Semeon Antonovich 1 Borsuk, Karol 1 Brown, Ronald 1 Budnitska, Tetiana 1 Cappell, Sylvain E. 1 Carlsson, Gunnar E. 1 Cencelj, Matija 1 Cepedello Boiso, Manuel 1 Čerin, Zvonko Tomislav 1 Chernoff, Paul R. 1 Clavier, Lucien 1 Connolly, Frank 1 Conway, Anthony 1 Cruz, Ricardo Nogueira da 1 Curtis, K. W. 1 da Fonseca, Carlos Martins 1 de Silva, Vin 1 De Vries, Jan 1 Degiovanni, Marco 1 Edmonds, Allan L. 1 Eells, James jun. 1 Eilers, Søren ...and 103 more Authors all top 5 #### Cited in 57 Serials 51 Topology and its Applications 23 Transactions of the American Mathematical Society 17 Proceedings of the American Mathematical Society 16 Bulletin of the American Mathematical Society 13 Compositio Mathematica 5 Journal of Mathematical Analysis and Applications 5 Mathematical Notes 5 Algebraic & Geometric Topology 4 Inventiones Mathematicae 4 Journal of Functional Analysis 4 Linear Algebra and its Applications 3 Journal of Soviet Mathematics 3 Mathematische Annalen 3 Acta Mathematica Hungarica 3 $$K$$-Theory 3 Journal of Mathematical Sciences (New York) 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Duke Mathematical Journal 2 Journal of the Mathematical Society of Japan 2 Manuscripta Mathematica 2 Ergodic Theory and Dynamical Systems 2 Bulletin of the American Mathematical Society. New Series 2 Mediterranean Journal of Mathematics 2 Groups, Geometry, and Dynamics 2 Journal of Topology and Analysis 1 Bulletin of the Australian Mathematical Society 1 Ukrainian Mathematical Journal 1 Chaos, Solitons and Fractals 1 Acta Mathematica 1 Advances in Mathematics 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Canadian Journal of Mathematics 1 Illinois Journal of Mathematics 1 Journal of Algebra 1 Journal of the London Mathematical Society. Second Series 1 Mathematische Zeitschrift 1 Mathematika 1 Memoirs of the American Mathematical Society 1 Michigan Mathematical Journal 1 Monatshefte für Mathematik 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Proceedings of the Japan Academy. Series A 1 Quaestiones Mathematicae 1 Advances in Applied Mathematics 1 Journal of the American Mathematical Society 1 Forum Mathematicum 1 Differential Geometry and its Applications 1 Expositiones Mathematicae 1 Journal of Dynamics and Differential Equations 1 Indagationes Mathematicae. New Series 1 Electronic Research Announcements of the American Mathematical Society 1 Sbornik: Mathematics 1 Izvestiya: Mathematics 1 Geometry & Topology 1 Acta Mathematica Sinica. English Series 1 Nonlinear Analysis. Real World Applications 1 Journal of Homotopy and Related Structures all top 5 #### Cited in 27 Fields 113 Manifolds and cell complexes (57-XX) 98 General topology (54-XX) 70 Algebraic topology (55-XX) 28 Global analysis, analysis on manifolds (58-XX) 16 Functional analysis (46-XX) 14 Dynamical systems and ergodic theory (37-XX) 12 Group theory and generalizations (20-XX) 8 $$K$$-theory (19-XX) 7 Topological groups, Lie groups (22-XX) 7 Differential geometry (53-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Category theory; homological algebra (18-XX) 3 Measure and integration (28-XX) 3 Geometry (51-XX) 3 Convex and discrete geometry (52-XX) 2 Combinatorics (05-XX) 2 Associative rings and algebras (16-XX) 2 Functions of a complex variable (30-XX) 2 Operator theory (47-XX) 2 Computer science (68-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Number theory (11-XX) 1 Nonassociative rings and algebras (17-XX) 1 Real functions (26-XX) 1 Potential theory (31-XX) 1 Calculus of variations and optimal control; optimization (49-XX) #### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2021-02-26T12:54:01	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42386990785598755, "perplexity": 7994.55027856029}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178357641.32/warc/CC-MAIN-20210226115116-20210226145116-00605.warc.gz"}
https://gea.esac.esa.int/archive/documentation/GDR1/datamodel/Ch2/phot_variable_time_series_gfov.html	# 2.2 phot_variable_time_series_gfov Field-of-view time series of sources that have phot_variable_flag = "VARIABLE" in the gaia_source table. Columns description: solution_id : Solution Identifier (long) The data in the MDB will be described by means of a ”Solution identifier” parameter. This will be a numeric field attached to each table row that can be used to unequivocally identify the version of all the subsystems that where used in the generation of the data as well as the input data used. Each DPC generating the data will have the freedom to choose the Solution identifier number, but they must ensure that given the Solution identifier they can provide detailed information about the ”conditions” used to generate the data: versions of the software, version of the data used… source_id : Unique source identifier (long) A unique single numerical identifier of the source obtained from gaia_source (for a detailed description see gaia_source.source_id) observation_time : Barycentric light-travel time corrected timestamp for each FOV observation (double, Time[Barycentric JD in TCB - 2455197.5 (day)]) Field-of-view transit averaged observation time in units of Barycentric JD (in TCB) in days -2 455 197.5, computed as follows. First the observation time is converted from On-board Mission Time (OBMT) into Julian date in TCB (Temps Coordonnée Barycentrique). Next a correction is applied for the light-travel time to the Solar system barycentre, resulting in Barycentric Julian Date (BJD). Finally, an offset of 2 455 197.5 days is applied (corresponding to a reference time $T_{0}$ at 2010-01-01T00:00:00) to have a conveniently small numerical value. Although the centroiding time accuracy of the individual CCD observations is (much) below 1 ms, this per-FoV observation time is averaged over typically 9 CCD observations taken in a time range of about 44 sec. g_flux : G-band flux for each FOV observation (double, Flux[e-/s]) G-band flux for the field-of-view transit observation. g_flux_error : Estimated G-band flux uncertainty for each FOV observation (double, Flux[e-/s]) Estimated uncertainty of G-band flux for the field-of-view transit observation. g_magnitude : G-band magnitude for each FOV observation (double, Magnitude[mag]) G-band magnitude for the field-of-view transit observation, computed from the g_flux field using magnitude zero-point defined in ExtPhotZeroPoint. rejected_by_variability_processing : True when this FOV observation was excluded from variability analyses (boolean, Dimensionless[see description]) Observations with this flag true have been excluded from the variability result in tables variable_summary, cepheid, rrlyrae, and phot_variable_time_series_gfov_statistical_parameters.	2021-08-02T02:32:05	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 1, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6176860332489014, "perplexity": 5121.086387546289}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154302.46/warc/CC-MAIN-20210802012641-20210802042641-00247.warc.gz"}
https://crd.lbl.gov/departments/computational-science/c3/c3-people/zarija-lukic/	Zarija Lukić Zarija Lukić Research Scientist Phone: +1 510 486 7378 Fax: +1 510 486 4300 Computational Research Division Zarija Lukić is a research scientist in the Computational Cosmology Center. He earned his astrophysics Ph.D. in 2008 from the University of Illinois at Urbana-Champaign and has been a postdoctoral researcher in the Theoretical Division of Los Alamos National Laboratory (2008-2011) and the Computational Research Division of Lawrence Berkeley Lab (2011-2013). Zarija's research combines (astro)physics, high-performance computing and "big data". He has published research articles in both physics and computational science venues. The main topics of his research are the formation and evolution of the structure of the Universe and different ways of determining cosmological parameters from sky surveys. His studies involve modeling the Lyman-alpha absorption observed in spectra of distant quasars, the evolution and properties of clusters of galaxies, and the internal structure and statistical properties of dark matter halos, among topics. An essential part of Zarija's research is finding new computational algorithms for modeling physical systems – building simulation codes that can efficiently run on the largest supercomputers, as well as algorithms for extracting scientific insights from big data sets produced with these simulation codes. Over the past 15+ years, he has used many leading machines at different supercomputer centers, including NERSC, the National Center for Supercomputing Applications (NCSA), the Los Alamos Supercomputer Center and the Oak Ridge Leadership Computing Facility (OLCF). He has been the principal investigator (P.I.) and co-P.I. on some of the largest computing allocations in the U.S. He is currently LBL P.I. on SciDAC-4 project "Accelerating HEP Science: Inference and Machine Learning at Extreme Scales", and on ECP project "Computing the Sky at Extreme Scales". In addition to astrophysics, Zarija's research also includes topics in applied nuclear physics. He has published research on the practical use of cosmic rays to identify materials and remotely diagnose the state of damaged reactor cores in the wake of the 2011 Fukushima Daiichi Nuclear Power Plant accident.	2021-03-08T03:04:00	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18672560155391693, "perplexity": 1903.6073319089835}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178381803.98/warc/CC-MAIN-20210308021603-20210308051603-00255.warc.gz"}
https://www.conicet.gov.ar/new_scp/detalle.php?keywords=&id=13074&inst=yes&congresos=yes&detalles=yes&congr_id=516350	IFLP 13074 INSTITUTO DE FISICA LA PLATA congresos y reuniones científicas Título: Structural, magnetic and hyperfine interactions at the Fe sites of Fe-doped SnO Autor/es: L. A. ERRICO Y M. WEISSMANN Lugar: Buenos Aires Reunión: Workshop; Workshop "At the Frontiers of Condensed Matter physics IV"; 2008 <!-- /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0pc; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman";} pre {margin:0pc; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Courier New"; mso-fareast-font-family:"Times New Roman";} @page Section1 {size:51.0pc 66.0pc; margin:6.0pc 7.5pc 6.0pc 7.5pc; mso-header-margin:3.0pc; mso-footer-margin:3.0pc; mso-paper-source:0;} div.Section1 {page:Section1;} --> Trabajo presentado en forma de poster durante la reunionTin oxides SnO and SnO$_2$ have been a topic of interest in the last few years due to their technological importance and industrial applications. In fact, tin dioxide is used in many devices where transparent semiconductors are needed, such as thin heat reflecting foils, transparent electrodes, gas sensors, and solar panels, among others. In most cases, impurities are included in order to improve the response of the material. As an example, the interest in SnO$_2$ was recently renewed due to the discovery of high-temperature ferromagnetism in Sn${1-x}$Co$_x$O$_2$ films [Ogale et al., Phys. Rev. Lett. {\bf 91}, 77205 (2003)] with potential applications in spintronics. Also, in 2005, Punnoose et al [Phys. Rev. B {\bf 72}, 054402 (2005)] reported the development of room-temperature ferromagnetism in chemically synthesized powder samples of Sn${1-x}$Co$_x$O$_2$ samples and paramagnetic behaviour in Sn${1-x}$Co$_x$O samples. Results for the hyperfine interactions at $^{57}$Fe (measured by M\"{o}ssbauer spectroscopy) were also reported. We present here our first results of a Density Functional Theory-based {\it ab initio} study of Fe-doped SnO. Calculations were performed assuming that Fe ions replace Sn indigenous atoms of the structure and including vacancies, in order to discuss their role in the hyperfine interactions and in the magnetic solutions. In all cases, the equilibrium atomic positions and electronic structure of the systems were determined and the hyperfine parameters at the Fe sites were obtained and compared with available experimental data.	2020-07-10T07:16:44	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7705156803131104, "perplexity": 9514.607101438907}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655906214.53/warc/CC-MAIN-20200710050953-20200710080953-00317.warc.gz"}
https://pages.nist.gov/feasst/plugin/shape/doc/Cylinder.html	# Cylinder¶ class Cylinder : public feasst::Shape A cylinder is given by an axis of rotational symmetry and a radius. The axis is described by two points. Public Functions Cylinder(const argtype &args, const Position point0, const Position point1) Parameters • args: radius : Set the radius of the cylinder. • point0: one point on the cylinder’s axis of symmetry • point1: a second point on the cylinder’s axis of symmetry double nearest_distance(const Position &point) const Return the distance from the point to the nearest point on the surface. The distance is negative if the point is inside of the shape and positive if it is outside.	2021-03-05T07:16:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5729972720146179, "perplexity": 1607.4165603350946}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178370239.72/warc/CC-MAIN-20210305060756-20210305090756-00134.warc.gz"}
https://par.nsf.gov/biblio/10273329-search-transitions-from-emission-meson	Search for transitions from $ϒ(4S)$ and $ϒ(5S)$ to $ηb(1S)$ and $ηb(2S)$ with emission of an $ω$ meson Authors: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more » Award ID(s): Publication Date: NSF-PAR ID: 10273329 Journal Name: Physical Review D Volume: 102 Issue: 9 ISSN: 2470-0010	2022-06-25T19:26:24	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 21, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6646614074707031, "perplexity": 6473.214029762418}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103036099.6/warc/CC-MAIN-20220625190306-20220625220306-00664.warc.gz"}
https://conferences.lbl.gov/event/36/contributions/2087/	# TAUP 2013 8-13 September 2013 Asilomar, California US/Pacific timezone ## Reexamination of the Reactor Antineutrino Anomaly 12 Sep 2013, 15:00 20m Asilomar, California #### Asilomar, California Asilomar Conference Grounds, 800 Asilomar Avenue, Pacific Grove, CA 93950-3704 Oral Low-Energy Neutrinos (solar, reactor, supernova, and geo neutrinos and also nuclear astrophysics associated with these sources) ### Speaker Anna Hayes (Los Alamos National Laboratory) ### Description The reactor neutrino anomaly [1] refers to a greater than 3 deficit between the number of neutrinos detected relative to the number that are predicted in short baseline reactor neutrino oscillation experiments. The prediction for the expected number of detected neutrinos has evolved upward over time, largely as a consequence of a predicted increased in the neutrino flux and an increased cross section associated with smaller values for the neutron lifetime. The changes in the predicted neutrino flux are mostly associated with improved knowledge of the beta decays of the isotopes created in fission reactors. If not an artifact, such an anomaly is potentially extremely significant, as a shortfall in the detected neutrino flux could be ascribed to oscillation into a light sterile neutrino with a mass ~ 1ev. An analysis [2] that sought to improve the earlier flux estimations based on the ILL on-line measurements [3-6] of the integral beta spectrum of the reactor fission products resulted in a systematic increase in the antineutrino flux. Because the beta spectra from reactor fission products involve about six thousand beta transitions, ~1500 of which forbidden transitions, some assumptions are required to deduce the antineutrino flux from a measured beta spectrum. A second independent analysis [7], that used similar assumptions to [2], confirmed the predicted increase in reactor antineutrino fluxes. The present contribution questions whether the previous analyses properly accounted for the forbidden nature of many (~30%) decays present in the aggregate fission spectra. We find that the uncertainty in how to treat these forbidden transitions is large, and our analysis indicates that the resulting uncertainty in the aggregate antineutrino spectra is larger than the size of the original anomaly. This suggests that earlier conclusions on the reactor neutrino anomaly need to be revisited. In addition, analyses of medium and long baseline reactor experiments, that placed small uncertainties on fission antineutrino spectra may also need to be revisited. [1] G. Mention et. al., Phys. Rev. D83 073006 (2011) [2] Th. A. Mueller et. al., Phys. Rev. C83 054615 (2011) [3] K. Schreckenbach et.al., Phys. Lett. B93 251 (1981) [4] F. von Feilitzsch et. al., Phys. Lett. B118 162 (1982) [5] K. Schreckenbach et.al., Phys. Lett. B160 325 (1985) [6] A.A. Hahn et.al., Phys. Lett. B218 365 (1989) [7] P. Huber, Phys. Rev. C84 024617 (2011) ### Primary author Anna Hayes (Los Alamos National Laboratory) ### Presentation Materials There are no materials yet.	2022-01-18T12:39:26	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8331223130226135, "perplexity": 3087.0083760020902}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300849.28/warc/CC-MAIN-20220118122602-20220118152602-00319.warc.gz"}
https://arrow.fandom.com/wiki/User_talk:Oilgof	8,606 Pages # Oilgof 0 Discussion posts My favorite wikis • I live in Leffe (Bg), Italy • I was born on September 21 • I am M ## RE:Welcome Hi, I'm an admin for the Arrowverse Wiki community. Welcome and thank you for your edit to Rex Tyler! If you need help getting started, check out our help pages or contact me or another admin here. For general help, you could also stop by Community Central to explore the forums and blogs. Please leave me a message if I can help with anything. Enjoy your time at Arrowverse Wiki! ## Images Can you please stop with the images. The point of importing the images is to maintain the histories so the people who initially uploaded them get the credit.TIMESHADE \|Talk/Wall\| - \|C\| 21:23, January 2, 2017 (UTC) ## Actors Hey! Thanks for helping add the categories for the Supergirl Actors! If you want you can help me with the rest! I am starting at "Category:Actors" and going through each page in alphabetical order and adding the appropriate categories for the different shows "The Flash Actors" "Arrow Actors" "DC's Legends of Tomorrow Actors" etc. If they are in multiple, make sure they get all of the categories. If you want we can keep a running total here of what we have already done. IHHeroes (talk) 17:17, January 4, 2017 (UTC) • A,B,C,R,S,T,U,V,W,Y,Z has already been completed. Dear Lord, stop consuming the feed in that one type of edit. Have to stroll down like 15 times before you can get to the main edits. So, please stop. -- ImperiexSeed, 1:26 PM, January 4th 2017 Don't ignore me, you're going against policy. -- ImperiexSeed, 3:08 PM, January 4th 2017 Really such a big category should've had admin consultation first. Also, if it's this big it should be done on a bot account, so it doesn't clog up recent changes or recent activity.TIMESHADE \|Talk/Wall\| - \|C\| 21:19, January 4, 2017 (UTC) ## Allies Generally speaking, being an ally of a particular group or organisation does not count as an occupation, thus should not be included under that parameter in a character's infobox. Of course, there's cases where this may not be the case, and being an ally may in fact be their occupation (eg. affiliated with and paid but not officially a member). However, for the most part, it's not (eg. allies of Team Arrow/Flash/Legends). —MakeShift (talk page) 13:29, January 5, 2017 (UTC) ## Screenshots Please license screenshots with the "Image-screenshot" template, and make sure to categorise them properly. Also, be careful with the names of them, though understandably English probably isn't your first language. Also, we don't allow filetypes other than PNGs. Please try reading the wiki image policy. —MakeShift (talk page) 05:35, January 16, 2017 (UTC) If you add a pipe after the template name and add the episode title (eg. {{Image-screenshot\|Stronger Together}}) then it'll categorise the screenshot under the appropriate episode. —MakeShift (talk page) 00:38, January 17, 2017 (UTC) ## RE: Floyd Lawton I'll get right on it. Thanks for the heads up. If you need anything else, you know where to reach me! Hambergite (talk) 02:23, January 23, 2017 (UTC) ## Actor categories Please stop adding those categories. I don't know if it was you that implemented them, but you ran nothing by any admin and it's frustrating to clean up. If you ever have that sort of idea in future, run it by an admin to make sure it's okay to do. It definitely is not to just implement mass changes cause you can. —MakeShift (talk page) 13:51, January 27, 2017 (UTC) ## Talia I had to remove that bit you used an external link to cite as it's against our spoiler policy, as it's not completely confirmed in aired/released content.TIMESHADE \|Talk/Wall\| - \|C\| 19:35, February 6, 2017 (UTC) ## Re:Talia's birthdate Yes, but Talia being born in 1950 is only an assumption based on how old she looked like. ## Images So you know, we don't use the "Images of Kara Danvers' apartment" category. Also, you're doubling up on the "Image-screenshot" template when you upload images. We just use the single template under a "Licensing" header. —MakeShift (talk page) 10:58, February 22, 2017 (UTC) Just a reminder that you're doubling up on the licensing template. An example of what I mean can be seen here. —MakeShift (talk page) 15:01, February 25, 2017 (UTC) ## Re:No such thing as Vixen the movie exists. The so called movie is basically all episodes put together, and we already have the episodes in appearences.Ninja72 (talk) 23:43, December 2, 2017 (UTC) Ok, your last point convinced me.Ninja72 (talk) 00:01, December 3, 2017 (UTC) ## Earth Two Laurel When exactly in the episode was it said that she was born sometime around 1985?Ninja72 (talk) 12:03, December 10, 2017 (UTC) Your generation does not necessarily mean, they are exactly the same age. It just means they are close in age. This is the second time you add a birth year, based on an assumption.Ninja72 (talk) 12:48, December 10, 2017 (UTC) Just because, they are close in age, it does not mean you should add one s birth year with a circa to the other. For example Helena Bertinelli is probably around the same age as Oliver, but we dont add it.Your source is very ambigious and unclear. As for Talia, as TimeShade said to Riyanjackson, we do not add our estimations of, when someone was born.Ninja72 (talk) 13:03, December 10, 2017 (UTC) Look at Felicity Smoak for example, she has born c.1989, because she said she was 25 years old,but we are not sure, when exactly she turned 25. Tony Woodward has c.1989, because if he is a classmate of Barry and Iris, he would have to be the same age as them, unless he started going to school one year later or earlier, or repeated a grade. Eobard Thawne has c.2151, because he said that he is born 136 years from now, but it might be 136 years as of this point of the year, which is why it has a c. All those sources are way more clear than yours.Ninja72 (talk) 13:16, December 10, 2017 (UTC) How exactly has Quentin implied that the Laurels have the same the birthday?Ninja72 (talk) 13:31, December 10, 2017 (UTC) Ok, this is a more clear implication than the generation thing. I will add it again.Ninja72 (talk) 13:37, December 10, 2017 (UTC)PS: the difference betwen classmate and generation, is that classmate is almost always the same age, while generation could mean 1-2 years older or 1-2 years younger. ## the joker I would very much like him to show up once in arrow as a main antagonist Rise akainu (talk) 21:24, December 25, 2017 (UTC) 21:24, December 25, 2017 (UTC)21:24, December 25, 2017 (UTC)~~ ## Gotham City population Hi, could you send me the episode and timestamp where the population of Gotham was mentioned? 'Cause there was this scene in the beginning of Elseworlds, Part 2 where Kara said that there were 1.6 million people. Yeah, sorry, I'm quite the information junkie. I just want to watch the scene because I somehow don't remember it. Thanks. ~ COƧMO THE CHOCOBO \| TALK? \| at 14:14, Dec 14, 2018 (UTC) Okay, then. Thanks! ~ COƧMO THE CHOCOBO \| TALK? \| at 14:40, Dec 14, 2018 (UTC) ## Tesmacher family It was never said that Mary is Bitsie s mother. Also, Bitsie called her "Mary" rather than my mother.Ninja72 (talk) 14:26, April 3, 2019 (UTC) I was going to suggest making a compromise and listing it as unclear relation, but it seems we both missed something. Bitsie said "I want you out of my aunt's house" after they discovered that Eve had given her the cure. You can see that here https://www.youtube.com/watch?v=w2zBU49gF7M.Ninja72 (talk) 17:59, April 3, 2019 (UTC) ## Images Hey, please do not manually add categories to images pages stating what episode they are from. The Image-screenshot template automatically adds this there. You should still add character categories such as "Images of Kara Danvers", but you should never be physically adding the category "Images from ___". You may normally not physically add it; it may just be today. If you have been paying attention to the announcements, you would have known that the Image-screenshot template was temporarily "dead" for a few hours, so these automatic categories were not live. They are now live again so it is automatically categorizing again. So please in the future do not physically add these categories for episodes and pay attention to the announcements. Thanks, $\int$ IHH dt 16:11, Mar 26, 2020 (UTC) But Kara actually knows who he really is, so "Bruce Wayne would never bail us out" seems to be something that really is part of his personality and she could have meant something different than "Bruce Wayne is (pretending to be) selfish". She could have meant it as in that he would never bail some random people that he does not even know. Plus Kate said that Bruce was the only one that was there for her after her mother and sister died and Jacob said Kate is like Bruce, so there really is not that much evidence he presents himself as a selfish person.Ninja72 (talk) 20:24, October 13, 2019 (UTC) ## Re:Eve Teschmacher.png I know you didn't delete it, and it's actually great you uploaded another pic for future use in case the file ever gets updated. If her current appearance is seen in an episode though, we usually update them, as evident in cases such as Kara's hairstyle. It's all good though. Keep up the good work, and happy editing! ~ COƧMO THE CHOCOBO \| TALK? \| at 16:52, Oct 16, 2019 (UTC) ## Moving Pages Hey, just to let you know the "copy/paste" method you used when you attempted to move a page is considered plagiarism and is illegal. What this does is it does not carry over the edit history, so it seems as though you are the one that wrote all of the code on that page (which you did not). In particular, I'm speaking about Wayne Tower concierge. Please do not "move" pages like this again because it is plagiarism which is not tolerated. Thanks, $\int$ IHH dt 16:11, Mar 26, 2020 (UTC) ## Re:2019 in current Batwoman episodes He actually says two weeks ago, not four. And we do not know when exactly in December Elseworlds took place, the episode aired on December 10th, so it could have been the 8th or the 9th in-universe and the current episode of Batwoman could still be in December 2018.Ninja72 (talk) 12:46, November 9, 2019 (UTC) ## Re:Why so? I got your point. But please include such info in the Behind the scenes section, where we can freely compare our articles to real world and comics parallels, as putting them in the main page body is too much of an assumption. Also, yes, we have Central and Star City, but so what? It doesn't mean there's a pattern to follow with the others. ~ COƧMO THE CHOCOBO \| TALK? \| at 13:20, Jan 28, 2020 (UTC) The location for Central and Star City is already confirmed to be official, so it's okay that their state is, well, stated in the intro. Again, if were talking real world parallels (key word: real world), it must always be placed in the Behind the scenes section, which includes out-of-universe trivia, as per our policy. The Trivia section is only used for in-universe facts. This is also not a polemic, it's what I often do, informing people of certain details of the policy. I actually think your deduction of the location is great, so please keep up the work. ~ COƧMO THE CHOCOBO \| TALK? \| at 13:41, Jan 28, 2020 (UTC) Hey, I saw that you moved back the "Location" trivia in the Gotham City (Earth-Prime) page to the Trivia section instead of the Behind the scenes section (back in late January). Again, if the factoid uses references to the real world and/or other media in the real world, it should be in the Behind the scenes section. Trivia is for in-universe content. As per the wiki's policies, "In-universe articles should be written without reference to behind the scenes. These sort of articles are written as if one were within the actual universe and detailing the events and surrounds of the world in an encyclopedic format." (link) Also, as I've previously explained, don't assume that we have exactly the same geography as Earth-Prime does. The only reason why we added the states of Central and Star City is because they were officially confirmed, just as all of the wiki's information is official, with the exception of the sometimes presumptive Behind the scenes section. ~ COƧMO THE CHOCOBO \| TALK? \| at 13:53, Feb 16, 2020 (UTC) ## Re:Trivia Well then, as per the wiki's policies, the "Location" section of each of the aforementioned pages should be in the the "Behind the scenes" section as well. And for your point regarding the map, it doesn't change the fact that the information uses out-of-universe info to support its claims. ~ COƧMO THE CHOCOBO \| TALK? \| at 15:33, Feb 16, 2020 (UTC) The map only showed an outline of the continents and dots where the cities are located. There weren't any outlines and names showing the states, and even if there were outlines, if there are no names of the locations, then naming them by going consulting with a real world map is definitely an assumption and considered as out-of-universe info. ~ COƧMO THE CHOCOBO \| TALK? \| at 16:17, Feb 16, 2020 (UTC) New York City and New York were mentioned in "Meet the Legends". Freeland being in Georgia is (for now) only applicable for the original multiverse, a logic that also applies for Metropolis. The United States of America is mentioned by the President in "Crisis on Infinite Earths: Part Five". Those locations (Wisconsin, Illinois, Indiana, Michigan, etc.) weren't mentioned. Central City is in Missouri, as seen in the address on Freddy's body bag ("Iron Heights Penitentiary, Central City, MO, USA" in "Slay Anything"), and the name Missouri is seen in "Slay Anything". These places aren't just pulled out from nothing, meaning they're obviously not assumptions. All the names of the locations on Earth-Prime are accounted for because they've been name dropped. No name drop of a major location obviously means it's an assumption. ~ COƧMO THE CHOCOBO \| TALK? \| at 17:11, Feb 16, 2020 (UTC) An exception to this rule is the location hierarchy of real world locations. Even if Hong Kong and China were mentioned separately and Hong Kong wasn't stated to be located in China, we can presume the hierarchy of these real world locations, so we can say that Hong Kong is a city in China. This doesn't include fictional locations of DC Comics. So yeah, if Central City wasn't mentioned to be in Missouri, then we just place United States; Earth as the location. ~ COƧMO THE CHOCOBO \| TALK? \| at 17:31, Feb 16, 2020 (UTC) Yes, that first statement is correct. Although, there has to be a map explicitly stating that Gotham is near Lake Michigan. For the other, simply Delaware being mentioned isn't enough for us to say that Metropolis is located there, but, food for thought: If there is a map (of Earth-Prime USA) with the outlines and names of the states being mentioned and is overlaid with what we got in "Marathon", then that's solid enough. (e.g. a separate map explicitly showing the location of Delaware that seems to also be the exact same position of Metropolis as seen in "Marathon"). Long story short, assume as if we've never seen a real world map, but we know the location hierarchy. Please let me know if that made sense or not, I'm not good with logical progression of ideas. ~ COƧMO THE CHOCOBO \| TALK? \| at 18:50, Feb 16, 2020 (UTC) ## Lara Van-El Where is she listed as "Lara Van-El"? You have shown links to imdb where she is listed as "Lara". Karl Meing (talk) 14:55, March 26, 2020 (UTC) Until you show the source, it should move to "Lara". If there is a source, you can move it back. Karl Meing (talk) 15:19, March 26, 2020 (UTC) • He is inactive and his email is not working. • You should ask him and specify the source on the page. Since you are the source of this name, undoing edits. Karl Meing (talk) 15:38, March 26, 2020 (UTC) If you are sure that this is her possible name, remove the tag for a move and add template {{Cite}} to the name. All responsibility will be yours. Karl Meing (talk) 16:10, March 26, 2020 (UTC) Community content is available under CC-BY-SA unless otherwise noted.	2020-04-01T12:12:30	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.41658565402030945, "perplexity": 2957.4448796837123}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370505730.14/warc/CC-MAIN-20200401100029-20200401130029-00445.warc.gz"}
https://par.nsf.gov/biblio/10051224-simultaneous-search-prompt-radio-emission-associated-short-grb-using-all-sky-imaging-capability-ovro-lwa	A simultaneous search for prompt radio emission associated with the short GRB 170112A using the all-sky imaging capability of the OVRO-LWA We have conducted the most sensitive low frequency (below 100 MHz) search to date for prompt, low-frequency radio emission associated with short-duration gamma-ray bursts (GRBs), using the Owens Valley Radio Observatory Long Wavelength Array (OVRO-LWA). The OVRO-LWA's nearly full-hemisphere field-of-view (∼20,000 square degrees) allows us to search for low-frequency (sub-100 MHz) counterparts for a large sample of the subset of GRB events for which prompt radio emission has been predicted. Following the detection of short GRB 170112A by Swift, we used all-sky OVRO-LWA images spanning one hour prior to and two hours following the GRB event to search for a transient source coincident with the position of GRB 170112A. We detect no transient source, with our most constraining 1σ flux density limit of 650 mJy for frequencies spanning 27 MHz−84 MHz. We place constraints on a number of models predicting prompt, low-frequency radio emission accompanying short GRBs and their potential binary neutron star merger progenitors, and place an upper limit of Lradio/Lγ≲7×10−16 on the fraction of energy released in the prompt radio emission. These observations serve as a pilot effort for a program targeting a wider sample of both short and long GRBs with the OVRO-LWA, including bursts with confirmed more » Authors: Award ID(s): Publication Date: NSF-PAR ID: 10051224 Journal Name: Astrophysical journal ISSN: 1538-4357 4. ABSTRACT We present a low-frequency (170–200 MHz) search for prompt radio emission associated with the long GRB 210419A using the rapid-response mode of the Murchison Widefield Array (MWA), triggering observations with the Voltage Capture System for the first time. The MWA began observing GRB 210419A within 89 s of its detection by Swift, enabling us to capture any dispersion delayed signal emitted by this gamma-ray burst (GRB) for a typical range of redshifts. We conducted a standard single pulse search with a temporal and spectral resolution of $100\, \mu$s and 10 kHz over a broad range of dispersion measures from 1 to $5000\, \text{pc}\, \text{cm}^{-3}$, but none were detected. However, fluence upper limits of 77–224 Jy ms derived over a pulse width of 0.5–10 ms and a redshift of 0.6 < z < 4 are some of the most stringent at low radio frequencies. We compared these fluence limits to the GRB jet–interstellar medium interaction model, placing constraints on the fraction of magnetic energy (ϵB ≲ [0.05–0.1]). We also searched for signals during the X-ray flaring activity of GRB 210419A on minute time-scales in the image domain and found no emission, resulting in an intensity upper limit of $0.57\, \text{Jy}\, \text{beam}^{-1}$, corresponding to a constraint ofmore » 5. Abstract We discuss observational strategies to detect prompt bursts associated with gravitational wave (GW) events using the Australian Square Kilometre Array Pathfinder (ASKAP). Many theoretical models of binary neutron stars mergers predict that bright, prompt radio emission would accompany the merger. The detection of such prompt emission would greatly improve our knowledge of the physical conditions, environment, and location of the merger. However, searches for prompt emission are complicated by the relatively poor localisation for GW events, with the 90% credible region reaching hundreds or even thousands of square degrees. Operating in fly’s eye mode, the ASKAP field of view can reach $\sim1\,000$ deg $^2$ at $\sim$ $888\,{\rm MHz}$ . This potentially allows observers to cover most of the 90% credible region quickly enough to detect prompt emission. We use skymaps for GW170817 and GW190814 from LIGO/Virgo’s third observing run to simulate the probability of detecting prompt emission for GW events in the upcoming fourth observing run. With only alerts released after merger, we find it difficult to slew the telescope sufficiently quickly as to capture any prompt emission. However, with the addition of alerts released before merger by negative-latency pipelines, we find that it should be possible to searchmore »	2022-10-02T09:01:27	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5467348694801331, "perplexity": 2963.2095284276875}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337307.81/warc/CC-MAIN-20221002083954-20221002113954-00629.warc.gz"}
https://zbmath.org/authors/?q=ai%3Amilicic.dragan	# zbMATH — the first resource for mathematics ## Miličić, Dragan Compute Distance To: Author ID: milicic.dragan Published as: Milicic, D.; Milicic, Dragan; Miličić, D.; Miličić, Dragan External Links: MGP · Wikidata Documents Indexed: 24 Publications since 1971 Reviewing Activity: 80 Reviews all top 5 #### Co-Authors 10 single-authored 4 Hecht, Henryk 2 Casselman, William A. 2 Kraljevic, Hrvoje 2 Pandžić, Pavle 2 Soergel, Wolfgang 1 Huang, Jing-Song 1 Primc, Mirko 1 Schmid, Wilfried 1 Sun, Binyong 1 Veselić, Krešimir 1 Wolf, Joseph Albert all top 5 #### Serials 9 Glasnik Matematički. Serija III 2 Duke Mathematical Journal 2 Proceedings of the American Mathematical Society 1 Commentarii Mathematici Helvetici 1 Inventiones Mathematicae 1 Mathematische Annalen 1 Pacific Journal of Mathematics 1 Journal of the European Mathematical Society (JEMS) all top 5 #### Fields 22 Topological groups, Lie groups (22-XX) 5 Nonassociative rings and algebras (17-XX) 3 Operator theory (47-XX) 2 Functional analysis (46-XX) 1 Number theory (11-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Abstract harmonic analysis (43-XX) #### Citations contained in zbMATH 19 Publications have been cited 214 times in 189 Documents Cited by Year Asymptotic behavior of matrix coefficients of admissible representations. Zbl 0524.22014 Casselman, William; Milicic, Dragan 1982 Localization and standard modules for real semisimple Lie groups. I: The duality theorem. Zbl 0699.22022 Hecht, Henryk; Miličić, Dragan; Schmid, Wilfried; Wolf, Joseph A. 1987 The composition series of modules induced from Whittaker modules. Zbl 0956.17004 Miličić, Dragan; Soergel, Wolfgang 1997 Asymptotic behaviour of matrix coefficients of the discrete series. Zbl 0398.22022 Milicic, Dragan 1977 Bruhat filtrations and Whittaker vectors for real groups. Zbl 0959.22010 Casselman, William; Hecht, Henryk; Miličić, Dragan 2000 On C$$^$$-algebras with bounded trace. Zbl 0265.46072 Milicic, Dragan 1973 Topological representation of the group $$C^ $$-algebra of SL(2,R). Zbl 0229.22010 Miličić, Dragan 1971 Twisted Harish-Chandra sheaves and Whittaker modules: the nondegenerate case. Zbl 1322.22018 Miličić, Dragan; Soergel, Wolfgang 2014 Equivariant derived categories, Zuckerman functors and localization. Zbl 0907.22019 Miličić, Dragan; Pandžić, Pavle 1998 Representations of almost connected groups. Zbl 0295.22011 Milicic, Dragan 1975 The C$$^$$-algebra of the universal covering group of SL(2,R). Zbl 0248.22014 Kraljevic, Hrvoje; Milicic, Dragan 1972 Algebraic $${\mathcal D}$$-modules and representation theory of semisimple Lie groups. Zbl 0821.22005 Miličić, Dragan 1993 The dual spaces of almost connected reductive groups. Zbl 0299.22006 Milicic, Dragan 1974 A note on invariant order ideals in the predual of a von Neumann algebra. Zbl 0217.16901 Miličić, D. 1971 Intertwining functors and irreducibility of standard Harish-Chandra sheaves. Zbl 0760.22019 Miličić, Dragan 1991 On the boundary of essential spectra. Zbl 0216.41701 Miličić, D.; Veselić, K. 1971 On the cohomological dimension of the localization functor. Zbl 0714.22011 Hecht, Henryk; Miličić, Dragan 1990 On the irreducibility of unitary principal series representations. Zbl 0477.22011 Milicic, Dragan; Primc, Mirko 1982 Elementary representations of the group SO(3,2). Zbl 0288.22023 Kraljevic, H.; Milicic, D. 1974 Twisted Harish-Chandra sheaves and Whittaker modules: the nondegenerate case. Zbl 1322.22018 Miličić, Dragan; Soergel, Wolfgang 2014 Bruhat filtrations and Whittaker vectors for real groups. Zbl 0959.22010 Casselman, William; Hecht, Henryk; Miličić, Dragan 2000 Equivariant derived categories, Zuckerman functors and localization. Zbl 0907.22019 Miličić, Dragan; Pandžić, Pavle 1998 The composition series of modules induced from Whittaker modules. Zbl 0956.17004 Miličić, Dragan; Soergel, Wolfgang 1997 Algebraic $${\mathcal D}$$-modules and representation theory of semisimple Lie groups. Zbl 0821.22005 Miličić, Dragan 1993 Intertwining functors and irreducibility of standard Harish-Chandra sheaves. Zbl 0760.22019 Miličić, Dragan 1991 On the cohomological dimension of the localization functor. Zbl 0714.22011 Hecht, Henryk; Miličić, Dragan 1990 Localization and standard modules for real semisimple Lie groups. I: The duality theorem. Zbl 0699.22022 Hecht, Henryk; Miličić, Dragan; Schmid, Wilfried; Wolf, Joseph A. 1987 Asymptotic behavior of matrix coefficients of admissible representations. Zbl 0524.22014 Casselman, William; Milicic, Dragan 1982 On the irreducibility of unitary principal series representations. Zbl 0477.22011 Milicic, Dragan; Primc, Mirko 1982 Asymptotic behaviour of matrix coefficients of the discrete series. Zbl 0398.22022 Milicic, Dragan 1977 Representations of almost connected groups. Zbl 0295.22011 Milicic, Dragan 1975 The dual spaces of almost connected reductive groups. Zbl 0299.22006 Milicic, Dragan 1974 Elementary representations of the group SO(3,2). Zbl 0288.22023 Kraljevic, H.; Milicic, D. 1974 On C$$^$$-algebras with bounded trace. Zbl 0265.46072 Milicic, Dragan 1973 The C$$^$$-algebra of the universal covering group of SL(2,R). Zbl 0248.22014 Kraljevic, Hrvoje; Milicic, Dragan 1972 Topological representation of the group $$C^ $$-algebra of SL(2,R). Zbl 0229.22010 Miličić, Dragan 1971 A note on invariant order ideals in the predual of a von Neumann algebra. Zbl 0217.16901 Miličić, D. 1971 On the boundary of essential spectra. Zbl 0216.41701 Miličić, D.; Veselić, K. 1971 all top 5 #### Cited by 198 Authors 9 Van den Ban, Erik Peter 8 Schmid, Wilfried 7 Schlichtkrull, Henrik 7 Wolf, Joseph Albert 5 Barchini, Leticia 5 Collingwood, David H. 5 Delorme, Patrick 5 Hecht, Henryk 5 Mazorchuk, Volodymyr 5 Sun, Binyong 5 Zierau, Roger 4 Aizenbud, Avraham 4 Archbold, Robert J. 4 Casian, Luis G. 4 Gourevitch, Dmitry 4 Guo, Xiangqian 4 Herb, Rebecca A. 4 Miličić, Dragan 4 Soergel, Wolfgang 4 Tadić, Marko 3 Chang, Jen-Tseh 3 Coulembier, Kevin 3 Knapp, Anthony William 3 Koelink, Erik 3 Krötz, Bernhard J. 3 Liu, Xuewen 3 Muić, Goran 3 Ondrus, Matthew 3 Plymen, Roger J. 3 Román, Pablo Manuel 3 Wiesner, Emilie B. 2 Bezrukavnikov, Roman 2 Brown, Adam R. 2 Brown, Jonathan S. 2 Casselman, William A. 2 Chen, Chih-Whi 2 Christodoulopoulou, Konstantina 2 Clare, Pierre 2 Crisp, Tyrone 2 Gaillard, Pierre-Yves 2 Goodwin, Simon M. 2 Higson, Nigel 2 Jiang, Dihua 2 Kaniuth, Eberhard 2 Ludwig, Jean 2 Matumoto, Hisayosi 2 Oda, Takayuki 2 Polo, Patrick 2 Renard, David A. 2 Sahi, Siddhartha 2 Schlichting, Günter 2 Somerset, Douglas W. B. 2 Speh, Birgit 2 Stroppel, Catharina H. 2 Taylor, Joseph L. 2 Van Pruijssen, Maarten 2 Vilonen, Kari 2 Zhao, Kaiming 2 Zhu, Chen-Bo 1 Adamović, Dražen 1 Aldenhoven, Noud 1 an Huef, Astrid 1 Ankabout, Karim 1 Arkhipov, Sergey M. 1 Avila Cordeiro de Melo, Artur 1 Backelin, Erik 1 Bagci, Irfan 1 Baggett, Larry W. 1 Baldoni-Silva, Maria Welleda 1 Barnes, Bruce A. 1 Batra, Punita 1 Bautista, Raymundo 1 Beltiţă, Daniel 1 Benkart, Georgia M. 1 Berkani, Mohammed 1 Boe, Brian Douglas 1 Bourgain, Jean 1 Bowen, Lewis Phylip 1 Božičević, Mladen 1 Brodzki, Jacek 1 Brylinski, Jean-Luc 1 Cai, Yanan 1 Chen, Hongjia 1 Chen, Yangyang 1 Chenevier, Gaëtan 1 Colarusso, Mark 1 Dang, Nguyen Viet 1 Deicke, Klaus 1 Din, Alexander Yom 1 Donley, Robert W. jun. 1 Dooley, Anthony Haynes 1 Duflo, Michel 1 Ebata, Mitsuhiko 1 Eguchi, Masaaki 1 Evens, Sam 1 Felińska, Ewa 1 Franke, Jens 1 Furusawa, Masaaki 1 Gaitsgory, Dennis 1 Golod, P. I. ...and 98 more Authors all top 5 #### Cited in 57 Serials 25 Journal of Functional Analysis 12 Journal of Algebra 11 Transactions of the American Mathematical Society 10 Advances in Mathematics 10 Mathematische Zeitschrift 10 Representation Theory 9 Mathematische Annalen 7 Compositio Mathematica 7 Duke Mathematical Journal 7 Inventiones Mathematicae 6 Proceedings of the American Mathematical Society 5 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 4 Annales de l’Institut Fourier 4 Journal of Pure and Applied Algebra 3 Communications in Algebra 3 Israel Journal of Mathematics 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 Bulletin of the American Mathematical Society. New Series 2 Journal of Mathematical Physics 2 Proceedings of the Japan Academy. Series A 2 Ergodic Theory and Dynamical Systems 2 Journal of the American Mathematical Society 2 Geometric and Functional Analysis. GAFA 2 Selecta Mathematica. New Series 2 Journal of the European Mathematical Society (JEMS) 2 Frontiers of Mathematics in China 1 Communications in Mathematical Physics 1 Moscow University Mathematics Bulletin 1 Ukrainian Mathematical Journal 1 Arkiv för Matematik 1 Reviews in Mathematical Physics 1 Acta Mathematica 1 Bulletin de la Société Mathématique de France 1 Canadian Journal of Mathematics 1 Functional Analysis and its Applications 1 Glasgow Mathematical Journal 1 Publications Mathématiques 1 Journal of Number Theory 1 Journal of Soviet Mathematics 1 Memoirs of the American Mathematical Society 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Acta Applicandae Mathematicae 1 Mémoires de la Société Mathématique de France. Nouvelle Série 1 Indagationes Mathematicae. New Series 1 Journal of Algebraic Combinatorics 1 Documenta Mathematica 1 Transformation Groups 1 The Ramanujan Journal 1 Algebras and Representation Theory 1 Annals of Mathematics. Second Series 1 Journal of the Institute of Mathematics of Jussieu 1 Journal of Algebra and its Applications 1 Complex Analysis and Operator Theory 1 Confluentes Mathematici 1 Japanese Journal of Mathematics. 3rd Series 1 São Paulo Journal of Mathematical Sciences 1 Annals of Functional Analysis all top 5 #### Cited in 24 Fields 126 Topological groups, Lie groups (22-XX) 49 Nonassociative rings and algebras (17-XX) 24 Abstract harmonic analysis (43-XX) 23 Group theory and generalizations (20-XX) 22 Functional analysis (46-XX) 18 Number theory (11-XX) 16 Algebraic geometry (14-XX) 13 Associative rings and algebras (16-XX) 12 Several complex variables and analytic spaces (32-XX) 10 Category theory; homological algebra (18-XX) 7 Differential geometry (53-XX) 7 Manifolds and cell complexes (57-XX) 6 Special functions (33-XX) 6 Dynamical systems and ergodic theory (37-XX) 6 Global analysis, analysis on manifolds (58-XX) 4 Operator theory (47-XX) 4 Quantum theory (81-XX) 2 Combinatorics (05-XX) 2 $$K$$-theory (19-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 1 Ordinary differential equations (34-XX) 1 Partial differential equations (35-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) #### Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.	2021-03-04T10:02:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3871363699436188, "perplexity": 8541.328030606317}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178368687.25/warc/CC-MAIN-20210304082345-20210304112345-00395.warc.gz"}
https://alldimensions.fandom.com/wiki/Kolmnasuperverse	## FANDOM 2,850 Pages Kolmnasuperverse (KSV) contains $\frac{1}{\mho^2}$ of the Super everything[1]. ## References 1. The Super Everything (TSE) is beyond everything. Everything are only contained up to The Absolute Existence. Community content is available under CC-BY-SA unless otherwise noted.	2019-11-23T02:59:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2571927309036255, "perplexity": 12758.270340425172}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496672313.95/warc/CC-MAIN-20191123005913-20191123034913-00404.warc.gz"}
https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Calculus_(Apex)/8%3A_Sequences_and_Series/8.8%3A_Taylor_Series	# 8.8: Taylor Series $$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$ In Section 8.6, we showed how certain functions can be represented by a power series function. In 8.7, we showed how we can approximate functions with polynomials, given that enough derivative information is available. In this section we combine these concepts: if a function $$f(x)$$ is infinitely differentiable, we show how to represent it with a power series function. Definition 39 taylor and maclaurin series Let $$f(x)$$ have derivatives of all orders at $$x=c$$. 1. The Taylor Series of $$f(x)$$, centered at $$c$$ is $\sum_{n=0}^\infty \frac{f\,^{(n)}(c)}{n!}(x-c)^n.$ 2. Setting $$c=0$$ gives the Maclaurin Series of $$f(x)$$: $\sum_{n=0}^\infty \frac{f\,^{(n)}(0)}{n!}x^n.$ The difference between a Taylor polynomial and a Taylor series is the former is a polynomial, containing only a finite number of terms, whereas the latter is a series, a summation of an infinite set of terms. When creating the Taylor polynomial of degree $$n$$ for a function $$f(x)$$ at $$x=c$$,we needed to evaluate $$f$$,and the first $$n$$ derivatives of $$f$$,at $$x=c$$.When creating the Taylor series of $$f$$, it helps to find a pattern that describes the $$n^\text{th}$$ derivative of $$f$$ at $$x=c$$.We demonstrate this in the next two examples. Example $$\PageIndex{1}$$: The Maclaurin series of $$f(x) = \cos x$$ Find the Maclaurin series of $$f(x)=\cos x$$. SOLUTION In Example 8.7.4 we found the $$8^\text{th}$$ degree Maclaurin polynomial of $$\cos x$$.In doing so, we created the table shown in Figure 8.29. Figure 8.29: A table of the derivatives of $$f(x)= \cos x$$ evaluated at $$x=0$$. Notice how $$f\,^{(n)}(0)=0$$ when $$n$$ is odd, $$f\,^{(n)}(0)=1$$ when $$n$$ is divisible by $$4$$,and $$f\,^{(n)}(0)=-1$$ when $$n$$ is even but not divisible by 4. Thus the Maclaurin series of $$\cos x$$ is $1-\frac{x^2}2+\frac{x^4}{4!}-\frac{x^6}{6!}+\frac{x^8}{8!} - \cdots$ We can go further and write this as a summation. Since we only need the terms where the power of $$x$$ is even, we write the power series in terms of $$x^{2n}$$: $\sum_{n=0}^\infty (-1)^{n}\frac{x^{2n}}{(2n)!}.$ Example $$\PageIndex{2}$$: The Taylor series of $$f(x)=\ln x$$ at $$x=1$$ Find the Taylor series of $$f(x) = \ln x$$ centered at $$x=1$$. SOLUTION Figure 8.30 shows the $$n^\text{th}$$ derivative of $$\ln x$$ evaluated at $$x=1$$ for $$n=0,\ldots,5$$,along with an expression for the $$n^\text{th}$$ term: $f\,^{(n)}(1) = (-1)^{n+1}(n-1)!\quad \text{for $$n\geq 1$$.}$ Remember that this is what distinguishes Taylor series from Taylor polynomials; we are very interested in finding a pattern for the $$n^\text{th}$$ term, not just finding a finite set of coefficients for a polynomial. Figure 8.30: Derivatives of $$\ln x$$ evaluated at $$x=1$$. Since $$f(1) = \ln 1 = 0$$,we skip the first term and start the summation with $$n=1$$,giving the Taylor series for $$\ln x$$,centered at $$x=1$$,as $\sum_{n=1}^\infty (-1)^{n+1}(n-1)!\frac{1}{n!}(x-1)^n = \sum_{n=1}^\infty (-1)^{n+1}\frac{(x-1)^n}{n}.$ It is important to note that Definition 39 defines a Taylor series given a function $$f(x)$$; however, we cannot yet state that $$f(x)$$ is equal to its Taylor series. We will find that "most of the time'' they are equal, but we need to consider the conditions that allow us to conclude this. Theorem 76 states that the error between a function $$f(x)$$ and its $$n^\text{th}$$--degree Taylor polynomial $$p_n(x)$$ is $$R_n(x)$$,where $\big\|R_n(x)\big\| \leq \frac{\max\left\|\,f\,^{(n+1)}(z)\right\|}{(n+1)!}\big\|(x-c)^{(n+1)}\big\|.$ If $$R_n(x)$$ goes to 0 for each $$x$$ in an interval $$I$$ as $$n$$ approaches infinity, we conclude that the function is equal to its Taylor series expansion. theorem 77 function and taylor series equality Let $$f(x)$$ have derivatives of all orders at $$x=c$$,let $$R_n(x)$$ be as stated in Theorem 76, and let $$I$$ be an interval on which the Taylor series of $$f(x)$$ converges. If $$\lim\limits_{n\to\infty} R_n(x) = 0$$ for all $$x$$ in $$I$$,then $f(x) = \sum_{n=0}^\infty \frac{f\,^{(n)}(c)}{n!}(x-c)^n\ \text{ on $$I$$.}$ We demonstrate the use of this theorem in an example. Example $$\PageIndex{3}$$: Establishing equality of a function and its Taylor series Show that $$f(x) = \cos x$$ is equal to its Maclaurin series, as found in Example 8.8.1, for all $$x$$. SOLUTION Given a value $$x$$,the magnitude of the error term $$R_n(x)$$ is bounded by $\big\|R_n(x)\big\| \leq \frac{\max\left\|\,f\,^{(n+1)}(z)\right\|}{(n+1)!}\big\|x^{n+1}\big\|.$ Since all derivatives of $$\cos x$$ are $$\pm \sin x$$ or $$\pm\cos x$$,whose magnitudes are bounded by $$1$$,we can state $\big\|R_n(x)\big\| \leq \frac{1}{(n+1)!}\big\|x^{n+1}\big\|$ which implies $-\frac{\|x^{n+1}\|}{(n+1)!} \leq R_n(x) \leq\frac{\|x^{n+1}\|}{(n+1)!}.\label{eq:coseqtaylor}$ For any $$x$$,$$\lim\limits_{n\to\infty} \frac{x^{n+1}}{(n+1)!} = 0$$. Applying the Squeeze Theorem to Equation \ref{eq:coseqtaylor}, we conclude that $$\lim\limits_{n\to\infty} R_n(x) = 0$$ for all $$x$$,and hence $\cos x = \sum_{n=0}^\infty (-1)^{n}\frac{x^{2n}}{(2n)!}\quad \text{for all $$x$$}.$ It is natural to assume that a function is equal to its Taylor series on the series' interval of convergence, but this is not the case. In order to properly establish equality, one must use Theorem 77. This is a bit disappointing, as we developed beautiful techniques for determining the interval of convergence of a power series, and proving that $$R_n(x)\to 0$$ can be cumbersome as it deals with high order derivatives of the function. There is good news. A function $$f(x)$$ that is equal to its Taylor series, centered at any point the domain of $$f(x)$$,is said to be an analytic function, and most, if not all, functions that we encounter within this course are analytic functions. Generally speaking, any function that one creates with elementary functions (polynomials, exponentials, trigonometric functions, etc.) that is not piecewise defined is probably analytic. For most functions, we assume the function is equal to its Taylor series on the series' interval of convergence and only use Theorem 77 when we suspect something may not work as expected. We develop the Taylor series for one more important function, then give a table of the Taylor series for a number of common functions. Example $$\PageIndex{4}$$: The Binomial Series Find the Maclaurin series of $$f(x) = (1+x)^k$$,$$k\neq 0$$. SOLUTION When $$k$$ is a positive integer, the Maclaurin series is finite. For instance, when $$k=4$$,we have $f(x) = (1+x)^4 = 1+4x+6x^2+4x^3+x^4.$ The coefficients of $$x$$ when $$k$$ is a positive integer are known as the binomial coefficients, giving the series we are developing its name. When $$k=1/2$$,we have $$f(x) = \sqrt{1+x}$$.Knowing a series representation of this function would give a useful way of approximating $$\sqrt{1.3}$$,for instance. To develop the Maclaurin series for $$f(x) = (1+x)^k$$ for any value of $$k\neq0$$,we consider the derivatives of $$f$$ evaluated at $$x=0$$: Thus the Maclaurin series for $$f(x) = (1+x)^k$$ is $1+ k + \frac{k(k-1)}{2!} + \frac{k(k-1)(k-2)}{3!} + \ldots + \frac{k(k-1)\cdots\big(k-(n-1)\big)}{n!}+\ldots$ It is important to determine the interval of convergence of this series. With $a_n = \frac{k(k-1)\cdots\big(k-(n-1)\big)}{n!}x^n,$ we apply the Ratio Test: \begin{align} \lim\limits_{n\to\infty}\frac{\|a_{n+1}\|}{\|a_n\|}&=\lim\limits_{n\to\infty} \left\|\frac{k(k-1)\cdots(k-n)}{(n+1)!}x^{n+1}\right\|\Bigg/\left\|\frac{k(k-1)\cdots\big(k-(n-1)\big)}{n!}x^n\right\|\\ &=\lim\limits_{n\to\infty} \left\|\frac{k-n}{n}x\right\|\\ &= \|x\|. \end{align} The series converges absolutely when the limit of the Ratio Test is less than 1; therefore, we have absolute convergence when $$\|x\|<1$$. While outside the scope of this text, the interval of convergence depends on the value of $$k$$.When $$k>0$$,the interval of convergence is $$[-1,1]$$.When $$-1<k<0$$,the interval of convergence is $$[-1,1)$$.If $$k\leq -1$$,the interval of convergence is $$(-1,1)$$. We learned that Taylor polynomials offer a way of approximating a "difficult to compute'' function with a polynomial. Taylor series offer a way of exactly representing a function with a series. One probably can see the use of a good approximation; is there any use of representing a function exactly as a series? While we should not overlook the mathematical beauty of Taylor series (which is reason enough to study them), there are practical uses as well. They provide a valuable tool for solving a variety of problems, including problems relating to integration and differential equations. In Key Idea 32 (on the following page) we give a table of the Taylor series of a number of common functions. We then give a theorem about the "algebra of power series,'' that is, how we can combine power series to create power series of new functions. This allows us to find the Taylor series of functions like $$f(x) = e^x\cos x$$ by knowing the Taylor series of $$e^x$$ and $$\cos x$$. Before we investigate combining functions, consider the Taylor series for the arctangent function (see Key Idea 32). Knowing that $$\tan^{-1}(1) = \pi/4$$,we can use this series to approximate the value of $$\pi$$: \begin{align} \frac{\pi}4 &= \tan^{-1}(1) = 1-\frac13+\frac15-\frac17+\frac19-\cdots\\ \pi &= 4\left(1-\frac13+\frac15-\frac17+\frac19-\cdots\right) \end{align} Unfortunately, this particular expansion of $$\pi$$ converges very slowly. The first 100 terms approximate $$\pi$$ as $$3.13159$$,which is not particularly good. KEY IDEA 32 IMPORTANT TAYLOR SERIES EXPASIONS THEOREM 78 ALGEBRA OF POWER SERIES Let $$f(x) = \sum_{n=0}^\infty a_nx^n$$ and $$g(x) = \sum_{n=0}^\infty b_nx^n$$ converge absolutely for $$\|x\|<R$$,and let $$h(x)$$ be continuous. 1. $$f(x)\pm g(x) = \sum_{n=0}^\infty (a_n\pm b_n)x^n$$ \quad for $$\|x\|<R$$. 2. $$f(x)g(x) = \left(\sum_{n=0}^\infty a_nx^n\right)\left(\sum_{n=0}^\infty b_nx^n\right) = \sum_{n=0}^\infty\big(a_0b_n+a_1b_{n-1}+\ldots a_nb_0\big)x^n \text{ for }\|x\|<R$$. 3. $$f\big(h(x)\big) = \sum_{n=0}^\infty a_n\big(h(x)\big)^n \quad \text{ for }\|h(x)\|<R$$. Example $$\PageIndex{5}$$: Combining Taylor series Write out the first 3 terms of the Taylor Series for $$f(x) = e^x\cos x$$ using Key Idea 32 and Theorem 78. SOLUTION Key Idea 32 informs us that $e^x = 1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\cdots\quad \text{and}\quad \cos x = 1-\frac{x^2}{2!}+\frac{x^4}{4!}+\cdots.$ Applying Theorem 78, we find that \begin{align} e^x\cos x &= \left(1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\cdots\right)\left(1-\frac{x^2}{2!}+\frac{x^4}{4!}+\cdots\right).\\ \text{Distribute}&\text{ the right hand expression across the left:} \\ &= 1\left(1-\frac{x^2}{2!}+\frac{x^4}{4!}+\cdots\right)+x\left(1-\frac{x^2}{2!}+\frac{x^4}{4!}+\cdots\right)+\frac{x^2}{2!}\left(1-\frac{x^2}{2!}+\frac{x^4}{4!}+\cdots\right)\\ &+\frac{x^3}{3!}\left(1-\frac{x^2}{2!}+\frac{x^4}{4!}+\cdots\right) + \frac{x^4}{4!}\left(1-\frac{x^2}{2!}+\frac{x^4}{4!}+\cdots\right)+\cdots \\ &\text{Distribute again and collect like terms.}\\ &= 1 + x -\frac{x^3}{3}-\frac{x^4}{6} - \frac{x^5}{30}+\frac{x^7}{630}+\cdots \end{align} While this process is a bit tedious, it is much faster than evaluating all the necessary derivatives of $$e^x\cos x$$ and computing the Taylor series directly. Because the series for $$e^x$$ and $$\cos x$$ both converge on $$(-\infty,\infty)$$,so does the series expansion for $$e^x\cos x$$. Example $$\PageIndex{6}$$: Creating new Taylor series Use Theorem 78 to create series for $$y=\sin(x^2)$$ and $$y=\ln (\sqrt{x})$$. SOLUTION Given that $\sin x = \sum_{n=0}^\infty (-1)^n\frac{x^{2n+1}}{(2n+1)!} = x-\frac{x^3}{3!}+\frac{x^5}{5!} -\frac{x^7}{7!}+\cdots,$ we simply substitute $$x^2$$ for $$x$$ in the series, giving $\sin (x^2) = \sum_{n=0}^\infty (-1)^n\frac{(x^2)^{2n+1}}{(2n+1)!} = x^2-\frac{x^6}{3!}+\frac{x^{10}}{5!} -\frac{x^{14}}{7!}\cdots.$ Since the Taylor series for $$\sin x$$ has an infinite radius of convergence, so does the Taylor series for $$\sin(x^2)$$. The Taylor expansion for $$\ln x$$ given in Key Idea 32 is centered at $$x=1$$,so we will center the series for $$\ln (\sqrt{x})$$ at $$x=1$$ as well. With $\ln x = \sum_{n=1}^\infty(-1)^{n+1}\frac{(x-1)^n}{n} = (x-1)- \frac{(x-1)^2}{2} +\frac{(x-1)^3}{3}-\cdots,$ we substitute $$\sqrt{x}$$ for $$x$$ to obtain $\ln (\sqrt{x}) = \sum_{n=1}^\infty(-1)^{n+1}\frac{(\sqrt{x}-1)^n}{n} = (\sqrt{x}-1)- \frac{(\sqrt{x}-1)^2}{2} +\frac{(\sqrt{x}-1)^3}{3}-\cdots.$ While this is not strictly a power series, it is a series that allows us to study the function $$\ln(\sqrt{x})$$.Since the interval of convergence of $$\ln x$$ is $$(0,2]$$,and the range of $$\sqrt{x}$$ on $$(0,4]$$ is $$(0,2]$$,the interval of convergence of this series expansion of $$\ln(\sqrt{x})$$ is $$(0,4]$$. Note: In Example 8.8.6, one could create a series for $$\ln(\sqrt{x})$$ by simply recognizing that $$\ln(\sqrt{x}) = \ln (x^{1/2}) = 1/2\ln x$$,and hence multiplying the Taylor series for $$\ln x$$ by $$1/2$$.This example was chosen to demonstrate other aspects of series, such as the fact that the interval of convergence changes. Example $$\PageIndex{7}$$: Using Taylor series to evaluate definite integrals Use the Taylor series of $$e^{-x^2}$$ to evaluate $$\int_0^1e^{-x^2}\ dx$$. SOLUTION We learned, when studying Numerical Integration, that $$e^{-x^2}$$ does not have an antiderivative expressible in terms of elementary functions. This means any definite integral of this function must have its value approximated, and not computed exactly. We can quickly write out the Taylor series for $$e^{-x^2}$$ using the Taylor series of $$e^x$$: \begin{align} e^x &= \sum_{n=0}^\infty \frac{x^n}{n!} = 1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\cdots \\ \text{and so}& \\ e^{-x^2} &= \sum_{n=0}^\infty \frac{(-x^2)^n}{n!} \\ &= \sum_{n=0}^\infty (-1)^n\frac{x^{2n}}{n!}\\ &= 1-x^2+\frac{x^4}{2!}-\frac{x^6}{3!}+\cdots. \end{align} We use Theorem 75 to integrate: $\int e^{-x^2}\ dx = C + x - \frac{x^3}{3}+\frac{x^5}{5\cdot2!}-\frac{x^7}{7\cdot3!}+\cdots +(-1)^n\frac{x^{2n+1}}{(2n+1)n!}+\cdots$ This is the antiderivative of $$e^{-x^2}$$;while we can write it out as a series, we cannot write it out in terms of elementary functions. We can evaluate the definite integral $$\int_0^1e^{-x^2}\ dx$$ using this antiderivative; substituting 1 and 0 for $$x$$ and subtracting gives $\int_0^1e^{-x^2}\ dx = 1-\frac{1}{3}+\frac{1}{5\cdot 2!}-\frac{1}{7\cdot3!} + \frac{1}{9\cdot4!}\cdots.$ Summing the 5 terms shown above give the approximation of $$0.74749.$$ Since this is an alternating series, we can use the Alternating Series Approximation Theorem, (Theorem 71), to determine how accurate this approximation is. The next term of the series is $$1/(11\cdot5!) \approx 0.00075758$$.Thus we know our approximation is within $$0.00075758$$ of the actual value of the integral. This is arguably much less work than using Simpson's Rule to approximate the value of the integral. Example $$\PageIndex{8}$$: Using Taylor series to solve differential equations Solve the differential equation $$y^{\prime}=2y$$ in terms of a power series, and use the theory of Taylor series to recognize the solution in terms of an elementary function. SOLUTION We found the first 5 terms of the power series solution to this differential equation in Example 8.6.5 in Section 8.6. These are: $a_0=1,\quad a_1 = 2,\quad a_2 = \frac42=2,\quad a_3=\frac{8}{2\cdot3}=\frac43,\quad a_4=\frac{16}{2\cdot3\cdot4} = \frac23.$ We include the "unsimplified'' expressions for the coefficients found in Example 8.6.5 as we are looking for a pattern. It can be shown that $$a_n = 2^n/n!$$.Thus the solution, written as a power series, is $y = \sum_{n=0}^\infty \frac{2^n}{n!}x^n = \sum_{n=0}^\infty \frac{(2x)^n}{n!}.$ Using Key Idea 32 and Theorem 78, we recognize $$f(x) = e^{2x}$$: $e^x = \sum_{n=0}^\infty \frac{x^n}{n!} \qquad \Rightarrow \qquad e^{2x} = \sum_{n=0}^\infty \frac{(2x)^n}{n!}.$ Finding a pattern in the coefficients that match the series expansion of a known function, such as those shown in Key Idea 32, can be difficult. What if the coefficients in the previous example were given in their reduced form; how could we still recover the function $$y=e^{2x}$$? Suppose that all we know is that $a_0=1,\quad a_1=2,\quad a_2=2,\quad a_3=\frac43,\quad a_4=\frac23.$ Definition 39 states that each term of the Taylor expansion of a function includes an $$n!$$.This allows us to say that $a_2=2=\frac{b_2}{2!},\quad a_3 = \frac43=\frac{b_3}{3!},\quad \text{and}\quad a_4 = \frac23=\frac{b_4}{4!}$ for some values $$b_2$$,$$b_3$$ and $$b_4$$. Solving for these values, we see that $$b_2=4$$,$$b_3 = 8$$ and $$b_4=16$$.That is, we are recovering the pattern we had previously seen, allowing us to write \begin{align} f(x) = \sum_{n=0}^\infty a_nx^n &= \sum_{n=0}^\infty \frac{b_n}{n!}x^n \\ &= 1+2x+ \frac{4}{2!}x^2 + \frac{8}{3!}x^3+\frac{16}{4!}x^4 + \cdots \end{align} From here it is easier to recognize that the series is describing an exponential function. There are simpler, more direct ways of solving the differential equation $$y^{\prime} = 2y$$.We applied power series techniques to this equation to demonstrate its utility, and went on to show how sometimes we are able to recover the solution in terms of elementary functions using the theory of Taylor series. Most differential equations faced in real scientific and engineering situations are much more complicated than this one, but power series can offer a valuable tool in finding, or at least approximating, the solution. This chapter introduced sequences, which are ordered lists of numbers, followed by series, wherein we add up the terms of a sequence. We quickly saw that such sums do not always add up to "infinity,'' but rather converge. We studied tests for convergence, then ended the chapter with a formal way of defining functions based on series. Such "series--defined functions'' are a valuable tool in solving a number of different problems throughout science and engineering. Coming in the next chapters are new ways of defining curves in the plane apart from using functions of the form $$y=f(x)$$.Curves created by these new methods can be beautiful, useful, and important. ### Contributors • Gregory Hartman (Virginia Military Institute). Contributions were made by Troy Siemers and Dimplekumar Chalishajar of VMI and Brian Heinold of Mount Saint Mary's University. This content is copyrighted by a Creative Commons Attribution - Noncommercial (BY-NC) License. http://www.apexcalculus.com/	2019-04-24T16:34:03	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9819880127906799, "perplexity": 274.4411517874412}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578650225.76/warc/CC-MAIN-20190424154437-20190424180437-00436.warc.gz"}
https://www.aimsciences.org/article/doi/10.3934/proc.2005.2005.784	Article Contents Article Contents Existence of guided modes on periodic slabs • We prove the existence of bound guided modes for the Helmholtz equation on lossless penetrable periodic slabs. We handle both robust modes, for which no Bragg harmonics propagate away from slab, as well as nonrobust standing modes, which exist in the presence of propagating Bragg harmonics. The latter are made possible by symmetries of the slab structure, which prevent coupling of energy to the propagating harmonics. These modes are isolated in wavevector-frequency space, as they disappear under a perturbation of the wavevector. The main tool is a volumetric integral equation of Lippmann-Schwinger type that has a self-adjoint kernel. Mathematics Subject Classification: 78A25. Citation: Open Access Under a Creative Commons license	2023-03-21T07:34:45	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.32623809576034546, "perplexity": 1817.1970470040933}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943637.3/warc/CC-MAIN-20230321064400-20230321094400-00330.warc.gz"}
https://survivor.togaware.com/datascience/function-call-layout.html	## 27.14 Function Call Layout 20200105 Don’t add spaces around for named arguments in parameter lists. Visually this ties the named arguments together and highlights this as a parameter list. This style is at odds with the default R printing style and is the only situation where I tightly couple a binary operator. In all other situations there should be a space around the operator. Preferred readr::read_csv(file="data.csv", skip=1e5, progress=FALSE) Discouraged read_csv(file = "data.csv", skip = 1e5, progress = FALSE) For long parameter lists improve readability using a table format aligning on the . Preferred readr::read_csv(file = "data.csv", skip = 1e5, progress = FALSE) All but the final argument to a function call can be easily commented out. However, the latter arguments are often optional and whilst exploring them we will likely comment them out. An alternative puts the comma at the beginning of the line to easily comment out specific arguments except for the first one, which is usually more important and often non-optional. This is common amongst SQL programmers and can be useful for R. Usual dialPlot(value = 78, label = "UseR!", label_cex = 3, label_color = "black") Alternative dialPlot(value = 78 , label = "UseR!" , label_cex = 3 , label_color = "black" ) Discouraged dialPlot( value=78, label="UseR!", label_cex=3, label_color="black") Your donation will support ongoing availability and give you access to the PDF version of this book. Desktop Survival Guides include Data Science, GNU/Linux, and MLHub. Books available on Amazon include Data Mining with Rattle and Essentials of Data Science. Popular open source software includes rattle, wajig, and mlhub. Hosted by Togaware, a pioneer of free and open source software since 1984. Copyright © 1995-2022 [email protected] Creative Commons Attribution-ShareAlike 4.0	2022-12-06T21:53:40	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17551015317440033, "perplexity": 4233.100350339893}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711114.3/warc/CC-MAIN-20221206192947-20221206222947-00734.warc.gz"}
https://journal.nafo.int/Volumes/Articles/ID/634/Files	03 # Spatiotemporal patterns of flatfish bycatch in two scallop access areas on Georges Bank ### Megan Winton1, 2, Carl Huntsberger1, 3, David Rudders4, Greg DeCelles2, 5, Katherine Thompson1, 6, Kathryn Goetting1, 7, and Ronald Smolowitz1 WINTON, M., C. HUNTSBERGER, D. RUDDERS, G. DECELLES, K. THOMPSON, K. GOETTING, and R. SMOLOWITZ. 2017. Spatiotemporal patterns of flatfish bycatch in two scallop access areas on Georges Bank. J. Northw. Atl. Fish. Sci., 49: 23–37. doi:10.2960/J.v49.m710 ## Abstract Bycatch is a constraint to the Atlantic sea scallop fishery, the most valuable single-species fishery along the eastern coast of the United States. To characterize trends in the bycatch of three flatfish species, a fishery-independent scallop dredge survey was conducted in two sea scallop access areas (Closed Areas I and II) on Georges Bank from 2011 to 2014. Generalized additive mixed models were used to identify seasonal bycatch hotspots of yellowtail, winter, and windowpane flounder. In all cases, spatially explicit models best fit the data (deviance explained: 47–73%) and provided insight into the spatial distribution underlying the seasonal trends in each area. Modeled catch rates for the three flatfish species suggested localized catches at discrete times of the year. Catches of yellowtail and windowpane flounder were highest in Closed Area II in the fall and winter, respectively. Winter flounder were caught in the highest numbers in Closed Area I during the summer and fall, and were largely absent from catches in Closed Area II. Our results suggest consistent seasonal trends that may help managers identify the optimal times to open the access areas to the scallop fleet in order to reduce flatfish bycatch. Keywords:catch per unit effort, GAMM, generalized additive mixed models, sea scallop, windowpane flounder, winter flounder, yellowtail flounder ## Introduction The Atlantic sea scallop (Placopecten magellanicus) fishery is the most valuable single-species fishery along the eastern coast of the United States (US; van Voorhees, MS 2014). The species is distributed along the northeastern US continental shelf from Cape Hatteras, North Carolina, to Maine, but the bulk of the fishery’s effort is concentrated on the productive scallop beds in the mid-Atlantic Bight and on Georges Bank (NEFMC, MS 2014). Since 2004, the resource has been harvested under a rotational area-based management strategy designed to increase the long-term yield and reproductive potential of the stock by identifying and protecting high-density beds of juvenile scallops from fishing mortality (NEFMC, MS 2003). Under the current plan, the fleet is also given limited access to two static closed areas on Georges Bank (Closed Areas I and II, hereafter also referred to as scallop access areas; Fig. 1) that were established in 1994 to protect spawning habitat of depleted groundfish stocks (Murawski et al., 2000). Although this management strategy has resulted in increased scallop yields (NEFSC, MS 2010), bycatch of several groundfish species remains a constraint to the fishery, both on Georges Bank and in the mid-Atlantic (O’Keefe and DeCelles, 2013). Fig. 1. In particular, catches of yellowtail flounder (Limanda ferruginea) have impacted the timing, location, and, ultimately, the allowable harvest of sea scallops over the past fifteen years (O’Keefe and DeCelles, 2013). The current regulatory framework mandates a strict accounting of fishery-specific bycatch. If the fleet exceeds its annual catch limit for a given species, accountability measures are implemented (e.g. in-season closures or quota reductions to account for previous overages; Magnuson-Stevens Fishery Conservation and Management Act; USDOC/NOAA/NMFS, MS 2007). Since 1999, the scallop fleet has been allocated an annual catch limit of Georges Bank yellowtail flounder. Between 1999 and 2009, in-season closures on Georges Bank have occurred several times due to yellowtail overages, resulting in economic losses to the fleet (O’Keefe and DeCelles, 2013). In addition to yellowtail flounder, bycatch of windowpane and winter flounder has also become a management concern in the scallop fishery; an accountability measure for windowpane was recently implemented in the mid-Atlantic (NEFMC, MS 2014). Although accountability measures for flatfish species other than yellowtail are not currently in place for the fishery on Georges Bank, it is plausible they may soon follow. Given the economic consequences of scallop fishery closures due to yellowtail bycatch (O’Keefe and DeCelles, 2013), numerous efforts to mitigate the fleet’s impact on non-target species have been implemented. The fishery funds its own observer program, and has invested heavily in approaches aimed at both reactive (e.g. real-time bycatch avoidance; O’Keefe and DeCelles, 2013) and proactive strategies (e.g. gear modifications; Davis et al., MS 201) to reduce bycatch. However, the current overfished status of the Georges Bank yellowtail flounder stock (TRAC, MS 2014) and the resulting low annual allocation to the scallop fleet (which was reduced by over 40% in 2014; NEFMC, MS 2014) means that existing approaches to bycatch reduction may not be sufficient to avoid exceeding catch limits. Documented seasonal variation in flatfish bycatch rates (Bachman, MS 2009) suggests that targeted time-area closures may be a viable option for the scallop fishery on Georges Bank. Given the relatively stationary nature of scallops (Hart and Chute, 2004) and the migratory patterns of the three flatfish species (Chang et al., 1999; Johnson et al., 1999; Pereira et al., 1999), it is plausible that periods of relative spatial segregation between target and non-target species could be identified based on spatiotemporal patterns in bycatch rates. However, the resolution of the data available is limited. Under the current management strategy, scallop access areas are only open to the fleet during certain periods of designated years, which limits the utility of fishery-dependent data for discerning seasonal trends in bycatch rates. Although the National Marine Fisheries Service-Northeast Fisheries Science Center biannual bottom trawl survey provides a continuous time series of fisheries-independent data for Georges Bank since 1963 (Despres-Patanjo et al., 1988), the survey is not conducted at the spatial resolution or temporal frequency required to assess seasonal patterns in flatfish distributions within the access areas. To collect the fine-scale, fishery-independent information needed to better understand the spatial and temporal dynamics of flatfish bycatch in the sea scallop fishery in Closed Areas I and II on Georges Bank, a seasonal dredge survey was conducted from 2011–2014. Generalized additive mixed models (Wood, 2006, 2011), which provide a flexible framework for the investigation of spatially continuous, non-linear trends (Swartzman et al., 1992; Augustin et al., 2013), were used to identify spatiotemporal patterns in flatfish bycatch rates. The results are considered in the context of possible time-area management strategies for the Georges Bank scallop access areas. ## Materials and Methods ### Survey Design Twenty-nine survey trips were conducted aboard eighteen commercial sea scallop vessels from 2011 to 2014. Survey trips were conducted monthly from March through November of 2011, and every six weeks from January 2012 to March 2014. Sampling locations in Closed Area I and Closed Area II were selected using a fixed station, systematic grid design to ensure uniform spatial coverage of each area (Fig. 1). However, some portions of each closed area could not be sampled due to bottom type (e.g. rocky substrate) or high densities of sand dollars (Echinarachnius parma. In order to evenly distribute sampling effort to areas with different spatial extents, the distance between stations in each area varied. In Closed Area I (CAI), the 31 stations were separated by 5.4 km east to west and 7.2 km north to south. The 30 stations in Closed Area II (CAII) were separated by 8.6 km east to west and 11.1 km north to south. On each trip, the vessel was outfitted with two commercial scallop dredges: one standardized 4.6 m wide Turtle Deflector Dredge (TDD) and one 4.6 m wide New Bedford-style dredge, which was supplied by the vessel. Each dredge had 10.2 cm rings and a 25.4 cm mesh twine top, but the TDD had a modified headbale designed to exclude sea turtles (Smolowitz et al., 2012). A more detailed description of the dredges used in this fishery as well as a description of the TDD frame is provided in Smolowitz et al. (2012). Only catch data from the standardized TDD used over the entire course of the survey are presented herein. It is important to note that the large mesh used on commercial scallop dredges has a low selectivity for small flatfish (Legault et al., MS 2010). Thus, the flatfish bycatch rates observed during the course of our survey are considered to be representative only of the portion of the population available and vulnerable to capture in commercial scallop dredges. At each station, standardized survey protocol specified that the vessel operator pass through the center of each grid cell at some point during the tow; tow direction was left to the discretion of the operator. The target tow duration was 30 minutes, with a minimum acceptable tow time of 20 minutes. Tows shorter than 20 minutes or those with gear or other operational issues were deemed invalid, and the station was resampled until an acceptable tow was completed. Target tow speed was 4.8 knots, and dredges were towed with a 3:1 wire to depth scope. Set-out and haul-back coordinates, depth, sea state, vessel speed, and weather conditions were recorded by the vessel operator. Beginning in May 2011, a temperature (Vemco Minilog) and a temperature-depth logger (Star-Oddi DST milli-TD) were attached to the dredge and programmed to acquire data every 30 seconds. Following each tow, the catch from each dredge was sorted by species. All yellowtail, winter, and windowpane flounder were counted and measured to the nearest cm. Bycatch rates for each flatfish species in each tow were expressed in terms of catch per unit effort (CPUE) as the ratio of the number of fish caught in the TDD and the time of the tow in minutes; CPUE values for tows that varied around the target tow duration of 30 minutes were scaled accordingly. ### Seasonal trends in flatfish catches Generalized additive mixed models (GAMMs; Wood, 2006, 2011) were used to investigate seasonal changes in the spatial distribution of flatfish catches. There were a large number of tows with zero flatfish catch in both areas (Table 1). Therefore, a Tweedie error distribution (which can accommodate continuous data with many zeros; Tweedie, 1984; Dunn and Smyth, 2005) and a log link function were assumed (Candy 2004; Shono 2008). The Tweedie distribution belongs to the family of exponential dispersion models, which generalize the exponential families used in generalized linear and additive modeling frameworks (Jørgensen 1992). The variance of a Tweedie-distributed random variable, Y, is given by Var(Y) =φ [E(Y)]p, where φ is a dispersion parameter and p is the Tweedie index parameter, which is a constant. When p is equal to 0, 1, or 2, the Tweedie is equivalent to the normal, Poisson, or gamma distribution, respectively. For values of p between 1 and 2, the model is a compound Poisson-gamma distribution. When p is closer to 1, the Tweedie distribution most closely resembles the Poisson and allows for a point mass at 0; as the value of p increases, the Tweedie more closely approximates the gamma (Candy 2004). Table 1 Because we were most interested in describing the spatial distribution of catches over the course of the year, we chose to model catch rates as a function of geographic location and month rather than environmental conditions. Additionally, depth and bottom temperature (the two available environmental variables we expected to correlate most highly with catch rates; Swartzman et al., 1992; Hyun et al., 2014) were not collected over the entire course of the survey and were highly correlated with longitude and month, respectively. Preliminary analyses also indicated that the results of models based on those covariates did not adequately describe the distribution of residuals; they are therefore not presented further here. For model fitting, tow location was estimated as the midpoint of the great circle distance between the start and end points of each tow using the “geosphere” package (Hijmans et al., 2012) in R (R Core Team, 2015). Midpoint coordinates were projected into the universal transverse Mercator coordinate system (UTM zone 19) using the R package “rgdal” (Bivand et al., 2013). Although we used standardized sampling protocols on each survey, different vessels were employed over the course of the study. Therefore, vessel was incorporated as a random effect to account for variability due to differences in vessel handling, engine power, or other technical characteristics of the vessels employed, as well as other inter-vessel differences not accounted for by the covariates of interest (Candy 2004; Augustin et al., 2013). The response, the CPUE of each flatfish species for tow j from vessel i (yij) was modelled as: $\mathrm{log}\left({y}_{ij}\right)={\beta }_{0}+{f}_{1}\left({\text{month}}_{ij},{\text{northing}}_{ij},{\text{easting}}_{ij}\right)+{\beta }_{1}\mathrm{}{{\text{year}}_{ij}+v}_{i}+{\epsilon }_{ij}$, where β0 is an intercept term; f1 is a smooth function of the covariates associated with vessel i and tow j; northing and easting are projected tow coordinates; β1 is a coefficient specifying the effect of survey year (note the distinction from calendar year); vi represents the random effect of vessel; and εij is an independently and identically distributed (i.i.d.) error term. It was assumed that vi~Normal(0,σi2) and i.i.d. The incorporation of vessel as a random effect term allows for marginal, “population-level” (i.e. vessel-averaged) predictions via integration of vi out of the conditional CPUE predictions (Candy 2004; Augustin et al., 2013). Table 2 Shifts in the spatial distribution of the catch by month are represented by f1, which is a tensor product interaction of a two-dimensional isotropic smooth for location and a one-dimensional smooth for month. The tensor product construction of this interaction term allows for CPUE to be modeled as a smooth function of location and month while being invariant to their relative scaling (Wood, 2006). Thin plate regression splines (Wood, 2006) were used to represent CPUE as a function of geographic coordinates (northing and easting). A cyclic cubic regression spline was used to represent trends in CPUE by month to avoid discontinuities between December and January (Zuur et al., 2009). Catches of winter flounder in CAII were too low (Table 2, Fig. 2; observed CPUE < 4.4 fish per tow in all cases; 3rd quantile = 0.0 fish per tow) and diffuse to se nsibly model in the framework used, as confirmed by residual diagnostics. Therefore, only the results for winter flounder catches in CAI are presented. Given that stations in CAI and CAII were separated by approximately 100 km, two unique models were constructed for CAI and CAII to avoid smoothing over areas that were not sampled. Simpler models nested within the above equation (e.g. models without month, models with the interaction term between geographic location and month replaced by additive effects; see Tables 3–5 for the full list of models fitted) were also considered. For each species, the Tweedie index parameter (p) was set to the value that maximized the penalized log-likelihood for all model variants (Tables 3–5). All models were fitted via maximum likelihood estimation using the R package “mgcv” (Wood, 2006, 2011). Fig. 2. ### Model selection and spatial prediction Model fit was evaluated based on the Akaike Information Criterion (AIC; Akaike, 1973). Interaction and individual terms were retained in the model if their inclusion resulted in lower AIC values and explained a higher proportion of the deviance. The AIC difference (Δi) of each model was calculated based on the lowest observed AIC value (AICmin) as Δi = AICi - AICmin. Models with Δi < 2 were considered indistinguishable in terms of fit (Burnham and Anderson, 2002). Residual plots were examined to assess model fit. Table 3 While location and time were included explicitly in the full models, there was still the possibility of unexplained residual correlation. Therefore, model fit was also assessed based on the mean absolute prediction error (MAPE) to corroborate the likelihood-based AIC approach (Augustin et al., 2013). Because the CPUE of each species varied widely over the course of the year, we chose to use the MAPE rather than the root mean square predictive error, which is more sensitive to large values (Willmott and Matsuura, 2005). Observed data were split into ten test sets based on randomly sampling fixed station locations. For each test set, models were fitted to the remaining data. Values predicted for the omitted set were then compared to observed values to estimate predictive error. The MAPE for each set was calculated as: . Table 4 The ten resulting MAPE values were then averaged to generate an overall MAPE for each model. The spatially explicit models used herein produce a smooth surface from which the expected flatfish CPUE can be estimated at any location within the study area. For models that included year as a fixed effect, the reference level was set to the last survey year (2013) for prediction. In instances when the best fitting models included geographic coordinates, prediction areas were roughly bounded based on the distribution of tow midpoints to avoid extrapolation into unsampled areas (Augustin et al., 1998). The expected flatfish CPUE was predicted over a high resolution grid (10 000 cells in each closed area). As our aim was to identify bycatch hotspots rather than to predict the number of flatfish that would be caught in a given tow, we decided to plot our estimates at this scale to ease interpretation. However, it is important to note that such fine-scale estimates would be prone to bias if used as the basis for field predictions of actual catches. Table 5 ## Results A total of 1 706 valid tows were completed from March 2011 to March 2014 (Table 2). Over the 29 survey trips, a total of 6 852 yellowtail flounder, 1 754 winter flounder, and 12 202 windowpane flounder were collected in the TDD. Catches of all three flounder species varied substantially between areas and seasons (Table 2; Fig. 2). Yellowtail and windowpane flounder catches were generally higher in CAII, with the greatest number of yellowtail caught in the fall and windowpane in the winter and spring (Fig. 2). Winter flounder catches were generally low throughout the year in both areas, but were highest in CAI in the summer and fall (Fig. 2). Yellowtail CPUE ranged from 0.0 to 12.0 in CAI and 0.0 to 143.0 in CAII. The CPUE of winter flounder and windowpane ranged from 0.0 to 48.0 and from 0.0 to 60.0 in CAI, respectively. In CAII, CPUE of winter flounder ranged from 0.0 to 4.4 and windowpane from 0.0 to 126.0. ### Seasonal trends in flatfish catches Fig. 3. The results of the GAMM analyses provided insight into the spatial distribution underlying the monthly trends in flatfish catches for each area. Variation in the CPUE of all three species was best described by models including the month-location smoother, indicating difference in the spatial distribution of flatfish catches by month (Tables 3–5). In all cases, the best fitting models also included survey year as a factor, suggesting differences in the magnitude of catches between years; however, differences in fit between the models including both survey year and the month-location smoother and those only including the month-location smoother were generally minimal (Tables 3–5). Model comparisons based on MAPE estimates supported the model selected based on AIC ranking in all cases (Tables 3–5). In general, the selected models explained a large proportion of the observed variance (deviance explained 0.47 to 0.73 for all cases; Tables 3–5), and residual plots indicated that the assumptions and the selected values of the Tweedie index parameter were appropriate. For yellowtail, model results for both closed areas suggested changes in the distribution and magnitude of bycatch by month (Fig. 3). In CAI, predicted CPUE was generally low in all months (mean CPUE < 2.0 fish per 30 minute tow for all locations) but was highest along the northwestern boundary from the spring into the fall (Fig. 3a-b). Catches in CAII exhibited greater variation over the year (Fig. 3c-d). The predicted CPUE was relatively low over large portions of CAII, with localized areas of higher catch (CPUE > 15.0) in the eastern portion of CAII during the fall (Fig. 3c-d). Predicted catches in both areas were lower in survey year 2013 than in the previous years (Table 6). Table 6 Model results also suggested seasonal changes in the distribution of winter flounder in CAI. Winter flounder were largely absent in predicted catches from February to April (Fig. 4). Predicted catches were highest along the northwestern and southern portions of the area from July to November (CPUE > 5.0; Fig. 4). The best fitting model suggested that predicted catches in CAI were lower in 2013 than in survey years 2011 and 2012 (Table 6). Fig. 4. Monthly variation in the predicted bycatch of windowpane flounder was greater than for the other two species (Fig. 5). The predicted range of windowpane catches was greater in CAII (CPUE: 0.0–69.9) than CAI (CPUE: 0.0–30.2) but was more episodic in CAII. In CAI, the highest predicted catches occurred in the southeastern portion of the area in the fall (September to December; Fig. 5a-b). The highest predicted catches in CAII occurred from January to April, and were relatively high over almost the entire area surveyed (Fig. 5c-d). From May to August, windowpane bycatch in CAII appeared to be minimal (Fig. 5c-d). Predicted catches in both areas were higher in survey year 2013 than in the previous two survey years (Table 6). Fig. 5. ## Discussion The results of our three-year dredge survey revealed considerable spatiotemporal variation in flatfish bycatch both within and between two scallop access areas on Georges Bank. By frequently sampling Closed Areas I and II over an extended period of time, we were able to document localized, seasonal shifts in the bycatch rates of three flatfish species. Our results suggest consistent seasonal patterns in flatfish bycatch that may help managers identify the optimal times to open the access areas to the scallop fleet in order to reduce bycatch of yellowtail, winter, and windowpane flounder. The selected models for flatfish bycatch explained a high degree of the variability observed over the three years of the survey. This was not surprising given our use of GAMMs, which allow for flexible, non-linear fits to explanatory variables (Wood, 2006). Additionally, by modeling bycatch rates as a function of location, which is inherently correlated with other factors (e.g. depth, bottom temperature, prey availability, substrate type), we were able to encompass a myriad of potential mechanistic drivers without explicitly including them in the model structure. While this certainly compromises a more holistic understanding of the observed trends, as well as the long-term predictive power of the models applied herein, we were most interested in identifying seasonal changes to inform management. Though we did not directly investigate the effect of environmental factors on bycatch, similar studies conducted in other regions may provide insight into the seasonal trends we characterized. Swartzman et al. (1992) used spatially-explicit GAMs to investigate inter-annual trends and environmental effects on flatfish catches from trawl survey data in the Bering Sea. They found that models based only on temperature and depth explained nearly as much of the observed variation in the spatial distribution of most species as did the models incorporating geographic coordinates. Limited information is available regarding environmental correlates to flatfish catch rates in CAI and CAII, but temperature and depth likely influence the spatial distribution of yellowtail, winter, and windowpane flounder in a similar fashion (Hyun et al., 2014). Habitat type may also be an important factor. Yellowtail and windowpane flounder typically occur on sand or sand-mud substrates (Chang et al., 1999; Johnson et al., 1999), such as those found along the southeastern edge of the access area in CAII (Murawski et al., 2000). Winter flounder occupy sandy substrates as well, but are more often associated with the mixed sand-gravel sediments typical of CAI (Pereira et al., 1999; Murawski et al., 2000). Alternatively, environmental covariates may operate via indirect effects by modifying the distribution and behavior of prey species, or by influencing the timing of flatfish migration to feeding or spawning grounds (Kotwicki et al., 2005). All three flatfish species are known to make seasonal migrations in response to both abiotic and biotic factors over some portion of their range (Chang et al., 1999; Johnson et al., 1999; Pereira et al., 1999). The survey CPUEs of all three species were relatively low during periods of peak spawning on Georges Bank (yellowtail flounder spawn from May to August, winter flounder from March to May, and windowpane from June to October; O’Brien et al., MS 1993), suggesting that neither area serves as a primary spawning ground for the species. Maturity data collected during the course of the survey corroborate this, as few flounder were observed to be in spawning condition (C. Huntsberger, unpublished data). Whatever the driving mechanisms may be, the spatio-temporal patterns of flatfish bycatch documented herein may be useful in terms of optimizing the harvest of sea scallops while avoiding bycatch, and hence accountability measures, in the Atlantic sea scallop fishery on Georges Bank. It is important to note that our results are only suggestive of relative trends in the availability of flatfish species to the scallop fishery, and are not necessarily related to actual trends in abundance in the two areas surveyed, particularly given the potential impact of large tows on estimated trends (Maunder et al., 2006). However, our results do suggest that predictable seasonal patterns in flatfish bycatch may provide a practical foundation for the formulation of effective time-area management strategies. Based in part on the survey results reported herein, CAII is now closed to the scallop fleet from August through November (NEFMC, MS 2013) in an effort to reduce high rates of yellowtail bycatch. ## Acknowledgements The authors thank the vessel owners, operators, and crew members of the F/Vs Anticipation, Arcturus, Atlantic, Celtic, Endeavor, Horizon, Kayla Rose, Liberty, Polaris, Ranger, Regulus, Resolution, Thor, Vanquish, Venture, Westport, Wisdom, and Zibet, who made this project possible. They are also grateful to survey staff from Coonamessett Farm Foundation (in particular F. Davis, B. Valenti, M. Weeks), the University of Massachusetts Dartmouth (E. Adams, C. Bank, A.Barkley, J. Garrity, S. Inglis, M. Levesque, R. Malloy, D. Zemeckis), the Virginia Institute of Marine Science (W. DuPaul), and Northeastern University (S. Heck). D. Kulka, D. Keith, and one anonymous reviewer provided helpful comments on an earlier draft of this manuscript. 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Climate Res. 30: 79–82. doi.org/10.3354/cr030079 WOOD, S. N. 2006. Generalized additive models: an introduction with R. Chapman and Hall/CRC, Boca Raton, FL. 2011. Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. J. Roy. Stat. Soc B 73(1): 3–36. doi.org/10.1111/j.1467-9868.2010.00749.x ZUUR, A. F., E. N. IENO, N. J. WALKER, A. A. SAVELIEV, and G. M. SMITH. 2009. Mixed effects models and extensions in ecology with R. Springer, New York, NY. doi.org/10.1007/978-0-387-87458-6 Citation: WINTON, M., C. HUNTSBERGER, D. RUDDERS, G. DECELLES, K. THOMPSON, K. GOETTING, and R. SMOLOWITZ. 2017. Spatiotemporal patterns of flatfish bycatch in two scallop access areas on Georges Bank. J. Northw. Atl. Fish. Sci., 49: 23–37. doi:10.2960/J.v49.m710. 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