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https://www.usgs.gov/media/images/us-atlantic-margin-seeps	# U.S. Atlantic Margin Seeps ### Detailed Description Schematic showing the general setting of seeps on the US Atlantic margin and related processes, such as gas hydrate degradation, groundwater seepage, leakage through fractured rocks, or emissions from the seafloor overlying salt diapirs. Pockmarks shown in white, and the nominal updip limit of gas hydrate stability is represented by the dashed black line. Analyses indicate that present-day seepage on this margin does not coincide with pockmarks. After the Nature Geoscience schematic. Public Domain.	2023-01-30T17:16:27	{"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": 0.8131141662597656, "perplexity": 9075.825318812878}, "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-2023-06/segments/1674764499826.71/warc/CC-MAIN-20230130165437-20230130195437-00539.warc.gz"}
https://pdglive.lbl.gov/Particle.action?node=M059&home=sumtabM	${\boldsymbol {\boldsymbol c}}$ ${\boldsymbol {\overline{\boldsymbol c}}}$ MESONS(including possibly non- ${\boldsymbol {\boldsymbol q}}$ ${\boldsymbol {\overline{\boldsymbol q}}}$ states) INSPIRE search # ${{\boldsymbol \eta}_{{c}}{(2S)}}$ $I^G(J^{PC})$ = $0^+(0^{- +})$ Quantum numbers are quark model predictions. ${{\mathit \eta}_{{c}}{(2S)}}$ MASS $3637.5 \pm1.1$ MeV (S = 1.2) ${{\mathit \eta}_{{c}}{(2S)}}$ WIDTH $11.3 {}^{+3.2}_{-2.9}$ MeV	2020-10-26T22:46:44	{"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": 0.9870617389678955, "perplexity": 8691.333312632965}, "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-2020-45/segments/1603107892062.70/warc/CC-MAIN-20201026204531-20201026234531-00130.warc.gz"}
https://par.nsf.gov/biblio/10372860-selection-substellar-companions-nearby-stars	3D Selection of 167 Substellar Companions to Nearby Stars Abstract We analyze 5108 AFGKM stars with at least five high-precision radial velocity points, as well as Gaia and Hipparcos astrometric data, utilizing a novel pipeline developed in previous work. We find 914 radial velocity signals with periods longer than 1000 days. Around these signals, 167 cold giants and 68 other types of companions are identified, through combined analyses of radial velocity, astrometry, and imaging data. Without correcting for detection bias, we estimate the minimum occurrence rate of the wide-orbit brown dwarfs to be 1.3%, and find a significant brown-dwarf valley around 40MJup. We also find a power-law distribution in the host binary fraction beyond 3 au, similar to that found for single stars, indicating no preference of multiplicity for brown dwarfs. Our work also reveals nine substellar systems (GJ 234 B, GJ 494 B, HD 13724 b, HD 182488 b, HD 39060 b and c, HD 4113 C, HD 42581 d, HD 7449 B, and HD 984 b) that have previously been directly imaged, and many others that are observable at existing facilities. Depending on their ages, we estimate that an additional 10–57 substellar objects within our sample can be detected with current imaging facilities, extending the imaged cold more » Authors: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more » Publication Date: NSF-PAR ID: 10372860 Journal Name: The Astrophysical Journal Supplement Series Volume: 262 Issue: 1 Page Range or eLocation-ID: Article No. 21 ISSN: 0067-0049 Publisher: DOI PREFIX: 10.3847 National Science Foundation ##### More Like this 1. Abstract The detection of satellites around extrasolar planets, so called exomoons, remains a largely unexplored territory. In this work, we study the potential of detecting these elusive objects from radial velocity monitoring of self-luminous, directly imaged planets. This technique is now possible thanks to the development of dedicated instruments combining the power of high-resolution spectroscopy and high-contrast imaging. First, we demonstrate a sensitivity to satellites with a mass ratio of 1%–4% at separations similar to the Galilean moons from observations of a brown-dwarf companion (HR 7672 B;Kmag= 13; 0.″7 separation) with the Keck Planet Imager and Characterizer (R∼ 35,000 in theKband) at the W. M. Keck Observatory. Current instrumentation is therefore already sensitive to large unresolved satellites that could be forming from gravitational instability akin to binary star formation. Using end-to-end simulations, we then estimate that future instruments such as the Multi-Object Diffraction-limited High-resolution Infrared Spectrograph, planned for the Thirty Meter Telescope, should be sensitive to satellites with mass ratios of ∼10−4. Such small moons would likely form in a circumplanetary disk similar to the Jovian satellites in the solar system. Looking for the Rossiter–McLaughlin effect could also be an interesting pathway to detecting the smallest moons on short orbitalmore » 2. Abstract Benchmark brown dwarf companions with well-determined ages and model-independent masses are powerful tools to test substellar evolutionary models and probe the formation of giant planets and brown dwarfs. Here, we report the independent discovery of HIP 21152 B, the first imaged brown dwarf companion in the Hyades, and conduct a comprehensive orbital and atmospheric characterization of the system. HIP 21152 was targeted in an ongoing high-contrast imaging campaign of stars exhibiting proper-motion changes between Hipparcos and Gaia, and was also recently identified by Bonavita et al. (2022) and Kuzuhara et al. (2022). Our Keck/NIRC2 and SCExAO/CHARIS imaging of HIP 21152 revealed a comoving companion at a separation of 0.″37 (16 au). We perform a joint orbit fit of all available relative astrometry and radial velocities together with the Hipparcos-Gaia proper motions, yielding a dynamical mass of$24−4+6MJup$, which is 1–2σlower than evolutionary model predictions. Hybrid grids that include the evolution of cloud properties best reproduce the dynamical mass. We also identify a comoving wide-separation (1837″ or 7.9 × 104au) early-L dwarf with an inferred mass near the hydrogen-burning limit. Finally, we analyze the spectra and photometry of HIP 21152 B using the Saumon & Marley (2008)more » 3. Abstract We observed HD 19467 B with JWST’s NIRCam in six filters spanning 2.5–4.6μm with the long-wavelength bar coronagraph. The brown dwarf HD 19467 B was initially identified through a long-period trend in the radial velocity of the G3V star HD 19467. HD 19467 B was subsequently detected via coronagraphic imaging and spectroscopy, and characterized as a late-T type brown dwarf with an approximate temperature ∼1000 K. We observed HD 19467 B as a part of the NIRCam GTO science program, demonstrating the first use of the NIRCam Long Wavelength Bar coronagraphic mask. The object was detected in all six filters (contrast levels of 2 × 10−4to 2 × 10−5) at a separation of 1.″6 using angular differential imaging and synthetic reference differential imaging. Due to a guide star failure during the acquisition of a preselected reference star, no reference star data were available for post-processing. However, reference differential imaging was successfully applied using synthetic point-spread functions developed from contemporaneous maps of the telescope’s optical configuration. Additional radial velocity data (from Keck/HIRES) are used to constrain the orbit of HD 19467 B. Photometric data from TESS are used to constrain the properties of the host star, particularly its age. NIRCammore » 4. Abstract Model-independent masses of substellar companions are critical tools to validate models of planet and brown dwarf cooling, test their input physics, and determine the formation and evolution of these objects. In this work, we measure the dynamical mass and orbit of the young substellar companion HD 984 B. We obtained new high-contrast imaging of the HD 984 system with Keck/NIRC2 that expands the baseline of relative astrometry from 3 to 8 yr. We also present new radial velocities of the host star with the Habitable-Zone Planet Finder spectrograph at the Hobby-Eberly Telescope. Furthermore, HD 984 exhibits a significant proper motion difference between Hipparcos and Gaia EDR3. Our joint orbit fit of the relative astrometry, proper motions, and radial velocities yields a dynamical mass of 61 ± 4MJupfor HD 984 B, placing the companion firmly in the brown dwarf regime. The new fit also reveals a higher eccentricity for the companion (e= 0.76 ± 0.05) compared to previous orbit fits. Given the broad age constraint for HD 984, this mass is consistent with predictions from evolutionary models. HD 984 B’s dynamical mass places it among a small but growing list of giant planet and brown dwarf companions with direct massmore » 5. Abstract We explore the fascinating eclipses and dynamics of the compact hierarchical triple-star system KOI-126 (KIC 5897826). This system is composed of a pair of M-dwarf stars (KOI-126 B and C) in a 1.74 day orbit that revolve around an F star (KOI-126 A) every 34 days. Complex eclipse shapes are created as the M stars transit the F star, due to two effects: (1) the duration of the eclipse is a significant fraction of the M-star orbital period, so the prograde or retrograde motion of the M stars in their orbit lead to unusually short or long duration eclipses; (2) due to 3-body dynamics, the M-star orbit precesses with an astonishingly quick timescale of 1.74 yr for the periastron (apsidal) precession, and 2.73 yr for the inclination and nodal angle precession. Using the full Kepler data set, supplemented with ground-based photometry, plus 29 radial velocity measurements that span 6 yr, our photodynamical modeling yields masses ofMA= 1.2713 ± 0.0047M(0.37%),MB= 0.23529 ± 0.00062M(0.26%), andMC= 0.20739 ± 0.00055M(0.27%) and radii ofRA= 1.9984 ± 0.0027R(0.14%),RB= 0.25504 ± 0.00076R(0.3%), andRC= 0.23196 ± 0.00069R(0.3%). We also estimate the apsidal motion constant of the M dwarfs, a parameter that characterizes the internal mass distribution. Althoughmore »	2023-03-20T09:53:03	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 5, "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": 0.6284297704696655, "perplexity": 5288.108500400228}, "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/1679296943471.24/warc/CC-MAIN-20230320083513-20230320113513-00735.warc.gz"}
https://nroer.gov.in/55ab34ff81fccb4f1d806025/file/58872394472d4a1fef8115d6	### Reaction Of Sodium Chloride With Sulphuric Acid: The aim of this reaction is to observe the reaction of sodium chloride with sulphuric acid. Let's see what happens next. License:[Source CIET, NCERT ]Feb. 20, 2017, 11:45 a.m.	2020-02-25T02:03:35	{"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": 0.9373248815536499, "perplexity": 6196.245901800491}, "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-2020-10/segments/1581875146004.9/warc/CC-MAIN-20200225014941-20200225044941-00462.warc.gz"}
https://math-physics-problems.wikia.org/wiki/Doppler_Effect	267 Pages ## Problem A police siren emits a frequency of 640 Hz. When the police car approaches you at a speed of 25 m/s, what frequency do you perceive when: 1) you are not moving 2) you are moving towards the police car at 5 m/s 3) you are moving away from the police car at 5 m/s. Assume the speed of sound is 343 m/s. ## Solution Use the doppler shift formula $f = f_0 \left(\frac{v \pm v_r}{v \pm v_s}\right)$ where $f$ is the shifted frequency, $f_0$ is the frequency of the source, $v$ is the speed of sound, $v_r$ is the speed of the receiver, and $v_s$ is the speed of the source. Part 1 $f = f_0 \left(\frac{v}{v - v_s}\right)$ $f = 640 \left(\frac{343}{343 - 25}\right)$ $f = 690 \: Hz$ Part 2 $f = f_0 \left(\frac{v + v_r}{v - v_s}\right)$ $f = 640 \left(\frac{343 + 5}{343 - 25 }\right)$ $f = 700.38 \: Hz$ Part 3 $f = f_0 \left(\frac{v - v_r}{v - v_s}\right)$ $f = 640 \left(\frac{343 - 5}{343 - 25 }\right)$ $f = 680.25 \: Hz$ Community content is available under CC-BY-SA unless otherwise noted.	2020-11-29T02:25:10	{"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": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6112251281738281, "perplexity": 530.4315526838748}, "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-2020-50/segments/1606141195967.34/warc/CC-MAIN-20201129004335-20201129034335-00282.warc.gz"}
https://bison.inl.gov/Documentation/source/materials/tensor_mechanics/U3Si2CreepUpdate.aspx	# Uvar element = document.getElementById("moose-equation-532453a6-b1f3-47fa-9e98-94218d7d891b");katex.render("_3", element, {displayMode:false,throwOnError:false});Sivar element = document.getElementById("moose-equation-4208116e-ec4b-4beb-aa97-03882f7644d0");katex.render("_2", element, {displayMode:false,throwOnError:false}); Thermal Creep Update Calculates the thermal creep behavior of U3Si2 fuel. This material must be run in conjunction with ComputeMultipleInelasticStress. ## Description Thermal creep of USi fuel is calculated by the U3Si2CreepUpdate model. This model must be run in conjunction with ComputeMultipleInelasticStress. The thermal creep correlation is in the form of an Arrhenius law based upon experiments completed at the University of South Carolina. Details of the derivation of the pre-exponential constant, stress exponent, and activation energy can be found in Freeman et al. (2018). The creep rate is given by: (1) where is the ideal gas constant with a value of 8.314 J/mol-K and is the temperature in Kelvin. ## Example Input Syntax [./u3si2creep] type = U3Si2CreepUpdate block = 1 temperature = temp [../] (test/tests/tensor_mechanics/u3si2_creep/thermal_creep_u3si2.i) U3Si2CreepUpdate must be run in conjunction with the inelastic strain return mapping stress calculator as shown below: [./stress] type = ComputeMultipleInelasticStress tangent_operator = elastic inelastic_models = 'u3si2creep' block = 1 [../] (test/tests/tensor_mechanics/u3si2_creep/thermal_creep_u3si2.i) ## Input Parameters • temperatureThe coupled temperature (K) C++ Type:std::vector Description:The coupled temperature (K) ### Required Parameters • max_inelastic_increment0.0001The maximum inelastic strain increment allowed in a time step Default:0.0001 C++ Type:double Description:The maximum inelastic strain increment allowed in a time step • base_nameOptional parameter that defines a prefix for all material properties related to this stress update model. This allows for multiple models of the same type to be used without naming conflicts. C++ Type:std::string Description:Optional parameter that defines a prefix for all material properties related to this stress update model. This allows for multiple models of the same type to be used without naming conflicts. • max_its30Maximum number of Newton iterations Default:30 C++ Type:unsigned int Description:Maximum number of Newton iterations • acceptable_multiplier10Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress Default:10 C++ Type:double Description:Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress • absolute_tolerance1e-11Absolute convergence tolerance for Newton iteration Default:1e-11 C++ Type:double Description:Absolute convergence tolerance for Newton iteration • boundaryThe list of boundary IDs from the mesh where this boundary condition applies C++ Type:std::vector Description:The list of boundary IDs from the mesh where this boundary condition applies • relative_tolerance1e-08Relative convergence tolerance for Newton iteration Default:1e-08 C++ Type:double Description:Relative convergence tolerance for Newton iteration • blockThe list of block ids (SubdomainID) that this object will be applied C++ Type:std::vector Description:The list of block ids (SubdomainID) that this object will be applied ### Optional Parameters • activation_energy_scale_factor1Scale factor to be applied to the thermal creep activation energy. Used for calibration and sensitivity studies. Default:1 C++ Type:double Description:Scale factor to be applied to the thermal creep activation energy. Used for calibration and sensitivity studies. • stress_exponent_scale_factor1Scale factor to be applied to the thermal creep stress exponent. Used for calibration and sensitivity studies. Default:1 C++ Type:double Description:Scale factor to be applied to the thermal creep stress exponent. Used for calibration and sensitivity studies. • pre_exponential_scale_factor1Scale factor to be applied to the thermal creep exponential prefactor. Used for calibration and sensitivity studies. Default:1 C++ Type:double Description:Scale factor to be applied to the thermal creep exponential prefactor. Used for calibration and sensitivity studies. • effective_inelastic_strain_nameeffective_creep_strainName of the material property that stores the effective inelastic strain Default:effective_creep_strain C++ Type:std::string Description:Name of the material property that stores the effective inelastic strain • enableTrueSet the enabled status of the MooseObject. Default:True C++ Type:bool Description:Set the enabled status of the MooseObject. • 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 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 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 Description:The seed for the master random number generator • implicitTrueDetermines whether this object is calculated using an implicit or explicit form Default:True C++ Type:bool Description:Determines whether this object is calculated using an implicit or explicit form • constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped Default:NONE C++ Type:MooseEnum Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped • internal_solve_output_onon_errorWhen to output internal Newton solve information Default:on_error C++ Type:MooseEnum Description:When to output internal Newton solve information • internal_solve_full_iteration_historyFalseSet true to output full internal Newton iteration history at times determined by internal_solve_output_on. If false, only a summary is output. Default:False C++ Type:bool Description:Set true to output full internal Newton iteration history at times determined by internal_solve_output_on. If false, only a summary is output. ### Debug Parameters • output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type) C++ Type:std::vector Description:List of material properties, from this material, to output (outputs must also be defined to an output type) • outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object Default:none C++ Type:std::vector Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object ## References 1. R. A. Freeman, T. Martin, E. Roberts, and T. W. Knight. Analysis of thermal creep for uranium silicide fuel using Bison. In Proceedings of the 2018 International Congress on Advances in Nuclear Power Plants (ICAPP 18). Charlotte, NC, 2018.[BibTeX]	2020-12-04T05:59:42	{"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": 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": 0.368560791015625, "perplexity": 4716.444974644061}, "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-2020-50/segments/1606141733122.72/warc/CC-MAIN-20201204040803-20201204070803-00493.warc.gz"}
https://gradschool.ncbj.gov.pl/seminars-2020-2021/	# Seminars in 2022/23 ## 12 May 2022 Speaker: Anatolii Koval (Studium Doktoranckie NCBJ) Title: How does one look inside of the proton? Abstract: Presently Generalized Parton Distributions allow us novel three-dimensional description of the proton structure when both transverse and longitudinal degrees of freedom are taken into account. A tool to experimentally constraint GPDs is Deeply Virtual Compton Scattering. Main steps in extracting DVCS cross-section in the framework of COMPASS experiment are discussed in detail hinting path towards the proton tomography. ## 5 May 2022 Speaker: Krzysztof Jodłowski (Studium Doktoranckie NCBJ) Title: Indirect detection of long-lived particles in a less-simplified dark Higgs portal Abstract: Simplified models of light new physics are an important theoretical and experimental benchmark. Models that extend minimal scenarios by introducing other degrees of freedom are well motivated ways to go beyond the Standard Model (SM). In this talk, I will focus on the light dark Higgs portal that connects the dark sector consisting of, e.g., TeV-scale secluded dark matter (DM) with the SM. I will illustrate the phenomenology of this model, focusing on the signatures of DM and long-lived particles (LLP) in complementary experimental searches. These include i) the intensity frontier searches for light new physics, ii) indirect detection (ID) of secluded WIMPs, and iii) future CMB radiation surveys. Finally, I will highlight the important role of non-local effects present in the ID of LLPs which significantly affects the detection strategies, usually tailored to WIMPs. These effects include a) an additional contribution to the photon flux due to the “GC diffusion” effect, b) a linear flux decrease in the long-lived regime due to finite DM density support, and c) a faster flux decrease with LLP decay length for observations focused on small regions of interest, compared to large ones. ## 28 April 2022 Speaker: Michał Mazurek (Szkoła Doktorska NCBJ) Title: Fast simulation interface and custom datasets in Gaussino Abstract: Monte Carlo simulations are key to the design and commissioning of new detectors as well as the interpretation of physics measurements. A new version of the LHCb Gauss simulation framework has been developed to better accommodate new simulation techniques and software technologies to produce the necessary samples required for the Run 3 physics program of the LHCb experiment. It provides the LHCb-specific functionality while the generic simulation infrastructure has been encapsulated in an experiment-independent framework, Gaussino. In this talk, I am going to present the fast simulation interface, the latest feature in Gaussino developed to interact with Geant4 to replace its detailed description of physics processes with fast simulation models. I will also present how the built-in mechanism that handles an additional geometry at configuration time can be used to produce custom datasets and, in particular, training and validation datasets for fast simulation models. ## 21 April 2022 Speaker: Grzegorz Żarnecki (Studium doktoranckie NCBJ) Title: Cross section measurement of the charged current muon antineutrino single π- production at T2K Abstract: T2K experiment is a long baseline neutrino oscillation experiment in Japan. Cross section measurements of (anti)neutrino interactions in sub-GeV to few GeV energy range allow to constrain the systematic uncertainties in the oscillation analysis. Single charged pion production is a relevant interaction mode at this energy scale. The biggest contribution to that mode is due to the baryonic resonance interaction, coherent interaction and deep inelastic scattering. In this seminar I will present the cross section measurement of single π- production in muon antineutrino CC interaction on hydrocarbon. The cross section is reported as double-differential in muon kinematical variables i.e. momentum and cosine of the muon emission polar angle. ## 7 April 2022 Speaker: Mahmoud Hamed (Szkoła Doktorska NCBJ) Title: Reverse-engineering galaxy spectra to decode the IRX-β relation at intermediate redshift Abstract: n galaxies, different components interact with each other on various timescales. An example of such interaction is the interplay between young and as well evolved stars with dust. This complex interplay influences the total spectra of galaxies. Dust affects the shape of the spectral energy distribution (SED) like no other component, despite its low contribution to the overall mass of the baryonic matter. At higher redshifts, the challenging measurements of FIR emission are overpowered by the easily available rest-frame UV emission. This in turn limits the wavelength range from which the physical properties are inferred, therefore, a correct understanding of physical processes that prevail at short wavelength domain, like dust attenuation, becomes critical. Observationally, many galaxies seem to follow what is known as the IRX-β relation, which links heavily-attenuated UV spectral slope (β) and the IR excess of galaxies characterised by the ratio between the IR (mainly dust) and UV (mostly composed of young stars) luminosities (L(FIR)/L(UV)). However, this relation is not universal, and outliers for it are often encountered. Understanding such relation and its connection to dust attenuation properties will help us uncover and understand the role of dust, and its attenuation at higher redshifts. Our study used a unique dataset from the “VIMOS Public Extragalactic Redshift Survey” (VIPERS), which mapped in detail 24 deg2 of the sky sampling galaxies at redshift~0.7. We use the robust Oii, Oiii, and Hβ line detections of our statistical sample from VIPERS to estimate the gas-phase metallicities at the redshift range 0.5<z<0.9. We derive key physical properties that are necessary to study galaxy evolution, such as the stellar masses and the star formation rates, from the SED fitting tool CIGALE. We find a strong dependence of the IRX-β relation on gas-phase metallicity in our sample and dependencies on stellar properties of galaxies like stellar ages, stellar masses, and specific star formation rates. We have also checked morphological parameters, and we find that the compactness of our sources characterised by the Sérsic indexes is also sensitive to the location on the IRX-β plane. ## 31 March 2022 Speaker: Francesco PISTIS (Szkoła Doktorska NCBJ) Title: The FMR up to z~0.7: investigating different methods Abstract: The studies of galaxy metallicity — as the outcome of the integrated star formation history and the evolution of the interstellar medium — can constrain the description of galaxy evolution. This subject has been widely studied in the local Universe, in particular using data from the Sloan Digital Sky Survey (SDSS). In this project, we develop such studies up to redshift z~0.7 with the data from VIMOS Public Extragalactic Redshift Survey (VIPERS) and quantify its possible evolution with high statistical precision. We test different methods to study the Fundamental Metallicity Relation (FMR) and compare samples to review if they can lead to the same conclusions on the metallicity evolution between different samples, showing the pros/cons of each method and analogies/dissimilarities between them. We built two control samples by cross-matching all SDSS galaxies on physical properties (stellar mass and star formation rate) and galaxy type. We compare three different methods: i) the different projections of the FMR, ii) a non-parametric method, and iii) an “evolutionary” method. The biggest result of the control sample on physical properties is to show the same projection of the data at z~0.7 in the metallicity vs SFR plane. Both the direct difference in metallicity — in each stellar mass-SFR bin between the local and intermediate redshift sample — and the non-parametric method show an increasing difference with increasing stellar mass, while the “evolutionary’’ method shows the samples diverging at lower stellar masses. ## 24 March 2022 Speaker: Jaime de Cabo Martin (Szkoła Doktorska NCBJ) Title: Inequivalent Quantum Cosmological bouncing models and the primordial structure Abstract: By quantising the background as well as the perturbations in a simple one fluid cosmological model, we show that there exists an ambiguity in the choice of relevant variables, potentially leading to incompatible observational physical predictions. In a classical inflationary background, the exact same canonical transformations lead to unique predictions, so the ambiguity we put forward demands a semiclassical background with a sufficiently strong departure from classical evolution. The latter condition is clearly satisfied by bouncing models. We propose coherent states as the tool for introducing the semiclassical universe. We solve the quantum dynamics of the perturbation modes both analytically and numerically and investigate the amplitude spectra of the perturbations. We study the underlying quantum state, the Bunch-Davies vacuum, from the point of view of late-time observers by means of the Bogolyubov transformations. In particular, we study the phase space probability distributions obtained with the standard coherent states built from instantaneous vacua. We discuss the issue of the temporal phase shift with which the modes emerge from the bounce as sine waves. Finally, we find that the model may be fitted to data and shed light on the physical universe, constraining free parameters of the bouncing universe. ## 17 March 2022 Speaker: Arantxa Tymowska (Szkoła Doktorska NCBJ) Title: DIS dijet production beyond eikonal accuracy Abstract: We derive subeikonal corrections to the quark propagator assuming that the quark is propagating through the whole medium in order to study DIS dijet production. We take into account NEik (Next-to-Eikonal) corrections from previous results for splitting before the medium and we calculate a new contribution coming from splitting inside the medium at NEik. This time we include not only corrections that contribute to Next-to-Eikonal accuracy that are due to considering a finite longitudinal width target and the interaction of the quark with the transverse component of the background field, here we also include the dynamics of the target. We then apply these corrections to the DIS dijet cross section for both inclusive and diffractive production. ## 10 March 2022 Speaker: Gabriele Riccio (Szkoła Doktorska NCBJ) Title: Star formation rate measurement in astrophysics Abstract: Star formation is one of the main mechanisms of energy production in the universe and one of the key processes that are linked to the evolution of galaxies. Over the past two decades we have witnessed an explosion of data from local and distant galaxies across the entire electromagnetic spectrum. These observations gave us an unprecedented picture of the star-forming activity in galaxies, the parameters it depends on (e.g. gas content, physical conditions in the interstellar medium, dynamical state of galaxies), and its evolution over cosmic time. The common denominator in all these studies is the use of diverse techniques for quantifying the recent star-forming activity in the different environments. The purpose of this talk is to provide an introduction of the methods used to measure the intensity of star-forming activity in galaxies (their star-formation rates), focusing on spectral energy distribution (SED) fitting methods and star formation rate evaluation from the galaxy X-ray emission. In this context, I will discuss my PhD project, dividing it into two parts: 1) how the upcoming Legacy Survey of Space and Time (LSST) data from the Vera C. Rubin Observatory can be employed, using SED fitting methods, to constrain the physical properties of normal star-forming galaxies (main-sequence galaxies); 2) Modeling of the X-ray emission and probing of X-ray luminosity versus star formation rate relation in galaxies. ## 3 March 2022 Speaker: Kamil Skwarczyński (Szkoła Doktorska NCBJ) Title: T2K Near Detector Fit Abstract: T2K (Tokai to Kamioka) is a long-baseline neutrino oscillation experiment located in Japan. One of the most challenging tasks of T2K is to study whether CP is violated in the lepton sector, which is suggested by recent T2K results. By utilizing the near detector (ND280) data, T2K can constrain neutrino interaction and flux uncertainties by fitting a parameterized model to data. This allows for a significant reduction of the systematic uncertainties in neutrino oscillation analyses. One of two fitters responsible for ND fit uses Bayesian Markov Chain Monte Carlo (MCMC) method. New T2K ND fit introduces many improvements, including new samples with proton and photon tag. Talk will present preliminary T2K results and method used including posteriori predictive distribution etc. ## 27 January 2022 Speaker: Artem Poliszczuk (Studium Doktoranckie NCBJ) Title: Introduction to Reverberation Mapping of Active Galactic Nuclei Abstract: During my presentation I will describe main concepts, observational results and open questions of Active Galactic Nuclei (AGN) reverberation mapping. Angular size of vast majority of active galaxy centers is way to small to be spatially resolved by modern instruments and thus cannot be directly observed via traditional methods. The reverberation mapping method allows to use variability properties of AGN to swap spatial resolution to time resolution and directly test vicinity of supermassive black holes in the centers of galaxies. Rapid development of reverberation mapping studies in the past two decades makes it a very promising tool for galaxy evolution and observational cosmology. ## 20 January 2022 Speaker: Hareesh Thuruthipilly (Szkoła Doktorska NCBJ) Title: Self-attention based encoder models for strong lens detection Abstract: The upcoming large scale surveys are expected to find approximately 10^5 strong gravitational systems by analysing data of many orders of magnitude larger than the current era. In this scenario, non-automated techniques will be highly challenging and time-consuming. We propose a new automated architecture based on self-attention, which can substitute the currently used CNNs to find strong gravitational lenses. The advantages of self-attention-based encoder models over convolution neural networks are investigated and encoder models are analysed to optimise performance using the data from the Bologna Lens Challenge. From our study, we pointed out that self-Attention-based models have a clear advantage compared to simpler CNNs. A low computational cost and complexity make it a highly competing architecture to currently used CNN architecture. Moreover, introducing the encoder layers can also tackle the over-fitting problem present in the CNN’s by acting as effective filters and providing better stability for the network. ## 13 January 2022 Speaker: Nora Salone (Szkoła Doktorska NCBJ) Title: The physics case for the CP-violation tests in hyperon decays at SCTF far detector Abstract: The observed matter-antimatter asymmetry in our universe can be explained theorizing the violation of the combined charge-conjugation–parity symmetry (CP), of which non-leptonic two-body weak decays of baryons are an important probe. We explain how and why the decays of strange baryons provide complementary information to the decays of kaons. We present a model-independent paramerization of the non-leptonic decays of the Λ- and Ξ-baryons produced at the at the next generation electron–positron J/ψ factories with luminosity of 10^35 cm^−2 s^−1. Using analytic approximations and numerical calculations we study the quantitative impact of spin correlations and polarization in CP tests built from the produced, spin-entangled hyperon-antihyperon pairs. We show that by using a longitudinally-polarized electron beam the statistical precision of the CP tests can be significantly improved. Furthermore, we map out further directions for possible improvements, like analysis of incompletely reconstructed events or a combination of the isospin related processes. Altogether these methods are promising for the observation of a statistically significant CP-violation signal with a strength corresponding to the standard model predictions. Finally, our results call for an update of the theory predictions with increased precision. ## 16 December 2021 Speaker: Yashwanth Prabhu (Szkoła Doktorska NCBJ) Title: Development of a multiring electron neutrino sample at the T2K far detector Abstract: The Tokai to Kamioka (T2K) experiment is a long-baseline accelerator neutrino experiment that measures electron neutrino appearance and muon neutrino disappearance from a muon neutrino beam by observing neutrino events at the near and far detectors. T2K uses the Super Kamiokande (SK) as the far detector, which is a 50-kilo ton water-Cherenkov detector that observes Cherenkov rings from charged particles produced in neutrino interactions with water. In the present oscillation analyses, T2K uses only single-ring electron neutrino events detected at SK. These single-ring events are dominated by charged current quasielastic interactions. Charged-current single pion events form the second most dominant signal events in electron neutrino appearance studies. In this mode, there can be two rings coming from electron and charged pion if the latter has a momentum above the Cherenkov threshold. The sample with no ring from the charged pion is already included in the oscillation analysis. My study is aimed at developing selection cuts for including the sample with two Cherenkov rings. Being the second most dominant signal event, its inclusion in the samples can increase the statistics of electron neutrino events at SK and possibly improve sensitivity to the CP violation phase. ## 9 December 2021 Speaker: Michał Jędrzejczyk (Szkoła Doktorska NCBJ) Title: Applying Approximate Bayesian Computation to reduce nuclear data uncertainties Abstract: The multiplication factor (keff) is a key parameter describing the dynamics of nuclear reactors. The uncertainty in its calculated value usually amounts to 1-2 %, measured in one relative standard deviation. It mostly originates from the imprecision with which neutron cross sections are known. 1 % in keff uncertainty is a lot. Reduction of this value would open a possibility to create more optimal nuclear reactor designs. There is a large database of well documented criticality benchmark experiments with precisely measured keff. It is called “International Handbook of Evaluated Criticality Safety Benchmark Experiments” and it is maintained by Nuclear Energy Agency. The goal of my research is to use the results of these experiments to decrease the uncertainties of neutron cross sections. In order to do that I will use a statistical tool called Approximate Bayesian Computation (ABC) and a criticality simulation software SCALE. In this seminar, I will discuss neutron cross section uncertainties and other nuclear data deficiencies. I will give an introduction to ABC and present a simple example of how it can be used to reduce uncertainties of any mathematical model parameters. I will then show how I am going to apply it to reduce neutron cross sections’ uncertainties (which are parameters in keff calculations). Finally, I will discuss to what extent we can reduce calculated keff uncertainties this way. ## 2 December 2021 Speaker: Luis Eduardo Suelves (Szkoła Doktorska NCBJ) Title: Photometry-based merger identification through Neural Network. Abstract: The evolution and dynamics of the galactic population are key elements for modeling the Universe history and structure. Within the Cold Dark Matter model, the gravitational pull between galaxies can lead to mergers: hierarchical growth interactions in which one galaxy “collides” with another, combining their stellar population, interstellar dust, and dark matter halos. This is likely to enhance the stellar formation in the daughter galaxy, influence its evolutionary history and modify strongly the shape of the original galaxies during the process. Identifying galaxy mergers (and galaxy morphologies in general) is a very elementary modern astronomy problem, and it is crucial to understand these phenomena, their time scale, and their implications. I will present the projects I have been working on during my PhD. I have been working on galaxy mergers classification by means of Machine Learning methods, using real astronomical images (Pearson, Suelves at al. 2021, submitted to A&A) and photometric measurements (Suelves et al. 2021, in preparation) ## 25 November 2021 Speaker: Mateusz Kmieć (Szkoła Doktorska NCBJ) Title: Practical Experimental Sensitivity for New Physics Discovery in LHC Abstract: Before announcing a discovery in particle physics we need to answer two fundamental questions. Firstly, we should ask ourselves what is the goodness of fit of our result to the tested theory (e.g. the Standard Model). Secondly, we need to check how well our measurement is described by the alternate theory (e.g. Beyond the Standard Model). In other words, we need to establish if our measurement is congruent with the chosen model and find the experimental sensitivity to discovery in the process of hypothesis testing. The sensitivity of an experiment is usually reported as the expected significance. It is typically obtained for a series of hypothesis tests on an ensemble of simulated data. In my current research work, I am trying to establish the sensitivity of high luminosity experiments such as LHCb to CPT violation (CPTV) measurement with neutral meson oscillations. In this seminar, I will present methods for finding the expected significance with which one would be able to reject different values of CPTV parameter. I will present both the approach employing the Monte Carlo (MC) simulations (computationally expensive) as well as approximate methods allowing us to obtain the expected significance without the need of performing weary MC simulations. ## 18 November 2021 Speaker: Victor Martínez-Fernández (Szkoła Doktorska NCBJ) Title: Inclusive and exclusive inelastic processes in QCD Abstract: For a long time, it was believed that fundamental constituents of atoms were electrons and nucleons until experiments conducted in the 1960s at Standford Linear Accelerator Center (SLAC) proved the existence of internal dynamics in the nucleons. With QCD as the fundamental theory for hadrons, we can describe hadronic structure via correlations between some degrees of freedom that we call quarks and gluons, collectively partons. The non-elementary nature of hadrons makes these correlators perturbatively unsolvable so we can only measure or model them. In this seminar, I review and compare 2 of these correlators/distributions, namely PDF and GPD, and discuss how to study phenomenology of a particular exclusive inelastic process (double deeply virtual Compton scattering) in order to extract information on the partonic distributions beyond leading-order accuracy. ## 4 November 2021 Speaker: Maitrayee Mandal (Szkoła Doktorska) Title: Detection of Tau Neutrinos at the Super-Kamiokande Experiment Abstract: The Super-Kamiokande experiment (SK) is the famed water Cherenkov detector which discovered the oscillation of atmospheric neutrinos. As a result of the oscillation of atmospheric muon neutrinos, tau neutrinos are expected to appear. Therefore, direct detection of tau neutrinos in the flux of atmospheric neutrinos provides unambiguous confirmation of the phenomenon of neutrino oscillation. In 2018, SK excluded the hypothesis of no tau appearance with a significance level of 4.6��. SK used machine learning techniques of neural networks (NNs) to classify the tau charged-current interactions from the interactions of the atmospheric muon and electron neutrinos. My research involves upgrading the NN for better classification. In particular, the signatures to classify these interactions are expected to be seen in neutrons, which are copiously produced in the particle showers arising from the tau and atmospheric neutrino interactions. So far, information related to neutrons has not been used at SK for discerning tau neutrinos. The prospect of expanding the NN with new inputs pertaining to neutron captures is under consideration, owing to the enhanced detection of neutrons with the recent addition of gadolinium in SK. Preliminary results show that this additional information shall improve the NN classification, and hence, the detection of tau neutrinos. ## 28 October 2021 Speaker: Paritosh Verma (Studium Doktoranckie NCBJ) Title: Probing GWs from pulsars in Brans-Dicke theory Abstract: A coupling constant determines how much force will be exerted in a given interaction. In renormalized I shall discuss the results of our recent paper on gravitational waves (GWs) from spinning neutron stars in Brans-Dicke (BD) theory. The BD theory attempts to modify the GR by varying gravitational constant G, and it has three polarization states. The first two states are the same as in GR, and the third is scalar polarization. We derive the response of a laser interferometric detector to the GW signal from a spinning neutron star in BD theory. We obtain a statistic based on the maximum likelihood principle to identify the signal in BD theory in the detector’s noise. This statistic generalizes the well known F-statistic used in the case of GR. We perform Monte Carlo simulations in Gaussian noise to test the detectability of the signal and the accuracy of estimation of its parameters. Finally, I shall present the total power radiated away in this theory and analytical formula to obtain the maximum limit of dipole amplitude. ## 21 October 2021 Speaker: Souvik Mondal (Szkoła Doktorska) Title: Vector Like extension of Standard Model Abstract: A coupling constant determines how much force will be exerted in a given interaction. In renormalized perturbation theory, a coupling receives contributions from higher-order loop diagrams. Therefore, one can define the effective coupling as the sum of tree-level coupling and all higher-order contributions. The goal of the project is to find the Zff effective coupling. At the tree level this coupling is determined by the electroweak gauge coupling and the quantum numbers of the fermion. The loop corrections in the Standard Model are known and consistent with the experimental measurements. That is not the case for a generic BSM scenario, where the contributions to the effective coupling need to be calculated and confronted with the data. In my talk, I will discuss contributions to Zff effective coupling in a class of BSM scenarios considering vector-like fermions. I will also show how these results could be used to indirectly look for the New Physics. ## 14 October 2021 Speaker: Patrycja Dyrcz (Studium Doktoranckie NCBJ) Title: Radiological characterization of metallic waste from particle accelerators for disposal after melting Abstract: The operation of high-energy particle accelerators like the ones at the European Organization for Nuclear Research (CERN) leads to the unavoidable production of radioactive materials. Activated materials that cannot be reused or recycled need to be disposed of in dedicated disposal facilities for radioactive waste. In this presentation, I describe a novel radiological characterization method of low and intermediate level (LL and IL) metallic waste produced at CERN, which will be melted into ingots at an external facility prior to disposal. I will give an overview of the main challenges and technical solutions associated with the radiological characterization at CERN: in-situ gamma spectrometry of massive items with multiple counting and dose-rate levels above 100 uSv/h at contact, modeling of activity concentrations in the spectrometry analyses, validation of scaling factors for LL and IL waste based on the analytical calculations and Monte Carlo simulations, and self-attenuation in waste packages. In addition, I will identify operational activity limits which take into account the acceptance criteria of the melting facility and of the final repositories, as well as the uncertainties associated with the characterization methodology. ## 10 June 2021 Speaker: Szymon Nakoneczny (Studium Doktoranckie NCBJ) Title: Large Scale Structure and Cosmic Microwave Background in study of the Universe Abstract: Astrophysicists are now facing some of the biggest mysteries in science. Dark Matter (DM), which interacts only gravitationally and makes up to about 27% of the Universe, and Dark Energy (DE), which accelerates expansion of the Universe and makes up to about 68% of it, both fit to the theoretical model, but we do not understand their nature. On the other hand, we measure different values of cosmic parameters from different probes, which creates cosmic tension not explainable by any known theory. In my talk, I will describe how observations of the Large Scale Structure (LSS) and Cosmic Microwave Background (CMB) are used to shed light on these unknown problems. I will explain the concept of the epoch of recombination, in which the CMB originates, and give an introduction to the theory of the gravitational collapse which led to the development of the LSS. Then, I will give an introduction to Integrated Sachs-Wolfe (ISW) effect which changes energy of CMB photons as they travel through the decisively expanding Universe. In terms of data, I will focus on one of the largest radio surveys to date, the International Low-Frequency Array (LOFAR), which operates in many countries across Europe, including Poland. Finally, I will show my initial results on cosmic inference using LOFAR and CMB data. ## 27 May 2021 Speaker: Viktor Svensson (Szkoła Doktorska NCBJ) Title: Divergent series and hydrodynamics Abstract: Hydrodynamics is a very useful theory of near equilibrium dynamics, but it is far from obvious what “near equilibrium” means in practice. Central to the formulation of hydrodynamics is a perturbative series, the gradient expansion. The applicability of hydrodynamics should be related to how well this perturbative expansion works. Many studies have shown that it is actually a divergent series. In this seminar, I’ll talk about why it diverges, and why this does not spell the end of hydrodynamics. ## 20 May 2021 Speaker: Andrea Bevilacqua (Szkoła Doktorska NCBJ) Title: κ-deformed complex fields and discrete symmetries Abstract: In this talk I will briefly describe a construction of κ-deformed complex scalar field theory with the objective of shedding light on the way discrete symmetries and CPT invariance are affected by the deformation. It is commonly expected that the usual description of spacetime as a smooth manifold is no longer reliable as we approach the Planck scale when quantum effects of the geometry can no longer be neglected. Since the prehistory of research on quantum gravity, noncommutativity of spacetime has been advocated as a possible way to effectively model quantum gravitational effects in regimes of negligible curvature. A widely studied incarnation of this idea suggests that the scale of noncommutativity should be seen as an observer-independent length scale and that, in order to accommodate such a fundamental scale, ordinary relativistic symmetries should be deformed in such a way that they should reproduce the usual Poincaré algebra in the limit of vanishing noncommutativity. The κ-Poincaré algebra is an example of such deformation. After a brief introduction to the formalism and the involved quantities, I will introduce the action and I will proceed to the calculation of the equations of motion (EOM). I will then discuss CPT transformation of the fields and present the translation charges, which will lead to a discussion of the one-particle states. I will then conclude with some comments and prospects for the future. ## 13 May 2021 Speaker: Piotr Kalaczyński (Szkoła Doktorska NCBJ) Title: Comparison of the measured atmospheric muon rate with Monte Carlo simulations and sensitivity study for detection of prompt atmospheric muons with KM3NeT Abstract: The KM3NeT Collaboration has successfully deployed the first detection units of the next generation undersea neutrino telescopes in the Mediterranean Sea at the two sites in Italy and in France. The data sample collected between December 2016 and January 2020 has been used to measure the atmospheric muon rate at two different depths under the sea level: 3.5 km with KM3NeT-ARCA and 2.5 km with KM3NeT-ORCA. Atmospheric muons represent an abundant signal in a neutrino telescope and can be used to test the reliability of the Monte Carlo simulation chain and to study the physics of extensive air showers caused by highly-energetic primary nuclei impinging the Earth’s atmosphere. At energies above PeV the contribution from prompt muons, created right after the first interaction in the shower, is expected to become dominant, however its existence was not yet experimentally confirmed. In this talk data collected with the first detection units of KM3NeT are compared to Monte Carlo simulations based on MUPAGE and CORSIKA codes. The main features of the simulation and reconstruction chains are discussed and presented. Additionally, sensitivities of both KM3NeT-ARCA and KM3NeT-ORCA to the prompt muon component are evaluated using CORSIKA code. ## 6 May 2021 Speaker: Grzegorz Żarnecki (Szkoła Doktorska NCBJ) Title: Muon antineutrino single charged pion production cross-section measurement. Abstract: The goal of the presented analysis is the measurement of the muon antineutrino single charged pion production interactions on CH in the T2K near detector ND280. This interaction mode is the second largest at T2K energies and studies are ongoing to include such events in T2K oscillation analyses. For this reason, a more detailed understanding of this interaction channel using near detector data becomes vital. The measurement will be a double differential cross-section in lepton kinematics and will be extracted using a binned likelihood fit. The event selection strategy developed for this analysis along with the validation studies performed to check the analysis robustness are discussed in this presentation. ## 29 April 2021 Speaker: Anatolii Koval (Szkoła Doktorska NCBJ) Title: How does one look inside of the proton? Abstract: Presently Generalized Parton Distributions allow us novel three-dimensional description of the proton structure when both transverse and longitudinal degrees of freedom are taken into account. A tool to experimentally constraint GPDs is Deeply Virtual Compton Scattering. Main steps in extracting DVCS cross-section in the framework of COMPASS experiment are discussed in detail hinting path towards the proton tomography. ## 22 April 2021 Speaker: Krzysztof Jodłowski (Szkoła Doktorska NCBJ) Title: Looking for Beyond Standard Model short-lived particles with secondary production Abstract: Many Beyond Standard Model (BSM) physics scenarios contain new long-lived particles (LLPs), leading to interesting experimental signatures such as e.g. highly-displaced decay signatures. Examples of such minimal models are so-called portals which include coupling of New Physics particle to SM particles through a renormalizable interaction. Going beyond such simple realisations of BSM physics, one can introduce non-minimal particle content where lighter particle can upscatter into heavier one in front of the detector, leading to interplay between short and long-lived regimes. We illustrate the prospects of such searches in FASER, MATHUSLA and SHiP for a representative models with inelastic dark matter, neutrino dipole portal and dark neutrino portal, among others. We also study signatures consisting of scattering off electrons or nuclei in tungsten detector followed by the decay outside both tungsten detector and the decaying vessel or inside tungsten detector, respectively. ## 15 April 2021 Speaker: Michał Mazurek (Szkoła Doktorska NCBJ) Title: New Software Technologies at the LHCb Experiment Abstract: The LHCb Experiment is one of the largest detectors located at the Large Hadron Collider (LHC) at CERN (The European Organization for Nuclear Research). With the data collected during LHC Run 1 and Run 2, the LHCb Experiment has successfully performed a large number of measurements in heavy flavour physics. In order to perform further measurements with higher precision, the LHCb Experiment is currently installing a major detector upgrade for Run 3 of data taking so that it will be able to process events with 5 times higher luminosity. It is also planning a further upgrade with another increase in luminosity by a factor of 5 to 10. Higher capacity in data storage, computing power, and data processing is needed to prepare the experiment for the changes in Run 3. The whole software of the experiment is being adapted to work in a multithreaded environment in order to exploit as many as possible of the available computing resources. Moreover, new software technologies have to be introduced in order to produce a sufficient number of Monte Carlo samples. In this talk, I am going to present recent investigations on how to integrate deep learning-based fast simulation techniques in the LHCb Gauss simulation framework and a new approach to cluster reconstruction in the electromagnetic calorimeter using convolutional neural networks. ## 8 April 2021 Speaker: Alice Boldrin (Szkoła Doktorska NCBJ) Title: Dirac method in Bianchi I Abstract: Observational data indicates that the Universe has emerged from its primordial phase in a very peculiar state: as a patch of flat, isotropic and homogeneous space furnished with small adiabatic density perturbations with a nearly scale-invariant amplitude spectrum. Our goal is to construct a theory of the primordial universe based on the assumption that it was dominated by quantum gravity effects, which led the Universe to avoid the initial singularity. Presently available quantum frameworks usually assume primordial isotropy. The driving idea behind this work is that alternative frameworks need to possess less primordial symmetries. In particular we will start by assuming a non-isotropic Universe which eventually will be described by the Bianchi IX metric. In this presentation I will focus on the first steps needed to reach our goals. I will explain how we can obtain a Hamiltonian formulation for a Bianchi I Universe, which is a homogeneous and anisotropic Universe whose description is simpler that the one needed for Bianchi IX. After a rather technical introduction I will present the Dirac method, how and why it is useful. Finally I will show our results focusing on the difference between a Bianchi I Universe and a FLRW one. ## 25 March 2021 Speaker: Mahmoud Hamed (Szkoła Doktorska NCBJ) Title: Dust attenuation in ALMA-detected Ultra Dusty Star-Forming galaxies up to z = 4 Abstract: Despite its low contribution to the total mass of the interstellar medium (ISM), dust plays a crucial role in the evolution of galaxies, and it has the biggest impact on the shape of their total emission. The affluence of infrared and radio detections of millions of galaxies in the COSMOS field, provided by powerful instruments such as Herschel and ALMA, has allowed us to study the cold dust in galaxies and its variation over a wide range of redshift. A key element in reproducing the total spectral energy distribution of galaxies, is assuming a dust attenuation law which accounts for the behaviour and the imprints of dust in the ISM. However, different studies have shown that a single law cannot fully model dust in a large sample of galaxies. This non-universality of attenuation laws should be considered in order to accurately account for dust, and therefore in deriving the physical properties of galaxies. In this work, we study different attenuation laws in a statistical sample of ALMA-detected galaxies in the COSMOS field. We probe the resulting variation of key physical properties of these galaxies such as the star formation rate, the stellar mass and the dust to stellar mass ratio. We also investigate the dust temperatures in the ISM and spatial extent of the dust continuum and the implication that it might have on the attenuation curve. We find that a bouquet of attenuation curves must be used in order to reproduce the UV spectrum. Although these curves are not redshift-dependent, they are correlated to the relative spatial distribution to the stellar population of heavily dust-obscured galaxies, and we find a dependence of attenuation laws on the cold dust emission temperatures constrained by ALMA. ## 18 March 2021 Speaker: Francesco PISTIS (Szkoła Doktorska NCBJ) Title: VIPERS: analysis of the FMR and its projections at z~0.7. Can observational biases affect their shapes? Abstract: Galaxy metallicity, a result of the integrated star formation history and evolution of the interstellar medium, is an important property describing galaxy evolution. As such it has been widely studied in the local Universe with the data from the SDSS, as well as its relations with galaxy stellar mass and SFR. The relation between these three galaxy physical properties, known as Fundamental Metallicity Relation (FMR), was shown not to undergo any significant evolution at least up to z~2. In spite of that, different studies find some differences in 2D projections of this relation. However, these studies are based on very different samples, with different data selection at different redshift ranges. In our work we aim at finding FMR evolution from z~0.6 to z~0, making use of the unprecedented statistics of the VIMOS Public Extragalactic Survey (VIPERS) and comparing it to the local SDSS sample. Having that goal in mind, we study the effect of different selection biases introduced into the SDSS sample on both the FMR and its 2D projections. We find significant differences occurring when different data selection, mimicking the selection of higher redshift samples, is applied. Then, we compare these results with the data from the VIPERS sample at z~0.6. We conclude that both FMR and its projection at z~0.6 to z~0 are not in agreement even when the data selection effects are carefully applied. This implies a small but statistically significant evolution of the FMR between z~0.6 to z~0 which needs to be taken into account in future studies. ## 11 March 2021 Speaker: Jaime de Cabo Martin (Szkoła Doktorska NCBJ) Title: Exploring the primordial power spectrum of scalar perturbations from quantum bounce cosmologies. Abstract: Observational data from the Cosmic Microwave Background indicates that the Universe has emerged from its primordial phase in a very peculiar state: as a patch of flat, isotropic and homogeneous space furnished with small adiabatic density perturbations with nearly scale invariant amplitude spectrum. In this talk we will briefly review the main problems of the standard cosmological model for the description of the primordial universe and we will try to solve them not within the usual inflationary solution but in the framework of quantum bounce cosmology. We will present the basic ideas for performing such a description using Hamiltonian formulation of General Relativity. We will derive the reduced scalar quantum Hamiltonian for the flat FLRW universe filled with a perfect fluid. We will introduce the so-called Natural and Mukhanov parametrizations for the description of the dynamics of the scalar perturbations. Finally, we will investigate the primordial power spectrum of such perturbations, trying to approach the solution both numerically and analytically. ## 4 March 2021 Speaker: Arantxa Tymowska (Szkoła Doktorska NCBJ) Title: Quarks at NEik accuracy in the CGC: Forward quark-nucleus scattering Abstract: Within the theory of Color Glass Condensate we derived the Next-to-Eikonal corrections to the background quark propagator from relaxing two Eikonal conditions. These two different corrections to the eikonal approximation combine together and provides a gauge covariant expression for the quark propagator at NEik accuracy. We then apply our results to quark (or antiquark) scattering on a nucleus at NEik accuracy, considering both unpolarized cross section and helicity asymmetry. ## 28 January 2021 Speaker: Ubaldo Cavazos (Studium Doktoranckie NCBJ) Title: Unification via vector-like fermions Abstract: The pursuit for an ultimate theory of nature has been driving the particle physicists for decades. One popular idea explored over the years is the unification of all the fundamental interactions into one common description. In this talk, I will discuss extensions of the Standard Model in which the gauge coupling unification is achieved by introducing new vector-like fermions and scalars with the masses in the TeV range. I will show how the long-lived particles searches can be employed to derive the mass limits for those exotic particles, and how those limits depend on the particle representation. ## 21 January 2021 Speaker: Gabriele Riccio (Studium Doktoranckie NCBJ) Title: Getting ready for the LSST data – estimating the physical properties of main sequence galaxies. Abstract: The upcoming Large Survey of Space and Time (LSST), conducted by Vera Rubin Observatory, will produce, over a 10-year period, multi-petabyte archive of images and catalogs of astrophysical sources on more than 18000 square degrees of the southern sky. Reaching magnitude depth of around 26.5 (AB) in the six bands ugrizy, LSST data will be useful to perform a wide variety of high precision statistical studies, allowing to obtain more accurate measurements of astrophysical quantities. I will present studies based on simulated LSST observations of real galaxies in the ELAIS-N1 and COSMOS fields of the Herschel Extragalactic Legacy Project (HELP) survey. Spectral Energy Distributions (SEDs) were fitted to the real and simulated photometric measurements of 65,889 galaxies in the redshift range 0 < z < 2.5, using the latest release of a galaxy SED fitting code CIGALE. We compare main galaxy physical parameters, such as star formation rate (SFR), stellar mass and dust luminosity obtained from real data using ultraviolet and infrared observations to the same parameters obtained from the simulated optical LSST measurements only. We conclude there is a possible overestimation of SFR, dust luminosity and dust mass if they are calculated with LSST photometric measurements only. This overestimation is found to depend on redshift, diminishing up to z = 2.5. The least sensitive parameter is the stellar mass which was found to be reliably estimated even if based only on the optical bands. ## 14 January 2021 Speaker: Kamil Skwarczyński (Studium Doktoranckie NCBJ) Title: Constraining T2K oscillation fit using proton information from ND280 Abstract: Tokai to Kamioka (T2K) is a long baseline accelerator neutrino experiment. T2K uses the near detector (ND280) to constrain cross-section models as well as flux model. This allows to significantly reduce the systematic error of the Far Detector event rate prediction. T2K cross-section models describe various neutrino interactions like CCQE, 2p2h, DIS. Model constraints are obtained by fitting parametrized model to data (so called ND280 fit). T2K is planning to expand ND280 fit by including proton information (so called proton samples). Proton samples showed improvement in constraints of many parameters describing the model. The crucial feature of proton samples is that they separate phase space of many key variables used in modeling of neutrino interactions. To fully utilize the new samples T2K is also expanding systematic uncertainty model, one of such new parameter is nucleon FSI. ## 7 January 2021 Speaker: Artem Poliszczuk (Studium Doktoranckie NCBJ) Title: Active Galactic Nuclei Catalog from the AKARI NEP-Wide field Abstract: I will present a new AGN catalog from the AKARI NEP-Wide field. Currently the standard method of Active Galactic Nuclei (AGN) selection in the data collected by the AKARI satellite is based on the near- and mid-infrared limits (Lee et al. 2007). This method allows to select AGN candidates with high efficiency at the expense of strong reduction of the catalog size. Our method is based on broad ensemble of supervised machine learning algorithms trained on spectroscopically confirmed sample. The AGN target selection for this sample was strongly influenced by the mid-IR selection. Our method shows high consistency with Lee et al. method, however it does not rely on mid-IR measurements, utilizing only near-IR AKARI passbands and new SUBARU/HSC optical data. New method gives more efficient way for AGN selection in optical and NIR data, being also an important preliminary study of upcoming surveys synergies such as LSST and Euclid. Further information on electromagnetic transition form factors can be acquired through the self-analyzing weak decay of the ground-state hyperon: computing the respective multi-differential four-body decay width results in an additional term containing a relative phase between combinations of the original form factors. ## 17 December 2020 Speaker: Hareesh Thuruthipilly (Studium Doktoranckie NCBJ) Title: Introduction to Emergent Gravity Paradigm and Emergence of Cosmic Space Abstract: On the backgrounds of connections between gravity and thermodynamics, the emergence of cosmic space as cosmic time progresses is an exciting idea advanced by Padmanabhan to explain the accelerated expansion of the universe. The generalisation of Padmanabhan’s conjecture to the non-flat universe has resulted in scepticism about the choice of volume such that the law of emergence can not be appropriately formulated if one uses proper invariant volume. The deep connection between the first law of thermodynamics and the law of emergence, motivate us to explore the status of the first law in a non-at universe when one uses proper invariant volume. We have shown that the first law of thermodynamics, dE = TdS+WdV cannot be formulated properly for a non-flat universe using proper invariant volume. The failure in formulating the first law of thermodynamics with invariant volume hints to why our universe is spatially flat. In this talk, I will give a brief introduction to the emergent gravity paradigm and its application in cosmology. ## 10 December 2020 Speaker: Nora Salone (Studium Doktoranckie NCBJ) Title: Electromagnetic transition form factors and Dalitz decays of hyperons Abstract: This project aims to gain information about the hyperon structure through the study of Dalitz decays of a hyperon resonance to a ground-state hyperon and an electron-positron pair. The usual framework of fixed target experiments, albeit very suitable for nucleons, is not as effective for hyperon resonances. One should consequently change the explored kinematical region, from space-like to time-like $q^2$, with the aid of crossing symmetry. After parametrizing the corresponding baryon-photon-baryon vertex through the use of electromagnetic transition form factors, we formulate double differential decay rates for different spin-parity combinations of the initial state resonance ($J^P = \frac{1}{2}^\pm, \frac{3}{2}^\pm$) transitioning to a ground-state hyperon ($J^P = \frac{1}{2}^+$). Such decay rates are then computed at $q^2=0$ (“QED-type” approximation) and compared to the original quantities where a “radius” structure has been implemented through a low-energy approximation of the form factors. This parallelism can give a rough estimate for the measurement accuracy needed to distinguish between a structure-less and a composite hyperon, namely the minimum requirements for the hyperon internal structure to be “seen”. Further information on electromagnetic transition form factors can be acquired through the self-analyzing weak decay of the ground-state hyperon: computing the respective multi-differential four-body decay width results in an additional term containing a relative phase between combinations of the original form factors. ## 3 December 2020 Speaker: Yashwanth Prabhu (Studium Doktoranckie NCBJ) Title: On the Determination of 𝛿CP with Accelerator Neutrinos Abstract: One of the most important open questions in particle physics is whether the CP symmetry is violated in the leptonic sector- more specifically in the neutrino sector. It is well known the CP symmetry is violated in the quark sector. Discovery of CP violation in the neutrino sector will have implications on the observed matter and antimatter asymmetry in the Universe. The leptonic CP violation arises through the phase 𝛿CP which is a parameter in the neutrino mixing matrix. If 𝛿CP takes a non-conserving value, it will result in CP violation. In my thesis, I studied the effect of 𝛿CP on neutrino and anti-neutrino oscillation probabilities and extended the same to the study of event rates at long baseline neutrino experiments. In this talk, I will discuss the results obtained from my analysis of accelerator neutrinos that travel 1,300 km before detection. ## 26 November 2020 Speaker: Michał Jędrzejczyk (Studium Doktoranckie NCBJ) Title: Establishment of reasonable model to simulate emergency passive coolant system in HTTR reactor Abstract: International Atomic Energy Agency (IAEA) Coordinated Research Program (CRP) on “Heat Transport and Afterheat Removal for Gas-cooled Reactors under Accident Conditions” started in November 1993. In this program, benchmark tasks were proposed for the analysis of passive afterheat removal from gas-cooled reactors (GCR) under accident conditions. The specific objective of the benchmark program is to capture the essential heat transfer features of reactor-to-reactor vessel cooling system (VCS) and provide useful information applicable to a wide variety of designs, operating conditions and model parameters. In the present study, a 1/6 scale model of VCS for High-Temperature Test Reactor (HTTR) was used to develop a reasonably accurate thermal-hydraulics model of a passive cooling system. HTTR is a graphite-moderated gas-cooled research reactor in Oarai, Ibaraki, Japan, operated by the Japan Atomic Energy Agency (JAEA). The reasonable 2D model was established by using ANSYS Fluent software. In the study temperature profiles of the outside of the scaled reactor vessel for three experiment configurations were obtained numerically and compared with experimental results. The numerical results showed good agreement with the experimental ones. Moreover, a simplified numerical approach has been proposed and new heat transfer coefficients were determined. The approach allows for a two-fluid system simulation with significantly reduced computational costs. ## 19 November 2020 Speaker: Luis Eduardo Suelves (Studium Doktoranckie NCBJ) Title: Anisotropic multiplicative bias in weak lensing shear estimates Abstract: Gravitational weak lensing, the weak regime of gravitational lensing phenomena, arises in the sky as a slight shape distortion of observed galaxies, quantified as a change in their ellipticity. As the only information of a galaxy’s ellipticity that we have is in the observation itself, the gravitational effect has to be extracted statistically. Simply speaking, the intrinsic shape of a set of galaxies at an astronomical frame would stack to that of a circle, therefore, any deviation from this stacked shape would be produced by some mass distribution. This Master Thesis project was dedicated to characterize the systematic effects that can bias the measurements in weak lensing and cosmic shear surveys of the shear, a main quantity to characterize weak lensing studies. We produced highly simplified simulations of astronomical frames, with a uniform shear applied to the galaxies, using the Stuff/SkyMaker package, and then applied the KSB shear estimation method. The formalism used to calibrate the measurement systematics, called calibration bias, differs from the one found usually in the literature by the introduction of extra cross-components. ## 12 November 2020 Speaker: Mateusz Kmieć (Studium Doktoranckie NCBJ) Title: Feasibility Studies of CPT Violation Measurement in Flavour Oscillations of the Neutral D Meson Abstract: Mesons are bound quark-antiquark pairs. Flavoured neutral mesons are defined as mesons with no electric charge and non-zero strangeness, charm or beauty content. The weak interactions mix neutral-mesons with their antiparticles leading to spontaneous transitions between meson and antimeson quantum states, which can serve as a sensitive interferometer facilitating precision testing of CPT invariance. The main objective of my master’s thesis was to perform feasibility studies of the CPT violation (CPTV) measurement in the system of the neutral D meson. CPT symmetry is one of the fundamental symmetries of the Standard Model (SM). The measurement of CPTV would mean that there exists physics beyond the SM. My goal was to probe the level of sensitivity of testing CPTV in the system of the neutral D meson. For this purpose, I created a Monte Carlo (MC) generator of neutral meson decays, where CPTV was controlled by a complex phenomenological parameter z. The MC generator was used to simulate the CPT violation effect at the level of z=0.1 for an ensemble of 100 pseudo-experiments. Each experiment consisted of N=6.5*107 of MC generated events corresponding to the number of D0 -> K+pi decays collected by the LHCb (2011-2012). For such statistics, the CPT violation effect would be seen at seven standard deviations level. This can be contrasted with the best experimental limit for the parameter z of order O(1) provided by the FOCUS collaboration. ## 5 November 2020 Speaker: Victor Martínez-Fernández (Studium Doktoranckie NCBJ) Title: CP violation in the Minimal Linear sigma Model Abstract: In this seminar we review the generalities of composite Higgs (CH) models that aim to solve the Standard Model hierarchy problem with the introduction of the Higgs as a Nambu-Goldstone boson as well as a new strong sector with new heavy particles. In particular we work with a renormalizable CH model, the Minimal Linear sigma model (MLsM). The phenomenology of this model is extended with the study of the electron electric dipole moment (eEDM) in accordance with the experimental constraints furnished by the ACME Collaboration in order to set limits on the MLsM CP-violating phases. Our interest in the eEDM stems from the fact that a non-zero value implies CP violation. Since it is a low-energy observable, we perform an integration-out of the heavy fields, obtaining an effective field theory that at 2 loop describes an eEDM (Barr-Zee diagram). ## 29 October 2020 Speaker: Maitrayee Mandal (Studium Doktoranckie NCBJ) Title: Improving the Tau Appearance Study in Atmospheric Neutrinos with Neutron Capture Information at the Super-Kamiokande Experiment Abstract: The Super-Kamiokande (SK) experiment is dedicated to the detection and understanding of neutrino physics. Currently, few experiments constrain the tau neutrino sector and therefore, improving the detection of the appearance of tau neutrinos in atmospheric neutrino flux at SK is an interesting problem. To identify the tau signal from the background, a neural network is utilised at SK. The predominant background consists of neutral current interactions of neutrinos of all flavors. Lesser neutron captures per event are expected in case of the tau signal than in the predominant background, however the present neural network does not include an input of neutron capture information. The recent SK-Gd upgrade will result in 90% of the neutrons produced in the detector being detected and recognised. In the presented study, we show that adding a new input corresponding to the number of neutron captures per event allows for better classification of the tau-signal. We also observe a positive correlation of initial kinetic energy of the event with the separation of signal and background due to neutron captures. ## 22 October 2020 Speaker: Paritosh Verma (Studium Doktoranckie NCBJ) Title: Searching for gravitational waves from pulsars in Jordan Brans Dicke theory Abstract: I shall talk about gravitational waves in Jordan Brans Dicke (JBD) theory. There are two tensor polarization states in the General theory of relativity (GR) but there can also be vector and scalar polarization states in alternative theories of gravity. The JBD theory is one of the attempts to modify the general theory of relativity by varying gravitational constant G and it has three polarization states. The first two states are the same as in GR and the third one is the scalar polarization. We have extracted these three polarizations for a particular case of a rotating neutron star with a mountain and then calculated the F-statistic. Finally, we have developed a simulation to estimate the amplitudes from quadrupole as well as dipole emission.	2022-11-30T01:27:58	{"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": 0.6584147214889526, "perplexity": 1716.6371040232152}, "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/1669446710712.51/warc/CC-MAIN-20221129232448-20221130022448-00846.warc.gz"}
https://par.nsf.gov/biblio/10391098-cosmic-conn-cosmic-ray-detection-deep-learning-framework-data-set-toolkit	Cosmic-CoNN: A Cosmic-Ray Detection Deep-learning Framework, Data Set, and Toolkit Abstract Rejecting cosmic rays (CRs) is essential for the scientific interpretation of CCD-captured data, but detecting CRs in single-exposure images has remained challenging. Conventional CR detectors require experimental parameter tuning for different instruments, and recent deep-learning methods only produce instrument-specific models that suffer from performance loss on telescopes not included in the training data. We present Cosmic-CoNN, a generic CR detector deployed for 24 telescopes at the Las Cumbres Observatory, which has been made possible by the three contributions in this work: (1) We build a large and diverse ground-based CR data set leveraging thousands of images from a global telescope network. (2) We propose a novel loss function and a neural network optimized for telescope imaging data to train generic CR-detection models. At 95% recall, our model achieves a precision of 93.70% on Las Cumbres imaging data and maintains a consistent performance on new ground-based instruments never used for training. Specifically, the Cosmic-CoNN model trained on the Las Cumbres CR data set maintains high precisions of 92.03% and 96.69% on Gemini GMOS-N/S 1 × 1 and 2 × 2 binning images, respectively. (3) We build a suite of tools including an interactive CR mask visualization and editing interface, console more » Authors: ; ; ; ; Publication Date: NSF-PAR ID: 10391098 Journal Name: The Astrophysical Journal Volume: 942 Issue: 2 Page Range or eLocation-ID: Article No. 73 ISSN: 0004-637X Publisher: DOI PREFIX: 10.3847 National Science Foundation ##### More Like this 1. Context. Fast radio bursts (FRBs) are extremely energetic pulses of millisecond duration and unknown origin. To understand the phenomenon that emits these pulses, targeted and un-targeted searches have been performed for multiwavelength counterparts, including the optical. Aims. The objective of this work is to search for optical transients at the positions of eight well-localized (< 1″) FRBs after the arrival of the burst on different timescales (typically at one day, several months, and one year after FRB detection). We then compare this with known optical light curves to constrain progenitor models. Methods. We used the Las Cumbres Observatory Global Telescope (LCOGT) network to promptly take images with its network of 23 telescopes working around the world. We used a template subtraction technique to analyze all the images collected at differing epochs. We have divided the difference images into two groups: In one group we use the image of the last epoch as a template, and in the other group we use the image of the first epoch as a template. We then searched for optical transients at the localizations of the FRBs in the template subtracted images. Results. We have found no optical transients and have therefore set limiting magnitudesmore » 2. ABSTRACT We present and study a large suite of high-resolution cosmological zoom-in simulations, using the FIRE-2 treatment of mechanical and radiative feedback from massive stars, together with explicit treatment of magnetic fields, anisotropic conduction and viscosity (accounting for saturation and limitation by plasma instabilities at high β), and cosmic rays (CRs) injected in supernovae shocks (including anisotropic diffusion, streaming, adiabatic, hadronic and Coulomb losses). We survey systems from ultrafaint dwarf ($M_{\ast }\sim 10^{4}\, \mathrm{M}_{\odot }$, $M_{\rm halo}\sim 10^{9}\, \mathrm{M}_{\odot }$) through Milky Way/Local Group (MW/LG) masses, systematically vary uncertain CR parameters (e.g. the diffusion coefficient κ and streaming velocity), and study a broad ensemble of galaxy properties [masses, star formation (SF) histories, mass profiles, phase structure, morphologies, etc.]. We confirm previous conclusions that magnetic fields, conduction, and viscosity on resolved ($\gtrsim 1\,$ pc) scales have only small effects on bulk galaxy properties. CRs have relatively weak effects on all galaxy properties studied in dwarfs ($M_{\ast } \ll 10^{10}\, \mathrm{M}_{\odot }$, $M_{\rm halo} \lesssim 10^{11}\, \mathrm{M}_{\odot }$), or at high redshifts (z ≳ 1–2), for any physically reasonable parameters. However, at higher masses ($M_{\rm halo} \gtrsim 10^{11}\, \mathrm{M}_{\odot }$) and z ≲ 1–2, CRs can suppress SF and stellar masses by factorsmore » 3. (Ed.) ABSTRACT We study the impact of cosmic rays (CRs) on the structure of virial shocks, using a large suite of high-resolution cosmological FIRE-2 simulations accounting for CR injection by supernovae. In Milky Way-mass, low-redshift (z ≲ 1−2) haloes, which are expected to form ‘hot haloes’ with slowly cooling gas in quasi-hydrostatic equilibrium (with a stable virial shock), our simulations without CRs do exhibit clear virial shocks. The cooler phase condensing out from inflows becomes pressure confined to overdense clumps, embedded in low-density, volume-filling hot gas with volume-weighted cooling time longer than inflow time. The gas thus transitions sharply from cool free-falling inflow, to hot and thermal-pressure supported at approximately the virial radius (≈Rvir), and the shock is quasi-spherical. With CRs, we previously argued that haloes in this particular mass and redshift range build up CR-pressure-dominated gaseous haloes. Here, we show that when CR pressure dominates over thermal pressure, there is no significant virial shock. Instead, inflowing gas is gradually decelerated by the CR pressure gradient and the gas is relatively subsonic out to and even beyond Rvir. Rapid cooling also maintains subvirial temperatures in the inflowing gas within ∼Rvir. 4. Abstract Background Microbiomes are now recognized as the main drivers of ecosystem function ranging from the oceans and soils to humans and bioreactors. However, a grand challenge in microbiome science is to characterize and quantify the chemical currencies of organic matter (i.e., metabolites) that microbes respond to and alter. Critical to this has been the development of Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS), which has drastically increased molecular characterization of complex organic matter samples, but challenges users with hundreds of millions of data points where readily available, user-friendly, and customizable software tools are lacking. Results Here, we build on years of analytical experience with diverse sample types to develop MetaboDirect, an open-source, command-line-based pipeline for the analysis (e.g., chemodiversity analysis, multivariate statistics), visualization (e.g., Van Krevelen diagrams, elemental and molecular class composition plots), and presentation of direct injection high-resolution FT-ICR MS data sets after molecular formula assignment has been performed. When compared to other available FT-ICR MS software, MetaboDirect is superior in that it requires a single line of code to launch a fully automated framework for the generation and visualization of a wide range of plots, with minimal coding experience required. Among the tools evaluated, MetaboDirect is alsomore » Conclusion Application of MetaboDirect to FT-ICR MS-based metabolomic data sets from a marine phage-bacterial infection experiment and aSphagnumleachate microbiome incubation experiment showcase the exploration capabilities of the pipeline that will enable the research community to evaluate and interpret their data in greater depth and in less time. It will further advance our knowledge of how microbial communities influence and are influenced by the chemical makeup of the surrounding system. The source code and User’s guide of MetaboDirect are freely available through (https://github.com/Coayala/MetaboDirect) and (https://metabodirect.readthedocs.io/en/latest/), respectively. 5. Abstract In pursuit of scientific discovery, vast collections of unstructured structural and functional images are acquired; however, only an infinitesimally small fraction of this data is rigorously analyzed, with an even smaller fraction ever being published. One method to accelerate scientific discovery is to extract more insight from costly scientific experiments already conducted. Unfortunately, data from scientific experiments tend only to be accessible by the originator who knows the experiments and directives. Moreover, there are no robust methods to search unstructured databases of images to deduce correlations and insight. Here, we develop a machine learning approach to create image similarity projections to search unstructured image databases. To improve these projections, we develop and train a model to include symmetry-aware features. As an exemplar, we use a set of 25,133 piezoresponse force microscopy images collected on diverse materials systems over five years. We demonstrate how this tool can be used for interactive recursive image searching and exploration, highlighting structural similarities at various length scales. This tool justifies continued investment in federated scientific databases with standardized metadata schemas where the combination of filtering and recursive interactive searching can uncover synthesis-structure-property relations. We provide a customizable open-source package (https://github.com/m3-learning/Recursive_Symmetry_Aware_Materials_Microstructure_Explorer) of thismore »	2023-03-28T14:19:34	{"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": 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": 0.3431496322154999, "perplexity": 4277.150003780315}, "config": {"markdown_headings": true, "markdown_code": false, "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-2023-14/segments/1679296948867.32/warc/CC-MAIN-20230328135732-20230328165732-00244.warc.gz"}
https://www.zbmath.org/authors/?q=ai%3Abonnet.alexis	# zbMATH — the first resource for mathematics ## Bonnet, Alexis Compute Distance To: Author ID: bonnet.alexis Published as: Bonnet, Alexis; Bonnet, A. External Links: IdRef · MGP · Wikidata · dblp Awards: EMS Prize (1996) Documents Indexed: 24 Publications since 1992, including 1 Book all top 5 #### Co-Authors 12 single-authored 4 Monneau, Régis 3 Berestycki, Henri 3 Chapman, Stephen Jonathan 2 Larrouturou, Bernard 1 David, Guy 1 Dkhil, Fathi 1 Hamel, François 1 Kamin, Shoshana 1 Logak, Elisabeth 1 Sainsaulieu, Lionel 1 van Duijn, Cornelis Johannes all top 5 #### Serials 6 Comptes Rendus de l’Académie des Sciences. Série I 3 SIAM Journal on Mathematical Analysis 1 Archive for Rational Mechanics and Analysis 1 Communications on Pure and Applied Mathematics 1 Manuscripta Mathematica 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Physica D 1 European Journal of Applied Mathematics 1 Comptes Rendus de l’Académie des Sciences. Série II 1 Communications on Applied Nonlinear Analysis 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Interfaces and Free Boundaries 1 Nonlinear Analysis. Real World Applications 1 Astérisque 1 Advances in Nonlinear Analysis 1 Nonlinear Analysis. Theory, Methods & Applications all top 5 #### Fields 10 Partial differential equations (35-XX) 8 Fluid mechanics (76-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 6 Classical thermodynamics, heat transfer (80-XX) 5 Ordinary differential equations (34-XX) 5 Biology and other natural sciences (92-XX) 4 Computer science (68-XX) 2 Manifolds and cell complexes (57-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Information and communication theory, circuits (94-XX) #### Citations contained in zbMATH Open 17 Publications have been cited 149 times in 132 Documents Cited by Year Existence of nonplanar solutions of a simple model of premixed Bunsen flames. Zbl 0942.35072 Bonnet, Alexis; Hamel, François 1999 On the regularity of edges in image segmentation. Zbl 0883.49004 Bonnet, A. 1996 A semi-elliptic system arising in the theory of type-II superconductivity. Zbl 0866.35030 Berestycki, H.; Bonnet, A.; Chapman, S. J. 1994 Cracktip is a global Mumford-Shah minimizer. Zbl 1014.49009 Bonnet, Alexis; David, Guy 2001 A deformation lemma on a $$C^ 1$$ manifold. Zbl 0801.57023 Bonnet, Alexis 1993 Convergence of Meissner minimizers of the Ginzburg-Landau energy of superconductivity as $$\kappa\to +\infty$$. Zbl 0970.35031 Bonnet, A.; Chapman, S. J.; Monneau, R. 2000 Distribution of vortices in a type-II superconductor as a free boundary problem: Existence and regularity via Nash-Moser theory. Zbl 0989.35146 Bonnet, A.; Monneau, R. 2000 Travelling waves for planar flames with complex chemistry reaction network. Zbl 0739.34034 Bonnet, Alexis 1992 On the stability of multiple steady planar flames when the Lewis number is less than 1. Zbl 0802.76090 Bonnet, Alexis; Larrouturou, Bernard; Sainsaulieu, Lionel 1993 Non-uniqueness for flame propagation when the Lewis number is less than 1. Zbl 0840.76088 Bonnet, Alexis 1995 On the regularity of the edge set of Mumford-Shah minimizers. Zbl 0916.49030 Bonnet, Alexis 1996 Propagation of flames in the limit of zero ignition temperature. Zbl 0884.34034 Bonnet, Alexis 1997 Travelling-wave solutions to combustion models for a reversible reaction. Zbl 0866.34017 Bonnet, Alexis 1996 Front instability in a condensed phase combustion model. Zbl 1330.35209 Bonnet, Alexis; Dkhil, Fathi; Logak, Elisabeth 2015 A stationary flow in a strip. Zbl 0921.35125 Bonnet, A.; Kamin, S. 1999 On the mushy region arising between two fluids in a porous medium. Zbl 1075.35114 Bonnet, A.; Monneau, R. 2004 Non-unicité dans le modèle de propagation de flamme plane quand le nombre de Lewis est inférieur à 1. (Non-uniqueness for planar flame propagation model when Lewis number is less than 1). Zbl 0753.34004 Bonnet, Alexis 1992 Front instability in a condensed phase combustion model. Zbl 1330.35209 Bonnet, Alexis; Dkhil, Fathi; Logak, Elisabeth 2015 On the mushy region arising between two fluids in a porous medium. Zbl 1075.35114 Bonnet, A.; Monneau, R. 2004 Cracktip is a global Mumford-Shah minimizer. Zbl 1014.49009 Bonnet, Alexis; David, Guy 2001 Convergence of Meissner minimizers of the Ginzburg-Landau energy of superconductivity as $$\kappa\to +\infty$$. Zbl 0970.35031 Bonnet, A.; Chapman, S. J.; Monneau, R. 2000 Distribution of vortices in a type-II superconductor as a free boundary problem: Existence and regularity via Nash-Moser theory. Zbl 0989.35146 Bonnet, A.; Monneau, R. 2000 Existence of nonplanar solutions of a simple model of premixed Bunsen flames. Zbl 0942.35072 Bonnet, Alexis; Hamel, François 1999 A stationary flow in a strip. Zbl 0921.35125 Bonnet, A.; Kamin, S. 1999 Propagation of flames in the limit of zero ignition temperature. Zbl 0884.34034 Bonnet, Alexis 1997 On the regularity of edges in image segmentation. Zbl 0883.49004 Bonnet, A. 1996 On the regularity of the edge set of Mumford-Shah minimizers. Zbl 0916.49030 Bonnet, Alexis 1996 Travelling-wave solutions to combustion models for a reversible reaction. Zbl 0866.34017 Bonnet, Alexis 1996 Non-uniqueness for flame propagation when the Lewis number is less than 1. Zbl 0840.76088 Bonnet, Alexis 1995 A semi-elliptic system arising in the theory of type-II superconductivity. Zbl 0866.35030 Berestycki, H.; Bonnet, A.; Chapman, S. J. 1994 A deformation lemma on a $$C^ 1$$ manifold. Zbl 0801.57023 Bonnet, Alexis 1993 On the stability of multiple steady planar flames when the Lewis number is less than 1. Zbl 0802.76090 Bonnet, Alexis; Larrouturou, Bernard; Sainsaulieu, Lionel 1993 Travelling waves for planar flames with complex chemistry reaction network. Zbl 0739.34034 Bonnet, Alexis 1992 Non-unicité dans le modèle de propagation de flamme plane quand le nombre de Lewis est inférieur à 1. (Non-uniqueness for planar flame propagation model when Lewis number is less than 1). Zbl 0753.34004 Bonnet, Alexis 1992 all top 5 #### Cited by 152 Authors 10 Wang, Zhi Cheng 9 Bu, Zhenhui 9 Hamel, François 7 Lemenant, Antoine 7 Pan, Xingbin 6 Monneau, Régis 6 Sheng, WeiJie 5 Berestycki, Henri 5 Wang, Zhi Cheng 4 Bonnet, Alexis 4 Fusco, Nicola 4 Leoni, Giovanni 4 Li, Wan-Tong 4 Morini, Massimiliano 3 Bao, Xiongxiong 3 Fonseca, Irene 3 Ma, Luyi 3 Maia, Liliane A. 3 Niu, Hong-Tao 3 Serfaty, Sylvia 3 Wick, Thomas 3 Xiang, Xingfei 3 Yu, Wanghui 2 Aftalion, Amandine 2 Carriero, Michele 2 Chambolle, Antonin 2 Daou, Joel 2 De Lellis, Camillo 2 Endtmayer, Bernhard 2 Focardi, Matteo 2 Haragus, Mariana 2 Khatib, Alireza 2 Leaci, Antonio 2 Léger, Jean-Christophe 2 Mikayelyan, Hayk 2 Molica Bisci, Giovanni 2 Ninomiya, Hirokazu 2 Roquejoffre, Jean-Michel 2 Ruan, Shigui 2 Sandier, Etienne 2 Scheel, Arnd 2 Sire, Yannick 2 Spirn, Daniel P. 2 Tomarelli, Franco 2 Volpert, Vitaly A. 1 Acerbi, Emilio 1 Ambrosio, Luigi 1 Bartolo, Rossella 1 Bates, Peter W. 1 Bourdin, Blaise 1 Brancolini, Alessio 1 Bulanyi, Bohdan 1 Cagnetti, Filippo 1 Cao, Meiling 1 Carioni, Marcello 1 Chapman, Stephen Jonathan 1 Chen, Xinfu 1 Clapp, Mónica 1 Collet, Pierre 1 Cremers, Daniel 1 Cuesta, Mabel 1 David, Guy 1 Davoli, Elisa 1 Guedes de Figueiredo, Djairo 1 De Pauw, Thierry 1 Degiovanni, Marco 1 Del Pino, Manuel A. 1 Dolbeault, Jean 1 D’Onofrio, Luigi 1 Du, Yihong 1 Ducrot, Arnaud 1 El Badia, Abdellatif 1 El Hajj, Ahmad 1 Fiscella, Alessio 1 Francfort, Gilles A. 1 Ghazaryan, Anna 1 Giovangigli, Vincent 1 Goel, Divya 1 Gossez, Jean-Pierre 1 Gravina, Giovanni 1 Gui, Changfeng 1 Guo, Hongjun 1 Guo, Jong-Shenq 1 Hao, Xiaoling 1 Horák, Jiri V. 1 Huang, Rui 1 Hupkes, Hermen Jan 1 Iyer, Gautam 1 Jazar, Mustapha 1 Kowalczyk, Michał 1 Kriventsov, Dennis 1 Lafortune, Stéphane 1 Lamboley, Jimmy 1 Lancelotti, Sergio 1 Langer, Ulrich 1 Larrouturou, Bernard 1 Laurent, Frédérique 1 Léger, Alain 1 Li, Kun 1 Li, Zhilin ...and 52 more Authors all top 5 #### Cited in 59 Serials 8 Journal of Differential Equations 6 Archive for Rational Mechanics and Analysis 6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 6 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 6 Journal de Mathématiques Pures et Appliquées. Neuvième Série 5 Communications on Pure and Applied Mathematics 5 Journal of Mathematical Analysis and Applications 5 Calculus of Variations and Partial Differential Equations 5 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 4 Nonlinear Analysis. Real World Applications 4 Communications on Pure and Applied Analysis 3 Journal of Mathematical Physics 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Physica D 3 Applied Mathematics Letters 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Computers & Mathematics with Applications 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Duke Mathematical Journal 2 Communications in Partial Differential Equations 2 Discrete and Continuous Dynamical Systems 2 Combustion Theory and Modelling 2 Advanced Nonlinear Studies 2 Milan Journal of Mathematics 2 Boundary Value Problems 2 Science China. Mathematics 1 Communications in Mathematical Physics 1 Nonlinearity 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Journal of Computational and Applied Mathematics 1 Manuscripta Mathematica 1 Numerische Mathematik 1 Rendiconti del Seminario Matematico della Università di Padova 1 Circuits, Systems, and Signal Processing 1 Computational Mechanics 1 European Journal of Applied Mathematics 1 Journal of Elasticity 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Journal on Mathematical Analysis 1 Journal of Dynamics and Differential Equations 1 Journal of Nonlinear Science 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Electronic Journal of Differential Equations (EJDE) 1 Journal of Inverse and Ill-Posed Problems 1 Journal of Convex Analysis 1 Fractional Calculus & Applied Analysis 1 Interfaces and Free Boundaries 1 Journal of the European Mathematical Society (JEMS) 1 Communications in Contemporary Mathematics 1 Discrete and Continuous Dynamical Systems. Series B 1 Computational Methods in Applied Mathematics 1 Journal of Numerical Mathematics 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Analysis and Applications (Singapore) 1 SIAM Journal on Imaging Sciences 1 Journal of Elliptic and Parabolic Equations 1 Bollettino dell’Unione Matematica Italiana all top 5 #### Cited in 25 Fields 97 Partial differential equations (35-XX) 29 Calculus of variations and optimal control; optimization (49-XX) 20 Statistical mechanics, structure of matter (82-XX) 14 Classical thermodynamics, heat transfer (80-XX) 11 Mechanics of deformable solids (74-XX) 11 Fluid mechanics (76-XX) 10 Information and communication theory, circuits (94-XX) 9 Numerical analysis (65-XX) 8 Ordinary differential equations (34-XX) 8 Biology and other natural sciences (92-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Operator theory (47-XX) 2 Difference and functional equations (39-XX) 2 Functional analysis (46-XX) 2 Differential geometry (53-XX) 2 Computer science (68-XX) 2 Operations research, mathematical programming (90-XX) 1 Real functions (26-XX) 1 Potential theory (31-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral equations (45-XX) 1 Probability theory and stochastic processes (60-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-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.	2021-09-17T13:17:45	{"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": 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": 0.34631332755088806, "perplexity": 8933.915922871585}, "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-2021-39/segments/1631780055645.75/warc/CC-MAIN-20210917120628-20210917150628-00609.warc.gz"}
https://pdglive.lbl.gov/DataBlock.action?node=B054W&home=sumtabB	#### ${{\mathit \Sigma}{(2620)}}$ WIDTH VALUE (MeV) DOCUMENT ID TECN COMMENT $221$ $\pm81$ 1975 DBC ${{\mathit K}^{-}}$ ${{\mathit N}}$ $\rightarrow$ ${{\mathit \Xi}}{{\mathit K}}{{\mathit \pi}}$ $175$ 1970 CNTR ${{\mathit K}^{-}}{{\mathit p}}$ , ${{\mathit K}^{-}}{{\mathit d}}$ total References: DIBIANCA 1975 NP B98 137 Study of ${{\mathit \Xi}^{-}}$ and ${{\mathit \Omega}^{-}}$ Production from ${{\mathit K}^{-}}$ ${{\mathit n}}$ and ${{\mathit K}^{-}}$ ${{\mathit p}}$ Interactions at 4.93 ${\mathrm {GeV/}}\mathit c$ ABRAMS 1970 PR D1 1917 Total Cross Sections of ${{\mathit K}^{\pm}}$ Mesons and Antiprotons on Nucleons up to 3.3 ${\mathrm {GeV/}}\mathit c$ Also PRL 19 259 New Structures in the ${{\mathit K}^{+}}$ ${{\mathit p}}$ and ${{\mathit K}^{+}}$ deuteron Cross Sections Between 1.55 and 3.30 ${\mathrm {GeV/}}\mathit c$ Also PRL 16 1228 New Structure in the ${{\mathit K}^{-}}{{\mathit p}}$ and ${{\mathit K}^{-}}{{\mathit d}}$ Total Cross Sections between 1 and 2.45 ${\mathrm {GeV/}}\mathit c$ Also PRL 19 678 New Structures in the ${{\mathit K}^{-}}{{\mathit p}}$ and ${{\mathit K}^{-}}{{\mathit d}}$ Total Cross Sections between 2.4 and 3.3 ${\mathrm {GeV/}}\mathit c$	2022-10-06T20:46:50	{"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": 0.6029000878334045, "perplexity": 1746.4182581603459}, "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-2022-40/segments/1664030337855.83/warc/CC-MAIN-20221006191305-20221006221305-00139.warc.gz"}
http://www.legisquebec.gouv.qc.ca/en/showversion/cr/H-4.2,%20r.%201?code=se:100&pointInTime=20210204	### H-4.2, r. 1 - Regulation respecting petroleum exploration, production and storage in a body of water 100. The authorization holder who proceeds with the sealing must ensure to seal the stratigraphic survey over its entire length. The holder must also ensure the following: (1) the absence of communication of fluids between the geological formations; (2) the absence of liquid flow and gas emanation or migration; (3) the absence of excessive pressure in the stratigraphic survey; (4) the long-term integrity of the stratigraphic survey, while considering the petroleum development potential of the adjacent sector and the impact of future activities. O.C. 1251-2018, s. 100. In force: 2018-09-20 100. The authorization holder who proceeds with the sealing must ensure to seal the stratigraphic survey over its entire length. The holder must also ensure the following: (1) the absence of communication of fluids between the geological formations; (2) the absence of liquid flow and gas emanation or migration; (3) the absence of excessive pressure in the stratigraphic survey; (4) the long-term integrity of the stratigraphic survey, while considering the petroleum development potential of the adjacent sector and the impact of future activities. O.C. 1251-2018, s. 100.	2021-04-22T00:13:32	{"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": 0.8658786416053772, "perplexity": 8137.143897035954}, "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-2021-17/segments/1618039554437.90/warc/CC-MAIN-20210421222632-20210422012632-00023.warc.gz"}
https://phys.libretexts.org/TextMaps/Introductory_Physics_TextMaps/Map%3A_Conceptual_Physics_(Crowell)/05._Thermodynamics	$$\require{cancel}$$ # 5: Thermodynamics $$S=k \log W$$ -- Inscription on the tomb of Ludwig Boltzmann, 1844-1906. Boltzmann, who originated the microscopic theory of thermodynamics, was driven to suicide by the criticism of his peers, who thought that physical theories shouldn't discuss purely hypothetical objects like atoms. In a developing country like China, a refrigerator is the mark of a family that has arrived in the middle class, and a car is the ultimate symbol of wealth. Both of these are heat engines: devices for converting between heat and other forms of energy. Unfortunately for the Chinese, neither is a very efficient device. Burning fossil fuels has made China's big cities the most polluted on the planet, and the country's total energy supply isn't sufficient to support American levels of energy consumption by more than a small fraction of China's population. Could we somehow manipulate energy in a more efficient way? Conservation of energy is a statement that the total amount of energy is constant at all times, which encourages us to believe that any energy transformation can be undone --- indeed, the laws of physics you've learned so far don't even distinguish the past from the future. If you get in a car and drive around the block, the net effect is to consume some of the energy you paid for at the gas station, using it to heat the neighborhood. There would not seem to be any fundamental physical principle to prevent you from recapturing all that heat and using it again the next time you want to go for a drive. More modestly, why don't engineers design a car engine so that it recaptures the heat energy that would otherwise be wasted via the radiator and the exhaust? Hard experience, however, has shown that designers of more and more efficient engines run into a brick wall at a certain point. The generators that the electric company uses to produce energy at an oil-fueled plant are indeed much more efficient than a car engine, but even if one is willing to accept a device that is very large, expensive, and complex, it turns out to be impossible to make a perfectly efficient heat engine --- not just impossible with present-day technology, but impossible due to a set of fundamental physical principles known as the science of thermodynamics. And thermodynamics isn't just a pesky set of constraints on heat engines. Without thermodynamics, there is no way to explain the direction of time's arrow --- why we can remember the past but not the future, and why it's easier to break Humpty Dumpty than to put him back together again. ### Contributors Benjamin Crowell (Fullerton College). Conceptual Physics is copyrighted with a CC-BY-SA license.	2018-03-21T10:33:57	{"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": 0.6047411561012268, "perplexity": 624.1668983571097}, "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-2018-13/segments/1521257647612.53/warc/CC-MAIN-20180321102234-20180321122234-00760.warc.gz"}
http://dlmf.nist.gov/13.16	# §13.16 Integral Representations ## §13.16(i) Integrals Along the Real Line In this subsection see §§10.2(ii), 10.25(ii) for the functions , , and , and §§15.1, 15.2(i) for . 13.16.4. where is arbitrary, . ## §13.16(ii) Contour Integrals For contour integral representations combine (13.14.2) and (13.14.3) with §13.4(ii). See Buchholz (1969, §2.3), Erdélyi et al. (1953a, §6.11.3), and Slater (1960, Chapter 3). See also §13.16(iii). ## §13.16(iii) Mellin–Barnes Integrals If , then where the contour of integration separates the poles of from those of . If , then where the contour of integration separates the poles of from those of . where the contour of integration passes all the poles of on the right-hand side.	2013-05-24T15:19:30	{"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": 0.9928532838821411, "perplexity": 7108.406761679937}, "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/1368704666482/warc/CC-MAIN-20130516114426-00034-ip-10-60-113-184.ec2.internal.warc.gz"}
https://par.nsf.gov/biblio/10224854-impact-tandem-redundant-sky-based-calibration-mwa-phase-ii-data-analysis	The impact of tandem redundant/sky-based calibration in MWA Phase II data analysis Abstract Precise instrumental calibration is of crucial importance to 21-cm cosmology experiments. The Murchison Widefield Array’s (MWA) Phase II compact configuration offers us opportunities for both redundant calibration and sky-based calibration algorithms; using the two in tandem is a potential approach to mitigate calibration errors caused by inaccurate sky models. The MWA Epoch of Reionization (EoR) experiment targets three patches of the sky (dubbed EoR0, EoR1, and EoR2) with deep observations. Previous work in Li et al. (2018) and (2019) studied the effect of tandem calibration on the EoR0 field and found that it yielded no significant improvement in the power spectrum (PS) over sky-based calibration alone. In this work, we apply similar techniques to the EoR1 field and find a distinct result: the improvements in the PS from tandem calibration are significant. To understand this result, we analyse both the calibration solutions themselves and the effects on the PS over three nights of EoR1 observations. We conclude that the presence of the bright radio galaxy Fornax A in EoR1 degrades the performance of sky-based calibration, which in turn enables redundant calibration to have a larger impact. These results suggest that redundant calibration can indeed mitigate some level of model more » Authors: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more » Award ID(s): Publication Date: NSF-PAR ID: 10224854 Journal Name: Publications of the Astronomical Society of Australia Volume: 37 ISSN: 1323-3580 The Canadian Hydrogen Intensity Mapping Experiment (CHIME) is a drift scan radio telescope operating across the 400–800 MHz band. CHIME is located at the Dominion Radio Astrophysical Observatory near Penticton, BC, Canada. The instrument is designed to map neutral hydrogen over the redshift range 0.8–2.5 to constrain the expansion history of the universe. This goal drives the design features of the instrument. CHIME consists of four parallel cylindrical reflectors, oriented north–south, each 100 m × 20 m and outfitted with a 256-element dual-polarization linear feed array. CHIME observes a two-degree-wide stripe covering the entire meridian at any given moment, observing three-quarters of the sky every day owing to Earth’s rotation. An FX correlator utilizes field-programmable gate arrays and graphics processing units to digitize and correlate the signals, with different correlation products generated for cosmological, fast radio burst, pulsar, very long baseline interferometry, and 21 cm absorber back ends. For the cosmology back end, the$Nfeed2$correlation matrix is formed for 1024 frequency channels across the band every 31 ms. A data receiver system applies calibration and flagging and, for our primary cosmological data product, stacks redundant baselines and integrates for 10 s. We present an overview of themore »	2023-03-24T22:34:23	{"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": 0.430035263299942, "perplexity": 4075.9951930257885}, "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/1679296945289.9/warc/CC-MAIN-20230324211121-20230325001121-00508.warc.gz"}
https://pdglive.lbl.gov/DataBlock.action?node=Q007SC	# ${\boldsymbol {\boldsymbol t}}$-quark EW Couplings ${{\mathit W}}$ helicity fractions in top decays. ${{\mathit F}_{{0}}}$ is the fraction of longitudinal and ${{\mathit F}_{{+}}}$ the fraction of right-handed ${{\mathit W}}$ bosons. ${{\mathit F}_{{{V+A}}}}$ is the fraction of $\mathit V+\mathit A$ current in top decays. The effective Lagrangian (cited by ABAZOV 2008AI) has terms f${}^{L}_{1}$ and f${}^{R}_{1}$ for $\mathit V−\mathit A$ and $\mathit V+\mathit A$ couplings, f${}^{L}_{2}$ and f${}^{R}_{2}$ for tensor couplings with b$_{R}$ and b$_{L}$ respectively. # Spin Correlation in ${{\boldsymbol t}}{{\overline{\boldsymbol t}}}$ Production in ${{\boldsymbol p}}{{\overline{\boldsymbol p}}}$ Collisions INSPIRE search C is the correlation strength parameter, f is the ratio of events with correlated ${{\mathit t}}$ and ${{\overline{\mathit t}}}$ spins (SM prediction: f = 1), and $\kappa$ is the spin correlation coefficient. See "The Top Quark" review for more information. VALUE DOCUMENT ID TECN COMMENT • • • We do not use the following data for averages, fits, limits, etc. • • • $0.89$ $\pm0.22$ 1 2016 A D0 f ( ${{\mathit \ell}}{{\mathit \ell}}$ +${}\geq{}$2 jets, ${{\mathit \ell}}$ +${}\geq{}$4 jets) $0.85$ $\pm0.29$ 2 2012 B D0 f ( ${{\mathit \ell}}{{\mathit \ell}}$ +${}\geq{}$2 jets, ${{\mathit \ell}}$ +${}\geq{}$4 jets) $1.15$ ${}^{+0.42}_{-0.43}$ 3 2012 B D0 f (${{\mathit \ell}}$ + $\not E_T$ + ${}\geq{}$4 jets) $0.60$ ${}^{+0.50}_{-0.16}$ 4 2011 AR CDF ${{\mathit \kappa}}$ (${{\mathit \ell}}$ + $\not E_T$ + ${}\geq{}$4 jets) $0.74$ ${}^{+0.40}_{-0.41}$ 5 2011 AE D0 f ( ${{\mathit \ell}}{{\mathit \ell}}$ +$\not E_T$ + ${}\geq{}$2 jets) $0.10$ $\pm0.45$ 6 2011 AF D0 C ( ${{\mathit \ell}}{{\mathit \ell}}$ +$\not E_T$ + ${}\geq{}$2 jets) 1 ABAZOV 2016A based on 9.7 fb${}^{-1}$ of data. A matrix element method is used. It corresponds to evidence of spin correlation at 4.2${{\mathit \sigma}}$ and is in agreement with the NLO SM prediction $0.80$ ${}^{+0.01}_{-0.02}$. 2 This is a combination of the lepton + jets analysis presented in ABAZOV 2012B and the dilepton measurement of ABAZOV 2011AE. It provides a 3.1 ${{\mathit \sigma}}$ evidence for the ${{\mathit t}}{{\overline{\mathit t}}}$ spin correlation. 3 Based on 5.3 fb${}^{-1}$ of data. The error is statistical and systematic combined. A matrix element method is used. 4 Based on 4.3 fb${}^{-1}$ of data. The measurement is based on the angular study of the top quark decay products in the helicity basis.The theory prediction is ${{\mathit \kappa}}$ $\approx{}$ 0.40. 5 Based on 5.4 fb${}^{-1}$ of data using a matrix element method. The error is statistical and systematic combined. The no-correlation hypothesis is excluded at the 97.7$\%$ CL. 6 Based on 5.4 fb${}^{-1}$ of data. The error is statistical and systematic combined. The NLO QCD prediction is C = $0.78$ $\pm0.03$. The neutrino weighting method is used for reconstruction of kinematics. References: ABAZOV 2016A PL B757 199 Measurement of Spin Correlation between Top and Antitop Quarks Produced in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV ABAZOV 2012B PRL 108 032004 Evidence for Spin Correlation in ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Production AALTONEN 2011AR PR D83 031104 Measurement of ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Spin Correlation in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions Using the CDF II Detector at the Tevatron ABAZOV 2011AF PL B702 16 Measurement of Spin Correlation in ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Production using Dilepton Final States ABAZOV 2011AE PRL 107 032001 Measurement of Spin Correlation in ${\mathit {\mathit t}}{\mathit {\overline{\mathit t}}}$ Production using a Matrix Element Approach	2020-11-29T15:54:29	{"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": 0.8698835372924805, "perplexity": 3736.169724178256}, "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-2020-50/segments/1606141201836.36/warc/CC-MAIN-20201129153900-20201129183900-00587.warc.gz"}
https://pdglive.lbl.gov/DataBlock.action?node=M249M&home=sumtabM	#### ${{\mathit D}_{{1}}^{}{(2760)}^{0}}$ MASS VALUE (MeV) EVTS DOCUMENT ID TECN COMMENT $2781$ $\pm18$ $\pm13$ 2k 1 2015 V LHCB ${{\mathit B}^{-}}$ $\rightarrow$ ${{\mathit D}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{-}}$ 1 From the amplitude analysis in the model describing the ${{\mathit D}^{+}}{{\mathit \pi}^{-}}$ wave together with virtual contributions from the ${{\mathit D}^{}{(2007)}^{0}}$ and ${{\mathit B}^{0}}$ states, nonresonant spin-0 and spin-1 components as well as the ${{\mathit D}_{{0}}^{}{(2400)}^{0}}$ , ${{\mathit D}_{{2}}^{}{(2460)}^{0}}$ and ${{\mathit D}_{{1}}^{}{(2760)}^{0}}$ resonances. References: AAIJ 2015V PR D91 092002 First Observation and Amplitude Analysis of the ${{\mathit B}^{-}}$ $\rightarrow$ ${{\mathit D}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{-}}$ Decay Also PR D93 119901 (errat.) Erratum to AAIJ 2015V: First Observation and Amplitude Analysis of the ${{\mathit B}^{-}}$ $\rightarrow$ ${{\mathit D}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{-}}$ Decay	2022-10-06T20:48:52	{"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": 0.9086150527000427, "perplexity": 3747.4183858110196}, "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/1664030337855.83/warc/CC-MAIN-20221006191305-20221006221305-00189.warc.gz"}
https://www.lessonplanet.com/teachers/direct-variation-1	# Direct Variation 1 This video solves a basic direct variation problem where the cost of buying gas for your car varies directly with the number of gallons you need to purchase. Sal shows how to write a direct variation equation based on this problem and solve a related question. Resource Details 6th - 9th Subjects Math 2 more... Resource Types Videos 1 more... Audiences For Teacher Use 1 more... Instructional Strategy Flipped Classroom Usage Permissions Creative Commons BY-NC-SA: 3.0	2019-04-20T08:15:37	{"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": 0.8056207895278931, "perplexity": 5471.3257680458655}, "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/1555578529472.24/warc/CC-MAIN-20190420080927-20190420102927-00380.warc.gz"}
https://zims-en.kiwix.campusafrica.gos.orange.com/wikipedia_en_all_nopic/A/Keulegan%E2%80%93Carpenter_number	# Keulegan–Carpenter number In fluid dynamics, the Keulegan–Carpenter number, also called the period number, is a dimensionless quantity describing the relative importance of the drag forces over inertia forces for bluff objects in an oscillatory fluid flow. Or similarly, for objects that oscillate in a fluid at rest. For small Keulegan–Carpenter number inertia dominates, while for large numbers the (turbulence) drag forces are important. The Keulegan–Carpenter number is important for the computation of the wave forces on offshore platforms. The Keulegan–Carpenter number KC is defined as:[1] ${\displaystyle K_{C}={\frac {V\,T}{L}},}$ where: • V is the amplitude of the flow velocity oscillation (or the amplitude of the object's velocity, in case of an oscillating object), • T is the period of the oscillation, and • L is a characteristic length scale of the object, for instance the diameter for a cylinder under wave loading. The Keulegan–Carpenter number is named after Garbis H. Keulegan (1890–1989) and Lloyd H. Carpenter. A closely related parameter, also often used for sediment transport under water waves, is the displacement parameter δ:[1] ${\displaystyle \delta ={\frac {A}{L}},}$ with A the excursion amplitude of fluid particles in oscillatory flow and L a characteristic diameter of the sediment material. For sinusoidal motion of the fluid, A is related to V and T as A = VT/(2π), and: ${\displaystyle K_{C}=2\pi \,\delta .\,}$ The Keulegan–Carpenter number can be directly related to the Navier–Stokes equations, by looking at characteristic scales for the acceleration terms: • convective acceleration: ${\displaystyle (\mathbf {u} \cdot \nabla )\mathbf {u} \sim {\frac {V^{2}}{L}},}$ • local acceleration: ${\displaystyle {\frac {\partial \mathbf {u} }{\partial t}}\sim {\frac {V}{T}}.}$ Dividing these two acceleration scales gives the Keulegan–Carpenter number. A somewhat similar parameter is the Strouhal number, in form equal to the reciprocal of the Keulegan–Carpenter number. The Strouhal number gives the vortex shedding frequency resulting from placing an object in a steady flow, so it describes the flow unsteadiness as a result of an instability of the flow downstream of the object. Conversely, the Keulegan–Carpenter number is related to the oscillation frequency of an unsteady flow into which the object is placed. ## Notes 1. Dean & Dalrymple (1991), p. 232. ## References • Keulegan, G. H.; Carpenter, L. H. (1958), "Forces on cylinders and plates in an oscillating fluid", Journal of Research of the National Bureau of Standards, 60 (5): 423–440, doi:10.6028/jres.060.043 • Dean, R.G.; Dalrymple, R.A. (1991), Water wave mechanics for engineers and scientists, Advanced Series on Ocean Engineering, 2, World Scientific, Singapore, ISBN 978-981-02-0420-4 This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.	2021-05-17T09:04:09	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 5, "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": 0.7788881063461304, "perplexity": 1560.1125285240687}, "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-2021-21/segments/1620243992159.64/warc/CC-MAIN-20210517084550-20210517114550-00633.warc.gz"}
https://math.libretexts.org/Bookshelves/Number_Theory/Book%3A_Elementary_Number_Theory_(Raji)/5%3A_Primitive_Roots_and_Quadratic_Residues/5.5%3A_Legendre_Symbol	# 5.5: Legendre Symbol $$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$ In this section, we define Legendre symbol which is a notation associated to quadratic residues and prove related theorems. Definition: Legendre symbol Let $$p\neq 2$$ be a prime and $$a$$ be an integer such that $$p\nmid a$$. The Legendre symbol $$\left(\frac{a}{p}\right)$$ is defined by $\left(\frac{a}{p}\right)=\left\{\begin{array}{lcr} \ 1 &\mbox{if a is a quadratic residue of p} \\ \ -1 &\mbox{if a is a quadratic nonresidue of p}. \\ \end{array}\right .$ Notice that using the previous example, we see that \begin{aligned} && \left(\frac{1}{7}\right)=\left(\frac{2}{7}\right)=\left(\frac{4}{7}\right)=1\\ && \left(\frac{3}{7}\right)=\left(\frac{5}{7}\right)=\left(\frac{6}{7}\right)=-1\end{aligned} In the following theorem, we present a way to determine wether an integer is a quadratic residue of a prime. Euler’s Criterion Let $$p\neq 2$$ be a prime and let $$a$$ be a positive integer such that $$p\nmid a$$. Then $\left(\frac{a}{p}\right)\equiv a^{\phi(p)/2}(mod \ p).$ Assume that $$\left(\frac{a}{p}\right)=1$$. Then the congruence $$x^2\equiv a(mod \ p)$$ has a solution say $$x=x'$$. According to Fermat’s theorem, we see that $a^{\phi(p)/2}=((x')^2)^{\phi(p)/2}\equiv 1(mod\ p).$ Now if $$\left(\frac{a}{p}\right)=-1$$, then $$x^2\equiv a(mod \ p)$$ is not solvable. Thus by Theorem 26, we have that for each integer k with $$(k,p)=1$$ there is an integer $$l$$ such that $$kl\equiv a(mod \ p)$$. Notice that $$i\neq j$$ since $$x^2\equiv a(mod \ p)$$ has no solutions. Thus we can couple the integers $$1,2,...,p-1$$ into $$(p-1)/2$$ pairs, each has product $$a$$. Multiplying these pairs together, we find out that $(p-1)!\equiv a^{\phi(p)/2}(mod \ p).$ Using Wilson’s Theorem, we get $\left(\frac{a}{p}\right)=-1\equiv a^{(p-1)/2}(mod \ p).$ Let $$p=13$$ and $$a=3$$. Then $$\left(\frac{3}{13}\right)=-1\equiv 3^{6}(mod \ 13).$$ We now prove some properties of Legendre symbol. Let $$p\neq 2$$ be a prime. Let $$a$$ and $$b$$ be integers such that $$p\nmid a$$, $$p\nmid b$$ and $$p\mid (a-b)$$ then $\left(\frac{a}{p}\right)=\left(\frac{b}{p}\right).$ Since $$p\mid (a-b)$$, then $$x^2\equiv a(mod \ p)$$ has a solution if and only if $$x^2\equiv b(mod \ p)$$ has a solution. Hence $\left(\frac{a}{p}\right)=\left(\frac{b}{p}\right)$ Let $$p\neq 2$$ be a prime. Let $$a$$ and $$b$$ be integers such that $$p\nmid a$$, $$p\nmid b$$ then $\left(\frac{a}{p}\right)\left(\frac{b}{p}\right)=\left(\frac{ab}{p}\right)$ By Euler’s criterion, we have $\left(\frac{a}{p}\right)\equiv a^{\phi(p)/2}(mod \ p)$ and $\left(\frac{b}{p}\right)\equiv b^{\phi(p)/2}(mod \ p).$ Thus we get $\left(\frac{a}{p}\right)\left(\frac{b}{p}\right) \equiv (ab)^{\phi(p)/2}\equiv \left(\frac{ab}{p}\right)(mod \ p).$ We now show when is $$-1$$ a quadratic residue of a prime $$p$$ . If $$p\neq 2$$ is a, then $\left(\frac{-1}{p}\right)=\left\{\begin{array}{lcr} \ 1 &{\mbox{if}\ p\equiv 1(mod \ 4)} \\ \ -1 &{\mbox{if}\ p\equiv -1(mod \ 4)}. \\ \end{array}\right .$ By Euler’s criterion, we know that $\left(\frac{a}{p}\right)=(-1)^{\phi(p)/2}(mod \ p)$ If $$4\mid (p-1)$$, then $$p=4m+1$$ for some integer $$m$$ and thus we get $(-1)^{\phi(p)/2}=(-1)^{2m}=1.$ and if $$4\mid (p-3)$$, then $$p=4m+3$$ for some integer $$m$$ and we also get $(-1)^{\phi(p)/2}=(-1)^{2m+1}=-1.$ We now determine when $$2$$ is a quadratic residue of a prime $$p$$. For every odd prime $$p$$ we have $\left(\frac{2}{p}\right)=\left\{\begin{array}{lcr} \ 1 &{\mbox{if}\ p\equiv \pm1(mod \ 8)} \\ \ -1 &{\mbox{if}\ p\equiv \pm 3(mod \ 8)}. \\ \end{array}\right .$ Consider the following $$(p-1)/2$$ congruences \begin{aligned} p-1&\equiv& 1(-1)^1 \ \ \ (mod \ p)\\ 2&\equiv& 2(-1)^2 \ \ \ (mod \ p)\\ p-3&\equiv& 3(-1)^3 \ \ \ (mod \ p)\\ 4&\equiv& 4(-1)^4 \ \ \ (mod \ p)\\ &.& \\ &.& \\ &.& \\ r&\equiv& \frac{p-1}{2}(-1)^{(p-1)/2} \ \ \ (mod \ p),\\\end{aligned} where $$r$$ is either $$p-(p-1)/2$$ or $$(p-1)/2$$. Multiplying all these equations we get, $2.4.6...(p-1)\equiv \left(\frac{p-1}{2}\right)!(-1)^{1+2+...+(p-1)/2} \ \ \ (mod \ p).$ This gives us $2^{(p-1)/2}\left(\frac{p-1}{2}\right)! \equiv \left(\frac{p-1}{2}\right)!(-1)^{(p^2-1)/8} (mod \ p).$ Now notice that $$\left(\frac{p-1}{2}\right)!\not\equiv 0(mod \ p)$$ and thus we get $2^{(p-1)/2}\equiv (-1)^{(p^2-1)/8}(mod \ p).$ Note also that by Euler’s criterion, we get $2^{\phi(p)/2}\equiv \left(\frac{2}{p}\right)(mod \ p),$ and since each member is 1 or -1 the two members are equal. We now present an important lemma that determines whether an integer is a quadratic residue of a prime or not. Gauss’s Lemma Let $$p\neq 2$$ be a prime and $$a$$ a relatively prime integer to $$p$$. If $$k$$ counts the number of least positive residues of the integers $$a, 2a,...,((p-1)/2)a$$ that are greater than $$p/2$$, then $\left(\frac{a}{p}\right)=(-1)^k.$ Let $$m_1,m_2,...,m_s$$ be those integers greater than $$p/2$$ in the set of the least positive residues of the integers $$a, 2a,...,((p-1)/2)a$$ and let $$n_1,n_2,...,n_t$$ be those less than $$p/2$$. We now show that $p-m_1,p-m_2,...,p-m_k,p-n_1,p-n_2,...,p-n_t$ are precisely the integers $1,2,...,(p-1)/2,$ in the same order. So we shall show that no two integers of these are congruent modulo $$p$$, because there are exactly $$(p-1)/2$$ numbers in the set, and all are positive integers less than or equal to $$(p-1)/2$$. Notice that $$m_i\not\equiv m_j (\mod \ p)$$ for all $$i\neq j$$ and $$n_i\not\equiv n_j (\mod \ p)$$ for all $$i\neq j$$. If any of these congruences fail, then we will have that $$r\equiv s(mod \ p)$$ assuming that $$ra\equiv sa(mod \ p)$$. Also any of the integers $$p-m_i$$ can be congruent to any of the $$n_i$$’s. Because if such congruence holds, then we have $$ra\equiv p-sa(mod \ p)$$, so that $$ra\equiv -sa(mod \ p)$$. Because $$p\nmid a$$, this implies that $$r\equiv -s(mod \ p)$$, which is impossible. We conclude that $\prod_{i=1}^k(p-m_i)\prod_{i=1}^tn_i\equiv \left(\frac{p-1}{2}\right)!(mod \ p),$ which implies $(-1)^sm_1m_2...(p-m_k)n_1n_2...n_t\equiv \left(\frac{p-1}{2}\right)!(mod \ p),$ Simplifying, we get $m_1m_2...(p-m_k)n_1n_2...n_t\equiv a.2a...((p-1)/2)= a^{(p-1)/2}((p-1)/2)!( mod \ p).$ As a result, we have that $a^{(p-1)/2}((p-1)/2)!\equiv ((p-1)/2)!(mod \ p)$ Note that since $$(p,((p-1)/2)!)=1$$, we get $(-1)^ka^{(p-1)/2}\equiv 1(mod \ p).$ Thus we get $a^{(p-1)/2}\equiv(-1)^k(mod \ p).$ Using Euler’s criterion, the result follows. To find $$\left(\frac{5}{13}\right)$$ using Gauss’s lemma, we calculate $\sum_{i=1}^6[5i/13]=[5/13]+[10/13]+[15/13]+[20/13]+[25/13]+[30/13]=5$ Thus we get $$\left(\frac{5}{13}\right)=(-1)^5=-1$$. Exercises 1. Find all quadratic residues of 3 2. Find all quadratic residues of 19. 3. Find the value of Legendre symbol $$\left(\frac{j}{7}\right)$$ for $$j=1,2,3,4,5,6$$. 4. Evaluate the Legendre symbol $$\left(\frac{7}{11}\right)$$by using Euler’s criterion. 5. Let $$a$$ and $$b$$ be integers not divisible by $$p$$. Show that either one or all three of the integers $$a,b$$ and $$ab$$ are quadratic residues of $$p$$. 6. Let $$p$$ be a prime and $$a$$ be a quadratic residue of $$p$$. Show that if $$p\equiv 1(mod \ 4)$$, then $$-a$$ is also a quadratic residue of $$p$$, whereas if $$p\equiv 3(mod \ 4)$$, then $$-a$$ is a quadratic nonresidue of $$p$$. 7. Show that if $$p$$ is an odd prime and a is an integer not divisible by $$p$$ then $$\left(\frac{a^2}{p}\right)=1$$. ### Contributors • Dr. Wissam Raji, Ph.D., of the American University in Beirut. His work was selected by the Saylor Foundation’s Open Textbook Challenge for public release under a Creative Commons Attribution (CC BY) license.	2019-02-21T02:46:53	{"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": 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": 0.9840074777603149, "perplexity": 111.46619533169533}, "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-2019-09/segments/1550247497858.46/warc/CC-MAIN-20190221010932-20190221032932-00083.warc.gz"}
https://bison.inl.gov/Documentation/source/materials/tensor_mechanics/UO2AxialRelocationEigenstrain.aspx	# UOvar element = document.getElementById("moose-equation-4003a859-f150-4ed9-af0d-f21865185eb4");katex.render("_2", element, {displayMode:false,throwOnError:false}); Axial Relocation Eigenstrain This model accounts for the in the effective diameter of a crumbled layer of fuel during axial relocation under Loss of Coolant Conditions. ## Description The UO2AxialRelocationEigenstrain computes a strain to be applied in the radial direction in axial layers of fuel that have crumbled determined by the AxialRelocationUserObject. The strain is calculated using the current inner cladding radius and original pellet radius for the layer. When a layer crumbles the effective diameter of the fuel moves into contact with the cladding. To ensure the domain on which the heat equation is applied is correct, the mesh must be moved. This is accomodated by this eigenstrain. Note that the inclusion of a ficticious strain does not affect the solution because after crumbling the stress and strain state within the fuel is meaningless. The eigenstrain is calculated by: (1) where is the cladding inner radius, is the residual gap size (default is 2), and is the fuel outer radius at the time fuel gain is first calculated to occur. The definition of the residual gap is illustrated in Figure 1: Figure 1: Change in fuel geometry and effective fuel density following fuel pellet collapse in the ballooned region of the cladding. A residual gap is assumed to remain. ## Example Input Syntax [./axial_relocation_strain] type = UO2AxialRelocationEigenstrain axial_relocation_object = axial_relocation eigenstrain_name = axial_relocation [../] (test/tests/axial_relocation/axial_relocation_eigenstrain.i) ## Input Parameters • axial_relocation_objectName of the AxialRelocationUserObject that determines whether the fuel has crumbled. C++ Type:UserObjectName Description:Name of the AxialRelocationUserObject that determines whether the fuel has crumbled. • eigenstrain_nameMaterial property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator. C++ Type:std::string Description:Material property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator. ### Required Parameters • computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies. Default:True C++ Type:bool Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies. • base_nameOptional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases C++ Type:std::string Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases • boundaryThe list of boundary IDs from the mesh where this boundary condition applies C++ Type:std::vector Description:The list of boundary IDs from the mesh where this boundary condition applies • axial_axis1Coordinate axis of the axial direction of the fuel stack (0, 1, or 2 for x, y, or z Default:1 C++ Type:unsigned int Description:Coordinate axis of the axial direction of the fuel stack (0, 1, or 2 for x, y, or z • blockThe list of block ids (SubdomainID) that this object will be applied C++ Type:std::vector 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 Description:Set the enabled status of the MooseObject. • 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 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 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 Description:The seed for the master random number generator • implicitTrueDetermines whether this object is calculated using an implicit or explicit form Default:True C++ Type:bool Description:Determines whether this object is calculated using an implicit or explicit form • constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped Default:NONE C++ Type:MooseEnum Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped • output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type) C++ Type:std::vector Description:List of material properties, from this material, to output (outputs must also be defined to an output type) • outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object Default:none C++ Type:std::vector Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object	2020-12-04T05:43:44	{"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": 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": 0.2984985411167145, "perplexity": 3200.0725900761754}, "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-2020-50/segments/1606141733122.72/warc/CC-MAIN-20201204040803-20201204070803-00307.warc.gz"}
http://pdglive.lbl.gov/DataBlock.action?node=M300J05	# $\mathbf {{{\boldsymbol \pi}_{{1}}{(2015)}}}$ $\boldsymbol I\boldsymbol G(\boldsymbol J{}^{PC}) = 1{}^{-}(1{}^{-+})$ INSPIRE search MASS ${\mathrm {(MeV)}}$ WIDTH ${\mathrm {(MeV)}}$ EVTS DOCUMENT ID TECN COMMENT $2014 \pm20 \pm16$ $230 \pm32 \pm73$ 145k 2005 B852 18 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \omega}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}{{\mathit p}}$ $2001 \pm30 \pm92$ $333 \pm52 \pm49$ 69k 2004 B852 18 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{-}}{{\mathit p}}$ References: LU 2005 PRL 94 032002 Exotic Meson Decay to ${{\mathit \omega}}{{\mathit \pi}^{0}}{{\mathit \pi}^{-}}$ KUHN 2004 PL B595 109 Exotic Meson Production in the ${{\mathit f}_{{1}}{(1285)}}{{\mathit \pi}^{-}}$ System Observed in the Reaction ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{-}}{{\mathit p}}$ at 18 GeV/$\mathit c$	2019-04-26T16:15:07	{"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": 0.8160114884376526, "perplexity": 9640.50608681286}, "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/1555578841544.98/warc/CC-MAIN-20190426153423-20190426175423-00195.warc.gz"}
http://www.mathguru.com/level1/comparing-quantities-%28ii%29-2008082500031634.aspx	If you like what you see in Mathguru Subscribe Today For 12 Months US Dollars 12 / Indian Rupees 600 Available in 20 more currencies if you pay with PayPal. Buy Now No questions asked full moneyback guarantee within 7 days of purchase, in case of Visa and Mastercard payment Example:Percentage and its Application Post to: Explanation: Percentage In mathematics, a percentage is a way of expressing a number as a fraction of 100 (per cent meaning "per hundred" in Latin). It is often denoted using the percent sign, "%", or the abbreviation "pct". For example, 45% (read as "forty-five percent") is equal to 45/100, or 0.45. (Our solved example in mathguru.com uses this concept) Percentages are used to express how large/small one quantity is, relative to another quantity. The first quantity usually represents a part of, or a change in, the second quantity, which should be greater than zero. For example, an increase of 0.15 on a price of 2.50 is an increase by a fraction of 0.15/2.50 = 0.06. Expressed as a percentage, this is therefore a 6% increase. ## Calculations The fundamental concept to remember when performing calculations with percentages is that the percent symbol can be treated as being equivalent to the pure number constant1 / 100 = 0.01 , for example 35% of 300 can be written as (35/100) × 300 = 105. (Our solved example in mathguru.com uses this concept) To find the percentage that a single unit represents out of a whole of N units, divide 100% by N. For instance, if you have 1250 apples, and you want to find out what percentage of these 1250 apples a single apple represents, 100%/1250 = (100/1250)% provides the answer of 0.08%. So, if you give away one apple, you have given away 0.08% of the apples you had. Then, if instead you give away 100 apples, you have given away 100 × 0.08% = 8% of your 1250 apples. To calculate a percentage of a percentage, convert both percentages to fractions of 100, or to decimals, and multiply them. For example, 50% of 40% is: (50/100) × (40/100) = 0.50 × 0.40 = 0.20 = 20/100 = 20%. It is not correct to divide by 100 and use the percent sign at the same time. (E.g. 25% = 25/100 = 0.25, not 25% / 100, which actually is (25/100) / 100 = 0.0025.) http://en.wikipedia.org/wiki/Percentage The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.	2017-05-24T23:20:38	{"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": 0.4493385851383209, "perplexity": 1269.2108810317166}, "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-2017-22/segments/1495463607871.54/warc/CC-MAIN-20170524230905-20170525010905-00182.warc.gz"}
http://pdglive.lbl.gov/Particle.action?node=M121&home=sumtabM	CHARMED, STRANGE MESONS($\boldsymbol C$ = $\boldsymbol S$ = $\pm1$) ${{\mathit D}_{{s}}^{+}}$ = ${\mathit {\mathit c}}$ ${\mathit {\overline{\mathit s}}}$, ${{\mathit D}_{{s}}^{-}}$ = ${\mathit {\overline{\mathit c}}}$ ${\mathit {\mathit s}}$, similarly for ${{\mathit D}_{{s}}^{}}$'s INSPIRE search # ${{\boldsymbol D}_{{s1}}{(2536)}^{\pm}}$ $I(J^P)$ = $0(1^{+})$ J, P need confirmation. Seen in ${{\mathit D}^{}{(2010)}^{+}}{{\mathit K}^{0}}$ , ${{\mathit D}^{}{(2007)}^{0}}{{\mathit K}^{+}}$ , and ${{\mathit D}_{{s}}^{+}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ . Not seen in ${{\mathit D}^{+}}{{\mathit K}^{0}}$ or ${{\mathit D}^{0}}{{\mathit K}^{+}}$ . $\mathit J{}^{P} = 1{}^{+}$ assignment strongly favored. ${{\mathit D}_{{s1}}{(2536)}^{\pm}}$ MASS $2535.11 \pm0.06$ MeV ${\mathit m}_{{{\mathit D}_{{s1}}{(2536)}^{\pm}}}–{\mathit m}_{{{\mathit D}_{{s}}^{}{(2111)}}}$ $422.9 \pm0.4$ MeV ${\mathit m}_{{{\mathit D}_{{s1}}{(2536)}^{\pm}}}–{\mathit m}_{{{\mathit D}^{}{(2010)}^{\pm}}}$ $524.85 \pm0.04$ MeV ${\mathit m}_{{{\mathit D}_{{s1}}{(2536)}^{\pm}}}–{\mathit m}_{{{\mathit D}^{}{(2007)}^{0}}}$ $528.26 \pm0.05$ MeV (S = 1.2) ${{\mathit D}_{{s1}}{(2536)}^{\pm}}$ WIDTH $0.92 \pm0.05$ MeV ${{\mathit D}_{{s1}}{(2536)}^{-}}$ modes are charge conjugates of the modes below.	2019-11-19T08:13:11	{"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": 0.9913243651390076, "perplexity": 1512.913318991143}, "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/1573496670036.23/warc/CC-MAIN-20191119070311-20191119094311-00423.warc.gz"}
http://pdglive.lbl.gov/DataBlock.action?node=B068M&home=BXXX030	# ${{\boldsymbol \Xi}{(2030)}}$ MASS INSPIRE search VALUE (MeV) EVTS DOCUMENT ID TECN CHG COMMENT $\bf{ 2025 \pm5}$ OUR ESTIMATE $\bf{ 2025.1 \pm2.4}$ OUR AVERAGE Error includes scale factor of 1.3. $2022$ $\pm7$ 1983 MPS - ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}^{+}}$ MM $2024$ $\pm2$ 200 1977 HBC - ${{\mathit K}^{-}}{{\mathit p}}$ 4.2 ${\mathrm {GeV/}}\mathit c$ $2044$ $\pm8$ 1975 DBC -0 ${{\mathit \Xi}}{{\mathit \pi}}{{\mathit \pi}}$ , ${{\mathit \Xi}^{*}}{{\mathit \pi}}$ $2019$ $\pm7$ 15 1973 C HBC -0 ${{\mathit \Sigma}}{{\overline{\mathit K}}}$ $2030$ $\pm10$ 42 1969 HBC - ${{\mathit K}^{-}}{{\mathit p}}$ 3.9$-$5 ${\mathrm {GeV/}}\mathit c$ $2058$ $\pm17$ 40 1969 HBC -0 ${{\mathit K}^{-}}{{\mathit p}}$ 10 ${\mathrm {GeV/}}\mathit c$ ${{\mathit \Xi}{(2030)}}$ mass (MeV) References: JENKINS 1983 PRL 51 951 Existence of ${{\mathit \Xi}}$ Resonances above 2 GeV HEMINGWAY 1977 PL 68B 197 ${{\mathit \Xi}{(2030)}^{-}}$ Production in ${{\mathit K}^{-}}{{\mathit p}}$ Reactions at 4.2 ${\mathrm {GeV/}}\mathit c$ DIBIANCA 1975 NP B98 137 Study of ${{\mathit \Xi}^{-}}$ and ${{\mathit \Omega}^{-}}$ Production from ${{\mathit K}^{-}}{{\mathit n}}$ and ${{\mathit K}^{-}}{{\mathit p}}$ Interactions at 4.93 ${\mathrm {GeV/}}\mathit c$ ROSS 1973C Purdue Conf. 345 Production of Strangeness -2 Baryons in the Mass Region 1600 to 2100 ${\mathrm {MeV}}/\mathit c$2 in ${{\mathit K}^{-}}{{\mathit p}}$ Interactions at 3.1, 3.3, and 3.6 ${\mathrm {GeV/}}\mathit c$ ALITTI 1969 PRL 22 79 Strangeness S = -2 Baryon Resonance BARTSCH 1969 PL 28B 439 Evidence for a New ${{\mathit \Xi}}$ Resonance at 2500 MeV in 10 ${\mathrm {GeV/}}\mathit c$ ${{\mathit K}^{-}}{{\mathit p}}$ Interactions	2019-12-16T04:47:21	{"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": 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": 0.5420733690261841, "perplexity": 10921.358727667965}, "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-2019-51/segments/1575541317967.94/warc/CC-MAIN-20191216041840-20191216065840-00152.warc.gz"}
https://docs.nersc.gov/filesystems/backups/	Skip to content # Backups¶ Danger All NERSC users should back up important files to HPSS on a regular basis. Ultimately, it is your responsibility to protect yourself from data loss. ### Snapshots¶ Global homes and project use a snapshot capability to provide users a seven-day history of their directories. Every directory and sub-directory in global homes contains a ".snapshots" entry. • .snapshots is invisble to ls, ls -a, find and similar commands • Contents are visible through ls -F .snapshots • Can be browsed normally after cd .snapshots • Files cannot be created, deleted or edited in snapshots • Files can only be copied out of a snapshot ### Backup/Restore¶ Global homes are backed up to HPSS on a regular basis. If you require a restoration of lost data that cannot be accomplished via the snapshots capability, please contact NERSC Consulting with pathnames and timestamps of the missing data. Such restore requests may take a few days to complete. ## Purging¶ Files in $SCRATCH directories may be purged if they are older than 12 weeks (defined by last access time). Warning $SCRATCH directories are not backed up	2019-03-26T11:55:50	{"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": 0.22848020493984222, "perplexity": 8866.57439779562}, "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-2019-13/segments/1552912205163.72/warc/CC-MAIN-20190326115319-20190326141319-00348.warc.gz"}
http://legisquebec.gouv.qc.ca/en/version/cr/T-11.2,%20r.%204%20?code=se:35&history=20211017	### T-11.2, r. 4 - Regulation respecting remunerated passenger transportation by automobile 35. Each month, the operator must send to the Commission, by technological means, a report presenting the following information for the preceding month concerning each trip requested by a technological means that does not require the intervention of a natural person: (1) the date and time when the request was received; (2) the transportation mode for the trip, whether exclusive, by adapted automobile, or shared transportation; (3) the file number entered on the driver’s licence of the driver who made the trip; (4) the starting date and time; (5) the starting point; (6) the end date and time; (7) the destination; (8) the amount billed to the customer; (9) the amount paid to the driver; (10) with respect to the automobile used for the trip: (a) the licence plate number; (b) the vehicle identification number; (c) the identifier of the automobile’s owner; (d) the make, model and model year; (e) the type of automobile (adapted, accessible, limousine, sedan); (f) whether or not it contains a taximeter; (g) whether or not it contains a domelight; (h) whether it is a low-emission automobile within the meaning of section 157 of the Act, or, if not, the automobile’s engine type. The report must specify the month covered, include the operator’s identifier as issued by the Commission and be consistent with the model provided by the Commission on its website. O.C. 1046-2020, s. 35. In force: 2020-10-10 35. Each month, the operator must send to the Commission, by technological means, a report presenting the following information for the preceding month concerning each trip requested by a technological means that does not require the intervention of a natural person: (1) the date and time when the request was received; (2) the transportation mode for the trip, whether exclusive, by adapted automobile, or shared transportation; (3) the file number entered on the driver’s licence of the driver who made the trip; (4) the starting date and time; (5) the starting point; (6) the end date and time; (7) the destination; (8) the amount billed to the customer; (9) the amount paid to the driver; (10) with respect to the automobile used for the trip: (a) the licence plate number; (b) the vehicle identification number; (c) the identifier of the automobile’s owner; (d) the make, model and model year; (e) the type of automobile (adapted, accessible, limousine, sedan); (f) whether or not it contains a taximeter; (g) whether or not it contains a domelight; (h) whether it is a low-emission automobile within the meaning of section 157 of the Act, or, if not, the automobile’s engine type. The report must specify the month covered, include the operator’s identifier as issued by the Commission and be consistent with the model provided by the Commission on its website. O.C. 1046-2020, s. 35.	2021-11-29T02:04:17	{"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": 0.8466176390647888, "perplexity": 9574.494096030203}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "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-2021-49/segments/1637964358685.55/warc/CC-MAIN-20211129014336-20211129044336-00005.warc.gz"}
http://www.airports-worldwide.com/articles/article0568.php	Gravitation By Wikipedia, the free encyclopedia, http://en.wikipedia.org/wiki/Gravity Gravitation keeps the planets in orbit about the Sun. (Not to scale) Gravitation is a natural phenomenon by which objects with mass attract one another. In everyday life, gravitation is most commonly thought of as the agency which lends weight to objects with mass. Gravitation compels dispersed matter to coalesce, thus it accounts for the very existence of the Earth, the Sun, and most of the macroscopic objects in the universe. It is responsible for keeping the Earth and the other planets in their orbits around the Sun; for keeping the Moon in its orbit around the Earth, for the formation of tides; for convection (by which fluid flow occurs under the influence of a temperature gradient and gravity); for heating the interiors of forming stars and planets to very high temperatures; and for various other phenomena that we observe. Modern physics describes gravitation using the general theory of relativity, in which gravitation is a consequence of the curvature of spacetime which governs the motion of inertial objects. The simpler Newton's law of universal gravitation provides an excellent approximation for most calculations. The terms gravitation and gravity are mostly interchangeable in everyday use, but a distinction is made in scientific usage. "Gravitation" is a general term describing the phenomenon by which bodies with mass are attracted to one another, while "gravity" refers specifically to the net force exerted by the Earth on objects in its vicinity as well as by other factors, such as the Earth's rotation. ## History of gravitational theory ### Scientific revolution Modern work on gravitational theory began with the work of Galileo Galilei in the late 16th and early 17th centuries. In his famous (though possibly apocryphal) experiment dropping balls from the Tower of Pisa, and later with careful measurements of balls rolling down inclines, Galileo showed that gravitation accelerates all objects at the same rate. This was a major departure from Aristotle's belief that heavier objects are accelerated faster. Galileo correctly postulated air resistance as the reason that lighter objects may fall more slowly in an atmosphere. Galileo's work set the stage for the formulation of Newton's theory of gravity. ### Newton's theory of gravitation In 1687, English mathematician Sir Isaac Newton published Principia, which hypothesizes the inverse-square law of universal gravitation. In his own words, “I deduced that the forces which keep the planets in their orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve: and thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the Earth; and found them answer pretty nearly.” Newton's theory enjoyed its greatest success when it was used to predict the existence of Neptune based on motions of Uranus that could not be accounted by the actions of the other planets. Calculations by John Couch Adams and Urbain Le Verrier both predicted the general position of the planet, and Le Verrier's calculations are what led Johann Gottfried Galle to the discovery of Neptune. Ironically, it was another discrepancy in a planet's orbit that helped to point out flaws in Newton's theory. By the end of the 19th century, it was known that the orbit of Mercury showed slight perturbations that could not be accounted for entirely under Newton's theory, but all searches for another perturbing body (such as a planet orbiting the Sun even closer than Mercury) had been fruitless. The issue was resolved in 1915 by Albert Einstein's new General Theory of Relativity, which accounted for the small discrepancy in Mercury's orbit. Although Newton's theory has been superseded, most modern non-relativistic gravitational calculations are still made using Newton's theory because it is a much simpler theory to work with than General Relativity, and gives sufficiently accurate results for most applications. ### Gravitational torsion, weak equivalence principle and gravitational gradient Loránd Eötvös published on surface tension between 1876 and 1886. The Torsion or Eötvös balance, designed by Hungarian Baron Loránd Eötvös, is a sensitive instrument for measuring the density of underlying rock strata. The device measures not only the direction of force of gravity, but the change in the force of gravity's extent in horizontal plane. It determines the distribution of masses in the Earth's crust. The Eötvös torsion balance, an important instrument of geodesy and geophysics throughout the whole world, studies the Earth's physical properties. It is used for mine exploration, and also in the search for minerals, such as oil, coal and ores. Eötvös' law of capillarity (weak equivalence principle) served as a basis for Einstein's theory of relativity. (Capillarity: the property or exertion of capillary attraction of repulsion, a force that is the resultant of adhesion, cohesion, and surface tension in liquids which are in contact with solids, causing the liquid surface to rise - or be depressed...) These experiments demonstrate that all objects fall at the same rate with negligible friction (including air resistance). The simplest way to test the weak equivalence principle is to drop two objects of different masses or compositions in a vacuum, and see if they hit the ground at the same time. More sophisticated tests use a torsion balance of a type invented by Loránd Eötvös. Satellite experiments are planned for more accurate experiments in space. They verify the weak principle. ### General relativity Fundamental concepts General relativity $G_{\mu \nu} + \Lambda g_{\mu \nu}= {8\pi G\over c^4} T_{\mu \nu}\,$ Einstein field equations Introduction to... Mathematical formulation of... Resources Special relativity Equivalence principle World line · Riemannian geometry In general relativity, the effects of gravitation are ascribed to spacetime curvature instead of a force. The starting point for general relativity is the equivalence principle, which equates free fall with inertial motion, and describes free-falling inertial objects as being accelerated relative to non-inertial observers on the ground. In Newtonian physics, however, no such acceleration can occur unless at least one of the objects is being operated on by a force. Einstein proposed that spacetime is curved by matter, and that free-falling objects are moving along locally straight paths in curved spacetime. These straight lines are called geodesics. Like Newton's First Law, Einstein's theory stated that if there is a force applied to an object, it would deviate from the geodesics in spacetime. For example, we are no longer following the geodesics while standing because the mechanical resistance of the Earth exerts an upward force on us. Thus, we are non-inertial on the ground. This explains why moving along the geodesics in spacetime is considered inertial. Einstein discovered the field equations of general relativity, which relate the presence of matter and the curvature of spacetime and are named after him. The Einstein field equations are a set of 10 simultaneous, non-linear, differential equations. The solutions of the field equations are the components of the metric tensor of spacetime. A metric tensor describes a geometry of spacetime. The geodesic paths for a spacetime are calculated from the metric tensor. Notable solutions of the Einstein field equations include: The tests of general relativity included: • General relativity accounts for the anomalous perihelion precession of Mercury. • The prediction that time runs slower at lower potentials has been confirmed by the Pound-Rebka experiment, the Hafele-Keating experiment, and the GPS. • The prediction of the deflection of light was first confirmed by Arthur Eddington in 1919. The Newtonian corpuscular theory also predicted a lesser deflection of light, but Eddington found that the results of the expedition confirmed the predictions of general relativity over those of the Newtonian theory. However this interpretation of the results was later disputed. More recent tests using radio interferometric measurements of quasars passing behind the Sun have more accurately and consistently confirmed the deflection of light to the degree predicted by general relativity. See also gravitational lensing. • The time delay of light passing close to a massive object was first identified by Irwin Shapiro in 1964 in interplanetary spacecraft signals. • Gravitational radiation has been indirectly confirmed through studies of binary pulsars. • Alexander Friedmann in 1922 found that Einstein equations have non-stationary solutions (even in the presence of the cosmological constant). In 1927 Georges Lemaître showed that static solutions of the Einstein equations, which are possible in the presence of the cosmological constant, are unstable, and therefore the static universe envisioned by Einstein could not exist. Later, in 1931, Einstein himself agreed with the results of Friedmann and Lemaître. Thus general relativity predicted that the Universe had to be non-static—it had to either expand or contract. The expansion of the universe discovered by Edwin Hubble in 1929 confirmed this prediction. ### Gravity and quantum mechanics Several decades after the discovery of general relativity it was realized that general relativity is incompatible with quantum mechanics. It is possible to describe gravity in the framework of quantum field theory like the other fundamental forces, such that the attractive force of gravity arises due to exchange of virtual gravitons, in the same way as the electromagnetic force arises from exchange of virtual photons. This reproduces general relativity in the classical limit. However, this approach fails at short distances of the order of the Planck length, where a more complete theory of quantum gravity (or a new approach to quantum mechanics) is required. Many believe the complete theory to be string theory, or more currently M Theory. ## Specifics ### Earth's gravity Every planetary body (including the Earth) is surrounded by its own gravitational field, which exerts an attractive force on all objects. Assuming a spherically symmetrical planet (a reasonable approximation), the strength of this field at any given point is proportional to the planetary body's mass and inversely proportional to the square of the distance from the center of the body. The strength of the gravitational field is numerically equal to the acceleration of objects under its influence, and its value at the Earth's surface, denoted g, is approximately expressed below as the standard average. g = 9.8 m/s = 32.2 ft/s This means that, ignoring air resistance, an object falling freely near the Earth's surface increases its velocity with 9.8 m/s (32.2 ft/s or 22 mph) for each second of its descent. Thus, an object starting from rest will attain a velocity of 9.8 m/s (32.2 ft/s) after one second, 19.6 m/s (64.4 ft/s) after two seconds, and so on, adding 9.8 m/s (32.2 ft/s) to each resulting velocity. Also, again ignoring air resistance, any and all objects, when dropped from the same height, will hit the ground at the same time. According to Newton's 3rd Law, the Earth itself experiences an equal and opposite force to that acting on the falling object, meaning that the Earth also accelerates towards the object (until the object hits the earth, then the Law of Conservation of Energy states that it will move back with the same acceleration with which it initially moved forward, canceling out the two forces of gravity.). However, because the mass of the Earth is huge, the acceleration of the Earth by this same force is negligible, when measured relative to the system's center of mass. ### Equations for a falling body near the surface of the Earth Ball falling freely under gravity. See text for description. Under an assumption of constant gravity, Newton’s law of gravitation simplifies to F = mg, where m is the mass of the body and g is a constant vector with an average magnitude of 9.81 m/s². The acceleration due to gravity is equal to this g. An initially-stationary object which is allowed to fall freely under gravity drops a distance which is proportional to the square of the elapsed time. The image on the right, spanning half a second, was captured with a stroboscopic flash at 20 flashes per second. During the first 1/20th of a second the ball drops one unit of distance (here, a unit is about 12 mm); by 2/20ths it has dropped at total of 4 units; by 3/20ths, 9 units and so on. Under the same constant gravity assumptions, the potential energy, Ep, of a body at height h is given by Ep = mgh (or Ep = Wh, with W meaning weight). This expression is valid only over small distances h from the surface of the Earth. Similarly, the expression $h = \tfrac{v^2}{2g}$ for the maximum height reached by a vertically projected body with velocity v is useful for small heights and small initial velocities only. ### Gravity and astronomy The discovery and application of Newton's law of gravity accounts for the detailed information we have about the planets in our solar system, the mass of the Sun, the distance to stars, quasars and even the theory of dark matter. Although we have not traveled to all the planets nor to the Sun, we know their masses. These masses are obtained by applying the laws of gravity to the measured characteristics of the orbit. In space an object maintains its orbit because of the force of gravity acting upon it. Planets orbit stars, stars orbit galactic centers, galaxies orbit a center of mass in clusters, and clusters orbit in superclusters. The force of gravity is proportional to the mass of an object and inversely proportional to the square of the distance between the objects. In general relativity, gravitational radiation is generated in situations where the curvature of spacetime is oscillating, such as is the case with co-orbiting objects. The gravitational radiation emitted by the solar system is far too small to measure. However, gravitational radiation has been indirectly observed as an energy loss over time in binary pulsar systems such as PSR 1913+16. It is believed that neutron star mergers and black hole formation may create detectable amounts of gravitational radiation. Gravitational radiation observatories such as LIGO have been created to study the problem. No confirmed detections have been made of this hypothetical radiation, but as the science behind LIGO is refined and as the instruments themselves are endowed with greater sensitivity over the next decade, this may change. ## Anomalies and discrepancies There are some observations that are not adequately accounted for, which may point to the need for better theories of gravity or perhaps be explained in other ways. • Pioneer anomaly: The two Pioneer spacecraft seem to be slowing down in a way which has yet to be explained. • Flyby anomaly: Various spacecraft have experienced greater accelerations during slingshot maneuvers than expected. • Accelerating expansion: The expansion of the universe seems to be speeding up. Dark energy has been proposed to explain this. A recent alternative explanation is that the geometry of space is not homogeneous (due to clusters of galaxies) and that when the data are reinterpreted to take this into account, the expansion is not speeding up after all, however this conclusion is disputed. • Anomalous increase of the AU: Recent measurements indicate that planetary orbits are expanding faster than if this was solely through the sun losing mass by radiating energy. • Extra energetic photons: Photons travelling through galaxy clusters should gain energy and then lose it again on the way out. The accelerating expansion of the universe should stop the photons returning all the energy, but even taking this into account photons from the cosmic background radiation gain twice as much energy as expected. This may indicate that gravity falls off faster than inverse-squared at certain distance scales. • Dark flow: Surveys of galaxy motions have detected a mystery dark flow towards an unseen mass. Such a large mass is too large to have accumulated since the big bang using current models and may indicate that gravity falls off slower than inverse-squared at certain distance scales. • Extra massive hydrogen clouds: The spectral lines of the Lyman alpha forest suggest that hydrogen clouds are more clumped together at certain scales than expected and, like dark flow, may indicate that gravity falls off slower than inverse-squared at certain distance scales. ## References Text from Wikipedia is available under the Creative Commons Attribution/Share-Alike License; additional terms may apply. Published - July 2009	2017-03-26T16:49:39	{"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 2, "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": 0.669937789440155, "perplexity": 484.94820970454515}, "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-2017-13/segments/1490218189244.95/warc/CC-MAIN-20170322212949-00539-ip-10-233-31-227.ec2.internal.warc.gz"}
https://jaspock.github.io/funicular/dnc.html?utm_campaign=Revue%20newsletter&utm_medium=Newsletter&utm_source=Deep%20Learning%20Weekly	# A bit-by-bit guide to the equations governing differentiable neural computers Written by Juan Antonio Pérez-Ortiz, researcher at Universidad de Alicante, Spain. Last update: October 20 2017. Comments and suggestions: feel free to send any comments or suggestions to enhance this guide through the comments section at the end of this page. This guide attempts to gradually present the various pieces involved in the mathematical formulation of the differentiable neural computer (DNC) model, a memory-augmented neural network first introduced in the paper by Alex Graves, Greg Wayne et al., researchers at DeepMind, published in the Nature journal in October 2016. The paper in question, along with certain others published before it, is relevant in that it sows the seeds for an even brighter future of neural networks, potentially leading to their application in algorithmic tasks that were formerly inaccessible. The DNC architecture is also a good example of how to move concepts that are not in principle differentiable (e.g., the management of a read-write memory) to the realm of differentiable models that can be trained by means of gradient descent. The guide provides a step-by-step analysis of the equations that make up the model at a slower pace than that originally followed in the methods section of the paper cited above, in the hope that doing so will facilitate the understanding of the model for those who require extra details in order to fully comprehend the whole story. I, personally, needed hours to feel comfortable with all of the equations used to describe the model in the aforementioned paper in spite of my expertise as regards neural networks; I therefore decided that it might be a good idea to prepare this document so as to help those (maybe you!) in a situation similar to mine. The primary source of information regarding the DNC model is obviously the original paper and its contents prevail over any statement made in this guide. Deeply understanding how DNCs are designed could also make it possible to suggest modifications to the architecture that could lead to alternative models better suited to specific tasks. This guide assumes that the reader understands the basics of machine learning and neural networks (weights and connections, activation functions, the gradient descent optimization algorithm, recurrent networks, LSTM cells, etc.) along with the fundamentals of matrix algebra, but, apart from that, no additional advanced knowledge is, in principle, required to follow the discussion. Many good introductions to the topic of neural networks can be found on the web. Another additional resources as regards DNCs are: • the webpage and the blog entry in the DeepMind website, • the source code (written in Python with the TensorFlow and Sonnet libraries) released by DeepMind six months after the publication of the paper, • the brief description of the Neural Turing Machine (a predecessor of DNCs sharing some features with them) in one of the papers in the Distill journal, • the video of the talk given by Alex Graves at the NIPS 2016 conference, • the video review of the architecture and the source code by Siraj Raval, • the presentation of the paper in the Nature journal, • the review work by the Stanford student Carol Hsin, • and the analysis of the analogy between DNCs and the human memory by Sam Greydanus. Throughout this guide, I will often use what I call dualistic simplification in order to introduce discussions regarding many of the components of a DNC in a educational manner. The idea behind this is to start by assuming that the model could behave like a binary (dualistic) system in the same sense that, for example, a conventional memory location is always either written or not written, but cannot be half written. This behavior is what a programmer expects in most programming languages, in which an assignment instruction writes to the memory location of a particular variable and leaves the remaining variables untouched; for instance, x=3 means that the variable x will be fully written, and its previous value completely removed, while the remaining variables that are visible from the current scope will not be written at all. Remarkably, however, real life in the DNC world is slightly different (half serious, half joking, we could say that things are slightly differentiable; see later) from this approximation: all the values streaming through the DNC are continuous real values, signifying that a switch is rarely completely on or off, or that a memory pointer hardly ever refers to a unique location in the memory. In some cases, it may occur that the switch is almost on or off, or that the memory pointer is almost exclusively referring to a single memory location, but in some other cases, the switch may have an intermediate degree of activation or the pointer may be simultaneously focusing on more than one memory location at the same time (paying a different degree of attention to each of them). If you have some knowledge of how a regular computer operates, this non-binary pluralistic behavior of DNCs is at the other end of many strong preconceptions you may have about how a computer and its memory work. Throughout this guide, you are expected to open your mind to fuzzier mechanisms and embrace a view of DNCs as a pluralistic approach to computing. In this document, the beginning of those fragments of text that assume the dualistic simplification are marked with a yin-yang symbol . I hope that the dualistic simplification will prove useful to the reader in order to attain a rough idea of how a particular operation works in the DNC model before learning it in its entire realization. #### Threshold activation functions The first neural networks proposed by Warren McCulloch and Walter Pitts back in the 1940s used linear threshold units, a form of neuron whose binary output is computed by means of a Heaviside step activation function (activation is exactly 0 or 1). This kind of activation function (or extensions of it) may, in principle, appear to be suitable as regards obtaining dualistic references to memory locations in DNCs. Why, then, are they not used to embrace the dualistic view? Because a step-like function is not adequate for the gradient descent training algorithm since its derivative is $0$ at every point (except at the step point) and, therefore, provides no useful information for common learning algorithms. Other forms of activation functions will consequently be used and the references to memory locations will be pluralistic rather than dualistic. I shall begin by describing the basic architecture of a DNC, after which I shall go on to discuss how the explicit memory is represented in a DNC and how data is read from and written to this memory. ## Architecture Seen from afar, a DNC is similar to many other neural networks: it reads an external input $\b{x}_t$ and produces an output $\b{y}_t$ which is intended to represent things such as the estimation of a class, the prediction of the next element in a sequence, etc. The mapping from inputs to outputs is computed as a set of differentiable operations which depend on a set of weights that are automatically learned in order to minimize a loss function that compares the outputs emitted by the model with the desirable outputs contained in a training set. Gradient descent can then be used to estimate those weights for a particular task. A more careful look will, however, reveal an explicit memory that is used to store vectors and later retrieve them. A DNC is composed of a controller, a memory and an output module. The controller is responsible for emitting a controller output vector $\b{\nu}_t$ given the current external input $\b{x}_t$, but also interacts with the memory by emitting a vector of interface parameters $\b{\xi}_t$ that are used to regulate the memory operation at each time step. These interface parameters include values that directly or indirectly determine which memory locations will be read or written at the current time step. The memory has a set of $R$ read heads and one write head; the values read by the $i$-th read head at time step $t$ are denoted as $\b{r}^{i}_t$. The controller can, in principle, be any differentiable system (e.g., a feedforward neural network or a recurrent neural network) that computes a function $\c{N}$ in order to emit both vectors (the controller output and the interface parameters) given the external input and the previously read vectors: In the paper published in Nature, Alex Graves, Greg Wayne et al. use an LSTM-based recurrent neural network for the controller function $\c{N}$ in all the experiments, as a result of which these DNC controllers also use the state information (a much simpler form of memory) corresponding to the past input vectors $\b{x}_{t-1},\b{x}_{t-2},\ldots$ The values read from the memory at time $t$ ($\b{r}^{i}_t$, with $i=1,\ldots,R$) are used not only to feed the controller at time $t+1$ but also to compute the global output $\b{y}_t$ of the DNC by means of another differentiable system that computes a function $\c{N}’$: In the paper, a simple single-layer feedforward neural network is used for the global output function $\c{N}’$. Note that the values of $\b{r}^{i}_t$ at time $t$ cannot be involved in the computation of the interface parameters $\b{\xi}_t$ because these parameters are precisely required to obtain each $\b{r}^{i}_{t}$. Note also that both neural networks $\c{N}$ and $\c{N}’$ are trained together (end-to-end) by simply using a training set made of inputs $\b{x}_t$ and the corresponding desired values for the global outputs $\b{y}_t$. ## Memory Differentiable neural computers (DNCs) are an example of memory augmented neural networks. These models can be traced back to the nineties when Sun, Giles, Chen and Lee introduced their connectionist pushdown automaton, which used differentiable non-dualistic mechanisms to allow a recurrent neural controller to interact with a continuous external stack. The memory $\b{M}_t$ of a DNC stores a collection of $N$ real-valued vectors in $\R^W$, such as $[0.2, 0.6, 1.2] \in \R^3$. The word size $W$ of the memory locations is, in principle, set as constant for a particular DNC, and all vectors stored in memory consequently have the same length. The $N$ vectors are deployed in an $N \times W$ matrix; the following $4 \times 3$ matrix, for example, represents a memory with $N=4$ rows or locations in which the previous example vector is stored at the memory location $2$ (in accordance with the original article, the indexes start at one): Rows arbitrarily represent locations, but locations could also have been represented using columns. The number of memory locations $N$ (i.e., the capacity of the memory; in this case $N=4$) is also usually kept constant but it could, in principle, be dynamically increased to enable the storage of extra vectors once all the positions have been allocated and new vectors need to be stored (the concept of memory allocation will be discussed later). In this case, all the other vectors and matrices in the DNC defined in terms of $N$ would obviously also need to be resized. The DNC memory is time-varying (like regular computer memories), repeatedly being read and written. This is why we use the subindex $t$: the matrix $\b{M}_t$ represents the memory contents at time step $t$. As will be explored later, at every time step $t$, the memory may be optionally read and optionally written. A series of read heads and a write head interact with the contents of the memory. These are discussed below. ## Read operation Each DNC integrates at least one read head which can be used to attain access to the content of the memory. Read heads use a vector called weighting to convey the particular memory locations to be read at each time. Let us first follow the dualistic simplification and assume that this weighting can refer to a single memory location by using the one-hot encoding which, in the case of a memory with a capacity $N=4$, implies that, rather than representing the different locations as $1, 2, 3, 4$, they will be represented as the one-hot vectors $[1;0;0;0]$, $[0;1;0;0]$, $[0;0;1;0]$, $[0;0;0;1]$, respectively. This representation seems particularly relevant to our interests, since retrieving the content of a particular location would be expressed as a well-known matrix product between the memory matrix and the vector representing the location; for example, it would be possible to retrieve the content of location $2$ (represented as the weighting $[0;1;0;0]$) in the memory configuration of equation \eqref{memo} with: where $\top$ denotes the transpose of a matrix. The vector representing the location to be read at time $t$ is called the read weighting for reasons that will become clear later, and is represented as $\b{w}^\r{r}_t$ (in the running example, $\b{w}^\r{r}_t = [0;1;0;0]$). A position in memory can, therefore, be read with the operation $\b{M}^\top_t \b{w}^\r{r}_t$. There is a companion notebook that allows you to check how these values are obtained and apply the formulae to your own inputs. #### Column vectors Unless otherwise stated, all vectors used in the equations governing DNCs are column vectors. In order to simplify their in-line writing, they will be represented in text as $[0;1;0;0]$, that is, as rows in which element vectors are separated using semicolons rather than commas. The formulation shown above belongs to the dualistic world, a world in which, as mentioned in the introduction, a memory location is fully read or is not read at all; when working with DNCs, however, the functional unit (i.e., the read head) that emits the read weighting will not generate this one-hot clean output, but rather a distribution (or, in other words, a weighting) over all the memory locations; some of the reasons behind this were presented in the introduction when I discussed why threshold activation functions are not a good choice. As a result of this, $\b{w}^\r{r}_t[i]$, that is, the $i$-th element of $\b{w}^\r{r}_t$, will be interpreted as the degree to which memory location $i \in [1,N]$ is involved in the reading operation. For example, a weighting $\b{w}^\r{r}_t= [0;0.8;0.1;0.1]$ indicates that the second memory location gets eight times more attention than the third or fourth locations, and the first location gets no attention at all; using this weighting to retrieve the contents of the memory configuration \eqref{memo} would give: Note that the resulting vector is still close to the content of the second memory location, but that the residual attention paid to the third and fourth locations prevents it from exactly matching the second location. The companion notebook allows you to check how these values are obtained. More specifically (as will be seen later), the operations performed by the read head produce weightings $\b{w}^\r{r}_t \in \Delta_N$, with $\Delta_N$ defined as: The DNC allows for more than one read head in the hope that multiple simultaneous readings may simplify the dynamics that would otherwise be needed to perform a series of consecutive readings at steps $t$, $t+1$, etc. A set of $R$ read weightings $\b{w}^{\r{r},i}_t$ with $i \in {1,2,\ldots,R}$ are consequently generated for the $R$ read heads. The vector read by the $i$-th read head at time $t$ is: Note that this mechanism employed to retrieve the contents of a particular location is differentiable. If no location has to be read at the current time step by the $i$-th read head, then the read weighting vector $\b{w}^{\r{r},i}_t$ will be $\b{0}$, as will $\b{r}^i_t$. #### Weightings As we will be seeing, DNCs have different weightings that are used to selectively focus on different memory locations. These weightings are vectors with components in the range of $[0,1]$ that may add up to exactly $1$ or to a value in $[0,1]$, depending on the purpose of the weighting. Most of the weightings belong to the second group, but a few of them belong to the first. For example, as will be seen later, at every time step, DNCs compute a similarity measure between a given lookup key vector and the content of each memory location; the result is a weighting whose elements indicate the proportion of the total similarity corresponding to each location. In this case, the weighting vector will be an element of $\c{S}_N$, a set defined as: $\c{S}_N$ is known in geometry as the unit $(N-1)$-simplex (or standard $N-1$ simplex). For example, in the case of $N=2$, the set $\c{S}_N$ will comprise the points of the line segment (a 1-simplex) which can be seen in this graph; for $N=3$, the corresponding $2$-simplex is the equilateral triangle (with vertices $[1,0,0]$, $[0,1,0]$ and $[0,0,1]$) that can be seen in this other graph; for a weighting with $N=4$, the corresponding 3-simplex is a tetrahedron, etc. The condition that the vector elements add up to $1$ may be relaxed in those scenarios in which attention is optional; for example, as it is not mandatory to write to a memory location at every time step, we should allow null weightings. In these cases, the components will add up to at most $1$, and the weighting vector will be an element of $\Delta_N$, a set which is defined as: $\Delta_N$ is known as the corner of the cube because it includes the points in the non-negative orthant of $\R^N$ that are under $\c{S}_N$, or, equivalently, all the points in the non-negative orthant with the $N-1$ unit simplex as a boundary. For example, in the case of weightings with $N=3$, the set $\Delta_N$ will be the tetrahedron (or triangular pyramid) under the triangular $2$-simplex shown above. ## Write operation DNCs have only one write head, meaning that they can only store one new vector in the memory at each time step. As with the read heads, the write head generates a write weighting $\b{w}^\r{w}_t \in \Delta_N$ in an analogous manner, and this contains the degree to which each memory location will be involved in the write operation. In the case of the read heads, the read weighting is the only thing needed to interact with the memory. The write head, however, also requires the vector to be written $\b{v}_t \in \R^W$ and an erase vector $\b{e}_t \in [0,1]^W$ which determines to what degree the elements of each of the locations involved in the write operation have to be erased before the update (note that this is analogous with the way in which LSTM cells use forget gates that have the ability to erase the content of the cell before the input gate opens). If $\b{e}_t[i] = 1$, the $i$-th element of the corresponding location in the memory will be completely erased; keep in mind that, as discussed for the read operation, the pluralistic nature of DNCs signifies that a location will rarely be completely erased. The equation that determines the new content of the memory is: where $\circ$ denotes the element-wise matrix product and $\b{E}$ is a matrix of ones with the same size as the memory $\b{M}$. The element-wise product (or Hadamard product) of two matrices is: With the dualistic simplification, our previous vector stored at memory location $2$ (represented as the weighting $\b{w}^\r{w}_t = [0;1;0;0]$) could be completely replaced (by using $\b{e}_t = \b{1}$) with the new vector $[-1.5;-1.3;-1.1]$ by using these parameters: For these values, \eqref{newm} would give: The companion notebook allows you to check how these values are obtained and apply the formulae to your own inputs. Note how the erasing and the updating have been wisely set out as a series of multiplications, additions and subtractions, all of which are differentiable. Obviously, $\b{v}_t \in \R^W$ like the other vectors stored in the memory. Although $\b{e}_t$ is a vector in $[0,1]^W$, we would expect it to always be a vector of ones, that is $\b{e}_t = \b{1}$, as it seems reasonable to completely erase the $W$ elements from a memory location before updating it. Again, this would be the case in a dualistic binary world, but it does not apply to actual DNCs for which a number of elements in the memory vector may be partially erased or not even erased at all. Add to this the fact that the write weighting could be focusing on different locations with different non-null degrees of attention and you will get a good idea of the pluralistic nature of DNCs. The learning algorithm will hopefully determine the best vectors for each time $t$ and they will consist of elements that are not as dualistic as in the running example. Let us now consider the same memory matrix $\b{M}_t$ and vector to be written $\b{v}_t$, but let us change the write weighting and erase vector to non-dualistic alternatives: With these pluralistic values, \eqref{newm} would give: Once again, the companion notebook allows you to check how these values are obtained. Equation \eqref{newm} is probably better understood if shown at the element level: where $[i,j]$ and $[i]$ refer to the corresponding element in a matrix or vector, respectively. #### New interface parameters in this section We have just introduced the first parameters emitted by the controller at time step $t$, namely, the write vector $\b{v}_t$ and the erase vector $\b{e}_t$. The controller actually emits two vectors, $\b{v}_t$ and $\hat{\b{e}}_t$, the first of which is used unaltered as the write vector. The logistic sigmoid function $\sigma$ is, meanwhile, applied to $\hat{\b{e}}_t$ in order to constrain its elements to $[0,1]$ and obtain $\b{e}_t$: where I shall add a block like that above to each section in which new interface parameters are presented. As seen above, the beginning of each of these blocks is marked with the astronomical symbol for Uranus . ## Intermezzo In the previous sections, we have explored the fundamentals of DNCs and their memory modus operandi. Basically, a matrix stores vectors, and weightings are used to decide which locations take part in the read or write operations. How these weightings are computed will be our main concern for the rest of the guide, so let’s go to it! ## Content-based addressing How do the read heads and the write head compute the corresponding read and write weightings? Various memory addressing schemes are used for this purpose, but for now, let me introduce the simplest: content-based addressing. Content-based addressing allows us to refer (via the read or write weightings) to the memory locations whose vectors are more similar to a given lookup key $\b{k} \in \R^W$. Recall that in a dualistic system, one would expect this kind of addressing mode to provide access to the most similar location only, but the pluralistic approach of DNC implies that all vectors will be affected to a greater or lesser extent. Given a lookup key vector $\b{k} \in \R^W$, a vector-valued function $\c{C}(\cdot)$ is used to produce a weighting in $\c{S}_N$ (see the discussion concerning weightings above) with a weight for each memory location, such that $\c{C}(\cdot)[i] > \c{C}(\cdot)[j]$ indicates that the content of location $i$ is more similar to $\b{k}$ than the content of location $j$. As mentioned previously, the sum of all the elements of a vector in $\c{S}_N$ is $1$; it is, therefore, possible to interpret $\c{C}(\cdot)$ as a probability distribution over the memory locations. Besides the memory matrix and the lookup key, the function $\c{C}$ also uses a scalar $\beta \in [1,\infty)$ that represents key strength as discussed later. The $i$-th element of $\c{C}$ is obtained as follows: $\b{M}[i,\cdot]$ denotes the $i$-th row of matrix $\b{M}$ (represented as a column vector); in our case, this corresponds to the vector stored at memory location $i$. $\c{D}$ is the cosine similarity, a scalar similarity measure between two vectors obtained as the cosine of the angle between them. If the two vectors have the same orientation (for example, $[0.5;0.5;0.5]$ and $[0.1;0.1;0.1]$), then this angle is $0^\circ$, and $\c{D}$ obtains its maximum value of $1$; if the vectors have exactly opposite orientations, then the angle is $180^\circ$, and $\c{D}$ obtains its minimum value of $-1$. Note that orientation and not magnitude is the relevant feature here: two vectors do not necessarily need to be equal to have a cosine similarity of $1$. For any two vectors, the value of $\c{D}$ will range between $-1$ and $1$. The cosine similarity $\c{D}$ is defined as follows: The numerator is the dot product of $\b{u}$ and $\b{v}$, computed as: where $W$ is the length of $\b{u}$ and $\b{v}$. The denominator is the product of the Euclidean norm (also known as the $2$-norm) of each vector: Let us assume that we have the following capacity 2 memory: Consider that the lookup vector is $\b{k}= [0.3;0.5;1]$ (which, as will intuitively be noted, is closer to location $2$ than to location $1$). The cosine similarity between the lookup vector and each of the memory vectors is: This is a graphical representation of the three vectors. It is now possible to calculate the values of $\c{C}$ for two different values of $\beta$, namely $\beta \in \{1,10\}$. The companion notebook allows you to check how all these values are obtained. Note the effect of the exponent $\beta$ on the exponential function $\r{exp}$. Closer values are more separated by the function as the value of $\beta$ grows. In both cases, the second element of the resulting vector is greater than the first, thus illustrating the fact that the second memory location is closer to $\b{k}= [0.3;0.5;1]$ than the first; the second element is, however, considerably greater than the first when a larger value of $\beta=10$ is used. Recall that the two elements have to add up to $1$. At each time $t$, the controller emits one lookup vector for each read head, namely $\b{k}^{\r{r},i}_{t}$ with $i=1,\ldots,R$, and a single lookup vector $\b{k}^{\r{w}}_t$ for the write head. It also emits $R$ read strengths $\beta^{\r{r},i}_t$ with $i=1,\ldots,R$, and a single write strength $\beta^{\r{w}}_t$. You may venture that the read and write heads compute the read and write weightings directly by using $\c{C}$, that is, The hourglass icon ⏳ is used throughout this guide to mark equations that are temporarily introduced for educational purposes but that are not part of the DNC model as presented in the Nature article. The previous two equations are an example of this, since, as will be seen later, the DNC computes the weightings in a more elaborate manner. Using only content-based addressing would considerably restrict the possibilities of the write and read heads to access the memory. For example, the task of copying an input vector sequence in such a way that the DNC repeats it completely once the input sequence has finished requires some kind of incremental addressing (i.e., reading at the next time step the vector that was written immediately after the last one read) that cannot be satisfied by means of content-based addressing. The heads consequently combine content-based addressing with more sophisticated schemes. In particular, content-based addressing is combined with dynamic memory allocation when writing and with temporal memory linkage when reading. The following section will focus on the latter. #### New interface parameters in this section The controller emits at time step $t$, among others, the following vectors and scalars corresponding to the discussion in this section: The vectors $\b{k}$ are used unaltered as the lookup vectors for the read and write heads. The scalars $\hat{\beta}$ are passed through a oneplus function before obtaining the corresponding strengths in order to ensure that the final values of the strengths lie in the domain $[1,\infty)$: with ## Temporal memory linkage This kind of memory reading scheme is mainly based on a temporal link matrix $\b{L}_t$ that keeps track of the order in which locations have been written. This matrix acts like a chronicler, saving the history of memory writes in the mathematical equivalent of a chronicle as follows: “In the beginning, memory location 2 was written. Then, location 4 was written after location 2. Then, location 1 was written after location 4.” The temporal link matrix $\b{L}_t$ is an $N \times N$ matrix in which the element $\b{L}_t[i,j]$ indicates whether memory location $i$ was written after location $j$. In our simplistic dualistic view, the chronicle above will be represented (assuming a memory with capacity $N=4$) as: The $1$ in the colored element $\b{L}_t[4,2]$ represents the sentence “Then, location 4 was written after location 2” in the narrative shown previously. Note that row $i$ holds backward information (namely, what was written before writing to location $i$; for example, the fourth row in the previous matrix lets us know that location $2$ was written before location $4$), whereas column $j$ contains forward information (namely, what was written after writing to location $j$; for example, the second column in the previous matrix lets us know that the write head moved to location $4$ after writing to location $2$). The fact that the second column has a non-zero element but the second row is made up of zeros indicates that memory location $2$ was the first to be written; the fact that both the third row and the third column are zero reveals that location $3$ has not yet been written. Bearing this in mind, given a generic weighting $\b{w}_t$ it can easily be deduced how we can move backward or forward in time in order to shift attention to those locations written before or after those represented by $\b{w}_t$; the resulting locations will be respectively represented by the backward weighting $\b{b}_t$ and the forward weighting $\b{f}_t$, which are computed as: For example, given the previous temporal link matrix $\b{L}_t$ in \eqref{lmatrix} and a dualistic weighting $\b{w}_t = [0;0;0;1]$ representing location 4, the backward weighting would be: which indicates that the location written before location 4 is location 2. The forward weighting would be analogously obtained as: which indicates that the location written after location 4 is location 1. Note again that although the previous example belongs to the simplistic dualistic world, DNCs deal with temporal link matrices and weightings that are pluralistic by nature. As a result of this, the element $\b{L}_t[i,j]$ in the temporal link matrix actually indicates to what degree memory location $i$ was written after location $j$; the backward and forward weightings also focus their attention on every location in a non-dualistic manner. In the special case of attempting to obtain the backward weighting for the second memory location ($\b{w}_t = [0;1;0;0]$), which is the first location written according to $\b{L}_t$, we will obtain: As stated previously, temporal memory linkage is an addressing mode that is intended for reading, but is based on information regarding writes that is provided by the chronicler matrix $\b{L}_t$ because the motivation here is to allow memory locations to be read in the same order as they were written (or in the reverse order, depending on the task). With this addressing scheme, and given $\b{L}_t$ and the locations $\b{w}^{\r{r},i}_{t-1}$ that were read at time $t-1$ by the $i$-th read head, the locations that the $i$-th read head should consequently pay attention to at time $t$ if the original write order is intended to be respected is represented by the forward weighting $\b{f}^i_t$, and the locations to be read by the $i$-th head at time $t$ if the reverse of the original write order needs to be followed is represented by the backward weighting $\b{b}^i_t$, both of which are computed as: The temporal memory linkage addressing mode, therefore, provides two (forward and backward) means to determine the next location to be read by a read head. We have already studied a third mode, namely, content-based addressing, which allows each read head to compute a content weighting $\b{c}^{\r{r},i}_t \in \c{S}_N$ (the paper wrongly indicates $\Delta_N$ in the “Read weighting” section on page 478) as follows: where the read (lookup) keys $\b{k}^{\r{r},i}_t$ and the key strengths $\beta^{\r{r},i}_t$ are parameters emitted by the controller, as discussed previously. How are these three addressing modes combined in order to determine the final weighting $\b{w}^{\r{r},i}_{t}$ to be used by the $i$-th read head? The three modes are interpolated using three scalar coefficients $\b{\pi}^i_t[1]$, $\b{\pi}^i_t[2]$ and $\b{\pi}^i_t[3]$ that are emitted by the controller: A read mode vector $\b{\pi}^i_t \in \c{S}_3$ is emitted by the controller for each read head. In a dualistic world, only one of the three coefficients would be one and the other two would be zero, but DNCs are pluralistic and much more flexible, and may actually combine different addressing schemes in a single read operation, the resulting weighting being a mixture of the contents of many different locations referred to via different addressing modes. As with the other weightings, $\b{b}^i_t \in \Delta_N$ and $\b{f}^i_t \in \Delta_N$, proof of which is omitted in this guide. If, however, proof is required, it is necessary to know that every row and column in $\b{L}_t$ is a weighting that belongs to $\Delta_N$, that is, $\b{L}_t[i,\cdot] \in \Delta_N$ and $\b{L}_t[\cdot,j] \in \Delta_N$ for all $i$, $j$ and $t$. This will be clearer after reading the next section. In the preceding discussion I have intentionally circumvented how the link matrix $\b{L}_t$ is computed. Recall that, although it is used to eventually compute the read weightings, this matrix contains information regarding writes. Details on how this is achieved are provided in the following section. #### New interface parameters in this section The controller emits a different vector $\hat{\b{\pi}}^i_t$ with $i=1,\ldots,R$ for each read head; in order to ensure that each of these vectors belongs to $\c{S}_3$, the softmax function is applied to obtain the $R$ read mode vectors $\b{\pi}^i_t$ with $i=1,\ldots,R$ in a such a way that the three elements of each vector add up to $1$ and are non-negative: Each element in $\b{\pi}^i_t$ is, therefore, obtained as: As stated in the previous section, $\b{L}_t \in [0,1]^{N \times N}$ is an $N \times N$ matrix in which the element $\b{L}_t[i,j]$ indicates to what degree memory location $i$ was written after location $j$ after time step $t$ and before time $t+1$. Let me begin by describing how things would work in the dualistic view when a single location is written at each time step, and let me also assume the (wrong) hypothesis that a write operation is always performed at each time step. With these simplifications $\b{L}_t$ would be a matrix of zeros and ones in which if $i$ is the last written location (at time $t$) and $j$ is the second-to-last written location (at time $t-1$), then $\b{L}_t[i,j]=1$ ; if neither $i$ has been written at time step $t$ nor $j$ has been written at time step $t-1$, then $\b{L}_t[i,j]$ remains unchanged with respect to its previous value at time step $t-1$; in the other cases (namely, either $i$ has been written at time $t$ or $j$ has been written at $t-1$ but both are not true), then $\b{L}_t[i,j]=0$ (recall that we are assuming that a write operation is always performed at each step), reflecting the fact that $i$ has not been written after writing to $j$: Also, $\b{L}_0[i,j]=0$ for all $i$ and $j$. Apart from the usual over-simplification that is intrinsic to the dualistic view, the previous equation ignores the fact that there may be an arbitrary number of time steps between one write and the next. In order to overcome these limitations, we need a more precise means to record the degree to which a memory location has been recently written. This objective is attained by first introducing a new weighting $\b{p}_t \in \Delta_N$, which is called the precedence weighting. The element $\b{p}_t[i]$ denotes the degree to which $i$ was the last location written and is computed recursively; a high value of $\b{p}_t[i]$ may indicate that $i$ has been written at time step $t$ with great dedication (that is, the other locations have not been written at all at time step $t$ or they have been written to a much lesser extent), but it may also indicate that location $i$ was written with great dedication at $t’<t$ but that no significant writes have been carried out in the memory since $t’$; it may also indicate that writing attention has been partially paid to $i$ at different recent time steps in the past and the total cumulative attention degree is greater than the degrees of attention paid to the other locations. A preliminary dualistic formulation of the precedence weighting would be: Note that $\b{p}_t$ is only updated when a write operation has been performed at time step $t$, and that it could consequently remain untouched for long read-only periods. To return to the pluralistic DNC reality, even a single read-only time step is notoriously difficult, as the write weighting $\b{w}^\r{w}_t$ will hardly be zero; we must, therefore, raise our sights and embrace this fact by introducing a continuous formulation of the precedence weighting as follows: Note that the previous equation would degenerate to \eqref{preced} in the limiting cases of a full-write or read-only time steps. In the first case, the summation of all the components of $\b{w}^\r{w}_t$ would have its greatest value (i.e., $1$), and $\b{p}_t$ would be reduced to $\b{w}^\r{w}_t$; in the second case, the summation of all the components of $\b{w}^\r{w}_t$ would be $0$, $\b{w}^\r{w}_t$ would also be $\b{0}$, and $\b{p}_t$ would then be a copy of $\b{p}_{t-1}$. Note that after a hypothetical full write, $\b{p}_t$ would reset and the past history (encoded in $\b{p}_{t-1}$) completely forgotten. The precedence weighting is initialized to $\b{p}_0 = \b{0}$. Bearing all this in mind, we are finally ready to set out a differentiable final formulation of $\b{L}_t[i,j]$ which surpasses the dualistic constraints of \eqref{Lsimp}. The equation must reflect the fact that if the memory location $i$ is significantly written at time step $t$ (i.e., $\b{w}^\r{w}_t[i]$ is high), then $\b{L}_t[i,j]$ must be given a value that is mostly proportional to the degree to which the memory location $j$ was the last location written before that (this information is represented by $\b{p}_{t-1}[j]$); one possibility for this is the product $\b{w}^\r{w}_t[i] p_{t-1}[j]$. If $\b{w}^\r{w}_t[i]$ is low (or, equivalently, $1-\b{w}^\r{w}_t[i]$ is high), then $\b{L}_t[i,j]$ will mostly maintain the value of $\b{L}_{t-1}[i,j]$; there is, however, an exception to the latter rule: if location $j$ has been significantly written at time step $t$ (i.e., $\b{w}^\r{w}_t[j]$ is high), then this situation has to trigger a non-dualistic reset of $\b{L}_t[i,j]$ to a low value, as the memory location that will be written after $j$ will not be known until time step $t+1$. The resulting differentiable equation that integrates all these aspects is: Note that as $\b{w}^\r{w}_t \in \Delta_N$, it is not possible for the subtractions in parenthesis to provide a negative value. In order to complete the specification of $\b{L}_t[i,j]$, the two following equations are required: This concludes the description of how the read weightings are computed as a combination of content-based addressing and temporal memory linkage. In the paper published in Nature there is a subsection entitled Sparse link matrix on page 478 which contains additional details on how to efficiently store and compute the link matrix $\b{L}_t$, but as these are implementation notes they will not be commented on in this guide. Let us now explore how the write weightings are computed. ## Dynamic memory allocation As already stated, content-based addressing is combined with dynamic memory allocation in order to obtain the write weighting $\b{w}^\r{w}_t$. Dynamic memory allocation in DNC represents the pluralistic equivalent of the memory allocation schemes in many programming languages. The objective of the dynamic memory allocation is to make DNCs compute a new kind of weighting at every time step, the allocation weighting, which is a vector $\b{a}_t \in \Delta_N$ that indicates to what degree each memory location is allocable (that is, not write protected). The fact that $\b{a}_t \in \Delta_N$ implies that the dualistic metaphor cannot be generally followed here. The allocation weighting corresponding to $N=4$ equally allocable memory locations would be, for example, $\b{a}_t = [0.1;0.1;0.1;0.1]$ rather than $[1;1;1;1]$; the fact that the second memory location is completely allocable but no other location can be reserved would be represented as $\b{a}_t = [0;1;0;0]$; the allocation weighting $\b{a}_t = [0.4;0.2;0;0]$ represents the situation in which the first location is more allocable than the second. If $\b{a}_t=\b{0}$, then the DNC has run out of free memory locations and no location can consequently be accessed for writing by means of dynamic memory allocation at time $t$; it is, however, important to note that it might still be possible to write to a location accessed by means of content-based addressing. The details regarding the computation of the allocation weighting vector $\b{a}_t$ will be provided in the next section. We shall, however, first see how it is used in order to determine the write weighting. In the same way that each read head computes a read content weighting $\b{c}^{\r{r},i}_t \in \Delta_N$ (see above), the write head computes a write content weighting $\b{c}^\r{w}_t \in \Delta_N$ as follows: where the write (lookup) key $\b{k}^\r{w}_t$ and the write key strength $\beta^\r{w}_t$ are parameters emitted by the controller. Observe the subindex of the memory matrix in the previous equation: $\b{c}^\r{w}_t$ is used to obtain $\b{M}_t$ and is, therefore, computed from $\b{M}_{t-1}$. It should be clear at this stage that there are three possible paths that can be followed at time $t$ regarding a write operation (and these will affect how the write weighting $\b{w}^\r{w}_t$ is obtained): 1. writing (via dynamic memory allocation) into the locations specified on the allocation weighting $\b{a}_t$; 2. writing (via content-based addressing) into the locations specified on the write content weighting $\b{c}^\r{w}_t$; 3. not writing at all at this time step. In line with the non-dualistic (pluralistic) nature of DNCs, a differentiable combination of the previous three schemes is used. In order to decide between the first two options, the DNC controller emits a scalar allocation gate $g^\r{a}_t \in [0,1]$ that governs the interpolation between $\b{a}_t$ and $\b{c}^\r{w}_t$ (the first two options), and a scalar write gate $g^\r{w}_t \in [0,1]$ that determines to what degree the memory is or is not written at this time step (the third option). The resulting write weighting is therefore computed as: In the limiting case in which $g^\r{w}_t=0$, $\b{w}^\r{w}_t$ would be $\b{0}$ meaning that no write operation would be performed at this time step; $g^\r{w}_t=1$ and $g^\r{a}_t=1$ correspond to dynamic memory addressing only (note that $\b{w}^\r{w}_t$ may still be $\b{0}$ if $\b{a}_t$ is also $\b{0}$); finally, $g^\r{w}_t=1$ and $g^\r{a}_t=0$ corresponds to content-base addressing only. The activation functions will not in fact produce these limiting values, thus resulting in gates that will be partially closed (or, equivalently, partially open). #### New interface parameters in this section The controller emits the scalars $\hat{g}^\r{a}_t$ and $\hat{g}^\r{w}_t$. In order to constrain them in the domain $[0,1]$ and to obtain the allocation and write gates, respectively, the logistic sigmoid function $\sigma$ is used: ## Computation of the allocation weighting vector As stated in the previous section, the allocation weighting $\b{a}_t$ indicates to what degree each memory location is allocable. As also stated, DNCs do not exist in a dualistic world, and the memory allocation scheme consequently deviates considerably from that found in many computer systems in which allocability is a binary property of each location (a location can or cannot be allocated). In order to compute $\b{a}_t$, a new vector $\b{u}_t \in [0,1]^N$, the usage vector, will first be introduced. Note that in this case the elements of $\b{u}_t$ may add up to much more than one (the maximum is $N$). As will be seen later, the formula used to obtain $\b{a}_t$ will then give significantly higher weights to those locations that appear closer to the head of the list of locations sorted in ascending order with respect to $\b{u}_t$. If all usages $\b{u}_t[i]$ are $1$, then no memory can be allocated until some locations have been freed and $\b{a}_t$ will be $\b{0}$. The usage vector $\b{u}_t$ is initialized to $\b{u}_0=\b{0}$. The main idea behind the computation of $\b{u}_t[i]$ is that of taking into account that different forces will act in opposite directions in order to determine whether the usage of location $i$ has to be increased at the current time step (to a maximum of $1$, which indicates that $i$ is completely in use and cannot be allocated at all) or decreased (to a minimum of $0$, which indicates that $i$ is completely allocable). On the one hand, the decremental force acts when the location $i$ has been read at time step $t-1$; this may be a good sign that the contents of location $i$ are no longer required (more details on this subject are provided below). On the other hand, the incremental force acts when location $i$ was written at time step $t-1$, which clearly indicates that the usage of $i$ needs to be strengthened as the value stored at location $i$ has not had yet the chance to be read. The decremental force is represented by the retention vector $\b{\psi}_t \in [0,1]^N$, which indicates to what degree each of the memory locations need to be retained at time step $t$ based on the information provided by the read operations at time step $t-1$: • A high value in the retention vector for location $i$ (when $\b{\psi}_t[i]$ is close to $1$) indicates that $i$ has to be retained (i.e., not freed) at time step $t$, because it was not read at time $t-1$. • A low value in the retention vector for location $i$ (when $\b{\psi}_t[i]$ is close to $0$) indicates that $i$ is available at time step $t$, because it was read at time $t-1$. Bearing all this in mind, the usage vector $\b{u}_t$ may be, in principle, formulated in a differentiable incremental manner as: Note how the two opposite forces act: $\b{w}^\r{w}_{t-1}[i]$ increases the previous usage score, but $\b{\psi}_t[i] \in [0,1]$ then decreases the result. The original paper adds a third term between the parentheses in the previous equation. I must admit that I am not completely certain about its purpose but my guess is that its mission is to cut off the result in order to ensure that $\b{u}_t[i] \in [0,1]^N$. The final equation that refines \eqref{firstu} is then: Note that if $\b{u}_{t-1}[i] \approx 1$, $\b{w}^\r{w}_{t-1} \approx 1$ and $\b{\psi}_t[i] \approx 1$, then $\b{u}_t[i]$ could easily be close to $2$ in \eqref{firstu}, but it will not be greater than $1$ in \eqref{secondu}. Note also that since none of the vector elements in \eqref{secondu} can be negative (they all belong to the range $[0,1]$), $\b{u}_t[i]$ cannot be negative either. Equation \eqref{secondu} can also be equivalently expressed in vector form as: where $\circ$ denotes the element-wise product (or Hadamard product) of two vectors.: We have yet to tackle two points. First, the formulation of the retention vector $\b{\psi}_t$, and second, the actual computation of the allocation weighting $\b{a}_t$. With regard to the retention vector $\b{\psi}_t \in [0,1]^N$, a preliminary proposal for it would be: With the dualistic simplification, the read weight $\b{w}^{\r{r},j}_{t-1}[i]$ would be $0$ or $1$; once one of the read weights for location $i$ was $1$ (indicating that the corresponding read head had performed a read operation on $i$ at time step $t-1$), the resulting $\b{\psi}_t[i]$ would be $0$; in other words, if $i$ was read by at least one read head at time $t-1$, then $i$ could be freed (not retained) at $t$. Real-word DNCs do not work under these extreme dualistic conditions and $\b{\psi}_t[i]$ will be higher or lower depending on the degree to which the previous read operations paid attention to $i$. Some readers may have noticed a limitation in the equation just formulated for the retention vector $\b{\psi}_t \in [0,1]^N$: if locations are freed immediately after a read operation is performed on them, then it might not be possible to read a particular value stored at a memory location more than once so that it is reused at different future time steps during the execution of the neural network. This would be a frustrating restriction that could limit the computational power of DNCs and leave many applications out of reach. In order to overcome this limitation, the controller emits a scalar free gate $f_t \in [0,1]$ to guarantee the possibility of the retention of a memory location even after a read operation. The resulting equation is: As is observed, there is a different free gate $f_t^j$ for each read head. If $f_t^j \approx 0$ for all read heads, then $\b{\psi}_t[i] \approx 1$ thus indicating that the location $i$ cannot be freed at time $t$ independently of whether or not $i$ was read at time step $t-1$. The last equation in vector form is: where the product of vectors represents the element-wise product as before. Finally, to conclude this section, let me discuss how the allocation weighting $\b{a}_t \in \Delta_N$ is computed. As already stated, higher weights will be given in $\b{a}_t$ to those locations that are closer to the head of the list of locations sorted with respect to $\b{u}_t$ in ascending order. The first step is, therefore, to obtain a free list $\b{\phi}_t \in \N^N$ made up of the indices of the memory locations (in the range of $1,\ldots,N$) in ascending order of usage at time $t$ as defined by $\b{u}_t$: For example, given the usage vector $\b{u}_t=[1;0;0.8;0.4]$, the resulting free list would be $\b{\phi}_t=[2;4;3;1]$; the least used memory location would be $\b{\phi}_t[1]$ (location $2$ in the example, with usage $\b{u}_t[\b{\phi}_t[1]]=0$) and the most used memory location would be $\b{\phi}_t[N]$ (location $1$ in the example, with usage $\b{u}_t[\b{\phi}_t[4]]=1$). Given $\b{\phi}_t$ and $\b{u}_t$ there are many different ways in which to obtain an allocation weighting $\b{a}_t$ that complies with the restrictions that a memory location stored at the $k$-th element of $\b{\phi}_t$ receives an allocation weight greater or equal than that received by the memory location stored at the $(k+1)$-th element of $\b{\phi}_t$, while the allocation weighting $\b{a}_t[i]$ is simultaneously $0$ for those locations with $\b{u}_t[i]=1$. One option would be: $\gamma$ is the value that satisfies $\b{\phi}_t[\gamma] = j$. If the vector $\b{u}_t=[1;0;0.8;0.4]$ is again employed, the resulting allocation weighting obtained from equation \eqref{myat} would be $\b{a}_t=[0;1;1/3;0.5]$: $j$ $\b{u}_t[j]$ $\gamma : \b{\phi}_t[\gamma] = j$ $\b{a}_t[j]$ $1$ $1$ $4$ $0$ $2$ $0$ $1$ $1/1$ $3$ $0.8$ $3$ $1/3$ $4$ $0.4$ $2$ $1/2$ The equation above, however, discards important information regarding the degree of usage contained in $\b{u}_t$; moreover, it does not guarantee that $\b{a}_t \in \Delta_N$. DNCs, in fact, use a different differentiable approach: in which $\gamma$ is again the value that satisfies $\b{\phi}_t[\gamma] = j$. For the running example, this equation will give $\b{a}_t[1] = 0$, $\b{a}_t[2] = 1$, $\b{a}_t[3] = 0$, $\b{a}_t[4] = 0$, that is, $\b{a}_t=[0;1;0;0]$. $j$ $\b{u}_t[j]$ $\gamma : \b{\phi}_t[\gamma] = j$ $1-\b{u}_t[j]$ $\prod_{i=1}^{\gamma-1} \b{u}_t[\b{\phi}_t[i]]$ $\b{a}_t[j]$ $1$ $1$ $4$ $0$ $0 \times 0.4 \times 0.8 = 0$ $0$ $2$ $0$ $1$ $1$ $1$ $1$ $3$ $0.8$ $3$ $0.2$ $0 \times 0.4 = 0$ $0$ $4$ $0.4$ $2$ $0.6$ $0$ $0$ Note that for those locations with full occupation (i.e., $\b{u}_t[\b{\phi}_t[j]] \approx 1$), the subtraction is approximately $0$ and it is, therefore, $\b{a}_t[\b{\phi}_t[j]]$. Note also that if at least one usage value of $0$ exists, then the first location in the list $\b{\phi}_t$ will be assigned a one in the allocation weighting and the remaining locations will be assigned a zero. No proof that the resulting allocation vector always belongs to $\Delta_N$ will be provided here. A further example. Note that the companion notebook allows you to check how these tables are obtained and get a table with your own data. In the case of the usage vector $\b{u}_t=[0.4;0.6;0.2;0.5]$, the resulting allocation weighting is $\b{a}_t=[0.12;0.016;0.8;0.04]$: $j$ $\b{u}_t[j]$ $\gamma : \b{\phi}_t[\gamma] = j$ $1-\b{u}_t[j]$ $\prod_{i=1}^{\gamma-1} \b{u}_t[\b{\phi}_t[i]]$ $\b{a}_t[j]$ $1$ $0.4$ $2$ $0.6$ $0.2$ $0.12$ $2$ $0.6$ $4$ $0.4$ $0.2 \times 0.4 \times 0.5 = 0.04$ $0.016$ $3$ $0.2$ $1$ $0.8$ $1$ $0.8$ $4$ $0.5$ $3$ $0.5$ $0.2 \times 0.4 = 0.08$ $0.04$ The original paper presents \eqref{atmod} in a slightly different, yet equivalent form, which avoids the need to define $\gamma$: Sorting is not a common operation in neural networks. It may even lead to some issues in the calculation of the gradient. But according to the authors of the paper, these issues are experimentally overlookable: “The sort operation induces discontinuities at the points at which the sort order changes. We ignore these discontinuities when calculating the gradient, as they do not seem to be relevant to learning” #### New interface parameters in this section The controller emits $R$ scalars $\hat{f}_t^i$ with $i=1,\ldots,R$; in order to constrain them in the domain $[0,1]$ and obtain the free gates, the logistic sigmoid function $\sigma$ is used: Upon integrating all the interface parameters introduced throughout this guide, we obtain the definition of the interface vector $\b{\xi}_t$: ## Conclusions Memory-augmented neural networks, such as DNCs, lead to interesting challenges in the interplay of machine learning, reasoning and algorithm inference. The purpose of this guide is not to point out these opportunities, but to simply present the motivations behind the equations that define how DNCs work in an pedagogical manner. I certainly hope that the objective has been achieved. Finally, it is interesting to note that many of these equations admit alternative formulations, which may pave the way for further curiosity, reflection and research. How to cite this work: Juan Antonio Pérez-Ortiz, “A bit-by-bit guide to the equations governing differentiable neural computers”. First published on October 20 2017. Last modified on October 20 2017. https://jaspock.github.io/funicular/dnc.html, accessed on October 23 2017 [replace with your current date; a bibtex file is also available] About the author: I work as an associate professor and researcher at Universidad de Alicante in Spain. I received my Ph.D. in computer science in 2002 with a thesis on recurrent neural models for sequence processing that used, among others, distributional representations for natural language processing (as devised by my thesis supervisor, Mikel L. Forcada) and LSTM cells (as devised by Jürgen Schmidhuber, who was my supervisor during my internship at the IDSIA research institute in 2000). I have also worked on machine translation and computer-assisted translation, especially as a member of the team involved in the development of the open-source machine translation platform Apertium. I have recently started to research on the topic of neural machine translation. I currently teach undergraduate and postgraduate courses on translation technologies, programming and web development. A list of my publications is available at my profile at Google Scholar. Sources: the source files of this document are available in a Github repository. License: «A bit-by-bit guide to the equations governing differentiable neural computers» by Juan Antonio Pérez-Ortiz is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.	2019-01-21T13:50:12	{"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": 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": 0.6866927146911621, "perplexity": 408.65283441716906}, "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-2019-04/segments/1547583792784.64/warc/CC-MAIN-20190121131658-20190121153658-00433.warc.gz"}
https://www.usgs.gov/media/files/tungsten-2019-tables-only-release	# Tungsten in 2019, tables-only release Tungsten in 2019, tables-only release ## Detailed Description Advance data tables (XLSX format) for the tungsten chapter of the Minerals Yearbook 2019. A version with an embedded text document and also a PDF of text and tables will follow.	2021-10-23T20:44:58	{"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": 0.9257502555847168, "perplexity": 9748.327516583055}, "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/1634323585768.3/warc/CC-MAIN-20211023193319-20211023223319-00591.warc.gz"}
https://www.nist.gov/programs-projects/quantum-information-and-quantum-limited-metrology	An official website of the United States government The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site. The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely. # Quantum Information and Quantum-Limited Metrology ## Summary The coherent control of quantum-mechanical systems holds promise for revolutionizing technologies including computing, simulation, secure communication and precision metrology. We pursue various aspects of these quantum-enabled applications using systems of trapped ions. Below are descriptions of several of our experiments and links to some key publications. The following links contain more complete lists of publications: Quantum Logic and Coherent Control, and Penning Traps and Non-Neutral Plasmas. Contact information for any current member of the group is available in the Time and Frequency Division Staff Listing. ## Paul Trap Experiments We pursue proof-of-concept experiments in quantum information processing and quantum control with trapped ions. In addition to pushing current limits on traditional quantum gate-based architectures for quantum computing we explore alternative approaches to entanglement generation and quantum information processing including microwave-based quantum gates and quantum simulation in 2-D arrays of rf microtraps. In one experiment we make use of a segmented three-dimensional Paul trap (Fig. 1) in which we confine magnesium and beryllium ions in linear arrays. The trap features two trapping zones to split and recombine ion crystals and an X-shaped junction, which can be used to reorder ions in a linear array [1]. We have demonstrated several elements of a scalable quantum information processor in this and similar traps, including fast, low-excitation transport [2] and a high-fidelity universal gate set [3]. In particular, we achieved single-qubit operations at a fault-tolerant level (with less than one error in 25000 operations) and two-qubit entangling operations with less than one error in 1000 operations. We have also demonstrated multi-species entangling operations between a magnesium and a beryllium ion [4], which are an integral part of a possible future trapped ion quantum computer. As an alternative to conventional laser-based quantum gates, we are also investigating microwave-driven gates [5]. This approach avoids a fundamental error source due to photon scattering and may be technologically easier to scale-up. In addition, breaking away from the traditional segmented linear traps, we develop micro-fabricated surface-electrode traps (Fig. 2) that enable flexible 2D geometries, and tunable interactions, which are useful for quantum computing and quantum simulation [6, 7]. Large-scale devices will need new methods for quantum state readout. In collaboration with colleagues at NIST, we are developing highly efficient superconducting photon detectors that are integrated into ion traps as part of the micro-fabrication process. [1] R. B. Blakestad et al., "Near-ground-state transport of trapped-ion qubits through a multidimensional array", Phys. Rev. A 84, 032314 (2011) [2] R. Bowler et al., "Coherent Diabatic Ion Transport and Separation in a Multizone Trap Array", Phys. Rev. Lett. 109, 080502 (2012) [3] T. R. Tan et al., "Multi-Element Logic Gates for Trapped-Ion Qubits", Nature 528, 380 (2015) [4] J. Gaebler et al. "High-Fidelity Universal Gate Set for 9Be+ Ion Qubits", Phys. Rev. Lett. 177, 060505 (2016) [5] C. Ospelkaus et al., "Microwave quantum logic gates for trapped ions", Nature 476, 181 (2011) [6] S. Seidelin et al., "A microfabricated surface-electrode ion trap for scalable quantum information processing", Phys. Rev. Lett. 96, 253003 (2006) [7] A.C. Wilson et al., "Tunable spin-spin interactions and entanglement of ions in separate controlled potential wells", Nature 512, 57 (2014) ## Penning trap quantum simulation experiments Entanglement between individual quantum objects exponentially increases the complexity of quantum many-body systems, so systems with more than 30-40 quantum bits cannot be fully studied using conventional techniques and computers. To make progress at this frontier of physics, we are pursuing Feynman’s pioneering idea of quantum simulation with two-dimensional, single-plane arrays of trapped ions. We use a Penning ion trap (Fig. 1(A)), which employs static electric and magnetic fields for ion confinement, to form single-plane, 2-dimensional triangular arrays of several hundred 9Be+ ions (Fig. 1(B)). Trapped-ions are naturally suited for simulating quantum magnetism. Long-range Ising interactions are engineered with spin-dependent forces on arrays up to ~300 ions. We implement a transverse magnetic field through the application of microwaves resonant with the qubit frequency. This enables simulations of the transverse Ising model $$\hat{H} = \frac{1}{N}\sum_{i<j}J_{i,j}\hat{\sigma}_i^z\hat{\sigma}_j^z + B_\perp\sum_i\hat{\sigma}_i^x$$ In recent experimental work we benchmark quantum dynamics and entanglement through measurements of the composite magnetization (or spin) of the system. We demonstrate quantum correlations and a detailed understanding of different sources of decoherence [1]. Recently, we implemented the multi-quantum coherence protocol invented in NMR. This enables a measurement of out-of-time-order correlation functions that quantify the spread of quantum information throughout the system [2]. [1] J. G. Bohnet et al., “Quantum spin dynamics and entanglement generation with hundreds of trapped ions”, Science 352, 1297 (2016) [2] M. Gärttner et al., "Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet", Nature Physics, 13, (2017) Created November 7, 2016, Updated February 4, 2019	2020-04-04T12:53:50	{"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": 0.6390137076377869, "perplexity": 4171.327256809467}, "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/1585370521876.48/warc/CC-MAIN-20200404103932-20200404133932-00525.warc.gz"}
http://lammps.sandia.gov/doc/compute_temp_deform_eff.html	# compute temp/deform/eff command ## Syntax compute ID group-ID temp/deform/eff • ID, group-ID are documented in compute command • temp/deform/eff = style name of this compute command ## Examples compute myTemp all temp/deform/eff ## Description Define a computation that calculates the temperature of a group of nuclei and electrons in the electron force field model, after subtracting out a streaming velocity induced by the simulation box changing size and/or shape, for example in a non-equilibrium MD (NEMD) simulation. The size/shape change is induced by use of the fix deform command. A compute of this style is created by the fix nvt/sllod/eff command to compute the thermal temperature of atoms for thermostatting purposes. A compute of this style can also be used by any command that computes a temperature, e.g. thermo_modify, fix npt/eff, etc. The calculation performed by this compute is exactly like that described by the compute temp/deform command, except that the formula for the temperature includes the radial electron velocity contributions, as discussed by the compute temp/eff command. Note that only the translational degrees of freedom for each nuclei or electron are affected by the streaming velocity adjustment. The radial velocity component of the electrons is not affected. Output info: This compute calculates a global scalar (the temperature) and a global vector of length 6 (KE tensor), which can be accessed by indices 1-6. These values can be used by any command that uses global scalar or vector values from a compute as input. See this section for an overview of LAMMPS output options. The scalar value calculated by this compute is “intensive”. The vector values are “extensive”. The scalar value will be in temperature units. The vector values will be in energy units. ## Restrictions This compute is part of the USER-EFF package. It is only enabled if LAMMPS was built with that package. See the Making LAMMPS section for more info.	2017-12-11T05:48:59	{"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": 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": 0.8109926581382751, "perplexity": 2123.001134958923}, "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-2017-51/segments/1512948512208.1/warc/CC-MAIN-20171211052406-20171211072406-00624.warc.gz"}
http://dlmf.nist.gov/15.9	# §15.9(i) Orthogonal Polynomials For the notation see §§18.3 and 18.19. # ¶ Jacobi 15.9.1 $\mathop{P^{(\alpha,\beta)}_{n}\/}\nolimits\!\left(x\right)=\frac{\left(\alpha+% 1\right)_{n}}{n!}\mathop{F\/}\nolimits\!\left({-n,n+\alpha+\beta+1\atop\alpha+% 1};\frac{1-x}{2}\right).$ # ¶ Gegenbauer (or Ultraspherical) 15.9.2 $\displaystyle\mathop{C^{(\lambda)}_{n}\/}\nolimits\!\left(x\right)$ $\displaystyle=\frac{\left(2\lambda\right)_{n}}{n!}\mathop{F\/}\nolimits\!\left% ({-n,n+2\lambda\atop\lambda+\frac{1}{2}};\frac{1-x}{2}\right).$ 15.9.3 $\displaystyle\mathop{C^{(\lambda)}_{n}\/}\nolimits\!\left(x\right)$ $\displaystyle=(2x)^{n}\frac{\left(\lambda\right)_{n}}{n!}\mathop{F\/}\nolimits% \!\left({-\frac{1}{2}n,\frac{1}{2}(1-n)\atop 1-\lambda-n};\frac{1}{x^{2}}% \right).$ 15.9.4 $\mathop{C^{(\lambda)}_{n}\/}\nolimits\!\left(\mathop{\cos\/}\nolimits\theta% \right)=e^{ni\theta}\frac{\left(\lambda\right)_{n}}{n!}\mathop{F\/}\nolimits\!% \left({-n,\lambda\atop 1-\lambda-n};e^{-2i\theta}\right).$ # ¶ Chebyshev 15.9.5 $\displaystyle\mathop{T_{n}\/}\nolimits\!\left(x\right)$ $\displaystyle=\mathop{F\/}\nolimits\!\left({-n,n\atop\frac{1}{2}};\frac{1-x}{2% }\right).$ 15.9.6 $\displaystyle\mathop{U_{n}\/}\nolimits\!\left(x\right)$ $\displaystyle=(n+1)\mathop{F\/}\nolimits\!\left({-n,n+2\atop\frac{3}{2}};\frac% {1-x}{2}\right).$ # ¶ Legendre 15.9.7 $\mathop{P_{n}\/}\nolimits\!\left(x\right)=\mathop{F\/}\nolimits\!\left({-n,n+1% \atop 1};\frac{1-x}{2}\right).$ # ¶ Krawtchouk 15.9.8 $\mathop{K_{n}\/}\nolimits\!\left(x;p,N\right)=\mathop{F\/}\nolimits\!\left({-n% ,-x\atop-N};\frac{1}{p}\right),$ $n=0,1,2,\dots,N$; compare also §15.2(ii). # ¶ Meixner 15.9.9 $\mathop{M_{n}\/}\nolimits\!\left(x;\beta,c\right)=\mathop{F\/}\nolimits\!\left% ({-n,-x\atop\beta};1-\frac{1}{c}\right).$ # ¶ Meixner–Pollaczek 15.9.10 $\mathop{P^{(\lambda)}_{n}\/}\nolimits\!\left(x;\phi\right)=\frac{\left(2% \lambda\right)_{n}}{n!}e^{ni\phi}\mathop{F\/}\nolimits\!\left({-n,\lambda+ix% \atop 2\lambda};1-e^{-2i\phi}\right).$ # §15.9(ii) Jacobi Function This is a generalization of Jacobi polynomials (§18.3) and has the representation 15.9.11 $\mathop{\phi^{(\alpha,\beta)}_{\lambda}\/}\nolimits\!\left(t\right)=\mathop{F% \/}\nolimits\!\left({\tfrac{1}{2}(\alpha+\beta+1-i\lambda),\tfrac{1}{2}(\alpha% +\beta+1+i\lambda)\atop\alpha+1};-{\mathop{\sinh\/}\nolimits^{2}}t\right).$ Defines: $\mathop{\phi^{(\alpha,\beta)}_{\lambda}\/}\nolimits\!\left(t\right)$: Jacobi function Symbols: $\mathop{F\/}\nolimits\!\left(a,b;c;z\right)$: hypergeometric function and $\mathop{\sinh\/}\nolimits z$: hyperbolic sine function Permalink: http://dlmf.nist.gov/15.9.E11 Encodings: TeX, pMML, png The Jacobi transform is defined as 15.9.12 $\widetilde{f}(\lambda)=\int_{0}^{\infty}f(t)\mathop{\phi^{(\alpha,\beta)}_{% \lambda}\/}\nolimits\!\left(t\right)(2\mathop{\sinh\/}\nolimits t)^{2\alpha+1}% (2\mathop{\cosh\/}\nolimits t)^{2\beta+1}dt,$ with inverse 15.9.13 $f(t)=\frac{1}{2\pi i}\int_{-i\infty}^{i\infty}\widetilde{f}(i\lambda)\mathop{% \Phi^{(\alpha,\beta)}_{i\lambda}\/}\nolimits\!\left(t\right)\frac{\mathop{% \Gamma\/}\nolimits\!\left(\tfrac{1}{2}(\alpha+\beta+1+\lambda)\right)\mathop{% \Gamma\/}\nolimits\!\left(\tfrac{1}{2}(\alpha-\beta+1+\lambda)\right)}{\mathop% {\Gamma\/}\nolimits\!\left(\alpha+1\right)\mathop{\Gamma\/}\nolimits\!\left(% \lambda\right)2^{\alpha+\beta+1-\lambda}}d\lambda,$ where the contour of integration is located to the right of the poles of the gamma functions in the integrand, and 15.9.14 $\mathop{\Phi^{(\alpha,\beta)}_{\lambda}\/}\nolimits\!\left(t\right)=(2\mathop{% \cosh\/}\nolimits t)^{i\lambda-\alpha-\beta-1}\mathop{F\/}\nolimits\!\left({% \tfrac{1}{2}(\alpha+\beta+1-i\lambda),\tfrac{1}{2}(\alpha-\beta+1-i\lambda)% \atop 1-i\lambda};{\mathop{\mathrm{sech}\/}\nolimits^{2}}t\right).$ For this result, together with restrictions on the functions $f(t)$ and $\widetilde{f}(\lambda)$, see Koornwinder (1984a). # §15.9(iii) Gegenbauer Function This is a generalization of Gegenbauer (or ultraspherical) polynomials (§18.3). It is defined by: 15.9.15 $\mathop{C^{(\lambda)}_{\alpha}\/}\nolimits\!\left(z\right)=\frac{\mathop{% \Gamma\/}\nolimits\!\left(\alpha+2\lambda\right)}{\mathop{\Gamma\/}\nolimits\!% \left(2\lambda\right)\mathop{\Gamma\/}\nolimits\!\left(\alpha+1\right)}\mathop% {F\/}\nolimits\!\left({-\alpha,\alpha+2\lambda\atop\lambda+\tfrac{1}{2}};\frac% {1-z}{2}\right).$ # §15.9(iv) Associated Legendre Functions; Ferrers Functions Any hypergeometric function for which a quadratic transformation exists can be expressed in terms of associated Legendre functions or Ferrers functions. For examples see §§14.3(i)14.3(iii) and 14.21(iii). The following formulas apply with principal branches of the hypergeometric functions, associated Legendre functions, and fractional powers. 15.9.16 $\displaystyle\mathop{\mathbf{F}\/}\nolimits\!\left({a,b\atop 2b};z\right)$ $\displaystyle=\frac{\sqrt{\pi}}{\mathop{\Gamma\/}\nolimits\!\left(b\right)}z^{% -b+(\ifrac{1}{2})}(1-z)^{(b-a-(\ifrac{1}{2}))/2}\\mathop{P^{-b+(\ifrac{1}{2})% }_{a-b-(\ifrac{1}{2})}\/}\nolimits\!\left(\frac{2-z}{2\sqrt{1-z}}\right),$ $b\neq 0,-1,-2,\dots$, $\|\mathop{\mathrm{ph}\/}\nolimits(1-z)\|<\pi$ and $\|1-z\|<1$. 15.9.17 $\displaystyle\mathop{\mathbf{F}\/}\nolimits\!\left({a,a+\tfrac{1}{2}\atop c};z\right)$ $\displaystyle=2^{c-1}z^{\ifrac{(1-c)}{2}}(1-z)^{-a+(\ifrac{(c-1)}{2})}\% \mathop{P^{1-c}_{2a-c}\/}\nolimits\!\left(\frac{1}{\sqrt{1-z}}\right),$ $\|\mathop{\mathrm{ph}\/}\nolimits z\|<\pi$ and $\|\mathop{\mathrm{ph}\/}\nolimits(1-z)\|<\pi$. 15.9.18 $\displaystyle\mathop{\mathbf{F}\/}\nolimits\!\left({a,b\atop a+b+\tfrac{1}{2}}% ;z\right)$ $\displaystyle=2^{a+b-(\ifrac{1}{2})}(-z)^{(-a-b+(\ifrac{1}{2}))/2}\\mathop{P^% {-a-b+(\ifrac{1}{2})}_{a-b-(\ifrac{1}{2})}\/}\nolimits\!\left(\sqrt{1-z}\right),$ $\left\|\mathop{\mathrm{ph}\/}\nolimits\!\left(-z\right)\right\|<\pi$. 15.9.19 $\displaystyle\mathop{\mathbf{F}\/}\nolimits\!\left({a,b\atop a-b+1};z\right)$ $\displaystyle=z^{\ifrac{(b-a)}{2}}(1-z)^{-b}\\mathop{P^{b-a}_{-b}\/}\nolimits% \!\left(\frac{1+z}{1-z}\right),$ $\|\mathop{\mathrm{ph}\/}\nolimits z\|<\pi$ and $\|\mathop{\mathrm{ph}\/}\nolimits(1-z)\|<\pi$. 15.9.20 $\displaystyle\mathop{\mathbf{F}\/}\nolimits\!\left({a,b\atop\tfrac{1}{2}(a+b+1% )};z\right)$ $\displaystyle=\left(-z(1-z)\right)^{\ifrac{(1-a-b)}{4}}\\mathop{P^{\ifrac{(1-% a-b)}{2}}_{\ifrac{(a-b-1)}{2}}\/}\nolimits\!\left(1-2z\right),$ $\left\|\mathop{\mathrm{ph}\/}\nolimits\!\left(-z\right)\right\|<\pi$. 15.9.21 $\displaystyle\mathop{\mathbf{F}\/}\nolimits\!\left({a,1-a\atop c};z\right)$ $\displaystyle=\left(\frac{-z}{1-z}\right)^{\ifrac{(1-c)}{2}}\\mathop{P^{1-c}_% {-a}\/}\nolimits\!\left(1-2z\right),$ $\left\|\mathop{\mathrm{ph}\/}\nolimits\!\left(-z\right)\right\|<\pi$. 15.9.22 $\mathop{\mathbf{F}\/}\nolimits\!\left({a,b\atop\tfrac{1}{2}};z\right)=\frac{2^% {a+b-(\ifrac{3}{2})}}{\pi}\mathop{\Gamma\/}\nolimits\!\left(a+\tfrac{1}{2}% \right)\mathop{\Gamma\/}\nolimits\!\left(b+\tfrac{1}{2}\right)\(z-1)^{(-a-b+(% \ifrac{1}{2}))/2}\\left(e^{\pm\pi i(a+b-(\ifrac{1}{2}))}\mathop{P^{-a-b+(% \ifrac{1}{2})}_{a-b-(\ifrac{1}{2})}\/}\nolimits\!\left(-\sqrt{z}\right)+% \mathop{P^{-a-b+(\ifrac{1}{2})}_{a-b-(\ifrac{1}{2})}\/}\nolimits\!\left(\sqrt{% z}\right)\right),$ $a,b\neq-\frac{1}{2},-\frac{3}{2},-\frac{5}{2},\ldots$, $0<\|\mathop{\mathrm{ph}\/}\nolimits z\|<\pi$, where the sign in the exponential is $\pm$ according as $\imagpart{z}\gtrless 0$. 15.9.23 $\mathop{\mathbf{F}\/}\nolimits\!\left({a,b\atop\tfrac{3}{2}};z\right)=\frac{2^% {a+b-(\ifrac{5}{2})}}{\pi\sqrt{z}}\mathop{\Gamma\/}\nolimits\!\left(a-\tfrac{1% }{2}\right)\mathop{\Gamma\/}\nolimits\!\left(b-\tfrac{1}{2}\right)\(z-1)^{(-a% -b+(\ifrac{3}{2}))/2}\\left(e^{\pm\pi i(a+b-(\ifrac{3}{2}))}\mathop{P^{-a-b+(% \ifrac{3}{2})}_{a-b-(\ifrac{1}{2})}\/}\nolimits\!\left(-\sqrt{z}\right)-% \mathop{P^{-a-b+(\ifrac{3}{2})}_{a-b-(\ifrac{1}{2})}\/}\nolimits\!\left(\sqrt{% z}\right)\right),$ $a,b\neq\frac{1}{2},-\frac{1}{2},-\frac{3}{2},\dots$, $0<\|\mathop{\mathrm{ph}\/}\nolimits z\|<\pi$, where the sign in the exponential is $\pm$ according as $\imagpart{z}\gtrless 0$.	2014-08-01T07:50:22	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 187, "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": 0.9768013954162598, "perplexity": 3304.468736198485}, "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-2014-23/segments/1406510274866.27/warc/CC-MAIN-20140728011754-00429-ip-10-146-231-18.ec2.internal.warc.gz"}
https://publications.drdo.gov.in/ojs/index.php/dsj/article/download/4207/2890	Real Time Mid-course Maneuver and Guidance of a Generic Reentry Vehicle The aim of any mission is to accomplish the final objective with desired accuracy and the same is valid for a generic launch vehicle. In many missions it is necessary to execute mid-course maneuvers with an intentional diversion trajectory to create a counter measure or to avoid certain specific known geographical locations. The current work elaborates a novel and practically implementable mid-course maneuver and an ascent phase guidance of a reentry vehicle executing an in-flight determined mid-course maneuver (trajectory reshaping) without compromising the accuracy of the final achieved target position. The robustness of the algorithm is validated with 6DoF simulation results by considering the dispersion of the burnout state vector conditions which arises due to variations in thrust profile, aerodynamics characteristics of the vehicle, atmosphere, etc. The primary objective of any launch vehicle is to deliver the Payload to the desired target within the given tolerance bounds. Since the first use of ballistic missile in 1940’s, a lot of innovation has gone in the development of more sophisticated guidance, control, navigation algorithm’s to enhance the range, accuracy, reliability, etc., In view of the current working scenario there is a demand for the maneuver during flight (trajectory reshaping) such that the mission objectives are achieved without any compromise on the mission end objective. A typical in-flight mid-course maneuver scenario is shown in Fig 1., where the trajectory in blue color is the one which is going to be followed by the vehicle if there is no intentional maneuver (non-maneuvering) is executed on board and the trajectory in green color is the intentional maneuver trajectory which is hard to predict as compared to the non-maneuvering trajectory. Figure 1. Normalized trajectory of a non-maneuvering and maneuver vehicle. A reentry vehicle approaches at a very high velocity, typical velocities varying from 5 Km/s - 7 Km/s based on the selected trajectory, downrange, guidance mechanism employed in the design procedure1. But with growth of computing power, more powerful and reliable estimation (prediction) and filtering techniques are available today by virtue of which it is possible to predict the trajectory of the reentry vehicle well ahead and take some advance corrective measures. Optimization based trajectory planning and tracking the reference trajectory using dynamic inversion guidance laws are proposed by Ran2, et al. In the paper the author describes the re-entry vehicle trajectory planning and guidance by considering the path constraints like aerodynamics heating, aerodynamic load, etc., in r-V plane with an aero assisted configuration.Gao Changsheng3, et al. describes a virtual displacement concept based reentry vehicle guidance using optimization technique and LQG based tracking of the reference trajectory. Page & Rogers4 summarizes a few investigations carried out in guidance and control of maneuvering reentry vehicles by considering cross-product, proportional and tangent cubic guidance mechanisms having cruciform, bank to turn and fixed trim control configurations. Explicit re-entry guidance equations for maneuvering re-entry vehicles (MaRVs) using characteristic curve approach is developed Cameron5. While formulating the guidance it is ensured that terminal trajectory constraints on path angles and lift acceleration and its derivatives are achieved. Variable gain vector guidance equations are established by forcing terminal equation structure to be similar to the characteristic curve equations. But the study doesn’t consider the limitation on aerodynamic capability, maximum acceleration limit nor did an energy management requirement and it assume that this type of characteristic curve calls for less acceleration for large range to go than that for small range to go. A practically implementable algorithm described in the current paper describes methodology to execute the in-flight determined maneuver of the vehicle and to guide the vehicle in the ascent phase to its predetermined target accurately with in the desired tolerance bounds. The basis of the current approach relies on the capability of simulating the real time scenario of the vehicle dynamics in the background simulation from the burnout point6,7 to the desired target point. Most of the classical launch vehicle guidance algorithms rely on required velocity vector concept8, which acts as basis for hit equation6 to be solved in order to reach the desired target. Once this required velocity vector is calculated, the desired burnout position and burnout flight path angle are determined9 . The innovative underlying concept of the proposed algorithm is performing an in-flight defined maneuver during the mid-course (after apogee i.e., decent phase) by keeping in view of the payload capabilities. The duration of maneuver can be decided based on temporal or spatial means. If the duration of maneuver is based on time then the maneuver will be open loop form, because the time of flight of the vehicle will vary based on the propulsion characteristics, range, burnout conditions. If the duration of maneuver is a function of altitude/range then the maneuver will be in closed form, because the aim of the payload to impact the desired coordinates at the predefined altitude, irrespective of time. The predetermined maneuver can be any realizable function like sinusoidal, pulse, triangular, exponential, etc. as shown in Fig 2. If the maneuver is of sinusoidal the variable parameters are maneuver amplitude and frequency, if the maneuver is pulse then the variable parameter is the pulse amplitude and if the maneuver is exponential then the variable parameter is the decay or rise slope of the maneuver. Maneuver can be executed by a variable or fixed thruster at center of gravity or close to center of gravity. Generic representation of the maneuver function is given below: Figure 2. Predetermined maneuver functions as a function of normalized time and altitude. Z=F (a, f, y)(1) where Z = Maneuver function a = Amplitude of the considered maneuver function f = Frequency of the considered maneuver function y = Independent variable (time, altitude, downrange) Values of the a & f are decided by the vehicle propulsive capability and the extent of dispersion planned and selection of maneuver function can be random in selection but definite once selected. Once the determined maneuver initiation point, duration and the maneuver function is finalized, initiate the background simulation from the burnout point to the target. During the simulation, initiate the determined maneuver from the determined initiation point up to maneuver duration point (time, altitude). With this maneuver, compute the difference in the desired and achieved latitude and longitude at the impact point. Augment the ascent phase target coordinates with the above computed difference values in latitude and longitude and solve the hit equation (initiate the ascent phase guidance) with this augmented coordinates and repeat the above procedure till convergence criteria is met. Because of the mid-course maneuver there will be a change in the guidance solution (burnout conditions) to reach the desired target, which can be seen as the perturbation on the initial solution as shown below7 $\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{{r}_{0}}{a}=\frac{1-\mathrm{cos}\left(\varphi +\Delta \varphi \right)}{\lambda {\mathrm{sin}}^{2}\gamma }+\frac{\mathrm{sin}\left(\gamma -\left(\varphi +\Delta \varphi \right)\right)}{\mathrm{sin}\gamma }$ (2) where r0 = (a+h) = missile position from the center of the earth a = equatorial radius (m), h = vehicle altitude from the surface of the earth $\lambda \text{\hspace{0.17em}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{\text{\hspace{0.17em}}{r}_{0}{v}^{2}}{GM}$ G = Universal gravitational constant φ= range angle γ = flight path angle at burn out $\Delta \varphi$ = Augmented range angle corresponding to change in final coordinates The steps involved in the proposed algorithm are given below: (i) With the desired burnout state vector as the initial states, simulate the vehicle trajectory up to the desired predetermined altitude, from where determined maneuver is planned. (ii) From predetermined altitude start of maneuver to the termination of the maneuver, superimpose a predetermined pseudo random maneuver (varying amplitude and frequency with altitude as the reference) to the actual attitude. During this maneuver period, activate thruster provided in the payload (typically called velocity package10) or side thrusters located at the center of gravity (if known accurately) can be used. (iii) Once the predetermined attitude maneuver period completed, deactivate the thruster and simulate the vehicle trajectory up to the impact point. Note the achieved latitude and longitude. (iv) Find the difference between the desired and achieved latitude and longitude, and augment the desired coordinates with this difference values. (v) Repeat the steps from I to IV till the difference between the desired and achieved latitude and longitude lie within the desired tolerance bounds. For the current work a standard nonlinear 6DoF mathematical model with 3 forces and 3 moments is considered11. In order to make the simulation more realistic a nonlinear aerodynamic model is considered, where the drag and aerodynamic forces are modeled as the functions of altitude, angle of attack and Mach number. The earth shape and rotational effects12 are included in the simulation as the time of travel is variable which, if not accounted correctly, leads to tens of kilometers range errors13. A universal earth gravity model up to J214 term is considered to take care of earth gravitational effects, which is a function of colatitude and altitude. Reentry atmospheric effects play a significant role during reentry, as the velocity with which the vehicle reenters is very high, in order to take care of this unwanted aerodynamic effects because of atmosphere, a more elaborate atmospheric model15 is considered for simulation. In order to take care of wind effects during the reentry phase, a realistic wind model16 is considered for studies. To assess the performance accurately a realistic inertial navigation model17 is included in the simulation taking care of real time hardware features (accelerometer for acceleration, gyroscope for rate). A nonlinear reaction control system and liquid velocity package models are considered for the simulation studies. $\left[\begin{array}{l}\stackrel{˙}{u}\\ \stackrel{˙}{v}\\ \stackrel{˙}{w}\\ \stackrel{˙}{p}\\ \stackrel{˙}{q}\\ \stackrel{˙}{r}\end{array}\right]\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left[\begin{array}{c}\left(\left({T}_{fx}-{D}_{fx}\right)}{m}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{g}_{x}\\ \left(\left({T}_{fy}-{A}_{fy}\right)}{m}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{g}_{y}\\ \left(\left({T}_{fz}-{A}_{fz}\right)}{m}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{g}_{z}\\ {M}_{x}}{{I}_{x}}\\ \left({M}_{y}+\left({I}_{z}-{I}_{x}\right)pr\right)}{{I}_{y}}\\ \left({M}_{z}+\left({I}_{x}-{I}_{y}\right)pq\right)}{{I}_{z}}\end{array}\right]\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}⇒\text{\hspace{0.17em}}\stackrel{˙}{X}=f\left(X,U\right)$ (3) where u, v, w and p, q, r are translation and rotational components. Tfx, Tfy, Tfz and Afy, Afz are thrust and aerodynamic force components. Dfx is the drag force action along the body axial direction. m is the mass of the pay load, gx, gy, gz are the gravitational components, and Mx, My, Mz and Ix, Iy, Iz are moment and inertia components respectively For the present study, a 2 stage solid propelled launch vehicle with flex nozzle actuated control system is considered. Once the solid propelled stages are separated after propellent got consumed, the payload is controlled by using a reaction control system powered by liquid thrusters, enabling the flexibility of switching on and off when desired. During the ascent phase the vehicle follows a preprogrammed attitude turn keeping in view the initial constraints like structural load &control limitation, etc., Once the vehicle attains the desired relaxed conditions usually out of atmosphere, an explicit closed loop guidance8 will guide and place the vehicle at burnout on a desired ellipse (function of burnout position, velocity, flight path angle &earth rotation rate compensated desired target position), by virtue of which the vehicles reaches the desired target. With these desired burnout state vector, a back ground 6DoF algorithm is initiated iteratively by using the proposed algorithm, till the 6DoF achieved impact latitude and longitude coincides with the desired one’s as per the specified tolerance bounds. To validate the proposed algorithm, different burnout conditions are considered for a given target as shown in Table 1.. For the study a sinusoid (quaternion18) with an amplitude and frequency of 0.0001 Hz and 0.15 Hz is considered for determined attitude maneuver. Here it should be noted that the maneuver activation is based on altitude not on time, since the trajectory varies with burnout conditions and the guidance problem considered for simulation is a free time problem (i.e., the aim is to reach the target without any constraint on the time of flight). The input amplitude and frequency are same for all the three cases considered for simulation, but the trajectory parameters vary based on burnout conditions i.e., velocity, position, flight path angle, etc. Table 1. Different burnout conditions are considered for a given target The thrust force can be provided by a small propulsion package with respect to altitude. During maneuver phase, a thruster with constant thrust force of 20 KN is considered. Once the maneuver period is completed the thruster gets deactivated and the vehicle follows the ballistic path there after. The execution of the determined maneuver for case 1 is shown in Fig. 3. The trajectory shown in blue color is the one which is generated by the payload without any deception maneuver and the green one is the one which is generated by the payload with a predetermined maneuver execution. From the Fig. 3 it is evident that the deception maneuver started at 150 km with a deviation from the predicted trajectory (blue trajectory). The trajectory shown in red colour is the background 6DoF trajectory which provides the reference for real time deception trajectory (green trajectory). The background and real time trajectory are in tight agreement because of which it is not possible to see the difference between red and green trajectory in the figure(s). Finally the realtime trajectory achieve’s the desired latitude and longitude with in the given tolerance bounds. Fig. 4 shows the altitude variation for with and without maneuver with respect to time. From the data markings in the figure, it is clear that the difference in the altitude between the non maneuvering and maneuvering trajectory is varying from 0 km to 9 km from 150 km altitude point to impact point. This magnitude can be increased by an additional impulse in the maneuvering vehicle. Figure 3. Case 1 Altitude vs latitude and longitude trajectory. Figure 4. Case 1 : Time vs altitude. The working of the algorithm for case 2 and case 3 are shown in Fig. 5 and Fig. 6Fig. 5 and Fig. 6shows the latitude and longitude variation with respect to altitude and it is clear from this figures that the algorithm drives the payload towards the desired target from the start of the deception point. Figure 5. Case 2 : Altitude vs latitude and longitude trajectory. Figure 6. Case 3 : Altitude vs latitude and longitude trajectory. The robustness of the proposed algorithm under model uncertainty is studied by perturbing the wind, atmosphere and aero models. The case studies are listed in Table 2. The burnout state vector consider for the simulation studies shown in Table 3. Table 4. shows the desired target point location, achieved terminal point location without (predictable trajectory) and with (deception trajectory) reentry maneuver. Table 2. Perturbation bands considered for robustness studies Table 3. Burnout state vector considering for robustness studies Table 4. Robustness test case simulation results Fig. 7 and Fig. 9 shows the wind, atmospheric density and drag variation with respect to the altitude. The curves in green shows the model considered for background trajectory simulation, while the red one is considered for fore ground simulation. Fig. 8 and Fig. 10 shows the latitude and longitude variation with respect to the altitude and it is clear from the figures that the final impact is achieved with in the prescribed tolerance bound, under model perturbations. Figure 7.Case 4 : Altitude vs wind velocity, density and drag. Figure 8.Case 4 : Altitude vs latitude and longitude. Figure 9. Case 5 : Altitude vs wind velocity, density, and drag.. Figure 10. Case 5 : Altitude vs latitude and longitude. A practically working and implementable algorithm for real time mid-course maneuver with pre-corrected ascent phase guidance is described in the current paper. The work describes in detail the implementation of the deception maneuver and guidance algorithm by means of a 6DoF simulation from burnout point to impact. With the practicable available subsystem’s the paper shows the robustness of the algorithm by means of some simulation cases by considering a wide band of burnout state vector values at the burnout. One of the flexibility of the proposed work is in selecting online the start and end point of maneuver with the variation of the amplitude and frequency of the maneuver, by keeping in view of the thrust force availability and capability. The present work can be extended to ascent phase guidance by virtue of which a wide band of dispersion at reentry can be taken care and it is also possible to use side thruster during the maneuver phase to decrease the payload response time for maneuver. 1. George, N. Lewis & Theodore A. Postol. Future challenges to the ballistic missile defense. IEEE Spectrum, 1997, 34(9), 60-68. [Full text via CrossRef] 2. Ran, Zhang; Huifeng, Li & Xudong, Cao. A new approach for re-entry vehicle trajectory planning and guidance, ICAS, 2012-5.7.5, 4, pp. 3158-3164. 3. Changsheng, Gao; Wuxing, Jing; & Chaoyong, Li. Optimal guidance law design for reentry vehicle using virtual displacement concept. In the Proceedings of the 26th Chinese Control Conference, Zhangjiajie, Hunan, China, July 26-31, 2007, pp. 507-510. [Full text via CrossRef] 4. Page, J.A. & Rogers, R.O. Guidance and control of maneuvering reentry vehicles. In the IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and a Special symposium on Fuzzy set theory and applications, Dec-1977, 16, pp. 659-664. [Full text via CrossRef] 5. Cameron, J.D.M. Explicit guidance equations for maneuvering reentry vehicles, re-entry and environmental systems divisions. General Electric Company, Philadelphia, Pa 19101, TP3-3:30. 6. George; R. & Pitman, J. Inertial Guidance. John Wiley & Sons, INC. Newyork, London, 1962. 7. Wheelon, Albert D. Free flight of a ballistic missile. ARS Journal, 1959, 29(12), 915-926. [Full text via CrossRef] 8. Siouris, George M. Missile guidance and control systems. Springer, 2004. [Full text via CrossRef] 9. Thomas, Tessy. Guidance scheme for solid propelled vehicle during atmospheric phase. Def. Sci. J., 2005, 55(3), 253-264. [Full text PDF] 10. Wilkey, John W. Velocity package. United States Patent No. 3,260,204. July 12, 1966. [Full text PDF] 11. Kadam, N.V. Practical design of flight control systems for launch vehicles and missiles. Allied Publishers Pvt Ltd. 2009. 12. Department of defence world geodetic system 1984. National Imagery and Mapping Agency, 3 January 2000. 13. Cornelisse, J.W.; Schoyer, H.F.R. & Wakker, K.F. Rocket propulsion and space flight dynamics. Pitman Publishing Limited, 1979. 14. Kenneth R. Britting, inertial navigation systems analysis, Wiley-Interscience, 1971. 15. Ananthasayanam, M.R. & Narasimha R. Standard atmosphere for aerospace applications. India. Dept. of Aerospace Engg. Indian Institute of Science, Bangalore. Report No. 79 FM 5. 16. Narasimha, R. The wind environment in India. NAL. Technical Memorandum Du 8501, 1985. 17. Titterton, David & Weston, John. Strapdown inertial navigation technology, IET, 2nd Ed, 2004. [Full text via CrossRef] 18. Kuipers, J.B. Quaternions and rotation sequences : A primer with application to orbits, aerospace, and virtual reality. Princeton University Press, Princeton, New Jersey. 2002. Mr Avinash Chander received his BE (Electrical Eng.) from IIT Delhi, in 1972 and MS (Spatial Information Technology) from Jawaharlal Nehru Technological University, Hyderabad. He is presently working as Distinguished Scientist in DRDO. He received many Awards like, DRDO Scientist of the Year-1989, Astronautical Society of India Award-1997, DRDO AGNI Self reliance Award-1999, Dr Biren Roy Space award-2000, DRDO Award for Path Breaking Research/Outstanding Technology Development-2007, Outstanding Technologist Award-2008 by Punjab Technical University. His areas of interest include: Navigation, guidance, mission design. Dr I.V. Murali Krishna received his MTech from IIT Madras and PhD from IISc, Bangalore in 1977. He is presently working as Director, Institute of Science and Technology and Coordinator of Centre for Atmospheric Sciences and Weather Modification Technologies at Jawaharlal Nehru Technological University, Hyderabad. His areas of interest includes: Geospatial technology and data mining, soft computing technologies, disaster management, satellite meteorology and weather informatics.	2020-08-11T16:04:03	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 4, "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": 0.5424745678901672, "perplexity": 2292.2447961220887}, "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-2020-34/segments/1596439738816.7/warc/CC-MAIN-20200811150134-20200811180134-00291.warc.gz"}
https://pos.sissa.it/174/085/	Volume 174 - 36th International Conference on High Energy Physics (ICHEP2012) - Parallel Session 1 - The Standard Model Improved sensitivity to charged Higgs searches un top quark decays $t \to bH^+ \to b(\tau^+\nu_\tau)$ at the LHC using $\tau$ polarisation and multivariate techniques J. Llorente Merino,* F. Barreiro Alonso, A. Ali *corresponding author Full text: pdf Published on: August 22, 2013 DOI: https://doi.org/10.22323/1.174.0085 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-ShareAlike.	2020-08-14T05:16:42	{"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": 0.28710058331489563, "perplexity": 8515.360519836917}, "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-2020-34/segments/1596439739177.25/warc/CC-MAIN-20200814040920-20200814070920-00170.warc.gz"}
https://par.nsf.gov/biblio/10085201-erratum-search-heavy-resonances-decaying-boson-higgs-boson-final-states-leptons-jets-fb1-sqrt-tev-pp-collisions-atlas-detector	Erratum to: Search for heavy resonances decaying into a W or Z boson and a Higgs boson in final states with leptons and b-jets in 36 fb−1 of s=13$$\sqrt{s}=13$$ TeV pp collisions with the ATLAS detector	2022-09-25T16:38:25	{"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": 0.945651113986969, "perplexity": 2732.914283471738}, "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-2022-40/segments/1664030334591.19/warc/CC-MAIN-20220925162915-20220925192915-00064.warc.gz"}
http://mathdl.maa.org/mathDL/19/?pa=reviews&sa=viewBook&bookId=73436	Search Keyword and/or # Book of Proof Richard Hammack Publisher: Creative Commons (2009) Details: 294 pages, Paperback Price: $12.95 ISBN: 978-0-9824062-0-5 Category: Textbook Topics: Proofs and Logic, Transition to Advanced Mathematics ## MAA Review [Reviewed by David Offner, on 08/20/2012] This is a wonderful book. Written as a text for a one-semester “transition to higher mathematics” course, it introduces the undergraduate to logic and proofs and to the basic objects and language used in higher mathematics. It is ideal for the many American undergraduates who come to college with little or no experience with proof or formal reasoning and need to be brought up to speed quickly in order to succeed in upper-level mathematics courses. The book is divided into four parts. The first part introduces sets and logic and includes a chapter on counting, which gives a brief introduction to elementary combinatorial techniques. The second section covers the basic techniques for proving conditional statements: direct proof, contrapositive proof, and proof by contradiction. The third part provides more examples of common proofs, such as proving non-conditional statements, proofs involving sets, and disproving statements, and also introduces mathematical induction. Finally the fourth part returns to basic mathematical structures, discussing relations, functions, and cardinality. Hammack clearly knows his audience, and writes about precise mathematical ideas in an inviting, conversational style that can be read by mathematically immature undergraduates. The exposition has the tone of a friendly office hour chat, as Hammack frequently addresses the reader as “you,” (e.g. “You should examine the following statements and make sure you understand how the answers were obtained.” p. 15) and sprinkles the text with references to what the reader has encountered in previous math courses, or will encounter in the future. The book contains many well-chosen examples, non-examples, and exercises that illustrate key concepts and clarify common confusions. The deliberate pace of the book allows Hammack to point out many of these explicitly, and give helpful advice about how to think about them (e.g. “You can think of statements as pieces of information that are either correct or incorrect.” p. 32). In explaining proof techniques or types of proofs, he gives helpful templates, and very nice discussions of not only the logic of proofs, but how one goes about constructing them in practice. Besides giving students the tools required to pursue advanced mathematics, the book also provides a nice introduction to the culture of mathematics. Engaging mathematical topics are sprinkled throughout. Many great theorems and proofs arise naturally in such a text: the ancient proofs that the square root of 2 is irrational and that there are an infinite number of primes are examples. Other engaging topics, such as Russell’s paradox, perfect numbers, Fibonacci numbers, and infinite cardinalities, are found in sections that shoot off from the main stream of the text. One last attraction of Book of Proof is its price, or lack thereof. It is freely available for download from the author’s website as a .pdf document, and is also available as a print on demand paperback at amazon.com for$12.95. There are many places where the author makes choices between rigor and accessibility, for example in deciding what properties of the integers should be assumed and what should be proved. While the book generally makes excellent choices in this regard, there are some proofs that do not give a significant pay-off given the investment. For example, much effort is put into building up to a proof of unique prime factorization of the integers which comes late in the book. While this is a spectacular result, many of the intermediate steps along the way are not well motivated as they arise, and may not be appreciated by students. This is surely a matter of taste, however, and much will depend on the particular students involved. It will probably come as no surprise that it is possible to skip certain sections of the book with no complaint from students. I have used the book as a text in a sophomore-level discrete mathematics course, where we have covered most but not all of the material in the book, and supplemented the text with additional topics in discrete mathematics. My students and I have both loved the book. They find it readable and interesting, and they learn enough from reading the book that I rarely need to explain any topic from scratch. I highly recommend this book as a text or supplement for an undergraduate transition course. Furthermore, it is readable and enjoyable enough that it would be interesting and useful independent reading for almost any undergraduate mathematics major. David Offner is Assistant Professor of Mathematics at Westminster College in New Wilmington, PA.	2013-05-18T10:21:44	{"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": 0.6214231848716736, "perplexity": 464.31158637487584}, "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/1368696382261/warc/CC-MAIN-20130516092622-00052-ip-10-60-113-184.ec2.internal.warc.gz"}
http://www.itl.nist.gov/div898/handbook/apr/section4/apr44.htm	8. Assessing Product Reliability 8.4. Reliability Data Analysis ## How do you compare reliability between two or more populations? Several methods for comparing reliability between populations are described Comparing reliability among populations based on samples of failure data usually means asking whether the samples came from populations with the same reliability function (or CDF). Three techniques already described can be used to answer this question for censored reliability data. These are: Comparing Sample Proportion Failures Assume each sample is a random sample from possibly a different lot, vendor or production plant. All the samples are tested under the same conditions. Each has an observed proportion of failures on test. Call these sample proportions of failures $$p_1, \, p_2, \, p_3, \, \ldots, \, p_n$$. Could these all have come from equivalent populations? This is a question covered in Chapter 7 for two populations, and for more than two populations, and the techniques described there apply equally well here. Likelihood Ratio Test Comparisons The Likelihood Ratio test was described earlier. In this application, the Likelihood ratio $$\lambda$$ has as a denominator the product of all the Likelihoods of all the samples assuming each population has its own unique set of parameters. The numerator is the product of the Likelihoods assuming the parameters are exactly the same for each population. The test looks at whether $$-2\mbox{ ln } \lambda$$ is unusually large, in which case it is unlikely the populations have the same parameters (or reliability functions). This procedure is very effective if, and only if, it is built into the analysis software package being used and this software covers the models and situations of interest to the analyst. Lifetime regression is similar to maximum likelihood and likelihood ratio test methods. Each sample is assumed to have come from a population with the same shape parameter and a wide range of questions about the scale parameter (which is often assumed to be a "measure" of lot-to-lot or vendor-to-vendor quality) can be formulated and tested for significance. For a complicated, but realistic example, assume a company manufactures memory chips and can use chips with some known defects ("partial goods") in many applications. However, there is a question of whether the reliability of "partial good" chips is equivalent to "all good" chips. There exists lots of customer reliability data to answer this question. However the data are difficult to analyze because they contain several different vintages with known reliability differences as well as chips manufactured at many different locations. How can the partial good vs all good question be resolved? A lifetime regression model can be constructed with variables included that change the scale parameter based on vintage, location, partial versus all good, and any other relevant variables. Then, a good lifetime regression program will sort out which, if any, of these factors are significant and, in particular, whether there is a significant difference between "partial good" and "all good".	2017-10-21T04:50:12	{"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": 0.6268041729927063, "perplexity": 707.8827314203382}, "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-2017-43/segments/1508187824570.79/warc/CC-MAIN-20171021043111-20171021063111-00186.warc.gz"}
https://pdglive.lbl.gov/DataBlock.action?node=S066CHR	#### ${{\mathit \nu}}$ CHARGE $\mathit e$ = electron charge is the unit of values listed below. VALUE ($\mathit e$) CL% DOCUMENT ID TECN COMMENT $\bf{<4 \times 10^{-35}}$ 95 1 2005 COSM charge neutral universe • • We do not use the following data for averages, fits, limits, etc. • • $<5.4 \times 10^{-12}$ 90 2 2020 E XMAS solar neutrinos $1.7 - 2.3 \times 10^{-12}$ 68 3 2020 spectral fit of XENON1T $<3 \times 10^{-8}$ 95 4 2016 LASR magnetic dichroism $<2.1 \times 10^{-12}$ 90 5 2014 A TEXO nuclear reactor $<1.5 \times 10^{-12}$ 90 6 2014 nuclear reactor $<3.7 \times 10^{-12}$ 90 7 2007 RVUE nuclear reactor $<2 \times 10^{-14}$ 8 1999 ASTR red giant luminosity $<6 \times 10^{-14}$ 9 1999 ASTR solar cooling $<4 \times 10^{-4}$ 10 1994 RVUE BEBC beam dump $<3 \times 10^{-4}$ 11 1991 RVUE SLAC ${{\mathit e}^{-}}$ beam dump $<2 \times 10^{-15}$ 12 1987 ASTR SN 1987A $<1 \times 10^{-13}$ 13 1963 ASTR solar energy losses 1 CAPRINI 2005 limit derived from the lack of a charge asymmetry in the universe. Limit assumes that charge asymmetries between particles are not anti-correlated. 2 ABE 2020E obtains this result by assuming that the low-energy excess events in the XMASS detector are produced by neutrino millicharge which is common for all three neutrino flavors. 3 KHAN 2020 performed a constrained spectral fit analysis of the excess observed in the electron recoil energy spectrum by the XENON1T experiment. This range of neutrino millicharge values is one of the possible interpretations of these excess events. For the individual flavor constraints at 90$\%$ C.L. see the original reference. 4 DELLA-VALLE 2016 obtain a limit on the charge of neutrinos valid for masses of less than 10 meV. For heavier neutrinos the limit increases as a power of mass, reaching $10^{-6}$ $\mathit e$ for $\mathit m$ = 100 meV. 5 CHEN 2014A use the Multi-Configuration RRPA method to analyze reactor ${{\overline{\mathit \nu}}_{{e}}}$ scattering on ${}^{}\mathrm {Ge}$ atoms with 300 eV recoil energy threshold to obtain this limit. 6 STUDENIKIN 2014 uses the limit on ${{\mathit \mu}_{{\nu}}}$ from BEDA 2013 and the 2.8 keV threshold of the electron recoil energy to obtain this limit. 7 GNINENKO 2007 use limit on ${{\overline{\mathit \nu}}_{{e}}}$ magnetic moment from LI 2003B to derive this result. The limit is considerably weaker than the limits on the charge of ${{\mathit \nu}_{{e}}}$ and ${{\overline{\mathit \nu}}_{{e}}}$ from various astrophysics considerations. 8 This RAFFELT 1999 limit applies to all neutrino flavors which are light enough ($<5~$keV) to be emitted from globular-cluster red giants. 9 This RAFFELT 1999 limit is derived from the helioseismological limit on a new energy-loss channel of the Sun, and applies to all neutrino flavors which are light enough ($<1~$keV) to be emitted from the sun. 10 BABU 1994 use COOPER-SARKAR 1992 limit on ${{\mathit \nu}}$ magnetic moment to derive quoted result. It applies to ${{\mathit \nu}_{{\tau}}}$ . 11 DAVIDSON 1991 use data from early SLAC electron beam dump experiment to derive charge limit as a function of neutrino mass. It applies to ${{\mathit \nu}_{{\tau}}}$ . 12 Exact BARBIELLINI 1987 limit depends on assumptions about the intergalactic or galactic magnetic fields and about the direct distance and time through the field. It applies to$~{{\mathit \nu}_{{e}}}$ . 13 The limit applies to all flavors. Conservation Laws: ELECTRIC CHARGE ($\mathit Q$) References: ABE 2020E PL B809 135741 Search for exotic neutrino-electron interactions using solar neutrinos in XMASS-I KHAN 2020 PL B809 135782 Can Nonstandard Neutrino Interactions explain the XENON1T spectral excess? DELLA-VALLE 2016 EPJ C76 24 The PVLAS Experiment: Measuring Vacuum Magnetic Birefringence and Dichroism with a Birefringent Fabry-Perot Cavity CHEN 2014A PR D90 011301 Constraints on Millicharged Neutrinos via Analysis of Data from Atomic Ionizations with Germanium Detectors at sub-keV Sensitivities STUDENIKIN 2014 EPL 107 21001 New Bounds on Neutrino Electric Millicharge from Limits on Neutrino Magnetic Moment GNINENKO 2007 PR D75 075014 New Limit on Millicharged Particles from Reactor Neutrino Experiments and the PVLAS Anomaly CAPRINI 2005 JCAP 0502 006 Constraints on the Electrical Charge Asymmetry of the Universe RAFFELT 1999 PRPL 320 319 Limits on Neutrino Electromagnetic Properties: An Update BABU 1994 PL B321 140 Closing the Windows on MeV ${{\mathit \tau}}$ Neutrinos DAVIDSON 1991 PR D43 2314 Limits on Particles of Small Electric Charge BARBIELLINI 1987 NAT 329 21 Electric Charge of the Neutrinos from SN1987A BERNSTEIN 1963 PR 132 1227 Electromagnetic Properties of the Neutrino	2023-03-21T23:58:55	{"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": 0.8553920984268188, "perplexity": 6137.847990737712}, "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-2023-14/segments/1679296943747.51/warc/CC-MAIN-20230321225117-20230322015117-00155.warc.gz"}
https://pdglive.lbl.gov/DataBlock.action?node=M173M&home=MXXX040	#### ${{\mathit D}_{{s1}}{(2460)}^{\pm}}$ MASS The fit includes ${{\mathit D}^{\pm}}$ , ${{\mathit D}^{0}}$ , ${{\mathit D}_{{s}}^{\pm}}$ , ${{\mathit D}^{\pm}}$ , ${{\mathit D}^{0}}$ , ${{\mathit D}_{{s}}^{\pm}}$ , ${{\mathit D}_{{1}}{(2420)}^{0}}$ , ${{\mathit D}_{{2}}^{}{(2460)}^{0}}$ , and ${{\mathit D}_{{s1}}{(2536)}^{\pm}}$ mass and mass difference measurements. VALUE (MeV) EVTS DOCUMENT ID TECN COMMENT $\bf{ 2459.5 \pm0.6}$ OUR FIT Error includes scale factor of 1.1. $\bf{ 2459.6 \pm0.9}$ OUR AVERAGE Error includes scale factor of 1.3. $2460.1$ $\pm0.2$ $\pm0.8$ 1 2006 P BABR 10.6 ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $2458.0$ $\pm1.0$ $\pm1.0$ 195 2004 E BABR 10.6 ${{\mathit e}^{+}}{{\mathit e}^{-}}$ • • We do not use the following data for averages, fits, limits, etc. • • $2459.5$ $\pm1.2$ $\pm3.7$ 920 2006 P BABR 10.6 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}_{{s}}^{+}}{{\mathit \gamma}}{{\mathit X}}$ $2458.6$ $\pm1.0$ $\pm2.5$ 560 2006 P BABR 10.6 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}_{{s}}^{+}}{{\mathit \pi}^{0}}{{\mathit \gamma}}{{\mathit X}}$ $2460.2$ $\pm0.2$ $\pm0.8$ 123 2006 P BABR 10.6 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}_{{s}}^{+}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit X}}$ $2458.9$ $\pm1.5$ 112 2 2004 S BABR ${{\mathit B}}$ $\rightarrow$ ${{\mathit D}_{{s1}}{(2460)}^{+}}{{\overline{\mathit D}}^{()}}$ $2461.1$ $\pm1.6$ 139 3 2004 S BABR ${{\mathit B}}$ $\rightarrow$ ${{\mathit D}_{{s1}}{(2460)}^{+}}{{\overline{\mathit D}}^{()}}$ $2456.5$ $\pm1.3$ $\pm1.3$ 126 4, 5 2004 BELL 10.6 ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $2459.5$ $\pm1.3$ $\pm2.0$ 152 6, 7 2004 BELL 10.6 ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $2459.9$ $\pm0.9$ $\pm1.6$ 60 6, 7 2004 BELL 10.6 ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $2459.2$ $\pm1.6$ $\pm2.0$ 57 2003 B BELL 10.6 ${{\mathit e}^{+}}{{\mathit e}^{-}}$ 1 The average of the values obtained from the ${{\mathit D}_{{s}}^{+}}{{\mathit \gamma}}$ , ${{\mathit D}_{{s}}^{+}}{{\mathit \pi}^{0}}{{\mathit \gamma}}$ , ${{\mathit D}_{{s}}^{+}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ final state. 2 Systematic errors not evaluated. From the decay to ${{\mathit D}_{{s}}^{+}}{{\mathit \pi}^{0}}$ . 3 Systematic errors not evaluated. From the decay to ${{\mathit D}_{{s}}^{+}}{{\mathit \gamma}}$ . 4 Not independent of the corresponding ${\mathit m}_{{{\mathit D}_{{s1}}{(2460)}^{\pm}}}–{\mathit m}_{{{\mathit D}_{{s}}^{\pm}}}$. 5 Using ${\mathit m}_{{{\mathit D}_{{s}}^{+}}}$ = $2112.4$ $\pm0.7$ MeV. 6 Not independent of the corresponding ${\mathit m}_{{{\mathit D}_{{s1}}{(2460)}^{\pm}}}–{\mathit m}_{{{\mathit D}_{{s}}^{\pm}}}$. 7 Using ${\mathit m}_{{{\mathit D}_{{s}}^{+}}}$ = $1968.5$ $\pm0.6$ MeV. References: AUBERT 2006P PR D74 032007 Study of the ${{\mathit D}_{{sJ}}^{}{(2317)}^{+}}$ and ${{\mathit D}_{{sJ}}{(2460)}^{+}}$ Mesons in Inclusive ${\mathit {\mathit c}}{\mathit {\overline{\mathit c}}}$ Production near $\sqrt {s }$=10.6 GeV AUBERT 2004E PR D69 031101 Observation of a Narrow Meson Decaying to ${{\mathit D}_{{s}}^{+}}{{\mathit \pi}^{0}}{{\mathit \gamma}}$ at a Mass of 2.458 GeV/$\mathit c{}^{2}$ AUBERT,B 2004S PRL 93 181801 Study of ${{\mathit B}}$ $\rightarrow$ ${{\mathit D}}{}^{()+}_{\mathit sJ}$ ${{\overline{\mathit D}}}{}^{()}$ Decays MIKAMI 2004 PRL 92 012002 Measurements of the ${{\mathit D}_{{sJ}}}$ Resonance Properties KROKOVNY 2003B PRL 91 262002 Observation of the ${{\mathit D}_{{sJ}}{(2317)}}$ and ${{\mathit D}_{{sJ}}{(2457)}}$ in ${{\mathit B}}$ Decays	2023-03-24T09:44:41	{"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": 0.8741786479949951, "perplexity": 1889.146638494944}, "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/1679296945279.63/warc/CC-MAIN-20230324082226-20230324112226-00273.warc.gz"}
https://pos.sissa.it/416/013/	Volume 416 - Loops and Legs in Quantum Field Theory (LL2022) - Plenary 3 Taming a resurgent ultra-violet renormalon M. Borinsky and D. Broadhurst* Full text: pdf Published on: October 20, 2022 Abstract Perturbative expansions in quantum field theory diverge for at least two reasons: the number of Feynman diagrams increases dramatically with the loop number and the process of renormalization may make the contribution of some diagrams large. We give an example of the second problem, from an ultra-violent renormalon of $\phi^3$ theory in 6 dimensions, where we can compute to very high loop-order. Taming this renormalon involves recent work on resurgence. This challenge is much more demanding than the corresponding problem for Yukawa theory in 4 dimensions. DOI: https://doi.org/10.22323/1.416.0013 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.	2022-12-07T23:43:38	{"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": 0.4462367594242096, "perplexity": 2593.4681592818306}, "config": {"markdown_headings": false, "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-2022-49/segments/1669446711221.94/warc/CC-MAIN-20221207221727-20221208011727-00442.warc.gz"}
https://mfix.netl.doe.gov/doc/vvuq-manual/main/html/pic/pic-05.html	# 5.5. PIC05: Evaporation¶ ## 5.5.1. Description¶ This case is used to verify the transport equations governing energy and species conservation. The setup consists of a single parcel representing a droplet suspended in a humidified air stream. This reflects the wet bulb phenomenon, where evaporation from the droplet results in a lowered humidified air temperature. The following reaction represents species transfer from the suspended droplet: (5.9)$H_{2} O (l) \rightarrow H_{2} O (g)$ Fifteen seconds of physical time is simulated to ensure the droplet achieves a steady-state (SS) temperature. The SS temperature should then compare with the theoretical wet-bulb temperature. ## 5.5.2. Setup¶ Table 5.10 PIC-05 Setup, Initial and Boundary Conditions. Computational/Physical model 3D, Transient Multiphase Gravity Turbulence equations are not solved Uniform mesh First order upqind discritization scheme Geometry Coordinate system Cartesian Grid partitions x-length 0.01 (m) 1 y-length 0.01 (m) 1 z-length 0.01 (m) 1 Material Gas density, $$\rho_{g}$$ Ideal gas law (kg·m-3) Solids Type PIC,DEM Diameter, $$d_{p}$$ 0.2 (mm) Density, $$\rho_{s}$$ 958.6 (kg·m-3) Solids Properties (PIC) Pressure linear scale factor, $$P_{s}$$ 0.0 (Pa) Exponential scale factor, $$\gamma$$ 1.0 (-) Statistical weight 25 (-) Solids Properties (DEM) Coefficient of friction, $$\mu_{pp},\mu_{pw}$$ 0.0 (-) Coefficient of restitution, $$e_{pp},e_{pw}$$ 1.0 (-) Spring constant, $$k_{pp},k_{pw}$$ 0.1 (kg·m-1) Initial Conditions x-velocity, $$u_{g}$$ 3.0 (m·s-1) y-velocity, $$v_{g}$$ 0.0 (m·s-1) z-velocity, $$w_{g}$$ 0.0 (m·s-1) Gas volume fraction, $$\epsilon_{g}$$ 0.999894 (-) Gas volume fraction at packing, $$\epsilon_{g}^{*}$$ 0.4 (-) Pressure, $$P_{g}$$ 101,325 (Pa) Gas temperature, $$T_{g}$$ 303.15 (K) Solid temperature, $$T_{s}$$ 303.15 (K) Species fraction of air, $$X_{g1}$$ Varied (-) Species fraction of water vapor, $$X_{g2}$$ Varied (-) Boundary Conditions West boundary $$u_{g}$$ Varied (kg·s-1) Mass inflow $$X_{g1},X_{g2}$$ Varied (-) East boundary 101,325 (Pa) Pressure outflow North and South boundaries Free-slip walls Top and Bottom boundaries Free-slip walls ## 5.5.3. Results¶ MFiX-PIC and MFiX-DEM simulations are performed by varying the relative humidity of surrounding air. Table 5.8 summarizes the different settings of relative humidity and the corresponding wet bulb temperatures. Based on the comparison of the data from [17] it can be concluded that the predictions from MFiX-PIC simulations are accurate Table 5.8. Also, the results are consistent with the predictions from MFiX-DEM. Rel. Humidity (%) $$X_{g1}$$ $$X_{g2}$$ Mass Flow Rate (g/s) Wet Bulb T (°C) 0 1.000000 0.000000 0.349315 10.5 10 0.997390 0.002610 0.348762 13.2 20 0.994771 0.005229 0.348208 15.7 30 0.992144 0.007856 0.347655 18.0 40 0.989509 0.010491 0.347102 20.1 50 0.986865 0.013135 0.346548 22.0 60 0.984212 0.015788 0.345995 23.8 70 0.981552 0.018448 0.345442 25.5 80 0.978882 0.021118 0.344888 27.1 90 0.976204 0.023796 0.344335 28.6 100 0.973518 0.026482 0.343281 30.0 Fig. 5.6 Comparison of wet bulb temperatures between data, MFiX-DEM and MFiX-PIC.	2022-07-03T17:53:58	{"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": 0.4316715896129608, "perplexity": 7155.358049795519}, "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/1656104248623.69/warc/CC-MAIN-20220703164826-20220703194826-00465.warc.gz"}
https://e-magnetica.pl/file/grains_in_go_steel_jpg	# Encyclopedia Magnetica ### Site Tools file:grains_in_go_steel_jpg Etched sample of grain-oriented electrical steel showing the grain structure. The length of the arrow is around 10 mm and its direction shows the rolling direction. grains_in_go_steel.jpg You are permitted and indeed encouraged to use this image freely, for any legal purpose including commercial, and with any modifications (the permission is hereby given, so there is no need to ask for it explicitly again), but you MUST always give the following credits: S. Zurek, Encyclopedia Magnetica, CC-BY-4.0 We would appreciate if you let us know of any use: [email protected]	2021-12-01T21:46:39	{"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": 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": 0.2512494623661041, "perplexity": 2509.3376726962615}, "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/1637964360951.9/warc/CC-MAIN-20211201203843-20211201233843-00274.warc.gz"}
https://par.nsf.gov/biblio/10349873-dark-energy-survey-year-results-cosmological-constraints-from-analysis-cosmic-shear-harmonic-space	This content will become publicly available on July 27, 2023 Dark energy survey year 3 results: cosmological constraints from the analysis of cosmic shear in harmonic space ABSTRACT We present cosmological constraints from the analysis of angular power spectra of cosmic shear maps based on data from the first three years of observations by the Dark Energy Survey (DES Y3). Our measurements are based on the pseudo-Cℓ method and complement the analysis of the two-point correlation functions in real space, as the two estimators are known to compress and select Gaussian information in different ways, due to scale cuts. They may also be differently affected by systematic effects and theoretical uncertainties, making this analysis an important cross-check. Using the same fiducial Lambda cold dark matter model as in the DES Y3 real-space analysis, we find ${S_8 \equiv \sigma _8 \sqrt{\Omega _{\rm m}/0.3} = 0.793^{+0.038}_{-0.025}}$, which further improves to S8 = 0.784 ± 0.026 when including shear ratios. This result is within expected statistical fluctuations from the real-space constraint, and in agreement with DES Y3 analyses of non-Gaussian statistics, but favours a slightly higher value of S8, which reduces the tension with the Planck 2018 constraints from 2.3σ in the real space analysis to 1.5σ here. We explore less conservative intrinsic alignments models than the one adopted in our fiducial analysis, finding no clear preference for a more complex model. We also include small more » Authors: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more » Award ID(s): Publication Date: NSF-PAR ID: 10349873 Journal Name: Monthly Notices of the Royal Astronomical Society Volume: 515 Issue: 2 Page Range or eLocation-ID: 1942 to 1972 ISSN: 0035-8711 National Science Foundation ##### More Like this 1. ABSTRACT We constrain the matter density Ωm and the amplitude of density fluctuations σ8 within the ΛCDM cosmological model with shear peak statistics and angular convergence power spectra using mass maps constructed from the first three years of data of the Dark Energy Survey (DES Y3). We use tomographic shear peak statistics, including cross-peaks: peak counts calculated on maps created by taking a harmonic space product of the convergence of two tomographic redshift bins. Our analysis follows a forward-modelling scheme to create a likelihood of these statistics using N-body simulations, using a Gaussian process emulator. We take into account the uncertainty from the remaining, largely unconstrained ΛCDM parameters (Ωb, ns, and h). We include the following lensing systematics: multiplicative shear bias, photometric redshift uncertainty, and galaxy intrinsic alignment. Stringent scale cuts are applied to avoid biases from unmodelled baryonic physics. We find that the additional non-Gaussian information leads to a tightening of the constraints on the structure growth parameter yielding $S_8~\equiv ~\sigma _8\sqrt{\Omega _{\mathrm{m}}/0.3}~=~0.797_{-0.013}^{+0.015}$ (68 per cent confidence limits), with a precision of 1.8 per cent, an improvement of 38 per cent compared to the angular power spectra only case. The results obtained with the angular power spectra and peak counts are found to be inmore » 2. ABSTRACT The CMB lensing signal from cosmic voids and superclusters probes the growth of structure in the low-redshift cosmic web. In this analysis, we cross-correlated the Planck CMB lensing map with voids detected in the Dark Energy Survey Year 3 (Y3) data set (∼5000 deg2), expanding on previous measurements that used Y1 catalogues (∼1300 deg2). Given the increased statistical power compared to Y1 data, we report a 6.6σ detection of negative CMB convergence (κ) imprints using approximately 3600 voids detected from a redMaGiC luminous red galaxy sample. However, the measured signal is lower than expected from the MICE N-body simulation that is based on the ΛCDM model (parameters Ωm = 0.25, σ8 = 0.8), and the discrepancy is associated mostly with the void centre region. Considering the full void lensing profile, we fit an amplitude $A_{\kappa }=\kappa _{{\rm DES}}/\kappa _{{\rm MICE}}$ to a simulation-based template with fixed shape and found a moderate 2σ deviation in the signal with Aκ ≈ 0.79 ± 0.12. We also examined the WebSky simulation that is based on a Planck 2018 ΛCDM cosmology, but the results were even less consistent given the slightly higher matter density fluctuations than in MICE. We then identified superclusters in the DES and the MICE catalogues,more » 3. ABSTRACT Measurements of large-scale structure are interpreted using theoretical predictions for the matter distribution, including potential impacts of baryonic physics. We constrain the feedback strength of baryons jointly with cosmology using weak lensing and galaxy clustering observables (3 × 2pt) of Dark Energy Survey (DES) Year 1 data in combination with external information from baryon acoustic oscillations (BAO) and Planck cosmic microwave background polarization. Our baryon modelling is informed by a set of hydrodynamical simulations that span a variety of baryon scenarios; we span this space via a Principal Component (PC) analysis of the summary statistics extracted from these simulations. We show that at the level of DES Y1 constraining power, one PC is sufficient to describe the variation of baryonic effects in the observables, and the first PC amplitude (Q1) generally reflects the strength of baryon feedback. With the upper limit of Q1 prior being bound by the Illustris feedback scenarios, we reach $\sim 20{{\ \rm per\ cent}}$ improvement in the constraint of $S_8=\sigma _8(\Omega _{\rm m}/0.3)^{0.5}=0.788^{+0.018}_{-0.021}$ compared to the original DES 3 × 2pt analysis. This gain is driven by the inclusion of small-scale cosmic shear information down to 2.5 arcmin, which was excluded in previous DES analyses that did not model baryonicmore » 4. ABSTRACT We present cosmological parameter constraints based on a joint modelling of galaxy–lensing cross-correlations and galaxy clustering measurements in the SDSS, marginalizing over small-scale modelling uncertainties using mock galaxy catalogues, without explicit modelling of galaxy bias. We show that our modelling method is robust to the impact of different choices for how galaxies occupy dark matter haloes and to the impact of baryonic physics (at the $\sim 2{{\ \rm per\ cent}}$ level in cosmological parameters) and test for the impact of covariance on the likelihood analysis and of the survey window function on the theory computations. Applying our results to the measurements using galaxy samples from BOSS and lensing measurements using shear from SDSS galaxies and CMB lensing from Planck, with conservative scale cuts, we obtain $S_8\equiv \left(\frac{\sigma _8}{0.8228}\right)^{0.8}\left(\frac{\Omega _\mathrm{ m}}{0.307}\right)^{0.6}=0.85\pm 0.05$ (stat.) using LOWZ × SDSS galaxy lensing, and S8 = 0.91 ± 0.1 (stat.) using combination of LOWZ and CMASS × Planck CMB lensing. We estimate the systematic uncertainty in the galaxy–galaxy lensing measurements to be $\sim 6{{\ \rm per\ cent}}$ (dominated by photometric redshift uncertainties) and in the galaxy–CMB lensing measurements to be $\sim 3{{\ \rm per\ cent}}$, from small-scale modelling uncertainties including baryonic physics. 5. 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 »	2022-11-30T04:23:14	{"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": 0.6743476390838623, "perplexity": 2277.607692406866}, "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/1669446710719.4/warc/CC-MAIN-20221130024541-20221130054541-00036.warc.gz"}
https://pdglive.lbl.gov/DataBlock.action?node=S056ZLF	#### Searches for ${{\mathit Z}^{\,'}}$ with Lepton-Flavor-Violating decays The following limits are obtained from ${{\mathit p}}{{\overline{\mathit p}}}$ or ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit Z}^{\,'}}{{\mathit X}}$ with ${{\mathit Z}^{\,'}}$ decaying to the mode indicated in the comments. VALUE DOCUMENT ID TECN COMMENT • • We do not use the following data for averages, fits, limits, etc. • • 1 2018 CM ATLS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit e}}{{\mathit \mu}}$ , ${{\mathit e}}{{\mathit \tau}}$ , ${{\mathit \mu}}{{\mathit \tau}}$ 2 2018 AT CMS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit e}}{{\mathit \mu}}$ 3 2016 P ATLS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit e}}{{\mathit \mu}}$ , ${{\mathit e}}{{\mathit \tau}}$ , ${{\mathit \mu}}{{\mathit \tau}}$ 4 2016 BE CMS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit e}}{{\mathit \mu}}$ 5 2015 O ATLS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit e}}{{\mathit \mu}}$ , ${{\mathit e}}{{\mathit \tau}}$ , ${{\mathit \mu}}{{\mathit \tau}}$ 6 2011 H ATLS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit e}}{{\mathit \mu}}$ 7 2011 Z ATLS ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit e}}{{\mathit \mu}}$ 8 2006 M CDF ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit e}}{{\mathit \mu}}$ 1 AABOUD 2018CM search for a new particle with lepton-flavor violating decay in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. See their Figs. 4, 5, and 6 for limits on $\sigma \cdot{}\mathit B$. 2 SIRUNYAN 2018AT search for a narrow resonance ${{\mathit Z}^{\,'}}$ decaying into ${{\mathit e}}{{\mathit \mu}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. See their Fig.5 for limit on $\sigma \cdot{}{{\mathit B}}$ in the range of 600 GeV $<$ $\mathit M_{{{\mathit Z}^{\,'}} }$ $<$ 5000 GeV. 3 AABOUD 2016P search for new particle with lepton flavor violating decay in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. See their Figs.2, 3, and 4 for limits on ${{\mathit \sigma}}$ $\cdot{}{{\mathit B}}$ . 4 KHACHATRYAN 2016BE search for new particle ${{\mathit Z}^{\,'}}$ with lepton flavor violating decay in ${{\mathit p}}{{\mathit p}}$ collisions at$\sqrt {s }$ = 8 TeV in the range of 200 GeV $<$ M$_{{{\mathit Z}^{\,'}} }<$ 2000 GeV. See their Fig.4 for limits on $\sigma \cdot{}\mathit B$ and their Table 5 for bounds on various masses. 5 AAD 2015O search for new particle ${{\mathit Z}^{\,'}}$ with lepton flavor violating decay in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV in the range of 500 GeV $<$ M$_{{{\mathit Z}^{\,'}} }$ $<$ 3000 GeV. See their Fig. 2 for limits on $\sigma \mathit B$. 6 AAD 2011H search for new particle ${{\mathit Z}^{\,'}}$ with lepton flavor violating decay in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV in the range of 700 GeV $<$ M$_{{{\mathit Z}^{\,'}} }$ $<$ 1000 GeV. See their Fig. 3 for limits on $\sigma \cdot{}\mathit B$. 7 AAD 2011Z search for new particle ${{\mathit Z}^{\,'}}$ with lepton flavor violating decay in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV in the range 700 GeV $<$ M$_{{{\mathit Z}^{\,'}} }$ $<$ 2000 GeV. See their Fig. 3 for limits on $\sigma \cdot{}\mathit B$. 8 ABULENCIA 2006M search for new particle ${{\mathit Z}^{\,'}}$ with lepton flavor violating decay in ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\sqrt {s }$ = 1.96$~$TeV in the range of 100 GeV $<$ M$_{{{\mathit Z}^{\,'}} }$ $<$ 800 GeV. See their Fig.$~$4 for limits in the mass-coupling plane. References: AABOUD 2018CM PR D98 092008 Search for lepton-flavor violation in different-flavor, high-mass final states in $pp$ collisions at $\sqrt s=13$ TeV with the ATLAS detector SIRUNYAN 2018AT JHEP 1804 073 Search for lepton-flavor violating decays of heavy resonances and quantum black holes to $e \mu$ final states in proton-proton collisions at $\sqrt{s}=13$ TeV AABOUD 2016P EPJ C76 541 Search for New Phenomena in Different-Flavour high-Mass Dilepton Final States in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 13 Tev with the ATLAS Detector KHACHATRYAN 2016BE EPJ C76 317 Search for Lepton Flavour Violating Decays of Heavy Resonances and Quantum Black Holes to an ${{\mathit e}}{{\mathit \mu}}$ Pair in Proton-Proton Collisions at $\sqrt {s }$ = 8 TeV PRL 115 031801 Search for a Heavy Neutral Particle Decaying to ${{\mathit e}}{{\mathit \mu}}$ , ${{\mathit e}}{{\mathit \tau}}$ , or ${{\mathit \mu}}{{\mathit \tau}}$ in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector EPJ C71 1809 Search for a Heavy Neutral Particle Decaying into an Electron and a Muon using 1 fb${}^{-1}$ of ATLAS Data PRL 106 251801 Search for a Heavy Particle Decaying into an Electron and a Muon with the ATLAS Detector in $\sqrt {s }$ = 7 TeV ${{\mathit p}}{{\mathit p}}$ collisions at the LHC. PRL 96 211802 Search for High-Mass Resonances Decaying to ${{\mathit e}}{{\mathit \mu}}$ in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV	2023-01-31T20:37:14	{"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": 0.9849359393119812, "perplexity": 1593.0552196633903}, "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-2023-06/segments/1674764499890.39/warc/CC-MAIN-20230131190543-20230131220543-00529.warc.gz"}
https://www.nist.gov/pml/diatomic-spectral-database/diatomic-spectral-database-2p-ground-state-molecules	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. # Diatomic Spectral Database, 2Π-Ground State Molecules ## Share ### 4. 2Π-Ground State Molecules As in the case of the 3Σ-molecules, the energy levels of a 2Π-molecule exhibit the additional splittings due to the electron spin and orbital angular momentum interactions. In order to describe the rotational spectra of this class. Hund's coupling case (a) is employed as a starting point. The rotational levels are defined with the quantum number Ω, the absolute value of the projection of the total electronic angular momentum on the molecular axis, with the quantum number J which represents the total angular momentum from rotation and electronic motion, and with the parity. For NO the parity, + or -, of the levels split by Ω-doubling follows the notation of ref. [12]. Although the parity is not known for the other 2Π diatomic molecules, it is necessary to distinguish transitions of + ← - and - ← +. Here the notation a and b is used, where a refers to transitions between the higher energy Λ-doubled levels and b to the lower energy levels. If the molecule contains nuclei with non-zero spin, the coupling of J with I results in the total angular momentum quantum number, F, assuming coupling case (aβ). The spectral line table for NO uses the headings F+ and F_ to indicate the Kronig symmetry and the total angular momentum quantum number. The electric dipole transitions are given by the following selection rules: ΔΩ = 0,ΔJ = 0, ± 1, and + ↔ - plus the normal selection rule for hyperfine splittings, ΔF = 0, ± 1. #### a. Molecular Parameters and Energy Level Formulation The rotational energies, derived from the observed rotational transitions, can be described with the Hamiltonian [12]: $$\begin{eqnarray} {\cal H}~=~B~(\textbf{J}^2~-~L_z^2~+~\textbf{S}^2)~+~AL_zS_z~-~2B \textbf{J} \cdot \textbf{S} \\ +~(B~+~A/2)~(L_+S_-~+~L_-S_+)~-~B(J_+L_-~+~J_-L_+)~+~ \gamma(\textbf{J - S}) \cdot \textbf{S} \end{eqnarray}$$ (eq 20) where a molecule-fixed cartesian coordinate system, with the z-axis along the molecular axis, is employed. The operators, Lz, L+, and L_ are the three spherical components of the electronic orbital angular momentum; Sz, S+, and S_ are the equivalent operators for electron spin and Jz, J+, J_ for the total angular momentum. The parameters B, A, and γ are functions of the internuclear distance and, thus, may be defined in terms of a power series in $$\zeta = \frac{r-r_{\rm e}}{r_{\rm e}}$$ as: $$\begin{eqnarray} B&=&B_{\rm e}(1 - 2\zeta + 3\zeta^3 + ...) ~ ,\\ A&=&A_{\rm e} + A_{(1)} \zeta + A_{(2)} \zeta^2 + ... ~ ,\\ \gamma&=&\gamma_{\rm e} + \gamma_{(1)} \zeta + ... ~ , \end{eqnarray}$$ (eq 20a) The eigenvalue solution of the Hamiltonian above is normally achieved by a perturbation method which takes into account the mixing of various vibrational states, and the mixing of various electronic states with the ground state. In this way centrifugal distortion terms, the vibrational dependence of the molecular parameters, l-uncoupling and Λ- or Ω-doubling can be determined. There are a variety of possible approximations employed to describe the observed microwave spectra. The method used depends on how close the angular momenta coupling in a specific: molecule corresponds to Hund's coupling case (a). Formulations employed for intermediate coupling cases, like that for OH and NO, are given in ref. [13] and [14]. The determinable parameters are Bv1 and Bv2, the effective rotational constants for the 2Π1/2 and 2Π3/2, respectively, the centrifugal distortion parameters Dv1 and Dv2, and the Λ-doubling parameters αp and βp. A very detailed analysis of the Λ-doubling alone is given in ref. [12] while ref. [15] introduces an additional centrifugal term, δ, for the electronic distribution. The appropriate formulation for coupling cases close to Hund's case (a), e.g., ClO and NS, are given in ref. [16]. The determinable parameters are Bv1,Bv2,Dv1,Dv2, where Dv1Dv2, is assumed in all cases, and the Λ-doubling constant peff for the 2Π1/2 state. Here peff is a function of αp and βp. The rotational constant Bv can be evaluated from Bv1 and Bv2, if additional assumptions are made. In a similar manner it is possible to estimate A and A(1) in a few instances. The hyperfine coupling Hamiltonian given in ref. [10] is evaluated in ref. [14] to first order for the magnetic and nuclear electric quadrupole interactions. Although the first order perturbation treatment is adequate for the interpretation of the microwave spectra, the more detailed analysis in ref. [12] is necessary to adequately describe the radiofrequency spectrum of NO. The determinable parameters are the magnetic coupling constants a, b, c, and d, as well as the quadrupole coupling constant, eQq, which is proportional to the electric field gradient at the nucleus in the direction of the molecular axis, and $$e Q \bar q ~ ,$$ which is proportional to the field gradient perpendicular to the molecular axis. In molecules with coupling cases close to case (a), the determinable parameters are functions of combinations of the constants a, b, c, and d. #### b. List of Symbols Symbols Definitions Bv1, Bv2 Effective rotational constants in the 2Π1/2 and 2Π3/2 state, respectively, for the vth vibrational state (MHz). Dv1, Dv2 Centrifugal distortion correction constants in the 2Π1/2 and 2Π3/2 state, respectively; Deff, if Dv1 = Dv2 is assumed. (MHz). αp, βp Ω-doubling parameters, $$\alpha_p = 4\Sigma(-1)^S {\displaystyle ~ \frac {\langle \Pi\|\, (A+2B) L_y\, \|\Sigma\rangle\,\langle\Sigma\|\, BL_y\, \|\Pi\rangle} {E_\Sigma - E_\Pi}}$$ (eq 21) $$\beta_p = \Sigma(-1)^S {\displaystyle ~ \frac {\| \langle\Pi\|\, BL_y\, \|\Sigma\rangle \|^2} {E_\Sigma - E_\Pi}}$$ (eq 22) peff Λ-type doubling constant in the 2Π1/2 state (MHz). a, b, c, d Magnetic hyperfine coupling constants (MHz) where, $$a = 2\mu_{\rm B} g_{\rm N}\mu_{\rm N} \langle 1/r^3\rangle$$ (eq 23) $$b = - \mu_{\rm B}g_{\rm N}\mu_{\rm N} ~\left\langle \frac{3\cos^2\chi-1}{r^3} \right\rangle + \frac{16}{3} ~ \pi \mu_{\rm B} g_{\rm N}\mu_{\rm N} ~ \mid\psi(0)\mid^2$$ (eq 24) $$c = 3\mu_{\rm B}g_{\rm N}\mu_{\rm N} ~\left\langle {\displaystyle \frac{3\cos^2\chi-1}{r^3}}\right\rangle$$ (eq 25) $$d = 3\mu_{\rm B}g_{\rm N}\mu_{\rm N} ~\left\langle {\displaystyle \frac{\sin^2\chi}{r^3}}\right\rangle ~ .$$ (eq 26) Here μB is the Bohr magneton, μN is the nuclear magneton, and gN is the nuclear g-value. eQq Quadrupole coupling constant along the molecular axis, where $$q = \left\langle {\displaystyle \frac{3\cos^2\chi-1}{r^3}}\right\rangle ~ (MHz).$$ $$e Q \bar q$$ Quadrupole coupling constant perpendicular to the molecular axis, where $$\bar q = \left\langle {\displaystyle \frac{3\sin^2\chi}{r^3}}\right\rangle ~ (MHz).$$ A Spin-orbit coupling constant defined by the power series, expansion, $$A = A_{\rm e} + A_{(1)} \zeta + A_{(2)} \zeta^2 + ... ~ .$$ γ Spin-rotation coupling constant defined by the power series $$\gamma = \gamma_{\rm e} + \gamma_{(1)} \zeta + ... ~ .$$ ## Contacts ### Sensor Science Division Created April 27, 2018, Updated November 15, 2019	2022-05-22T20:43:40	{"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": 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": 0.8338584899902344, "perplexity": 1925.4808602463036}, "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-2022-21/segments/1652662546071.13/warc/CC-MAIN-20220522190453-20220522220453-00752.warc.gz"}
https://pos.sissa.it/282/527/	Volume 282 - 38th International Conference on High Energy Physics (ICHEP2016) - Quark and Lepton Flavor Physics CP asymmetries in $D$ decays to two pseudoscalars U. Nierste,* S. Schacht *corresponding author Full text: pdf Pre-published on: February 06, 2017 Published on: April 19, 2017 Abstract This talk addresses two topics related to CP asymmetries in $D$ meson decays to two pseudoscalar mesons. First I discuss how new physics can be distinguished from the Standard Model through two sum rules relating three direct CP asymmetries each, using the sum rule correlating $D^0\to K^+K^-$, $D^0\to \pi^+ \pi^-$, and $D^0\to \pi^0 \pi^0$ for illustration. The other sum rule involves $a_{CP}^{\mathrm{dir}}(D^+\rightarrow \bar{K}^0K^+)$, $a_{CP}^{\mathrm{dir}}(D_s^+\rightarrow K^0\pi^+)$, and $a_{CP}^{\mathrm{dir}}(D_s^+\to K^+ \pi^0)$. The second topic is the direct CP asymmetry in the decay $D^0 \to K_S K_S$, which is expected to be large in the Standard Model for two reasons: Flavor-SU(3) symmetry suppresses the tree amplitude which enhances the crucial penguin-to-tree'' ratio and the penguin'' amplitude is dominated by the tree-level $W$ boson exchange between $c$ and $u$ quarks. We find that $\|a_{CP}^{\mathrm{dir}} (D^0 \to K_S K_S)\|$ can be as large as $1.1 \%$ in the Standard Model. We advocate $D^0 \to K_S K_S$ as a discovery channel for charm CP violation. DOI: https://doi.org/10.22323/1.282.0527 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.	2020-11-28T20:34:56	{"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": 0.7350974082946777, "perplexity": 2944.1484440503527}, "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/1606141195745.90/warc/CC-MAIN-20201128184858-20201128214858-00367.warc.gz"}
https://tjyj.stats.gov.cn/CN/10.19343/j.cnki.11-1302/c.2020.04.007	• • 中国老年人低就业率成因：与俄罗斯的跨国比较 • 出版日期:2020-04-25 发布日期:2020-04-15 The Reason for the Low Elderly Employment Rate in China: Comparison with Russia Wan Haiyuan Han Lili Shen Meng • Online:2020-04-25 Published:2020-04-15 Abstract: It is important to explore the elderly human resource in the background of rapid aging in China. Using the household survey data in China and Russia from 1988 to 2013, we find that China’s elderly employment rate is much lower than its counterpart and the disadvantage even expands in the past 25 years. We then use the Oaxaca method to decompose the contribution sources of the decline in employment rate, thus explaining the reason for the low employment of urban elderly in China. Generally, we argue that the cultural and institutional factors are not sufficient to explain the low employment rate in China, while the labor market and its changes are the main reasons. Compared to Russia, economic growth in China leads to diversified income structure and stable wealth accumulation, while the increasing young migrants crowd out the elderly from the market. The labor market changes lead to decline in the employment willingness and employment competitiveness for the elderly, so it is possible to explain the low and declining employment rate for the elderly in China. Therefore, we should break the labor market segmentation, help the elderly realize job transformation, improve the self-employment environment, increase irregular employment opportunities and employment training for the elderly, encourage the elderly with educational expertise to become an important complement to the labor force in China.	2022-06-26T14:37:46	{"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": 0.30450889468193054, "perplexity": 3097.516110173758}, "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-2022-27/segments/1656103269583.13/warc/CC-MAIN-20220626131545-20220626161545-00643.warc.gz"}
https://zbmath.org/authors/?q=ai%3Acaffarelli.luis-a	# zbMATH — the first resource for mathematics ## Caffarelli, Luis Ángel Compute Distance To: Author ID: caffarelli.luis-a Published as: Caffarelli, Luis A.; Caffarelli, Luis; Caffarelli, L. A.; Caffarelli, L.; Caffarelli, Luis Ángel; Cafferelli, L. A. Homepage: http://www.ma.utexas.edu/users/caffarel/ External Links: MGP · ORCID · Wikidata · Google Scholar · Math-Net.Ru · dblp · GND · IdRef Awards: Wolf Prize (2012) · Shaw Prize (2018) Documents Indexed: 308 Publications since 1974, including 8 Books Biographic References: 1 Publication all top 5 #### Co-Authors 58 single-authored 43 Friedman, Avner 18 Nirenberg, Louis 13 Spruck, Joel 12 Alt, Hans Wilhelm 12 Athanasopoulos, Ioannis 11 Salsa, Sandro 10 Silvestre, Luis E. 8 Mellet, Antoine 8 Vazquez, Juan Luis 6 Li, YanYan 6 Markowich, Peter Alexander 6 Sire, Yannick 6 Vasseur, Alexis F. 5 Berestycki, Henri 5 Kenig, Carlos Eduardo 5 Lee, Ki-Ahm 5 Lin, Fang Hua 5 Riviere, Nestor M. 5 Roquejoffre, Jean-Michel 5 Savin, Ovidiu V. 5 Shahgholian, Henrik 5 Valdinoci, Enrico 4 Aronson, Donald G. 4 Cabré, Xavier 4 Córdoba Barba, Antonio Juan 4 Crandall, Michael G. 4 Figalli, Alessio 4 Gutiérrez, Cristian E. 4 Souganidis, Panagiotis E. 4 Wang, Lihe 4 Wolanski, Noemi I. 3 Aguilera, Néstor E. 3 Arapostathis, Aristotle 3 Burger, Martin 3 De Silva, Daniela 3 Huang, Qingbo 3 Jerison, David S. 3 Wolfram, Marie-Therese 2 Allen, Mark G. 2 Ambrosio, Luigi 2 Biswas, Anup 2 Bjorland, Clayton 2 Bonforte, Matteo 2 Calderón, Calixto Pedro 2 de la Llave, Rafael 2 Fabes, Eugene B. 2 Gidas, Basilis 2 Grillo, Gabriele 2 Karakhanyan, Aram L. 2 Kohn, Robert Vita 2 Lederman, Claudia B. 2 McCann, Robert J. 2 Milakis, Emmanouil 2 Milman, Mario Marcos 2 Oliker, Vladimir I. 2 Patrizi, Stefania 2 Quitalo, Veronica 2 Salazar, Jorge A. 2 Stinga, Pablo Raúl 2 Torelli, Alessandro 2 Urbano, José Miguel 1 Brenier, Yann 1 Brézis, Haïm 1 Brezzi, Franco 1 Buttazzo, Giuseppe 1 Cagnetti, Filippo 1 Chan, Chi Hin 1 Charro, Fernando 1 Dávila, Gonzalo 1 Dipierro, Serena 1 Dolbeault, Jean 1 E, Weinan 1 Feldman, Mikhail 1 Garofalo, Nicola 1 Gilardi, Gianni 1 Glowinski, Roland 1 González, María del Mar 1 Gualdani, Maria Pia 1 Guan, Pengfei 1 Hardt, Robert M. 1 Jin, Tianling 1 Kamin, Shoshana 1 Karp, Lavi 1 Kinderlehrer, David 1 Kocan, Maciej 1 Kochengin, Sergey A. 1 Kohn, Joseph J. 1 Kriventsov, Dennis 1 Leitão, Raimundo A. 1 Lieb, Elliott H. 1 Littman, Walter 1 Ma, Xi-Nan 1 Manasevich, Raul F. 1 Maugeri, Antonino 1 Monneau, Régis 1 Mortola, Stefano 1 Muler, Nora E. 1 Nguyen, Truyen Van 1 Pang, Guodong 1 Peral Alonso, Ireneo ...and 26 more Co-Authors all top 5 #### Serials 35 Communications on Pure and Applied Mathematics 21 Archive for Rational Mechanics and Analysis 21 Indiana University Mathematics Journal 18 Communications in Partial Differential Equations 12 Annals of Mathematics. Second Series 10 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 8 Transactions of the American Mathematical Society 8 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 5 Advances in Mathematics 5 Duke Mathematical Journal 5 Journal of Differential Equations 5 Journal für die Reine und Angewandte Mathematik 5 Proceedings of the American Mathematical Society 5 Journal of the American Mathematical Society 4 American Journal of Mathematics 4 Calculus of Variations and Partial Differential Equations 4 Discrete and Continuous Dynamical Systems 3 Communications in Mathematical Physics 3 Acta Mathematica 3 Inventiones Mathematicae 3 Revista Matemática Iberoamericana 3 Differential and Integral Equations 3 SIAM Journal on Mathematical Analysis 3 Journal of the European Mathematical Society (JEMS) 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Pacific Journal of Mathematics 2 SIAM Journal on Control and Optimization 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 Communications in Analysis and Geometry 2 Journal of Mathematical Sciences (New York) 2 St. Petersburg Mathematical Journal 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Fixed Point Theory and Applications 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Analysis and Applications 1 Journal of Statistical Physics 1 Rocky Mountain Journal of Mathematics 1 Studia Mathematica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Calcolo 1 Colloquium Mathematicum 1 Compositio Mathematica 1 Illinois Journal of Mathematics 1 Journal of Functional Analysis 1 Manuscripta Mathematica 1 Mathematische Annalen 1 RAIRO. Analyse Numérique 1 Rendiconti del Seminario Matemàtico e Fisico di Milano 1 Chinese Annals of Mathematics. Series B 1 Journal of Scientific Computing 1 The Journal of Geometric Analysis 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the National Academy of Sciences of the United States of America 1 Bulletin of the American Mathematical Society. New Series 1 Expositiones Mathematicae 1 Bollettino della Unione Matemàtica Italiana. Serie VII. B 1 Journal of Partial Differential Equations 1 Journal of Dynamics and Differential Equations 1 Topological Methods in Nonlinear Analysis 1 The Journal of Fourier Analysis and Applications 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Interfaces and Free Boundaries 1 Journal of Numerical Mathematics 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Communications in Mathematical Sciences 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Bollettino della Unione Matematica Italiana. Series V. A 1 Bulletin of the American Mathematical Society 1 Colloquium Publications. American Mathematical Society 1 Contemporary Mathematics 1 Graduate Studies in Mathematics 1 Lecture Notes in Mathematics 1 IAS/Park City Mathematics Series 1 Networks and Heterogeneous Media 1 Discrete and Continuous Dynamical Systems. Series S 1 Kinetic and Related Models 1 Annals of PDE 1 Philosophical Transactions A. Royal Society of London all top 5 #### Fields 255 Partial differential equations (35-XX) 68 Calculus of variations and optimal control; optimization (49-XX) 42 Fluid mechanics (76-XX) 17 Differential geometry (53-XX) 16 Potential theory (31-XX) 12 Operator theory (47-XX) 11 Global analysis, analysis on manifolds (58-XX) 11 Mechanics of deformable solids (74-XX) 10 Classical thermodynamics, heat transfer (80-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 General and overarching topics; collections (00-XX) 8 Optics, electromagnetic theory (78-XX) 7 Real functions (26-XX) 7 Functional analysis (46-XX) 7 Numerical analysis (65-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Probability theory and stochastic processes (60-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Integral equations (45-XX) 4 History and biography (01-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Systems theory; control (93-XX) 3 Measure and integration (28-XX) 3 Quantum theory (81-XX) 2 Ordinary differential equations (34-XX) 2 Convex and discrete geometry (52-XX) 2 Operations research, mathematical programming (90-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Sequences, series, summability (40-XX) 1 Approximations and expansions (41-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX) #### Citations contained in zbMATH Open 271 Publications have been cited 13,618 times in 7,901 Documents Cited by Year An extension problem related to the fractional Laplacian. Zbl 1143.26002 Caffarelli, Luis; Silvestre, Luis 2007 Partial regularity of suitable weak solutions of the Navier-Stokes equations. Zbl 0509.35067 Caffarelli, L.; Kohn, R.; Nirenberg, Louis 1982 Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth. Zbl 0702.35085 Caffarelli, Luis A.; Gidas, Basilis; Spruck, Joel 1989 Fully nonlinear elliptic equations. Zbl 0834.35002 Caffarelli, Luis A.; Cabré, Xavier 1995 First order interpolation inequalities with weights. Zbl 0563.46024 Caffarelli, L.; Kohn, R.; Nirenberg, Louis 1984 Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Zbl 1204.35063 Caffarelli, Luis A.; Vasseur, Alexis 2010 The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian. Zbl 0654.35031 Caffarelli, L.; Nirenberg, L.; Spruck, J. 1985 Existence and regularity for a minimum problem with free boundary. Zbl 0449.35105 Alt, H. W.; Caffarelli, L. A. 1981 Interior a priori estimates for solutions of fully nonlinear equations. Zbl 0692.35017 Caffarelli, Luis A. 1989 On $$W^{1,p}$$ estimates for elliptic equations in divergence form. Zbl 0906.35030 Caffarelli, L. A.; Peral, I. 1998 Regularity theory for fully nonlinear integro-differential equations. Zbl 1170.45006 Caffarelli, Luis; Silvestre, Luis 2009 The Dirichlet problem for nonlinear second-order elliptic equations. I: Monge-Ampère equation. Zbl 0598.35047 Caffarelli, L.; Nirenberg, Louis; Spruck, J. 1984 Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian. Zbl 1148.35097 Caffarelli, Luis A.; Salsa, Sandro; Silvestre, Luis 2008 Interior $$W^{2,p}$$ estimates for solutions of the Monge-Ampère equation. Zbl 0704.35044 Caffarelli, Luis A. 1990 Variational problems with two phases and their free boundary. Zbl 0844.35137 Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner 1984 Nonlocal minimal surfaces. Zbl 1248.53009 Caffarelli, L.; Roquejoffre, J.-M.; Savin, O. 2010 The obstacle problem revisited. Zbl 0928.49030 Caffarelli, L. A. 1998 Non-local diffusions, drifts and games. Zbl 1266.35060 Caffarelli, Luis 2012 A geometric approach to free boundary problems. Zbl 1083.35001 Caffarelli, Luis; Salsa, Sandro 2005 Boundary behavior of nonnegative solutions of elliptic operators in divergence form. Zbl 0512.35038 Caffarelli, L.; Fabes, E.; Mortola, S.; Salsa, S. 1981 The regularity of free boundaries in higher dimensions. Zbl 0386.35046 Caffarelli, Luis A. 1978 On viscosity solutions of fully nonlinear equations with measurable ingredients. Zbl 0854.35032 Caffarelli, L.; Crandall, M. G.; Kocan, M.; Świȩch, A. 1996 A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity. Zbl 0704.35045 Caffarelli, L. A. 1990 Further qualitative properties for elliptic equations in unbounded domains. Zbl 1079.35513 Berestycki, Henri; Caffarelli, Luis; Nirenberg, Louis 1997 Variational problems with free boundaries for the fractional Laplacian. Zbl 1221.35453 Caffarelli, Luis A.; Roquejoffre, Jean-Michel; Sire, Yannick 2010 The Dirichlet problem for nonlinear second-order elliptic equations. II: Complex Monge-Ampère, and uniformly elliptic, equations. Zbl 0598.35048 Caffarelli, L.; Kohn, J. J.; Nirenberg, Louis; Spruck, J. 1985 Monotonicity for elliptic equations in unbounded Lipschitz domains. Zbl 0906.35035 Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. 1997 The regularity of mappings with a convex potential. Zbl 0753.35031 Caffarelli, Luis A. 1992 Vortex condensation in the Chern-Simons Higgs model: An existence theorem. Zbl 0846.58063 Caffarelli, Luis A.; Yang, Yisong 1995 Regularity results for nonlocal equations by approximation. Zbl 1231.35284 Caffarelli, Luis; Silvestre, Luis 2011 Some regularity properties of solutions of Monge Ampère equation. Zbl 0761.35028 Caffarelli, Luis A. 1991 A Harnack inequality approach to the regularity of free boundaries. II: Flat free boundaries are Lipschitz. Zbl 0676.35086 Caffarelli, Luis A. 1989 A Harnack inequality approach to the regularity of free boundaries. I: Lipschitz free boundaries are $$C^{1,\alpha}$$. Zbl 0676.35085 Caffarelli, Luis A. 1987 Convexity of solutions of semilinear elliptic equations. Zbl 0599.35065 Caffarelli, Luis A.; Friedman, Avner 1985 Nonlinear porous medium flow with fractional potential pressure. Zbl 1264.76105 Caffarelli, Luis; Vazquez, Juan Luis 2011 Convexity properties of solutions to some classical variational problems. Zbl 0508.49013 Caffarelli, Luis A.; Spruck, Joel 1982 The initial trace of a solution of the porous medium equation. Zbl 0556.76084 Aronson, D. G.; Caffarelli, L. A. 1983 Fractional elliptic equations, Caccioppoli estimates and regularity. Zbl 1381.35211 Caffarelli, Luis A.; Stinga, Pablo Raúl 2016 Inequalities for second-order elliptic equations with applications to unbounded domains. I. Zbl 0860.35004 Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. 1996 Boundary regularity of maps with convex potentials. II. Zbl 0916.35016 Caffarelli, Luis A. 1996 Properties of the solutions of the linearized Monge-Ampère equation. Zbl 0878.35039 Caffarelli, Luis A.; Gutiérrez, Cristian E. 1997 A parabolic problem with a fractional time derivative. Zbl 1338.35428 Allen, Mark; Caffarelli, Luis; Vasseur, Alexis 2016 Uniform estimates and limiting arguments for nonlocal minimal surfaces. Zbl 1357.49143 Caffarelli, Luis; Valdinoci, Enrico 2011 Regularity of the free boundary of a gas flow in an $$n$$-dimensional porous medium. Zbl 0439.76085 Caffarelli, Luis A.; Friedman, Avner 1980 Boundary regularity of maps with convex potentials. Zbl 0778.35015 Caffarelli, Luis A. 1992 Nonlinear second-order elliptic equations. V: The Dirichlet problem for Weingarten hypersurfaces. Zbl 0672.35028 Caffarelli, Luis; Nirenberg, Louis; Spruck, Joel 1988 The Evans-Krylov theorem for nonlocal fully nonlinear equations. Zbl 1232.49043 Caffarelli, Luis; Silvestre, Luis 2011 Regularity theory for parabolic nonlinear integral operators. Zbl 1223.35098 Caffarelli, Luis; Chan, Chi Hin; Vasseur, Alexis 2011 Constructing optimal maps for Monge’s transport problem as a limit of strictly convex costs. Zbl 1053.49032 Caffarelli, Luis A.; Feldman, Mikhail; McCann, Robert J. 2002 Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries. Zbl 1194.35138 Caffarelli, L. A.; Lin, Fang-Hua 2008 Continuity of the temperature in the two-phase Stefan problem. Zbl 0516.35080 Caffarelli, L. A.; Evans, L. C. 1983 Regularity of a free boundary with application to the Pompeiu problem. Zbl 0960.35112 Caffarelli, Luis A.; Karp, Lavi; Shahgholian, Henrik 2000 A Harnack inequality approach to the regularity of free boundaries. III: Existence theory, compactness, and dependence on X. Zbl 0702.35249 Caffarelli, Luis A. 1988 Further regularity for the Signorini problem. Zbl 0427.35019 Caffarelli, L. A. 1979 Homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media. Zbl 1063.35025 Caffarelli, Luis A.; Souganidis, Panagiotis E.; Wang, L. 2005 Lipschitz continuity of solutions and interfaces of the N-dimensional porous medium equation. Zbl 0644.35058 Caffarelli, L. A.; Vazquez, J. L.; Wolanski, N. I. 1987 Partial regularity of the zero-set of solutions of linear and superlinear elliptic equations. Zbl 0593.35047 Caffarelli, Luis A.; Friedman, Avner 1985 Monotonicity properties of optimal transportation and the FKG and related inequalities. Zbl 0978.60107 Caffarelli, Luis A. 2000 An extension to a theorem of Jörgens, Calabi, and Pogorelov. Zbl 1236.35041 Caffarelli, L.; Li, YanYan 2003 Uniform estimates for regularization of free boundary problems. Zbl 0702.35252 Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. 1990 A free boundary problem for quasi-linear elliptic equations. Zbl 0554.35129 Alt, Hans Wilhelm; Caffarelli, Luis A.; Friedman, Avner 1984 An $$L^ \infty$$ bound for solutions of the Cahn-Hilliard equation. Zbl 0851.35010 Caffarelli, Luis A.; Muler, Nora E. 1995 An optimal partition problem for eigenvalues. Zbl 1123.65060 Cafferelli, L. A.; Lin, Fang Hua 2007 Optimal transportation and applications. Lectures given at the C. I. M. E. summer school, Martina Franca, Italy, September 2–8, 2001. Zbl 1013.00028 Ambrosio, Luigi; Brenier, Yann; Buttazzo, Giusseppe; Caffarelli, Luis A.; Salsa, S. (ed.); Villani, Cédric 2003 A free-boundary problem for the heat equation arising in flame propagation. Zbl 0814.35149 Caffarelli, Luis A.; Vázquez, Juan L. 1995 Some new monotonicity theorems with applications to free boundary problems. Zbl 1142.35382 Caffarelli, Luis A.; Jerison, David; Kenig, Carlos E. 2002 Uniform convergence of a singular perturbation problem. Zbl 0829.49013 Caffarelli, Luis A.; Córdoba, Antonio 1995 Global energy minimizers for free boundary problems and full regularity in three dimensions. Zbl 1330.35545 Caffarelli, Luis A.; Jerison, David; Kenig, Carlos E. 2004 The structure of the free boundary for lower dimensional obstacle problems. Zbl 1185.35339 Athanasopoulos, I.; Caffarelli, L. A.; Salsa, S. 2008 Completely singular elliptic-harmonic measures. Zbl 0482.35020 Caffarelli, Luis A.; Fabes, Eugene B.; Kenig, Carlos E. 1981 Regularity of solutions of the fractional porous medium flow. Zbl 1292.35312 Caffarelli, Luis A.; Soria, Fernando; Vázquez, Juan Luis 2013 The obstacle problem for the biharmonic operator. Zbl 0405.31007 Caffarelli, Luis A.; Friedman, Avner 1979 Nonlocal tug-of-war and the infinity fractional Laplacian. Zbl 1235.35278 Bjorland, Clayton; Caffarelli, Luis; Figalli, Alessio 2012 Non-local gradient dependent operators. Zbl 1252.35099 Bjorland, C.; Caffarelli, L.; Figalli, A. 2012 Compactness methods in free boundary problems. Zbl 0437.35070 Caffarelli, Luis A. 1980 Regularity of solutions to the parabolic fractional obstacle problem. Zbl 1277.35088 Caffarelli, Luis; Figalli, Alessio 2013 A gradient bound for entire solutions of quasi-linear equations and its consequences. Zbl 0819.35016 Caffarelli, Luis; Garofalo, Nicola; Segala, Fausto 1994 Continuity of the density of a gas flow in a porous medium. Zbl 0425.35060 Caffarelli, Luis A.; Friedman, Avner 1979 Regularity properties of nonlocal minimal surfaces via limiting arguments. Zbl 1284.53008 Caffarelli, Luis; Valdinoci, Enrico 2013 Free boundaries in optimal transport and Monge-Ampère obstacle problems. Zbl 1196.35231 Caffarelli, Luis A.; McCann, Robert J. 2010 Asymptotic behaviour of a porous medium equation with fractional diffusion. Zbl 1211.35043 Caffarelli, Luis; Vázquez, Juan-Luis 2011 Rates of convergence for the homogenization of fully nonlinear uniformly elliptic PDE in random media. Zbl 1192.35048 Caffarelli, Luis A.; Souganidis, Panagiotis E. 2010 Symmetry for elliptic equations in a half space. Zbl 0793.35034 Berestycki, H.; Caffarelli, L. A.; Nirenberg, L. 1993 Real analysis related to the Monge-Ampère equation. Zbl 0858.35034 Caffarelli, Luis A.; Gutiérrez, Cristian E. 1996 An optimization problem with volume constraint. Zbl 0588.49005 Aguilera, N.; Alt, H. W.; Caffarelli, L. A. 1986 Regularity of a free boundary in parabolic potential theory. Zbl 1054.35142 Caffarelli, Luis; Petrosyan, Arshak; Shahgholian, Henrik 2004 The blow-up boundary for nonlinear wave equations. Zbl 0638.35053 Caffarelli, Luis A.; Friedman, Avner 1986 Allocation maps with general cost functions. Zbl 0883.49030 Caffarelli, Luis A. 1996 Optimal regularity of lower dimensional obstacle problems. Zbl 1108.35038 Athanasopoulos, I.; Caffarelli, L. A. 2004 Planelike minimizers in periodic media. Zbl 1036.49040 Caffarelli, Luis A.; de la Llave, Rafael 2001 How an initially stationary interface begins to move in porous medium flow. Zbl 0542.76119 Aronson, D. G.; Caffarelli, L. A.; Kamin, S. 1983 Nonlinear second order elliptic equations. IV. Starshaped compact Weingarten hypersurfaces. Zbl 0672.35027 Caffarelli, L.; Nirenberg, L.; Spruck, J. 1986 Potential methods in variational inequalities. Zbl 0455.49010 Caffarelli, L. A.; Kinderlehrer, D. 1980 Regularity of the free boundary in parabolic phase-transition problems. Zbl 0891.35164 Athanasopoulos, I.; Caffarelli, L.; Salsa, S. 1996 Smoothness and analyticity of free boundaries in variational inequalities. Zbl 0363.35009 Caffarelli, L. A.; Riviere, N. M. 1976 Continuity of the temperature in boundary heat control problems. Zbl 1190.35125 Athanasopoulos, I.; Caffarelli, L. A. 2010 Caloric functions in Lipschitz domains and the regularity of solutions to phase transition problems. Zbl 0853.35049 Athanasopoulos, I.; Caffarelli, L.; Salsa, S. 1996 Asymptotic estimates for the plasma problem. Zbl 0466.35033 Caffarelli, Luis A.; Friedman, Avner 1980 On the case of equality in the Brunn-Minkowski inequality for capacity. Zbl 0847.31005 Caffarelli, Luis A.; Jerison, David; Lieb, Elliott H. 1996 Regularity of the free boundary for the one-dimensional flow of gas in a porous medium. Zbl 0439.76084 Caffarelli, Luis A.; Friedman, Avner 1979 Regularity for $$C^{1, \alpha}$$ interface transmission problems. Zbl 1467.35169 Caffarelli, Luis Ángel; Soria-Carro, María; Stinga, Pablo Raúl 2021 Minimal surfaces and free boundaries: recent developments. Zbl 1433.35464 Caffarelli, Luis A.; Sire, Yannick 2020 Fully nonlinear integro-differential equations with deforming kernels. Zbl 1452.35055 Caffarelli, Luis; Teymurazyan, Rafayel; Urbano, José Miguel 2020 Optimal regularity and structure of the free boundary for minimizers in cohesive zone models. Zbl 1442.49005 Caffarelli, L.; Cagnetti, F.; Figalli, A. 2020 Existence of weak solutions to a continuity equation with space time nonlocal Darcy law. Zbl 1459.35233 Caffarelli, Luis; Gualdani, Maria; Zamponi, Nicola 2020 Parabolic obstacle problems, quasi-convexity and regularity. Zbl 1432.35264 Athanasopoulos, Ioannis; Caffarelli, Luis; Milakis, Emmanouil 2019 Ergodic control of a class of jump diffusions with finite Lévy measures and rough kernels. Zbl 1415.93288 Arapostathis, Ari; Caffarelli, Luis; Pang, Guodong; Zheng, Yi 2019 On uniqueness of solutions to viscous HJB equations with a subquadratic nonlinearity in the gradient. Zbl 1428.35125 Arapostathis, Ari; Biswas, Anup; Caffarelli, Luis 2019 Interior regularity for fractional systems. Zbl 1411.35111 Caffarelli, Luis; Dávila, Gonzalo 2019 On the regularity of the non-dynamic parabolic fractional obstacle problem. Zbl 1394.35588 Athanasopoulos, Ioannis; Caffarelli, Luis; Milakis, Emmanouil 2018 A minimization problem with free boundary related to a cooperative system. Zbl 1395.35226 Caffarelli, Luis A.; Shahgholian, Henrik; Yeressian, Karen 2018 Bounds on the Green function for integral operators and fractional harmonic measure with applications to boundary Harnack. Zbl 1387.35071 Caffarelli, Luis A.; Sire, Yannick 2018 Two-phase anisotropic free boundary problems and applications to the Bellman equation in 2D. Zbl 1393.35247 Caffarelli, L.; De Silva, D.; Savin, O. 2018 Obstacle problems for integro-differential operators: regularity of solutions and free boundaries. Zbl 1371.35361 Caffarelli, Luis; Ros-Oton, Xavier; Serra, Joaquim 2017 Porous medium flow with both a fractional potential pressure and fractional time derivative. Zbl 1372.35328 Allen, Mark; Caffarelli, Luis; Vasseur, Alexis 2017 On some pointwise inequalities involving nonlocal operators. Zbl 06703883 Caffarelli, Luis A.; Sire, Yannick 2017 A logistic equation with nonlocal interactions. Zbl 1356.35261 Caffarelli, Luis; Dipierro, Serena; Valdinoci, Enrico 2017 The two membranes problem for different operators. Zbl 1368.35045 Caffarelli, L.; De Silva, D.; Savin, O. 2017 On a long range segregation model. Zbl 1386.35084 Caffarelli, L.; Patrizi, S.; Quitalo, V. 2017 Fractional elliptic equations, Caccioppoli estimates and regularity. Zbl 1381.35211 Caffarelli, Luis A.; Stinga, Pablo Raúl 2016 A parabolic problem with a fractional time derivative. Zbl 1338.35428 Allen, Mark; Caffarelli, Luis; Vasseur, Alexis 2016 A free boundary problem related to thermal insulation. Zbl 1351.35268 Caffarelli, Luis A.; Kriventsov, Dennis 2016 Obstacle-type problems for minimal surfaces. Zbl 1370.35070 Caffarelli, L.; De Silva, D.; Savin, O. 2016 The Dirichlet problem for stable-like operators and related probabilistic representations. Zbl 1352.60080 Arapostathis, Ari; Biswas, Anup; Caffarelli, Luis 2016 Regularity of solutions of the fractional porous medium flow with exponent $$1/2$$. Zbl 1335.35273 Caffarelli, L.; Vázquez, J. L. 2016 A non-local Monge-Ampère equation. Zbl 1361.35067 Caffarelli, Luis; Silvestre, Luis 2016 Minimization of a fractional perimeter-Dirichlet integral functional. Zbl 1323.35216 Caffarelli, Luis; Savin, Ovidiu; Valdinoci, Enrico 2015 On a fractional Monge-Ampère operator. Zbl 1393.35268 Caffarelli, Luis; Charro, Fernando 2015 Regularity of free boundaries a heuristic retro. Zbl 1353.35319 Caffarelli, Luis A.; Shahgholian, Henrik 2015 A bifurcation phenomenon in a singularly perturbed one-phase free boundary problem of phase transition. Zbl 1334.35439 Caffarelli, Luis A.; Wang, Peiyong 2015 Local analysis of solutions of fractional semi-linear elliptic equations with isolated singularities. Zbl 1296.35208 Caffarelli, Luis; Jin, Tianling; Sire, Yannick; Xiong, Jingang 2014 Partial differential equation models in the socio-economic sciences. Zbl 1353.00004 Burger, Martin; Caffarelli, Luis; Markowich, Peter A. 2014 Hölder regularity for generalized master equations with rough kernels. Zbl 1312.45013 Caffarelli, Luis; Silvestre, Luis 2014 On the asymptotic behavior of a Boltzmann-type price formation model. Zbl 1307.35302 Burger, Martin; Caffarelli, Luis; Markowich, Peter A.; Wolfram, Marie-Therese 2014 Regularity for anisotropic fully nonlinear integro-differential equations. Zbl 1304.35730 Caffarelli, Luis A.; Leitão, Raimundo; Urbano, José Miguel 2014 Counter-example in three dimension and homogenization of geometric motions in two dimension. Zbl 1293.35026 Caffarelli, L. A.; Monneau, R. 2014 A perturbation argument for a Monge-Ampère type equation arising in optimal transportation. Zbl 1294.35170 Caffarelli, Luis; Del Mar González, María; Nguyen, Truyen 2014 Relations between geometric convexity, doubling measures and property $$\Gamma$$. Zbl 1307.46006 Caffarelli, Luis A.; Crandall, Michael G. 2014 Regularity of solutions of the fractional porous medium flow. Zbl 1292.35312 Caffarelli, Luis A.; Soria, Fernando; Vázquez, Juan Luis 2013 Regularity of solutions to the parabolic fractional obstacle problem. Zbl 1277.35088 Caffarelli, Luis; Figalli, Alessio 2013 Regularity properties of nonlocal minimal surfaces via limiting arguments. Zbl 1284.53008 Caffarelli, Luis; Valdinoci, Enrico 2013 Some remarks on singular solutions of nonlinear elliptic equations. III: Viscosity solutions including parabolic operators. Zbl 1279.35044 Caffarelli, Luis; Li, Yanyan; Nirenberg, Louis 2013 On a Boltzmann-type price formation model. Zbl 1372.91039 Burger, Martin; Caffarelli, Luis; Markowich, Peter A.; Wolfram, Marie-Therese 2013 A priori bounds for solutions of a nonlocal evolution PDE. Zbl 1273.35067 Caffarelli, Luis; Valdinoci, Enrico 2013 Non-local diffusions, drifts and games. Zbl 1266.35060 Caffarelli, Luis 2012 Nonlocal tug-of-war and the infinity fractional Laplacian. Zbl 1235.35278 Bjorland, Clayton; Caffarelli, Luis; Figalli, Alessio 2012 Non-local gradient dependent operators. Zbl 1252.35099 Bjorland, C.; Caffarelli, L.; Figalli, A. 2012 Some remarks on singular solutions of nonlinear elliptic equations. II: Symmetry and monotonicity via moving planes. Zbl 1325.35044 Caffarelli, Luis; Li, YanYan; Nirenberg, Louis 2012 Traveling waves for a boundary reaction-diffusion equation. Zbl 1255.35072 Caffarelli, L.; Mellet, A.; Sire, Y. 2012 The De Giorgi method for nonlocal fluid dynamics. Zbl 1357.35249 Caffarelli, Luis A.; Vasseur, Alexis 2012 The problem of two sticks. Zbl 1257.46009 Caffarelli, Luis A.; Crandall, Michael G. 2012 Regularity results for nonlocal equations by approximation. Zbl 1231.35284 Caffarelli, Luis; Silvestre, Luis 2011 Nonlinear porous medium flow with fractional potential pressure. Zbl 1264.76105 Caffarelli, Luis; Vazquez, Juan Luis 2011 Uniform estimates and limiting arguments for nonlocal minimal surfaces. Zbl 1357.49143 Caffarelli, Luis; Valdinoci, Enrico 2011 The Evans-Krylov theorem for nonlocal fully nonlinear equations. Zbl 1232.49043 Caffarelli, Luis; Silvestre, Luis 2011 Regularity theory for parabolic nonlinear integral operators. Zbl 1223.35098 Caffarelli, Luis; Chan, Chi Hin; Vasseur, Alexis 2011 Asymptotic behaviour of a porous medium equation with fractional diffusion. Zbl 1211.35043 Caffarelli, Luis; Vázquez, Juan-Luis 2011 On a price formation free boundary model by Lasry and Lions. Zbl 1216.91012 Caffarelli, Luis A.; Markowich, Peter A.; Pietschmann, Jan-F. 2011 On a price formation free boundary model by Lasry and Lions: the Neumann problem. Zbl 1233.91336 Caffarelli, Luis A.; Markowich, Peter A.; Wolfram, Marie-Therese 2011 Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Zbl 1204.35063 Caffarelli, Luis A.; Vasseur, Alexis 2010 Nonlocal minimal surfaces. Zbl 1248.53009 Caffarelli, L.; Roquejoffre, J.-M.; Savin, O. 2010 Variational problems with free boundaries for the fractional Laplacian. Zbl 1221.35453 Caffarelli, Luis A.; Roquejoffre, Jean-Michel; Sire, Yannick 2010 Free boundaries in optimal transport and Monge-Ampère obstacle problems. Zbl 1196.35231 Caffarelli, Luis A.; McCann, Robert J. 2010 Rates of convergence for the homogenization of fully nonlinear uniformly elliptic PDE in random media. Zbl 1192.35048 Caffarelli, Luis A.; Souganidis, Panagiotis E. 2010 Continuity of the temperature in boundary heat control problems. Zbl 1190.35125 Athanasopoulos, I.; Caffarelli, L. A. 2010 Convergence of nonlocal threshold dynamics approximations to front propagation. Zbl 1190.65132 Caffarelli, Luis A.; Souganidis, Panagiotis E. 2010 The De Giorgi method for regularity of solutions of elliptic equations and its applications to fluid dynamics. Zbl 1210.76039 Caffarelli, Luis A.; Vasseur, Alexis F. 2010 Distance functions and almost global solutions of eikonal equations. Zbl 1187.35024 Caffarelli, Luis A.; Crandall, Michael G. 2010 Analysis on the junctions of domain walls. Zbl 1193.35255 Caffarelli, Luis A.; Lin, Fang Hua 2010 On the Evans-Krylov theorem. Zbl 1180.35229 Caffarelli, Luis; Silvestre, Luis 2010 Smooth approximations of solutions to nonconvex fully nonlinear elliptic equations. Zbl 1208.35047 Caffarelli, Luis; Silvestre, Luis 2010 Regularity theory for fully nonlinear integro-differential equations. Zbl 1170.45006 Caffarelli, Luis; Silvestre, Luis 2009 Some remarks on singular solutions of nonlinear elliptic equations. I. Zbl 1215.35068 Caffarelli, Luis; Li, Yan Yan; Nirenberg, Louis 2009 The geometry of solutions to a segregation problem for nondivergence systems. Zbl 1217.35015 Caffarelli, L. A.; Karakhanyan, A. L.; Lin, Fang-Hua 2009 Nonlocal heat flows preserving the $$L^2$$ energy. Zbl 1154.35364 Caffarelli, Luis; Lin, Fanghua 2009 Random homogenization of an obstacle problem. Zbl 1180.35069 Caffarelli, L. A.; Mellet, A. 2009 Surfaces minimizing nonlocal energies. Zbl 1182.53055 Caffarelli, Luis A. 2009 Reflector problem in $${\mathbb R^n}$$ endowed with non-Euclidean norm. Zbl 1173.78003 Caffarelli, Luis A.; Huang, Qingbo 2009 Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian. Zbl 1148.35097 Caffarelli, Luis A.; Salsa, Sandro; Silvestre, Luis 2008 Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries. Zbl 1194.35138 Caffarelli, L. A.; Lin, Fang-Hua 2008 The structure of the free boundary for lower dimensional obstacle problems. Zbl 1185.35339 Athanasopoulos, I.; Caffarelli, L. A.; Salsa, S. 2008 A rate of convergence for monotone finite difference approximations to fully nonlinear, uniformly elliptic PDEs. Zbl 1140.65075 Caffarelli, Luis A.; Souganidis, Panagiotis E. 2008 Weak solutions of one inverse problem in geometric optics. Zbl 1202.78003 Caffarelli, L. A.; Oliker, V. I. 2008 On the regularity of reflector antennas. Zbl 1140.35009 Caffarelli, Luis A.; Gutiíerrez, Cristian E.; Huang, Qingbo 2008 Random homogenization of fractional obstacle problems. Zbl 1156.74359 Caffarelli, Luis; Mellet, Antoine 2008 A counterexample to $$C^{2,1}$$ regularity for parabolic fully nonlinear equations. Zbl 1162.35042 Caffarelli, Luis A.; Stefanelli, Ulisse 2008 Numerical solution of the Dirichlet problem for a Pucci equation in dimension two. Application to homogenization. Zbl 1155.65097 Caffarelli, L. A.; Glowinski, R. 2008 Viscosity method for homogenization of highly oscillating obstacles. Zbl 1158.35109 Caffarelli, Luis; Lee, Ki-Ahm 2008 Some nonlinear problems involving nonlocal diffusions. Zbl 1419.35203 Caffarelli, Luis A. 2008 An extension problem related to the fractional Laplacian. Zbl 1143.26002 Caffarelli, Luis; Silvestre, Luis 2007 An optimal partition problem for eigenvalues. Zbl 1123.65060 Cafferelli, L. A.; Lin, Fang Hua 2007 A constant rank theorem for solutions of fully nonlinear elliptic equations. Zbl 1191.35127 Caffarelli, Luis A.; Guan, Pengfei; Ma, Xinan 2007 Uniform Hölder estimates in a class of elliptic systems and applications to singular limits in models for diffusion flames. Zbl 1189.35084 Caffarelli, Luis A.; Roquejoffre, Jean-Michel 2007 Capillary drops: contact angle hysteresis and sticking drops. Zbl 1168.76007 Caffarelli, L. A.; Mellet, A. 2007 Capillary drops on an inhomogeneous surface. Zbl 1200.76053 Caffarelli, L. A.; Mellet, A. 2007 Homogenization of oscillating free boundaries: the elliptic case. Zbl 1122.35156 Caffarelli, L.; Lee, K. 2007 Flame propagation in one-dimensional stationary ergodic media. Zbl 1110.76054 Caffarelli, L. A.; Lee, K.-A.; Mellet, A. 2007 Free boundary problems for fractional powers of the Laplacian. Zbl 1253.35224 Caffarelli, Luis 2007 Phase transitions: uniform regularity of the intermediate layers. Zbl 1090.49019 Caffarelli, Luis A.; Córdoba, Antonio 2006 Homogenization and flame propagation in periodic excitable media: the asymptotic speed of propagation. Zbl 1093.35010 Caffarelli, L. A.; Lee, K.-A.; Mellet, A. 2006 ...and 171 more Documents all top 5 #### Cited by 5,645 Authors 121 Caffarelli, Luis Ángel 102 Valdinoci, Enrico 76 Vazquez, Juan Luis 60 Wei, Juncheng 58 Byun, Sun-Sig 56 Shahgholian, Henrik 56 Wang, Lihe 49 Figalli, Alessio 48 Lin, Chang-Shou 46 Sire, Yannick 45 Dipierro, Serena 45 Savin, Ovidiu V. 43 Zhang, Binlin 40 Quaas, Alexander 39 Ambrosio, Vincenzo 39 Li, YanYan 38 Lee, Ki-Ahm 38 Xiang, Mingqi 35 Friedman, Avner 33 Bao, Jiguang 33 Dong, Hongjie 33 Teixeira, Eduardo V. O. 33 Wang, Xu-Jia 32 Li, Dongsheng 32 Rădulescu, Vicenţiu D. 31 Farina, Alberto 31 Garofalo, Nicola 31 Trudinger, Neil Sidney 29 Ros-Oton, Xavier 28 Rossi, Julio Daniel 27 Kenig, Carlos Eduardo 27 Kim, Inwon Christina 27 Li, Congming 27 Novaga, Matteo 27 Petrosyan, Arshak 27 Squassina, Marco 26 Ferrari, Fausto 26 Kang, Dongsheng 26 Nyström, Kaj 26 Silvestre, Luis E. 25 Felmer, Patricio L. 25 Weiss, Georg Sebastian 24 Del Pino, Manuel A. 24 Musso, Monica 24 Peral Alonso, Ireneo 24 Terracini, Susanna 24 Vitolo, Antonio 23 De Silva, Daniela 23 Dolbeault, Jean 23 González, María del Mar 23 Gutiérrez, Cristian E. 23 Ivochkina, Nina Mikhaĭlovna 23 Nochetto, Ricardo Horacio 22 Chen, Wenxiong 22 Miyagaki, Olimpio Hiroshi 22 Seregin, Gregory A. 22 Sirakov, Boyan Slavchev 21 Hebey, Emmanuel 21 Niu, Pengcheng 21 Salsa, Sandro 21 Sciunzi, Berardino 21 Velichkov, Bozhidar 21 Wang, Kelei 21 Wolanski, Noemi I. 20 Abdellaoui, Boumediene 20 Bucur, Dorin 20 Karakhanyan, Aram L. 20 Lin, Fang Hua 20 Mingione, Giuseppe 20 Monneau, Régis 20 Serra Montolí, Joaquim 20 Stinga, Pablo Raúl 20 Yao, Fengping 20 Zhang, Lei 19 Bonforte, Matteo 19 Maldonado, Diego 19 McCann, Robert J. 19 Musina, Roberta 19 Salani, Paolo 19 Tang, Xianhua 18 Cabré, Xavier 18 Chen, Huyuan 18 da Silva, João Vítor 18 Dai, Limei 18 Krylov, Nicolaĭ Vladimirovich 18 Lu, Guozhen 18 Molica Bisci, Giovanni 18 Shivaji, Ratnasingham 18 Wang, Yanqing 18 Xiong, Jingang 18 Zou, Wenming 17 Chen, Caisheng 17 Chen, Zhen-Qing 17 De Philippis, Guido 17 Du, Lili 17 Fall, Mouhamed Moustapha 17 Guan, Pengfei 17 Gui, Changfeng 17 Liu, Jianguo 17 Ma, Xi-Nan ...and 5,545 more Authors all top 5 #### Cited in 456 Serials 518 Journal of Differential Equations 418 Nonlinear Analysis. 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Updates and corrections should be made in Wikidata.	2021-12-02T06:42:28	{"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": 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": 0.5934563875198364, "perplexity": 7733.609660700927}, "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/1637964361169.72/warc/CC-MAIN-20211202054457-20211202084457-00418.warc.gz"}
https://www.anl.gov/article/doe-approves-technical-plan-and-cost-estimate-to-upgrade-argonne-facility-project-will-create-xrays	# .argonne-logo-style0{fill:#231F20;} .argonne-logo-style1{fill:#FFFFFF;} .argonne-logo-style2{fill:#007836;} .argonne-logo-style3{fill:#0082CA;} .argonne-logo-style4{fill:#0B1F8F;} .argonne-logo-style5{fill:none;} .argonne-logo-style6{fill:#A12B2F;} .argonne-logo-style7{fill:#CD202C;} .argonne-logo-style8{fill:#77B300;} Argonne National Laboratory Press Release \| Argonne National Laboratory # DOE approves technical plan and cost estimate to upgrade Argonne facility; Project will create X-rays that illuminate the atomic scale, in 3D Upgrade to Advanced Photon Source will open new frontiers in science and help solve pressing problems across industries. The U.S. Department of Energy (DOE) has approved the technical scope, cost estimate and plan of work for an upgrade of the Advanced Photon Source (APS), a major storage-ring X-ray source at DOE’s Argonne National Laboratory, Argonne announced on December 14, 2018. The resulting facility will allow researchers to view matter at the atomic scale, in three dimensions, opening new frontiers in discovery science, from advances in pharmaceuticals to new materials for better rechargeable batteries. The APS, a DOE Office of Science User Facility, produces extremely bright, extremely focused X-rays that can peer through dense materials and illuminate matter at the molecular level. By way of comparison, the X-rays produced at today’s APS are up to one billion times brighter than the X-rays produced in a typical dentist’s office. The APS Upgrade project (APS-U) will increase the brightness of these super-bright X-rays another 100 to 1,000 times, depending on the technique used, which will allow scientists to map any atom’s position, identity and dynamics. The APS-U will lead to game-changing research across scientific disciplines,” said Robert Hettel, Director of the APS Upgrade project. The scientific advances from the APS have already made life better for countless Americans and have benefited businesses with new techniques and products. The APS-U will build on this foundation and drive even greater advances.” The goal of the $815 million project is to replace the APS accelerator and develop or update X-ray beamlines and other equipment to create a much more powerful X-ray facility. The APS-U will have a new design, a multi-bend achromat” lattice, with many more bending magnets and magnet-focusing cells than the present machine, resulting in much brighter X-ray production. The APS is already one of the crown jewels at Argonne, and the APS Upgrade ensures that this resource will keep its important place in the national laboratory system,” said Paul Kearns, Argonne Laboratory Director. The APS-U is a tremendous example of how cross-disciplinary teams, from Argonne and across the scientific community, come together to solve problems and drive future opportunities.” X-rays at the APS are produced by electrons that are accelerated to very high energies, moving at nearly the speed of light as they pass though magnet arrays around a 1.1-kilometer circular storage ring. X-rays are extracted from the storage ring into beamlines, which are equipped with experimental endstations. There, researchers use varying instrumentation to investigate the structure and chemistry of matter in a wide variety of systems across a broad spectrum of time and energy scales. Every year, more than 5,500 researchers from across the world conduct experiments at the APS. Studies at the APS have led to two Nobel Prizes, numerous pharmaceutical drugs (including the first drug to treat HIV), improved processes for oil extraction from shale and new insights into additive manufacturing. Scientists at the APS have also studied the composition of an ancient Egyptian mummy and the arms of SUE, the Tyrannosaurus rex specimen at The Field Museum of Chicago. The Advanced Photon Source is one of the most powerful X-ray facilities in the world, and the APS-U will ensure that the U.S. keeps this leadership position. New or upgraded facilities similar to the APS are being planned or are under construction in France, Brazil, China, Japan and other countries. The APS was commissioned in 1996, at Argonne’s campus, and the APS-U builds on the$1.5 billion of infrastructure that is already in place. We’re grateful to the Department of Energy for moving this important project forward,” said Stephen Streiffer, Director of the APS and Associate Laboratory Director for Photon Sciences at Argonne. This ambitious effort will ensure that the U.S. remains at the forefront of hard X-ray sciences for decades to come.” The approval from DOE is formally called Critical Decision 2, or CD-2, and indicates that the project has received baseline approval for its design and implementation. Another critical decision, CD-3, is needed in the future in order for the project to receive full spending authority for the baseline funding approved by CD-2. Depending on the Congressional appropriation process, removal of the old storage ring and installation of the new one could begin in 2022. This installation dark time” and subsequent ring commissioning period will last for about one year, after which the APS-U X-ray beamlines will be brought online for researchers. 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 https://energy.gov/science.	2021-10-18T23:08:41	{"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": 0.37007659673690796, "perplexity": 3584.281912438633}, "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/1634323585215.14/warc/CC-MAIN-20211018221501-20211019011501-00406.warc.gz"}
https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Map%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/4%3A_Diffraction/4.5%3A_Circular_Apertures_and_Resolution	$$\require{cancel}$$ # 4.5: Circular Apertures and Resolution Light diffracts as it moves through space, bending around obstacles, interfering constructively and destructively. This can be used as a spectroscopic tool—a diffraction grating disperses light according to wavelength, for example, and is used to produce spectra—but diffraction also limits the detail we can obtain in images. Figure $$\PageIndex{1a}$$ shows the effect of passing light through a small circular aperture. Instead of a bright spot with sharp edges, we obtain a spot with a fuzzy edge surrounded by circles of light. This pattern is caused by diffraction, similar to that produced by a single slit. Light from different parts of the circular aperture interferes constructively and destructively. The effect is most noticeable when the aperture is small, but the effect is there for large apertures as well. Figure $$\PageIndex{1}$$: (a) Monochromatic light passed through a small circular aperture produces this diffraction pattern. (b) Two point-light sources that are close to one another produce overlapping images because of diffraction. (c) If the sources are closer together, they cannot be distinguished or resolved. How does diffraction affect the detail that can be observed when light passes through an aperture? Figure $$\PageIndex{1b}$$ shows the diffraction pattern produced by two point-light sources that are close to one another. The pattern is similar to that for a single point source, and it is still possible to tell that there are two light sources rather than one. If they are closer together, as in Figure $$\PageIndex{1c}$$, we cannot distinguish them, thus limiting the detail or resolution we can obtain. This limit is an inescapable consequence of the wave nature of light. Diffraction limits the resolution in many situations. The acuity of our vision is limited because light passes through the pupil, which is the circular aperture of the eye. Be aware that the diffraction-like spreading of light is due to the limited diameter of a light beam, not the interaction with an aperture. Thus, light passing through a lens with a diameter D shows this effect and spreads, blurring the image, just as light passing through an aperture of diameter D does. Thus, diffraction limits the resolution of any system having a lens or mirror. Telescopes are also limited by diffraction, because of the finite diameter D of the primary mirror. Just what is the limit? To answer that question, consider the diffraction pattern for a circular aperture, which has a central maximum that is wider and brighter than the maxima surrounding it (similar to a slit) (Figure $$\PageIndex{1a}$$). It can be shown that, for a circular aperture of diameter D, the first minimum in the diffraction pattern occurs at $$\theta = 1.22 \lambda/D$$ (providing the aperture is large compared with the wavelength of light, which is the case for most optical instruments). The accepted criterion for determining the diffraction limit to resolution based on this angle is known as the Rayleigh criterion, which was developed by Lord Rayleigh in the nineteenth century. RAYLEIGH CRITERION The diffraction limit to resolution states that two images are just resolvable when the center of the diffraction pattern of one is directly over the first minimum of the diffraction pattern of the other (Figure $$\PageIndex{1b}$$). The first minimum is at an angle of $$\theta = 1.22 \lambda/D$$, so that two point objects are just resolvable if they are separated by the angle $\theta = 1.22 \lambda/D \label{Rayleigh}$ where λ is the wavelength of light (or other electromagnetic radiation) and D is the diameter of the aperture, lens, mirror, etc., with which the two objects are observed. In this expression, θ has units of radians. This angle is also commonly known as the diffraction limit. Figure $$\PageIndex{2}$$: (a) Graph of intensity of the diffraction pattern for a circular aperture. Note that, similar to a single slit, the central maximum is wider and brighter than those to the sides. (b) Two point objects produce overlapping diffraction patterns. Shown here is the Rayleigh criterion for being just resolvable. The central maximum of one pattern lies on the first minimum of the other. All attempts to observe the size and shape of objects are limited by the wavelength of the probe. Even the small wavelength of light prohibits exact precision. When extremely small wavelength probes are used, as with an electron microscope, the system is disturbed, still limiting our knowledge. Heisenberg’s uncertainty principle asserts that this limit is fundamental and inescapable, as we shall see in the chapter on quantum mechanics. Example $$\PageIndex{1}$$: Calculating Diffraction Limits of the Hubble Space Telescope The primary mirror of the orbiting Hubble Space Telescope has a diameter of 2.40 m. Being in orbit, this telescope avoids the degrading effects of atmospheric distortion on its resolution. (a) What is the angle between two just-resolvable point light sources (perhaps two stars)? Assume an average light wavelength of 550 nm. (b) If these two stars are at a distance of 2 million light-years, which is the distance of the Andromeda Galaxy, how close together can they be and still be resolved? (A light-year, or ly, is the distance light travels in 1 year.) Strategy The Rayleigh criterion stated in Equation \ref{Rayleigh}, $$\theta = 1.22 \lambda/D$$, gives the smallest possible angle θ between point sources, or the best obtainable resolution. Once this angle is known, we can calculate the distance between the stars, since we are given how far away they are. Solution 1. The Rayleigh criterion for the minimum resolvable angle is $\theta = 1.22 \dfrac{\lambda}{D}.$ Entering known values gives $\theta = 1.22\dfrac{550 \times 10^{-9} m}{2.40 \,m} = 2.80 \times 10^{-7} rad.$ 2. The distance s between two objects a distance r away and separated by an angle θ is $$s = r\theta$$. Substituting known values gives$s = (2.0 \times 10^6 \,ly)(2.80 \times 10^{-7} \,rad) = 0.56 \,ly.$ Significance The angle found in part (a) is extraordinarily small (less than 1/50,000 of a degree), because the primary mirror is so large compared with the wavelength of light. As noticed, diffraction effects are most noticeable when light interacts with objects having sizes on the order of the wavelength of light. However, the effect is still there, and there is a diffraction limit to what is observable. The actual resolution of the Hubble Telescope is not quite as good as that found here. As with all instruments, there are other effects, such as nonuniformities in mirrors or aberrations in lenses that further limit resolution. However, Figure $$\PageIndex{3}$$ gives an indication of the extent of the detail observable with the Hubble because of its size and quality, and especially because it is above Earth’s atmosphere. Figure $$\PageIndex{3}$$: These two photographs of the M82 Galaxy give an idea of the observable detail using (a) a ground-based telescope and (b) the Hubble Space Telescope. (credit a: modification of work by “Ricnun”/Wikimedia Commons) The answer in part (b) indicates that two stars separated by about half a light-year can be resolved. The average distance between stars in a galaxy is on the order of five light-years in the outer parts and about one light-year near the galactic center. Therefore, the Hubble can resolve most of the individual stars in Andromeda Galaxy, even though it lies at such a huge distance that its light takes 2 million years to reach us. Figure $$\PageIndex{4}$$ shows another mirror used to observe radio waves from outer space. Figure $$\PageIndex{4}$$: A 305-m-diameter paraboloid at Arecibo in Puerto Rico is lined with reflective material, making it into a radio telescope. It is the largest curved focusing dish in the world. Although D for Arecibo is much larger than for the Hubble Telescope, it detects radiation of a much longer wavelength and its diffraction limit is significantly poorer than Hubble’s. The Arecibo telescope is still very useful, because important information is carried by radio waves that is not carried by visible light. (credit: Jeff Hitchcock) Exercise $$\PageIndex{1}$$ What is the angular resolution of the Arecibo telescope shown in Figure $$\PageIndex{4}$$ when operated at 21-cm wavelength? How does it compare to the resolution of the Hubble Telescope? Solution $$8.4 \times 10^{-4} \,rad$$, 3000 times broader than the Hubble Telescope Diffraction is not only a problem for optical instruments but also for the electromagnetic radiation itself. Any beam of light having a finite diameter D and a wavelength λ exhibits diffraction spreading. The beam spreads out with an angle θ given by Equation \ref{Rayleigh}, $$\theta = 1.22 \lambda/D$$. Take, for example, a laser beam made of rays as parallel as possible (angles between rays as close to θ = 0° as possible) instead spreads out at an angle $$\theta = 1.22 \lambda/D$$, where D is the diameter of the beam and λ is its wavelength. This spreading is impossible to observe for a flashlight because its beam is not very parallel to start with. However, for long-distance transmission of laser beams or microwave signals, diffraction spreading can be significant (Figure $$\PageIndex{5}$$). To avoid this, we can increase D. This is done for laser light sent to the moon to measure its distance from Earth. The laser beam is expanded through a telescope to make D much larger and θ smaller. Figure $$\PageIndex{5}$$: The beam produced by this microwave transmission antenna spreads out at a minimum angle $$\theta = 1.22 \lambda/D$$ due to diffraction. It is impossible to produce a near-parallel beam because the beam has a limited diameter. In most biology laboratories, resolution is an issue when the use of the microscope is introduced. The smaller the distance x by which two objects can be separated and still be seen as distinct, the greater the resolution. The resolving power of a lens is defined as that distance x. An expression for resolving power is obtained from the Rayleigh criterion. Figure $$\PageIndex{6a}$$ shows two point objects separated by a distance x. According to the Rayleigh criterion, resolution is possible when the minimum angular separation is $\theta = 1.22 \dfrac{\lambda}{D} = \dfrac{x}{d},$ where d is the distance between the specimen and the objective lens, and we have used the small angle approximation (i.e., we have assumed that x is much smaller than d), so that $$tan \,\theta \approx sin \,\theta$$. Therefore, the resolving power is $$x= 1.22 \dfrac{\lambda d}{D}.$$ Another way to look at this is by the concept of numerical aperture (NA), which is a measure of the maximum acceptance angle at which a lens will take light and still contain it within the lens. Figure $$\PageIndex{1b}$$ shows a lens and an object at point P. The NA here is a measure of the ability of the lens to gather light and resolve fine detail. The angle subtended by the lens at its focus is defined to be $$\theta = 2\alpha$$. From the figure and again using the small angle approximation, we can write $sin \,\alpha = \dfrac{D/2}{d} = \dfrac{D}{2d}.$ The NA for a lens is $$NA = n \,sin \,\alpha$$, where n is the index of refraction of the medium between the objective lens and the object at point P. From this definition for NA, we can see that $x = 1.22 \dfrac{\lambda d}{D} = 1.22 \dfrac{\lambda}{2 \,sin \,\alpha} = 0.61 \dfrac{\lambda n}{NA}.$ In a microscope, NA is important because it relates to the resolving power of a lens. A lens with a large NA is able to resolve finer details. Lenses with larger NA are also able to collect more light and so give a brighter image. Another way to describe this situation is that the larger the NA, the larger the cone of light that can be brought into the lens, so more of the diffraction modes are collected. Thus the microscope has more information to form a clear image, and its resolving power is higher. Figure $$\PageIndex{6}$$: (a) Two points separated by a distance x and positioned a distance d away from the objective. (b) Terms and symbols used in discussion of resolving power for a lens and an object at point P (credit a: modification of work by “Infopro”/Wikimedia Commons). One of the consequences of diffraction is that the focal point of a beam has a finite width and intensity distribution. Imagine focusing when only considering geometric optics, as in Figure $$\PageIndex{7a}$$. The focal point is regarded as an infinitely small point with a huge intensity and the capacity to incinerate most samples, irrespective of the NA of the objective lens—an unphysical oversimplification. For wave optics, due to diffraction, we take into account the phenomenon in which the focal point spreads to become a focal spot (Figure $$\PageIndex{7b}$$) with the size of the spot decreasing with increasing NA. Consequently, the intensity in the focal spot increases with increasing NA. The higher the NA, the greater the chances of photodegrading the specimen. However, the spot never becomes a true point. Figure $$\PageIndex{7}$$:(a) In geometric optics, the focus is modelled as a point, but it is not physically possible to produce such a point because it implies infinite intensity. (b) In wave optics, the focus is an extended region. In a different type of microscope, molecules within a specimen are made to emit light through a mechanism called fluorescence. By controlling the molecules emitting light, it has become possible to construct images with resolution much finer than the Rayleigh criterion, thus circumventing the diffraction limit. The development of super-resolved fluorescence microscopy led to the 2014 Nobel Prize in Chemistry. Optical Resolution Simulation In this Optical Resolution Model, two diffraction patterns for light through two circular apertures are shown side by side in this simulation by Fu-Kwun Hwang. Watch the patterns merge as you decrease the aperture diameters. ## 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).	2019-02-20T22:33:48	{"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": 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": 0.6776722073554993, "perplexity": 520.2870227366853}, "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-2019-09/segments/1550247496694.82/warc/CC-MAIN-20190220210649-20190220232649-00523.warc.gz"}
https://www.conicet.gov.ar/new_scp/detalle.php?keywords=&id=05415&inst=yes&articulos=yes&detalles=yes&art_id=1458768	CEQUINOR 05415 CENTRO DE QUIMICA INORGANICA "DR. PEDRO J. AYMONINO" artículos Título: Density Functional Study on the Geometric Features and Growing Pattern of B$_n$P$_m$ Clusters ($n = 1-4$, $m = 1-4$, $n + m \leq 5$) Autor/es: V. FERRARESI CUROTTO; REINALDO PIS DIEZ Revista: INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY Editorial: JOHN WILEY & SONS INC Referencias: Lugar: New York; Año: 2012 vol. 112 p. 3261 - 3261 ISSN: 0020-7608 Resumen: The bonding features of BnPm clusters (n = 1?4, m = 1?4, n + m <= 5) are studied within the framework of the density functional theory following a systematic growing mechanism. Some stable geometries are found to agree well with results reported previously in the literature. Other geometries are found to be more stable than structures reported elsewhere for small B/P aggregates. To the best of our knowledge, stable geometries for BP4 are reported for the first time. It is found that small B/P clusters with up to five atoms tend to grow mainly toward nonlinear bidimensional structures. The existence of BAB and BAP bonds seems to be of importance for the relative stability of clusters as they grow. The growing patterns could be explained mainly in terms of electrophilicattacks of B atoms to BAB and BAP bonds. It is found thatthe growing is in general accompanied by geometryreorganization and atomic charge rearrangements.Electrophilic attacks of P atoms to BAB bonds seems to be agood alternative to grow for aggregates with many B atoms.Atomic charges derived from molecular electrostatic potentialsare useful to understand the growing paths followed in terms of electrophilic or nucleophilic attacks.	2019-11-16T21:30:05	{"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": 0.35519570112228394, "perplexity": 8221.158360684514}, "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/1573496668765.35/warc/CC-MAIN-20191116204950-20191116232950-00005.warc.gz"}
https://www.nist.gov/publications/static-and-dynamic-magnetic-properties-sputtered-fe-ga-thin-films	# Static and dynamic magnetic properties of sputtered Fe-Ga thin films Published: May 03, 2017 ### Author(s) We present measurements of the static and dynamic properties of iron-gallium films, ranging from 20~nm to 80~nm and sputtered from an $\mathrm{Fe_{0.8}Ga_{0.2}}$ target. Using a broadband ferromagnetic resonance setup in a wide frequency range, perpendicular standing spin-wave resonances were observed with the external static magnetic field applied in--plane. The field corresponding to the strongest resonance peak at each frequency is used to determine the effective magnetization, the $g$--factor and the Gilbert damping. Furthermore, the dependence of spin- wave mode on field-position is observed for several frequencies. The analysis of broadband dynamic properties allows determination of the exchange stiffness $A = \left ( 18 \pm 4 \right ) \mathrm{pJ/m}$ and Gilbert damping $\alpha = 0.042 \pm 0.005$ for 40~nm and 80~nm thick films. These values are approximately consistent with values seen in epitaxially grown films, indicating the potential for industrial fabrication of magnetostrictive FeGa films for microwave applications.	2019-10-14T22:06:24	{"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": 0.3459598422050476, "perplexity": 3853.4347479111802}, "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-2019-43/segments/1570986655310.17/warc/CC-MAIN-20191014200522-20191014224022-00305.warc.gz"}
https://shadowfight.fandom.com/wiki/Shogun	## FANDOM 694 Pages “ Did you really think you could match my power? I have conquered countless lands! Enslaved whole nations! Even Kings bow before me! ” – Shogun demonstrating his authority Shogun is the sixth demon boss in Shadow Fight 2, first appearing in Act VI: Iron Reign. He is a military warlord and the ruler of Ivory City, a town near the Gates of Shadows. He seized power from the former ruler of the city, known as the Prince, after he assassinated the said Prince. ## Appearance Shogun appears as a traditional Japanese Samurai, and is armed with a daisho - katana and a wakizashi which he wears on his hip. He is covered in black armor, and dons a Kabuto which is equipped with a Mempo that covers his whole face, excluding his white, featureless eyes. ## Storyline ### Sensei's Story Part 6. The Monster Shogun is the servant of the Prince, a man of royal birth. He is the warlord of Prince's army. After he met Widow and was manipulated by her, he sets a scheme to betray the Prince, so he could claim his throne and become Widow's liege. He hired Butcher to kidnap Prince and ordered Hermit to train his soldier. However, Shogun did not see that the Prince made a bargain with Butcher, causing the latter to let him go. He is also not aware if the Prince is saved by Sensei later. Shogun plans to become a great warlord by using the magical Sphere that Widow has promised him. After Widow obtained the Sphere, Prince comes to her place and seizes the Sphere. Shogun attempts to stop him, but he fails. Prince, who has lost his mind after getting the Sphere, takes Shogun to be executed and controls his mind with the Sphere. When Sensei arrives there, Prince makes Shogun fight Sensei. But, Sensei is able to defeat Shogun. ### Act VI: Iron Reign Shadow and his team head on to obtain the final seal which will lock the Gates of Shadow. Making their way to Ivory City, they learn that Shogun has taken over the city and has made it the seat of his vast empire. The city though, appears to be burning in flames. Sensei narrates that once the land surrounding the city was fertile. A wasteland is all that remains in its place now due to the effect of the Gates of Shadows. Shadow begins his fight against Shogun's bodyguards and when each one is defeated, they mistake Shadow for their missing Prince and move on to higher authority for help. Sly encourages Shadow to play along with this mistaken identity. Shogun first makes an appearance in conversation with General. After Shadow defeats Colonel, Shogun orders General to use whatever resources necessary to find and execute the rebel, who calls himself the Prince, and his associates. General responds by telling him that he will round up the best mercenary unit around and have them hunt down Shadow and the others. Shadow then faces five mercenaries in a row in a survival style fight lasting five rounds. After their defeat, he fights General and then finally reaches Shogun. Shogun fights Shadow, still believing that he is the lost prince. After his defeat, Shogun is left in disbelief that he was bested in combat. Before Shadow moves on, Shogun surrenders his Jade Seal, claiming that even though he lost, the people will not follow a petty 'prince'. Shogun teams up with the previous demons to halt Shadow's plans to close the Gates of Shadow. He battles Shadow last in line (sixth). ### Interlude Shadow returns in Interlude to fight Shogun for a third time to break the seal. Shogun, like the previous demons, is not pleased that Shadow wants to reopen the Gates. Before the fight, he declares that this realm and empire is his and therefore if Shadow reopens the gates, Titan will be released and Shogun will lose power and influence and he will not allow this. Shogun tries to stop Shadow in his quest and the fight ensues. After his defeat, he tells Shadow to leave as he does not have much time now before Titan destroys his world. ## Personality Shogun is extremely aggressive and hates failures. He refuses to tolerate any shortcomings or failure when it comes to the matters of his empire. He is a warlord who rules a vast empire, and claims to have conquered thousands and entire factions. He has an extreme hatred of Shadow, whom he believes to be the Prince responsible for causing chaos in his empire. He thinks of himself as the ruler of the realm until Titan is set loose. Shogun takes pride in his strength, and is devastated when he is beaten in combat. He values his empire very highly, falling apart when he believes it will be taken away from him. Shogun is fearsome, and his bodyguards fear him and his capabilities, proving that he is actually very strong. Shogun is shown to be quite arrogant, as he does not deign to deal with the enemy until he has no choice. Even when Shadow proves to be a highly dangerous threat to his empire, he prefer to assigns General to do the dirty work for him. It is shown how much the empire means to Shogun when Shogun threatens to fight Shadow just to keep his empire under his command. As re-opening the Gate of Shadows would release Titan and cause Shogun to be evicted from his seat of high power, he fights Shadow in an attempt to stop him from opening the Gates so he can remain in his powerful position. ## Bodyguards Shogun's bodyguards' names are actually their ranks in their military. 1. Corporal, bodyguard armed with a Jumonji Yari 2. Captain bodyguard armed with an Nodachi 3. Major, bodyguard armed with Wakizashi 4. Colonel, bodyguard armed with a Bisento 5. General, bodyguard armed with a straight-edged Glaive • Before fighting General, the player has to defeat his mercenaries first. ## Equipment Shogun wields a pair of weapons consisting of a Katana and a Wakizashi as his melee weapon. Of the pair, primarily the Katana is used for most attacks and the Wakizashi is only used to serves a finishing move to his double slash and super-slash. He also wears Crescent Helm. For ranged weapons, Shogun uses Kunai of the Wind. He then switches to Dragon Wings after getting defeated once and Keen Chakram after getting defeated twice. Shogun mostly uses fire-based magic. He uses Fire Ball, Fire Pillar (after getting defeated once), and Asteroid (after getting defeated twice). When fought in Gates of Shadows and Interlude, Shogun uses Keen Chakram and Asteroid. ## Perks and Enchantments • Summoning Shogun can call his bodyguards which appear from either side of the screen, do a single strike to attack Shadow and then disappear. These summoned bodyguards cannot be attacked. Their attacks cannot be blocked as well. However, they can be dodged. Shogun uses this perk after being defeated once. The bodyguard is summoned depending upon Shogun and Shadow's position on the battlefield: CorporalCorporal, along with General, has the strongest attack than other summoned bodyguards. Shogun jumps backward when calling Corporal. Upon summoning, Corporal dashes forward, while thrusting his Yari forward. Shogun calls him when Shadow is close to him. CaptainCaptain's attack is stronger than Colonel's attack, but weaker as compared to Corporal's and General's attack. His attack also has the longest range than other bodyguards' attack. Shogun rolls backward when calling him. Upon summoned, Captain jumps forward. He then steps forward, bends down, and swings his Nodachi. Shogun summons him if Shadow is too far from him. MajorMajor is not summoned by Shogun. ColonelColonel's attack is the weakest than other bodyguards' attack. Shogun rolls backward when calling him. Upon summoning, Colonel jumps forwards while thrusting his Bisento forward. Shogun calls him when Shadow is close to him. GeneralGeneral, along with Corporal, has the strongest attack than other bodyguards. Shogun stands still when calling him. Upon summoning, General comes from behind Shadow, rolls towards Shadow, pivots on one foot and swings his Glaive. Shogun summons him if he is cornered. • Damage Absorption Shogun's armor and Helm are enchanted with Damage Absorption, giving a chance to absorb all damage dealt to Shogun's body/head by a single strike. • Overheat Shogun's Katana and ranged weapons are enchanted with Overheat, giving Shogun a chance in each strike to put a buff on himself that makes his next strike inflict 200% more damage. Appears after Shogun is defeated twice. ## Quotes • General, find this rebel who calls himself 'the Prince.' He and his associates are to be arrested and executed. Use whatever resources you deem necessary. - Shogun giving orders to General • So... Here you are, after all of these years. What took you so long? Have you found another realm to ruin with your greed and incompetence? • I see my assassins haven't failed completely. You're only a shadow of the Prince I knew. - Before fight • No... This is impossible... I am invincible! I cannot lose, not now! And you... you think you can take my empire away from me? Hah! • They used your name to scare children, yes. But I brought them order; I gave them the Empire! My people won't follow a petty prince now... - Shogun defeated • We were the strongest warriors who ever lived and yet we failed to defeat you... - Gates of Shadows, after defeated ### Interlude • Until Titan finds the way through the Gates, this is my realm, and I will not allow you to take it from me! - Interlude, before fight • Why do you hasten your own demise? Leave now and enjoy what little time your world has left before Titan destroys you all. - Interlude, after defeated ### Old Wounds • Weakling! You're not even good enough to be my lord's court jester. I'll crush you with a single blow! - Shogun, under Prince's mind control, belittling Sensei ## Rewards • Normal: • 601 green orbs • 378 red orbs • Eclipse: • 10905 green orbs • 5040 red orbs • 142 purple orbs ### Eclipse Mode Reward Player can obtain Shogun's Katana by defeating him once more in Eclipse mode. It can be obtained at any level, as early as level 37. The Katana is enchanted with Overheat. The formula for the power of the Overheat enchantment is as follows: $[3639 / 100 * level + 105]$ ### Achievements • Conqueror Awarded for defeating Shogun. • Long Live The King! Awarded for winning a fight with Shogun once more in Eclipse mode. ## Soundtrack During the battle with Shogun and his bodyguards, the track “Burning Town“ plays. ## Trivia • Shogun's perk, summoning bodyguards, is the only demon's perk which is not performed by the other demons themselves. • The summoned bodyguards wear Centurion Mail and Crescent Helm. • His and Butcher's achievement icons are the only ones which are not merely silhouettes of their avatars. • There is a weapon that has the same movesets as Shogun's Katana, called Daisho. They only differ in appearance and enchantments. • Shogun's chest armor resembles European armor rather than the ones normally worn by Samurai. • "Shogun" means Military Leader in Japanese. • His counterpart in Shadow Fight 1 is Samurai. • In Old Wounds, Shogun is one of the two opponents who use Magic. The other is Prince. • In Old Wounds, Shogun is the only demon of Shadow Fight 2 who does not have any bodyguard to be fought before he can be fought and is himself a bodyguard of Prince. Community content is available under CC-BY-SA unless otherwise noted.	2020-02-28T14:43:55	{"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": 0.3582504391670227, "perplexity": 11008.424983094827}, "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/1581875147234.52/warc/CC-MAIN-20200228135132-20200228165132-00358.warc.gz"}
https://www.aimsciences.org/article/doi/10.3934/proc.2009.2009.349	Article Contents Article Contents # Nonexistence of weak solutions of quasilinear elliptic equations with variable coefficients • In this paper, we are concerned with the following quasilinear elliptic equations: -div${a(x)\|\nabla u\|^{p-2}\nabla u$ $=b(x)\|u\|^(q-2)u$ in $\Omega$ $u(x)$ $= 0$ on $\partial\Omega$ where $\Omega$ is a domain in $\mathbf R^N$ $(N \ge 1)$ with smooth boundary. When $a$ and $b$ are positive constants, there are many results on the nonexistence of nontrivial solutions for the equation (E). The main purpose of this paper is to discuss the nonexistence results for (E) with a class of weak solutions under some assumptions on $a$ and $b$. Mathematics Subject Classification: Primary: 35J25; Secondary: 35J20, 35J70. Citation: Open Access Under a Creative Commons license	2023-03-29T06:11:36	{"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": 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": 0.29416128993034363, "perplexity": 213.19076480015406}, "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-20230329054547-20230329084547-00079.warc.gz"}
https://www.usgs.gov/center-news/volcano-watch-clague-leaving-volcano-observatory	# Volcano Watch — Clague leaving volcano observatory Release Date: The "Volcano Watch" column first appeared on November 3, 1991. In the last four plus years, the staff and I have written 207 columns covering a wide range of topics, including updates on the ongoing eruption of Kīlauea, hazards posed by that eruption, long-term volcanic and seismic hazards in Hawaii, as well as descriptions of volcanic and seismic events worldwide. The "Volcano Watch" column first appeared on November 3, 1991. In the last four plus years, the staff and I have written 207 columns covering a wide range of topics, including updates on the ongoing eruption of Kīlauea, hazards posed by that eruption, long-term volcanic and seismic hazards in Hawaii, as well as descriptions of volcanic and seismic events worldwide. Through these columns, we have kept people informed about geologic events in a timely manner. More importantly, through the discussions of geologic hazards, we have enabled people to prepare for the earthquakes of the future, to avoid hazardous and potentially life-threatening areas near the eruption, and to plan development and growth on Hawaii with an awareness of, and respect for, the types and frequencies of geologic events that occur here, including the ones that disrupt their lives. This column will be the next-to-the-last that I will write because I will be leaving my current position as Scientist-in-Charge of the Hawaiian Volcano Observatory at the end of February and will be returning to the Mainland to a new job in early June. The staff of the Observatory will continue to write the "Volcano Watch" column, as we all feel it is an important mechanism to inform the public about changes in volcanic activity, as well as about the geology of Hawaii. I want to take this opportunity to reflect a bit on my four-and-a- half years here. These ruminations will form the basis of the remainder of this column and the column next week. The Hawaiian Volcano Observatory plays a critical role in real-time monitoring of volcanic and seismic events in Hawaii. We maintain the field instruments that warn of impending eruptions on Kīlauea, Mauna Loa, Hualālai, and Haleakalā. Each of these volcanoes has erupted in the past, and each will erupt again in the future. The question is when they will erupt, not if they will erupt. When they erupt, each will cause losses and disruption to life in the islands. Many people on the island have been born since the current eruption of Kīlauea began in January 1983. They cannot remember a time when Kīlauea was not in eruption. For those a bit older, the present state of activity seems unusual, because Kīlauea erupted only rarely, and usually briefly, prior to the current eruption. Likewise, most people on the island think of Mauna Loa as erupting infrequently because there have been only two eruptions since 1950. However, in the hundred years before 1950, Mauna Loa erupted roughly every three years. Hualālai is also a potentially dangerous volcano because it erupts every several hundred years. The occurrence of the last eruption in 1801 does not reduce the likelihood that it will erupt again in the next 50 to 100 years. Haleakalā, whose last eruption occurred in about 1790, has a similar eruptive history to Hualālai, with eruptions every several hundred years. The need to quantify this information about the volcanic hazards on the islands led us to develop a lava flowhazard map for the Big Island that delineates the relative hazards of the different parts of the island. This hazard information should be one of many considerations for land-use planning and development of public and private infrastructure, such as schools, roads, telephone, water wells and water distribution systems, power plants and electric distribution systems. The staff of the Hawaiian Volcano Observatory (past and present) has worked honestly and without bias to create a map that reflects the lava flow hazards on this island as best as we can determine them. Unfortunately, the misapplication of the hazards map has led to great frustration for many people living in the higher hazard zones due to unavailability of property insurance. The average lava flow coverage in hazard zones 1 and 2 on Kīlauea Volcano is slightly less than 30% in a 150-year period. Such coverage translates to a roughly 4.5% chance that any property will be lost to lava flows during the average life span of a house of 33 years in Hawai`i. These rough calculations indicate that the chance of loss each year is 0.14%. This is not a huge risk and certainly one that can be accommodated by insurance rates that reflect the increased risk. I hope the insurance industry will rise to the challenge to fairly assess the added risks associated with properties located in more hazardous lava flow zones and to set rates that accurately reflect their increased risk. The lava hazard zones have begun to be used in public or private land-use planning. In particular, the Puna Development Plan has incorporated lava hazards as an integral part of the plan. I feel that real reduction of future losses from eruptions will come about mainly through improved land-use planning and maintenance of low-density development in the highest hazard zones. Thank you for reading these columns over the last several years. May all the geologic events in your future be ones for which you are prepared. Aloha, Dave Clague.	2019-11-22T18:31:15	{"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": 0.3221128284931183, "perplexity": 2317.4328440748636}, "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/1573496671411.14/warc/CC-MAIN-20191122171140-20191122200140-00547.warc.gz"}
https://lammps.sandia.gov/doc/Speed_gpu.html	# 7.4.1. GPU package The GPU package was developed by Mike Brown while at SNL and ORNL and his collaborators, particularly Trung Nguyen (now at Northwestern). It provides GPU versions of many pair styles and for parts of the kspace_style pppm for long-range Coulombics. It has the following general features: • It is designed to exploit common GPU hardware configurations where one or more GPUs are coupled to many cores of one or more multi-core CPUs, e.g. within a node of a parallel machine. • Atom-based data (e.g. coordinates, forces) are moved back-and-forth between the CPU(s) and GPU every timestep. • Neighbor lists can be built on the CPU or on the GPU • The charge assignment and force interpolation portions of PPPM can be run on the GPU. The FFT portion, which requires MPI communication between processors, runs on the CPU. • Force computations of different style (pair vs. bond/angle/dihedral/improper) can be performed concurrently on the GPU and CPU(s), respectively. • It allows for GPU computations to be performed in single or double precision, or in mixed-mode precision, where pairwise forces are computed in single precision, but accumulated into double-precision force vectors. • LAMMPS-specific code is in the GPU package. It makes calls to a generic GPU library in the lib/gpu directory. This library provides NVIDIA support as well as more general OpenCL support, so that the same functionality is supported on a variety of hardware. Required hardware/software: To compile and use this package in CUDA mode, you currently need to have an NVIDIA GPU and install the corresponding NVIDIA CUDA toolkit software on your system (this is primarily tested on Linux and completely unsupported on Windows): • Check if you have an NVIDIA GPU: cat /proc/driver/nvidia/gpus/*/information • Install a driver and toolkit appropriate for your system (SDK is not necessary) • Run lammps/lib/gpu/nvc_get_devices (after building the GPU library, see below) to list supported devices and properties To compile and use this package in OpenCL mode, you currently need to have the OpenCL headers and the (vendor neutral) OpenCL library installed. In OpenCL mode, the acceleration depends on having an OpenCL Installable Client Driver (ICD) installed. There can be multiple of them for the same or different hardware (GPUs, CPUs, Accelerators) installed at the same time. OpenCL refers to those as ‘platforms’. The GPU library will select the first suitable platform, but this can be overridden using the device option of the package command. run lammps/lib/gpu/ocl_get_devices to get a list of available platforms and devices with a suitable ICD available. Building LAMMPS with the GPU package: See the Build extras doc page for instructions. Run with the GPU package from the command line: The mpirun or mpiexec command sets the total number of MPI tasks used by LAMMPS (one or multiple per compute node) and the number of MPI tasks used per node. E.g. the mpirun command in MPICH does this via its -np and -ppn switches. Ditto for OpenMPI via -np and -npernode. When using the GPU package, you cannot assign more than one GPU to a single MPI task. However multiple MPI tasks can share the same GPU, and in many cases it will be more efficient to run this way. Likewise it may be more efficient to use less MPI tasks/node than the available # of CPU cores. Assignment of multiple MPI tasks to a GPU will happen automatically if you create more MPI tasks/node than there are GPUs/mode. E.g. with 8 MPI tasks/node and 2 GPUs, each GPU will be shared by 4 MPI tasks. Use the “-sf gpu” command-line switch, which will automatically append “gpu” to styles that support it. Use the “-pk gpu Ng” command-line switch to set Ng = # of GPUs/node to use. lmp_machine -sf gpu -pk gpu 1 -in in.script # 1 MPI task uses 1 GPU mpirun -np 12 lmp_machine -sf gpu -pk gpu 2 -in in.script # 12 MPI tasks share 2 GPUs on a single 16-core (or whatever) node mpirun -np 48 -ppn 12 lmp_machine -sf gpu -pk gpu 2 -in in.script # ditto on 4 16-core nodes Note that if the “-sf gpu” switch is used, it also issues a default package gpu 1 command, which sets the number of GPUs/node to 1. Using the “-pk” switch explicitly allows for setting of the number of GPUs/node to use and additional options. Its syntax is the same as same as the “package gpu” command. See the package command doc page for details, including the default values used for all its options if it is not specified. Note that the default for the package gpu command is to set the Newton flag to “off” pairwise interactions. It does not affect the setting for bonded interactions (LAMMPS default is “on”). The “off” setting for pairwise interaction is currently required for GPU package pair styles. Or run with the GPU package by editing an input script: The discussion above for the mpirun/mpiexec command, MPI tasks/node, and use of multiple MPI tasks/GPU is the same. Use the suffix gpu command, or you can explicitly add an “gpu” suffix to individual styles in your input script, e.g. pair_style lj/cut/gpu 2.5 You must also use the package gpu command to enable the GPU package, unless the “-sf gpu” or “-pk gpu” command-line switches were used. It specifies the number of GPUs/node to use, as well as other options. Speed-ups to expect: The performance of a GPU versus a multi-core CPU is a function of your hardware, which pair style is used, the number of atoms/GPU, and the precision used on the GPU (double, single, mixed). Using the GPU package in OpenCL mode on CPUs (which uses vectorization and multithreading) is usually resulting in inferior performance compared to using LAMMPS’ native threading and vectorization support in the USER-OMP and USER-INTEL packages. See the Benchmark page of the LAMMPS web site for performance of the GPU package on various hardware, including the Titan HPC platform at ORNL. You should also experiment with how many MPI tasks per GPU to use to give the best performance for your problem and machine. This is also a function of the problem size and the pair style being using. Likewise, you should experiment with the precision setting for the GPU library to see if single or mixed precision will give accurate results, since they will typically be faster. Guidelines for best performance: • Using multiple MPI tasks per GPU will often give the best performance, as allowed my most multi-core CPU/GPU configurations. • If the number of particles per MPI task is small (e.g. 100s of particles), it can be more efficient to run with fewer MPI tasks per GPU, even if you do not use all the cores on the compute node. • The package gpu command has several options for tuning performance. Neighbor lists can be built on the GPU or CPU. Force calculations can be dynamically balanced across the CPU cores and GPUs. GPU-specific settings can be made which can be optimized for different hardware. See the package command doc page for details. • As described by the package gpu command, GPU accelerated pair styles can perform computations asynchronously with CPU computations. The “Pair” time reported by LAMMPS will be the maximum of the time required to complete the CPU pair style computations and the time required to complete the GPU pair style computations. Any time spent for GPU-enabled pair styles for computations that run simultaneously with bond, angle, dihedral, improper, and long-range calculations will not be included in the “Pair” time. • When the mode setting for the package gpu command is force/neigh, the time for neighbor list calculations on the GPU will be added into the “Pair” time, not the “Neigh” time. An additional breakdown of the times required for various tasks on the GPU (data copy, neighbor calculations, force computations, etc) are output only with the LAMMPS screen output (not in the log file) at the end of each run. These timings represent total time spent on the GPU for each routine, regardless of asynchronous CPU calculations. • The output section “GPU Time Info (average)” reports “Max Mem / Proc”. This is the maximum memory used at one time on the GPU for data storage by a single MPI process. None.	2019-08-18T01:19:46	{"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": 0.2386728674173355, "perplexity": 3740.082555401937}, "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-2019-35/segments/1566027313536.31/warc/CC-MAIN-20190818002820-20190818024820-00505.warc.gz"}
https://par.nsf.gov/biblio/10211995-layer-gate-tunable-spin-orbit-coupling-high-mobility-few-layer-semiconductor	skip to main content Layer- and gate-tunable spin-orbit coupling in a high-mobility few-layer semiconductor Spin-orbit coupling (SOC) is a relativistic effect, where an electron moving in an electric field experiences an effective magnetic field in its rest frame. In crystals without inversion symmetry, it lifts the spin degeneracy and leads to many magnetic, spintronic, and topological phenomena and applications. In bulk materials, SOC strength is a constant. Here, we demonstrate SOC and intrinsic spin splitting in atomically thin InSe, which can be modified over a broad range. From quantum oscillations, we establish that the SOC parameter α is thickness dependent; it can be continuously modulated by an out-of-plane electric field, achieving intrinsic spin splitting tunable between 0 and 20 meV. Unexpectedly, α could be enhanced by an order of magnitude in some devices, suggesting that SOC can be further manipulated. Our work highlights the extraordinary tunability of SOC in 2D materials, which can be harnessed for in operando spintronic and topological devices and applications. Authors: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; Award ID(s): Publication Date: NSF-PAR ID: 10211995 Journal Name: Science Advances Volume: 7 Issue: 5 Page Range or eLocation-ID: eabe2892 ISSN: 2375-2548 Sponsoring Org: National Science Foundation ##### More Like this 1. Abstract Current-induced spin-orbit torques (SOTs) are of interest for fast and energy-efficient manipulation of magnetic order in spintronic devices. To be deterministic, however, switching of perpendicularly magnetized materials by SOT requires a mechanism for in-plane symmetry breaking. Existing methods to do so involve the application of an in-plane bias magnetic field, or incorporation of in-plane structural asymmetry in the device, both of which can be difficult to implement in practical applications. Here, we report bias-field-free SOT switching in a single perpendicular CoTb layer with an engineered vertical composition gradient. The vertical structural inversion asymmetry induces strong intrinsic SOTs and a gradient-driven Dzyaloshinskii–Moriya interaction (g-DMI), which breaks the in-plane symmetry during the switching process. Micromagnetic simulations are in agreement with experimental results, and elucidate the role of g-DMI in the deterministic switching processes. This bias-field-free switching scheme for perpendicular ferrimagnets with g-DMI provides a strategy for efficient and compact SOT device design. 2. A major recent breakthrough in materials science is the emergence of intrinsic magnetism in two-dimensional (2D) crystals, which opens the door to more cutting-edge fields in the 2D family and could eventually lead to novel data-storage and information devices with further miniaturization. Herein we propose an experimentally feasible 2D material, Fe 2 I 2 , which is an intrinsic room-temperature ferromagnet exhibiting perpendicular magnetic anisotropy (PMA). Using first-principles calculations, we demonstrate that single-layer (SL) Fe 2 I 2 is a spin-gapless semiconductor with a spin-polarized Dirac cone and linear energy dispersion in one spin channel, exhibiting promising dissipation-less transport properties with a Fermi velocity up to 6.39 × 10 5 m s −1 . Our results reveal that both strain and ferroelectric polarization switching could induce an out-of- to in-plane spin reorientation in the 2D Fe 2 I 2 layer, revealing its advantage in assembling spintronic devices. In addition, spin–orbit coupling (SOC) triggers a topologically nontrivial band gap of 301 meV with a nonzero Chern number (\| C \| = 2), giving rise to a robust quantum anomalous Hall (QAH) state. The 2D crystal also exhibits high carrier mobilites of 0.452 × 10 3 and 0.201 × 10 3 cmmore » 3. Abstract Nonlinear photocurrent in time-reversal invariant noncentrosymmetric systems such as ferroelectric semimetals sparked tremendous interest of utilizing nonlinear optics to characterize condensed matter with exotic phases. Here we provide a microscopic theory of two types of second-order nonlinear direct photocurrents, magnetic shift photocurrent (MSC) and magnetic injection photocurrent (MIC), as the counterparts of normal shift current (NSC) and normal injection current (NIC) in time-reversal symmetry and inversion symmetry broken systems. We show that MSC is mainly governed by shift vector and interband Berry curvature, and MIC is dominated by absorption strength and asymmetry of the group velocity difference at time-reversed ±kpoints. Taking$${\cal{P}}{\cal{T}}$$$PT$-symmetric magnetic topological quantum material bilayer antiferromagnetic (AFM) MnBi2Te4as an example, we predict the presence of large MIC in the terahertz (THz) frequency regime which can be switched between two AFM states with time-reversed spin orderings upon magnetic transition. In addition, external electric field breaks$${\cal{P}}{\cal{T}}$$$PT$symmetry and enables large NSC response in bilayer AFM MnBi2Te4, which can be switched by external electric field. Remarkably, both MIC and NSC are highly tunable under varying electric field due to the field-induced large Rashba and Zeeman splitting, resulting in large nonlinear photocurrent response down to a few THz regime, suggesting bilayer AFM-zMnBi2Te4as amore » 4. Abstract Giant spin-orbit torque (SOT) from topological insulators (TIs) provides an energy efficient writing method for magnetic memory, which, however, is still premature for practical applications due to the challenge of the integration with magnetic tunnel junctions (MTJs). Here, we demonstrate a functional TI-MTJ device that could become the core element of the future energy-efficient spintronic devices, such as SOT-based magnetic random-access memory (SOT-MRAM). The state-of-the-art tunneling magnetoresistance (TMR) ratio of 102% and the ultralow switching current density of 1.2 × 105 A cm−2have been simultaneously achieved in the TI-MTJ device at room temperature, laying down the foundation for TI-driven SOT-MRAM. The charge-spin conversion efficiencyθSHin TIs is quantified by both the SOT-induced shift of the magnetic switching field (θSH = 1.59) and the SOT-induced ferromagnetic resonance (ST-FMR) (θSH = 1.02), which is one order of magnitude larger than that in conventional heavy metals. These results inspire a revolution of SOT-MRAM from classical to quantum materials, with great potential to further reduce the energy consumption. 5. Abstract Spin-orbit torques (SOT) enable efficient electrical control of the magnetic state of ferromagnets, ferrimagnets and antiferromagnets. However, the conventional SOT has severe limitation that only in-plane spins accumulate near the surface, whether interpreted as a spin Hall effect (SHE) or as an Edelstein effect. Such a SOT is not suitable for controlling perpendicular magnetization, which would be more beneficial for realizing low-power-consumption memory devices. Here we report the observation of a giant magnetic-field-like SOT in a topological antiferromagnet Mn3Sn, whose direction and size can be tuned by changing the order parameter direction of the antiferromagnet. To understand the magnetic SHE (MSHE)- and the conventional SHE-induced SOTs on an equal footing, we formulate them as interface spin-electric-field responses and analyzed using a macroscopic symmetry analysis and a complementary microscopic quantum kinetic theory. In this framework, the large out-of-plane spin accumulation due to the MSHE has an inter-band origin and is likely to be caused by the large momentum-dependent spin splitting in Mn3Sn. Our work demonstrates the unique potential of antiferromagnetic Weyl semimetals in overcoming the limitations of conventional SOTs and in realizing low-power spintronics devices with new functionalities.	2023-03-28T07:58:12	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "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": 0.545484721660614, "perplexity": 3210.6231851912826}, "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/1679296948817.15/warc/CC-MAIN-20230328073515-20230328103515-00449.warc.gz"}
http://pdglive.lbl.gov/Particle.action;jsessionid=713CDCCEA231F9B59ECE13077BF54AB5?node=S067&init=0	LEPTONS INSPIRE search # Neutrino Mixing See related reviews: Introductory Text to Neutrino Mixing Three-Neutrino Mixing Parameters (A) Neutrino fluxes and event ratios Events (observed/expected) from accelerator ${{\mathit \nu}_{{\mu}}}$ experiments. Events (observed/expected) from reactor ${{\overline{\mathit \nu}}_{{e}}}$ experiments. Atmospheric neutrinos R(${{\mathit \mu}}/{{\mathit e}}$) = (Measured Ratio ${{\mathit \mu}}/{{\mathit e}}$) $/$ (Expected Ratio ${{\mathit \mu}}/{{\mathit e}}$) R(${{\mathit \nu}_{{\mu}}}$) = (Measured Flux of ${{\mathit \nu}_{{\mu}}}$) $/$ (Expected Flux of ${{\mathit \nu}_{{\mu}}}$) R(${{\mathit \mu}}$/total) = (Measured Ratio ${{\mathit \mu}}$/total) $/$ (Expected Ratio ${{\mathit \mu}}$/total) $\mathit N_{{\mathrm {up}}}({{\mathit \mu}})/\mathit N_{{\mathrm {down}}}({{\mathit \mu}}$) $\mathit N_{{\mathrm {up}}}({{\mathit e}})/\mathit N_{{\mathrm {down}}}({{\mathit e}}$) R(up/down; ${{\mathit \mu}}$) = (Measured up/down; ${{\mathit \mu}}$) $/$ (Expected up/down; ${{\mathit \mu}}$) N(${{\mathit \mu}^{+}})/N({{\mathit \mu}^{-}}$) R(${{\mathit \mu}^{+}}/{{\mathit \mu}^{-}}$) = (Measured N(${{\mathit \mu}^{+}})/N({{\mathit \mu}^{-}}$)) $/$ (Expected N(${{\mathit \mu}^{+}})/N({{\mathit \mu}^{-}}$)) Solar neutrinos ${{\mathit \nu}_{{e}}}$ Capture Rates from Radiochemical Experiments $\phi _{\mathit ES}$ (${}^{8}\mathrm {B}$) $\phi _{\mathit CC}$ (${}^{8}\mathrm {B}$) $\phi _{\mathit NC}$ (${}^{8}\mathrm {B}$) $\phi _{{{\mathit \nu}_{{\mu}}}+{{\mathit \nu}_{{\tau}}}}$ (${}^{8}\mathrm {B}$) Total Flux of Active ${}^{8}\mathrm {B}$ Solar Neutrinos Day-Night Asymmetry (${}^{8}\mathrm {B}$) $0.033 \pm0.011$ $\phi _{\mathit ES}$ (${}^{7}\mathrm {Be}$) $\phi _{\mathit ES}$ ( ${{\mathit p}}{{\mathit e}}{{\mathit p}}$ ) $\phi _{\mathit ES}$ (CNO) $\phi _{ES}({{\mathit p}{\mathit p}}$) $\phi _{CC}({{\mathit p}{\mathit p}}$) $\phi _{\mathit ES}$ (hep) $\phi _{{{\overline{\mathit \nu}}_{{e}}}}$ (${}^{8}\mathrm {B}$) (B) Three-neutrino mixing parameters sin$^2(\theta _{12})$ $0.307 \pm0.013$ $\Delta$m${}^{2}_{21}$ $(7.53 \pm0.18) \times 10^{-5}$ eV${}^{2}$ sin$^2(\theta _{23})$ $0.417 {}^{+0.025}_{-0.028}$ (S = 1.2) ... $\Delta$m${}^{2}_{32}$ $0.00251 \pm0.00005$ eV${}^{2}$ (S = 1.1) ... sin$^2(\theta _{13})$ $0.0212 \pm0.0008$ $\boldsymbol CP$ violating phase $\delta$, $\mathit CP$ violating phase (C) Other neutrino mixing results $\Delta \mathit m{}^{2}$ for sin$^2(2{}\theta )$ = 1 ( ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{e}}}$ ) sin$^2(2{}\theta )$ for Large'' $\Delta \mathit m{}^{2}$ ( ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{e}}}$ ) $\Delta \mathit m{}^{2}$ for sin$^2(2{}\theta )$ = 1 ( ${{\overline{\mathit \nu}}_{{\mu}}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{e}}}$ ) sin$^2(2{}\theta )$ for Large'' $\Delta \mathit m{}^{2}$ ( ${{\overline{\mathit \nu}}_{{\mu}}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{e}}}$ ) $\Delta \mathit m{}^{2}$ for sin$^2(2{}\theta )$ = 1 ( ${{\mathit \nu}_{{\mu}}}$ ( ${{\overline{\mathit \nu}}_{{\mu}}}$ ) $\rightarrow$ ${{\mathit \nu}_{{e}}}$ ( ${{\overline{\mathit \nu}}_{{e}}}$ )) $<0.075$ eV${}^{2}$ CL=90.0% sin$^2(2{}\theta )$ for Large'' $\Delta \mathit m{}^{2}$ ( ${{\mathit \nu}_{{\mu}}}$ ( ${{\overline{\mathit \nu}}_{{\mu}}}$ ) $\rightarrow$ ${{\mathit \nu}_{{e}}}$ ( ${{\overline{\mathit \nu}}_{{e}}}$ )) $<1.8 \times 10^{-3}$ CL=90.0% $\Delta \mathit m{}^{2}$ for sin$^2(2{}\theta )$ = 1 ( ${{\overline{\mathit \nu}}_{{e}}}$ $\nrightarrow$ ${{\overline{\mathit \nu}}_{{e}}}$ ) sin$^2(2{}\theta )$ for Large'' $\Delta \mathit m{}^{2}$ ( ${{\overline{\mathit \nu}}_{{e}}}$ $\nrightarrow$ ${{\overline{\mathit \nu}}_{{e}}}$ ) Sterile neutrino limits $\Delta \mathit m{}^{2}$ for sin$^2(2{}\theta )$ = 1 (${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{s}}}$) Search for ${{\mathit \nu}_{{\mu}}}$ or ${{\mathit \nu}_{{e}}}$ $\rightarrow$ ${{\mathit \nu}_{{s}}}$ $\boldsymbol CPT$ tests $\langle \Delta {{\mathit m}^{2}}_{\mathrm {21}}−\Delta {{\overline{\mathit m}}}{}^{2}_{21}\rangle$ $\langle \Delta {{\mathit m}^{2}}_{\mathrm {32}}−\Delta {{\overline{\mathit m}}}{}^{2}_{32}\rangle$	2018-06-19T12:08:56	{"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": 0.9039550423622131, "perplexity": 5878.924101841162}, "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-2018-26/segments/1529267862929.10/warc/CC-MAIN-20180619115101-20180619135101-00606.warc.gz"}
https://tjyj.stats.gov.cn/CN/Y2014/V31/I6/17	• 论文 • 农民工收入统计归属对城乡收入差距的影响 • 出版日期:2014-06-15 发布日期:2014-07-14 Impact of Statistical Belongings of Migrants’ Income on the Urban-Rural Income Gap Shulan Fei & Jiqiang Guo • Online:2014-06-15 Published:2014-07-14 Abstract: As there are different opinions about the belongings of migrants’ income, this paper compares the urban-rural income gap under different statistical belongings of migrants’ income, and their implications. First, we did some mathematical derivation of the urban-rural income gap under different statistical belongings of migrants’ income, and proposed three hypotheses. Then, we use CHIP2007 data to examine these hypotheses. Among different belongings of migrants’ income, the resident principle is more reasonable. In addition, we adjust the income caliber to see the variation of urban-rural income gap.	2022-07-05T06:29:26	{"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": 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": 0.2356278896331787, "perplexity": 14718.799642648399}, "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-2022-27/segments/1656104514861.81/warc/CC-MAIN-20220705053147-20220705083147-00722.warc.gz"}
http://indico.vecc.gov.in/confAuthorIndex.py%3Fview=full&letter=r&confId=1.html	# ICPAQGP-2010 5-10 December 2010 6th International Conference on Physics and Astrophysics of Quark Gluon Plasma (ICPAQGP 2010) Home > Author Index Display options View mode use contribution ids and titlesuse contribution ids Authors a \| b \| c \| d \| e \| f \| g \| h \| i \| j \| k \| l \| m \| n \| o \| p \| q \| r \| s \| t \| u \| v \| w \| x \| y \| z \| [all] RAHA, Sibaji 86-Entropy scaling from chaotically produced particles in p+p collisions at LHC energies RAI, Ajay Kumar 55-E1 and M1 radiative transitions of heavy quarkonia111-Quarkonium decay to Light Hadrons RAINA, P. K. 46-Chromomagnetism in quark-gluon plasma RAJARSHI RAY, Rajarshi 40-QCD phase diagram using PNJL model with eight-quark interactions RAKOTOZAFINDRABE, Andry 5-Cold Nuclear Matter effects on Quarkonium production with extrinsic transverse momentum RAMADAS, sineeba 67-QGP In Astrophysics RAMANATHAN, R 65-A Phenomenological Quark-Gluon Density of States and its Implications for QGP-Hadron Phase Properties RANJAN, Akhilesh 46-Chromomagnetism in quark-gluon plasma RAY, Rajarshi 86-Entropy scaling from chaotically produced particles in p+p collisions at LHC energies RAY, RAJARSHI 160-Heavy di-lepton pair production in nucleus-nucleus collisions at LHC energy RAY, Rajarshi 75-CORRELATION BETWEEN CONSERVED CHARGES IN PNJL MODEL130-Study of scale anomaly on two colour QCD192-Models for strong interaction physics RICHTER, Matthias 135-The ALICE High Level Trigger RITTER, Hans Georg 51-Energy dependence of high-moments of net-proton distributions at RHIC ROY, Victor 104-Charged particle’s pT spectra and elliptic flow in \sqrt{s}=200 GeV Au+Au collisions: QGP vs. hadronic resonance gas.142-Elliptic flow ($v_2$) in $pp$ collisions at energies available at the CERN Large Hadron Collider: A hydrodynamical approach105-Initial energy density scaling and transverse momentum spectra and elliptic flow of charged particles in \sqrt{s}=200 GeV Au+Au collisions	2021-09-25T20:44:53	{"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": 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": 0.6480828523635864, "perplexity": 10545.896289937613}, "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-2021-39/segments/1631780057775.50/warc/CC-MAIN-20210925202717-20210925232717-00716.warc.gz"}
https://www.scstatehouse.gov/sess121_2015-2016/sj16/20160224.htm	South Carolina General Assembly 121st Session, 2015-2016 Journal of the Senate Wednesday, February 24, 2016 (Statewide Session) Indicates Matter Stricken Indicates New Matter The Senate assembled at 11:45 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: Hear this word from the Lord: "The Lord is my shepherd, I shall not want. He makes me lie down in green pastures; he leads me beside still waters; he restores my soul. He leads me in right paths for his name's sake." (Psalm 23:1-3) Join me as we bow in prayer, please: We indeed praise You, O Loving God, for having led us and cared for us in wondrous ways, in fashion far beyond our deserving, time and time again. We likewise thank You, Lord, for the commitment of each one of these Senators as they labor to lead all of the people of South Carolina in directions that are fair, worthy and decent. May these officials and their staff members never cease to be grateful to You for Your teachings and Your wisdom, dear God. May they always embrace in heartfelt ways their own responsibilities as caring shepherds -- solely doing those things that are pleasing in Your sight. We pray this in Your wondrous name, dear Lord. Amen. The PRESIDENT called for Petitions, Memorials, Presentments of Grand Juries and such like papers. Committee to Escort The PRESIDENT appointed Senators FAIR, NICHOLSON, PEELER, SABB and SHEALY to escort the Honorable Costa Pleicones, Chief Justice of the South Carolina Supreme Court, and members of her party to the House of Representatives for the Joint Assembly. RECESS At 11:50 A.M., on motion of Senator LARRY MARTIN, the Senate receded from business for the purpose of attending the Joint Assembly. JOINT ASSEMBLY Chief Justice of the South Carolina Supreme Court At 12:00 Noon, 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. 4824, a Concurrent Resolution adopted by both Houses. The Honorable Costa Pleicones, Chief Justice of the South Carolina Supreme Court, and members of her party, were escorted to the rostrum by Senators FAIR, NICHOLSON, PEELER, SABB and SHEALY and Representatives Delleney, Rutherford, W. McLeod, Cole and Pope. The PRESIDENT introduced the Honorable Costa Pleicones, Chief Justice of the South Carolina Supreme Court. Chief Justice Pleicones addressed the Joint Assembly as follows: State of the Judiciary Address by the Honorable Costa Pleicones Chief Justice of South Carolina Preamble Mr. PRESIDENT, Mr. Speaker, distinguished members of the General Assembly. I appear before you today to present a broad overview of the current state of the least powerful, most vulnerable, co-equal branch of government. Least powerful because we have no purse, no police, and no veto pen. Most vulnerable, because given the aforementioned absence of power, there always exists the possibility of a threat to our independence. The only thing that legitimates the authority of the Judicial Branch is its credibility which I pledge to you will be maintained during my tenure as your Chief Justice, as it should be. I know that you share my concern that we observe and maintain the constitutionally mandated separation of powers, a doctrine fundamental to our form of government. I look forward to working with you to insure that the judiciary remains an independent coequal branch. I thank you for bestowing upon me the greatest honor of my professional career, the privilege of serving our great State as Chief Justice, and I begin with the inescapable observation that the Supreme Court is an institution in transition. Less than two months ago we said goodbye to a long-serving member of the Court, and only three weeks ago you elected our newest member. Soon you will elect my successor as well as a justice to fill the vacancy created by my departure. Thus, we will experience a 40% turnover in the composition of the Court in just over the space of one year. Through it all, the institution abides. The men and women who serve the institution come and go, and it is vital that you continue to elect people of character, possessed of intellectual honesty, not those who may simply pass an ideological purity test. No less a sage than the late Antonin Scalia observed, "The judge who always likes the result he reaches is a bad judge." Scalia was himself an ideologue, but a brilliant one who knew that a judge must subordinate personal biases to the dictates of the law. I agree. In America, judicial systems are purposefully designed to be the non-political branch and we are committed to insuring that our branch remains an evenhanded, nonpartisan dispenser of justice both in perception and in practice. The turnover on the Court is not a cause for concern because of the stability of the institution itself. That institution, and indeed the entire judicial system of South Carolina, endures and succeeds owing to the commitment to justice on the part of our judges and the staff who support us. I am extremely proud of the successes achieved by our state's hard working and talented judiciary in the recent past. As we are all aware, our court system remains the most out of balance nationally in terms of ratio of judges to case filings. Since that is a circumstance unlikely to change in the foreseeable future, I have determined to put it aside and stop dwelling on it, and instead redouble our efforts to utilize our existing human and technical resources in the most efficient manner possible. In that regard, it has been estimated that thousands of new domestic violence cases will soon be adjudicated in circuit court. I am wholeheartedly committed to supporting Governor Haley's laudable initiative regarding the processing of these cases. This will require the Judicial Department to devote more circuit court resources to these cases, a task we will accomplish in the short-term with or without additional judicial resources. Why? Because that is our job. I will see to it that our Courts fully meet the requirements of this new program in a manner that is fair to victim and defendant alike. Recent Programs and Accomplishments I would now call to your attention a number of programs and projects that we have implemented in order to deliver justice to the citizens of South Carolina more expeditiously, while maintaining the fairness that undergirds the legitimacy of any court system: * Alternative Dispute Resolution was recently made mandatory in circuit court civil cases statewide. While this program is not a perfect solution, its expanded reach will serve to further reduce stressors on our adjudicative process. * The Docket Management Task Force, under the overall direction of Justice Hearn, has made great progress, resulting in significant improvement in the percentage of trial courts which are meeting their case disposition benchmarks. In the Family Courts, whose docketing subcommittee is chaired by Judge Aphrodite Konduros with the assistance of Judge Dottie Mobley Jones, all 16 circuits have achieved a processing time benchmark of disposing of at least 80% of cases within 365 days of filing. This is a phenomenal achievement when one considers how far we had to come. While recognizing this success, we continue to seek refinements that will enhance the quality of justice delivered by our hardworking Family Court judges, compatible with enhanced processing times. * Improvements have likewise been experienced in General Sessions' benchmarks, whose docketing subcommittee is led by Justice Don Beatty. General Sessions continues to be the most problematic area for improving processing times because of complicating systemic components, such as prisoner transport, over which we have no control. Nonetheless, over the past year we have doubled the number of circuits, albeit only from 2 to 4, which are hitting their 80% benchmarks. * In Common Pleas, processing times continue to improve, with 15 of the 16 circuits at the 80% mark. Credit is due to subcommittee chair Judge Cliff Newman. * For our part, my colleagues on the Supreme Court gave special emphasis during the past year to reducing pending petitions for review. As a result of the hard work done by the Court and our staff, we were able to reduce pending post-conviction relief petitions by 27% and pending Court of Appeals petitions by 44%. We continue our efforts to further pare down the time between when certiorari petitions are ready to be considered, and their disposition by the Court. * Another initiative, which helps to deliver justice more efficiently, is our Business Court program. We have expanded that program statewide. Further, I issued an order on January 1, which appointed Judge Roger Young of Charleston as CJAP of the business court, and which named 7 additional judges on a regional basis to hear business court cases. Notably, one of those judges, Clifton Newman, is president-elect of the American Congress and Business Court Judges, by virtue of which our State will host the annual meeting of that organization in 2017. My order also streamlined the processing of requests for business court designation. Business courts are a key consideration to the location and expansion of economic development in our State. The more confidence business has in a state's court system, the more likely they are to locate there. * In addition to these concrete achievements, we have instituted a number of pilot programs. I would like to emphasize the pilot nature of these programs, as it is my intent to conduct a thorough review of each pilot program before expanding it beyond the original impact area. While this review may slow "progress," I hope it will also give us time to reflect on the value of the project, and to consider changes to address issues exposed during pilot status. * In October 2015, a Civil Motions Pilot Program began in the 3rd and 15th Circuits. This pilot requires that parties file and serve supporting memoranda contemporaneous with written motions, and authorizes the resolution of motions in civil actions without a hearing. We are in the process of gathering data to assess the merits of this pilot. * In order to expedite consideration of post-conviction relief cases, we have instituted a pilot docket management program in the 5th and 11th Circuits aimed at establishing a streamlined process for dealing with PCR applications. These PCR applications are of the type that increases exponentially every year. We anticipate that the current pilot program will allow us to assess ways in which to process this growing caseload. * Turning from docket management successes and pilot programs, I wish to recognize a number of significant achievements during the past year beginning with several attributable to the work of the Chief Justice's Commission on the Profession, led by Justice John Kittredge. Most relevant to my own situation as I approach the age of presumptive senility, is the Court's adoption of Rule 428, SCACR, which is intended to achieve more sensitive handling of cases in which cognitive impairment of attorneys or judges may be at issue. It provides for interventions not unlike those currently in place for substance abuse issues. The desired end is to keep cases out of the disciplinary process if assistance to the impaired person can be brought about in a more compassionate manner. * Also adopted on recommendation of the Commission is Rule 429, SCACR, which establishes a certification program for paralegals. Last month I signed an order establishing the first Board of Paralegal Certification, which will administer the program, with support from the South Carolina Bar. The Board is composed of five attorneys and four paralegals, all of whom are currently certified by national organizations. This program will recognize the professional status of paralegals and the important work they do. * The Commission of the Profession has also had a significant impact on the quality of legal services received by the citizens of South Carolina, owing to the success story of our mentoring program. I was initially skeptical about this program, conceived by the legendary Dewey Oxner, but I am now a believer. You will be pleased to learn that disciplinary sanctions imposed upon lawyers admitted to practice for 5 years or less have been reduced from an average of 29 in the five years preceding implementation of the program, to one per year from 2012-2014. I am happy to announce that figure was reduced to zero in 2015! A remarkable result! * On another front, we are all aware of the pervasive and insidious evil that human trafficking presents in our society. We applaud Attorney General Wilson's efforts to combat this blight, and our Court Administration will convene a human trafficking summit in August 2016 for judges, prosecutors, social workers, and other stakeholders with interest in combatting this problem area. * Technical Accomplishments Turning from the human side to the technical, our IT department continues its exemplary performance. Just before her retirement, Chief Justice Toal saw her career-long goal of e-filing reach fruition in December 2015, when Clarendon County's pilot program was initiated. Since then, the other counties of the Third Circuit, Lee, Sumter, and Williamsburg have come on line. Just last Friday, our IT team appeared before an audience of well over a hundred attorneys, paralegals, and court personnel to announce the roll out on March 22, of e-filing in Greenville County, our first large county endeavor. I emphasize the pilot nature of this e-filing program which presents an enormous learning curve for lawyers, judges, clerks of court and their staffs, as well as significant technological challenges. E-filing is finally here, and it is here to stay, but it will be years before it is expanded statewide. * As for future technical programs, we are planning to expand public access to our appellate case management system. Of course, this expansion carries with it a requirement for security measures to restrict access to sensitive Family Court and other confidential matters. We are working diligently on this balance between transparency and privacy. * New Initiative A major initiative undertaken by our Court is our adoption in January, of the Uniform Bar Exam, components of which are already used in all 54 American jurisdictions, including South Carolina. Under the UBE: * We maintain strict control over who takes our exam, and how many times that person may take it. * We maintain our own character and fitness requirements. * We set our own passing score. * We will have our own state -- specific component, which is currently under development, to insure familiarity with South Carolina specific legal concepts. * Our law schools will have an additional recruiting tool, in that... * The UBE allows greater portability of a certificate -- not reciprocity -- for persons who take the UBE in South Carolina, and we may restrict the time limits for those seeking to transfer into South Carolina. In short, we protect our borders while expanding opportunities for our lawyers. * Fiscal Matters Turning now to the absence of the purse I mentioned at the beginning of this talk, I have submitted a budget for the upcoming fiscal year which is in keeping with the responsible fiscal stewardship traditionally observed by our branch. With regard to the future, I respectfully commend to your thoughtful consideration, the proposition that the court system be funded by a more stable mechanism than is currently the case. I'll be gone soon, but I am deeply concerned about our heavy dependence upon fines and fees, and though a greater dollar amount, relatively modest general fund revenues. I realize this is a condition that will not change this year, but I again respectfully suggest that you begin the dialogue on a formula-based method of funding the judiciary that reduces our heavy dependency on fines and fees. Regarding fines and fees, and to illustrate the disparate impact of the court system upon the fisc of the State, vis a vis its funding level; the most recent figures reported by the Treasurer's Office reveal that in 2015, fines and fees collected by all levels of the court system was $96.1 million, of which the Judicial Branch received$14.5 million, while $12.1 million went to the general fund, and$69.5 million was distributed to other state agencies. Please note that collections were down year over year, in 2015, demonstrating the unstable financial foundation upon which the budgetary needs of your court system in part rests. In short, I am suggesting exploration into the desirability of formula-based funding from general fund revenues. * Anyone looking at our budget will quickly understand that our system is labor intensive with more than 80% of our expenditures being consumed by personnel costs. Thus if fees and fines do not generate sufficient funds, we have little capacity in our budget to absorb such a downturn. * With regard to personnel costs, in fiscal 2015, our Finance and Personnel Department conducted a comprehensive review of salaries of our non-judicial staff, comparing their work to that of other employees in the state system with similar responsibilities. This study resulted in a significant, long overdue, and much deserved pay raise for 400 employees. With that accomplished, I have included a proposal -- modest in relative terms -- for a fair increase in judicial compensation. I respectfully submit to you that the evidence is irrefutable that, as with our staff, the time for such a readjustment is merited and overdue. A comprehensive review of judicial salaries in South Carolina has not been undertaken since 1995. While there have been minor incremental increases in the ensuing twenty years, judicial salaries have not kept pace with the economy, and pale in comparison percentage wise to the respective, and I would hasten to add, well-deserved, raises given to teachers, police, and general state employees. Think of our compensation request as a matter of deferred maintenance, to remedy years of gradual deterioration. Why should you, as representatives of the citizens of our great State, be concerned about the low level of judicial compensation? Substantial financial rewards have always been more available to seasoned practitioners -- the pool from which we traditionally attracted judicial candidates, and the pool from which we should continue to attract judicial candidates. The disparity in compensation between that pool and current judicial compensation is perilously close to being so great as to discourage the highest caliber of candidates. While no one believes that judicial pay should be on par with the compensation earned by private practitioners, it should be sufficient to encourage an experienced, civic-minded practitioner to opt for public service. Please keep in mind that unlike members of the two political branches of government, judicial officials may not, with limited exceptions, have outside sources of compensation. Further, and importantly, judges typically do not have careers following their judicial service. As I mentioned earlier, the only thing the Judicial Branch has to legitimate its authority is its credibility. The better the candidate pool, the greater the confidence of the business community and the person on the street. The business community, as you know, considers a state's court system -- a core function of government -- a key component of location and expansion. The competence level engendered by fair compensation will lift the confidence in our court system in both the loftiest industrial giants, and that of the ordinary citizen. I urge your thoughtful consideration of my proposal and I am happy to provide any detailed information you may require as you weigh the merits of this proposal. Judicial Selection Before I end my first and last address to you, I feel compelled to address the method we use to select judicial candidates. With regard to the composition of the judiciary, I have long been on record as favoring the current legislative election of judges. To paraphrase Winston Churchill, it is the worst of all methods of judicial selection . . . except for all the others. One of the primary virtues of our system is the absence of the influence of money, and the unseemly media campaigns that attend popular election of judges. Thank you for maintaining it, and thank you too for considering refinements that could improve the system. Thanks too for continuing measures designed to maintain a judiciary independent of political influence, by not countenancing pledge or promise requirements which poison the process in those states that popularly elect judges. Conclusion Finally, let me again thank the General Assembly for the opportunity you have given me to serve our State. I know you join me and our Court in steadfast adherence to the separation of powers which the framers of our national constitution provided as a template for our own system. As long as we each continue to observe that wholly salutary dichotomy, we will continue to have a system in which all of our citizens may be confident. My heartfelt thanks to the members of this honorable Body for affording me the privilege of addressing you. God bless our State and all of you. The purposes 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. At 12:25 P.M., by prior motion of Senator LEATHERMAN, the Senate receded until 2:00 P.M. AFTERNOON SESSION The Senate reassembled at 2:06 P.M. and was called to order by the PRESIDENT. MESSAGE FROM THE GOVERNOR The following appointments were transmitted by the Honorable Nikki Randhawa Haley: Local Appointment Reappointment, Allendale County Master-in-Equity, with the term to commence December 31, 2014, and to expire December 31, 2020 Walter H. Sanders, Jr., P. O. Box 840, Fairfax, SC 29827 Withdrawal of Statewide Appointment Initial Appointment, South Carolina State Board of Cosmetology, with the term to commence March 20, 2013, and to expire March 20, 2017 Cosmetologist: Tony V. Nguyen, 308 Live Oak Road, Aiken, SC 29803 VICE Selena M. Brown Appointment Withdrawn On motion of Senator LARRY MARTIN, the Senate acceded to the Governor's request and the Clerk was directed to return the appointment to the Governor. Point of Quorum At 2:12 P.M., Senator BRIGHT made the point that a quorum was not present. It was ascertained that a quorum was not present. Call of the Senate Senator LEATHERMAN moved that a Call of the Senate be made. The following Senators answered the Call: Bright Campbell Cleary Coleman Corbin Cromer Davis Fair Gregory Grooms Hembree Hutto Johnson Kimpson Leatherman Malloy Martin, Larry Martin, Shane Massey Matthews, Margie McElveen Peeler Sabb Scott Setzler Shealy Thurmond Turner Young A quorum being present, the Senate resumed. Doctor of the Day Senator CORBIN introduced Dr. Steven Samoya of Greenville, S.C., Doctor of the Day. Leave of Absence On motion of Senator HEMBREE, at 4:17 P.M., Senators MASSEY and GREGORY were granted a leave of absence for the balance of the day. Leave of Absence On motion of Senator SABB, at 6:41 P.M., Senator ALLEN was granted a leave of absence for the balance of the day. Expression of Personal Interest Senator J. MATTHEWS rose for an Expression of Personal Interest. S. 853 (Word version) Sen. Bright S. 929 (Word version) Sen. Bright INTRODUCTION OF BILLS AND RESOLUTIONS The following were introduced: S. 1109 (Word version) -- Senator L. Martin: A SENATE RESOLUTION TO RECOGNIZE AND COMMEND THE HONORABLE ALVIN D. JOHNSON, RESIDENT FAMILY COURT JUDGE FOR THE THIRTEENTH JUDICIAL CIRCUIT, UPON THE OCCASION OF HIS RETIREMENT FROM THE BENCH AND TO WISH HIM CONTINUED SUCCESS AND HAPPINESS IN ALL HIS FUTURE ENDEAVORS. l:\council\bills\rm\1511sd16.docx S. 1110 (Word version) -- Senator Massey: A BILL TO AMEND SECTION 23-3-430(C)(20) OF THE 1976 CODE, RELATING TO THE PLACEMENT OF A PERSON ON THE SEX OFFENDER REGISTRY FOR SEXUAL INTERCOURSE AGAINST A PATIENT OR TRAINEE, SO AS TO EXPAND THE POTENTIAL VICTIMS TO INCLUDE INMATES; AND TO BROADEN THE OFFENSE TO INCLUDE SEXUAL MISCONDUCT INSTEAD OF SEXUAL INTERCOURSE. l:\s-res\asm\028sex .eb.asm.docx Read the first time and referred to the Committee on Judiciary. S. 1111 (Word version) -- Senator Peeler: A BILL TO AMEND SECTION 56-3-2332, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO LICENSE PLATES FOR CERTAIN MANUFACTURERS, SO AS TO REVISE THE METHOD BY WHICH THE LICENSE PLATE FEE IS CALCULATED AND CREDITED; AND TO SET THE LICENSE PLATE FEE FOR 2017 AND 2018. l:\council\bills\nbd\11204dg16.docx Read the first time and referred to the Committee on Transportation. S. 1112 (Word version) -- Senator Campsen: A BILL TO AMEND SECTION 50-5-1710, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO SIZE LIMITS FOR CERTAIN FISH THAT MAY BE LAWFULLY TAKEN, POSSESSED, LANDED, SOLD, OR PURCHASED, SO AS TO INCREASE THE SIZE LIMIT FOR FLOUNDER THAT MAY BE LAWFULLY TAKEN, POSSESSED, LANDED, OR SOLD. l:\council\bills\gt\5079cm16.docx Read the first time and referred to the Committee on Fish, Game and Forestry. S. 1113 (Word version) -- Senators Alexander, Campbell, Corbin, Grooms, S. Martin, Massey, Peeler, Sheheen, Turner and L. Martin: A SENATE RESOLUTION TO DECLARE TUESDAY, MARCH 1, 2016, AS "CLEMSON DAY" IN SOUTH CAROLINA. l:\s-res\tca\053clem.kmm.tca.docx S. 1114 (Word version) -- Senator Williams: A SENATE RESOLUTION TO CONGRATULATE MRS. MAMIE THOMAS WEST OF MULLINS UPON THE OCCASION OF HER ONE HUNDREDTH BIRTHDAY AND TO WISH HER A JOYOUS BIRTHDAY CELEBRATION AND MUCH HAPPINESS IN THE DAYS TO COME. l:\s-res\kmw\007mami.kmm.kmw.docx H. 4092 (Word version) -- Reps. Loftis, H. A. Crawford, Allison, Burns, Chumley, Hardwick, Long, Kirby, Brannon, Goldfinch, Southard, Erickson, Johnson, Hill, Kennedy, Horne, Murphy, Spires, Limehouse, Anderson, Bedingfield, Clemmons, Delleney, Finlay, Forrester, Hayes, Herbkersman, Hicks, Hosey, Lowe, V. S. Moss, Newton, Norrell, Pope, Putnam, Rivers, Simrill, G. M. Smith, G. R. Smith, Sottile, Taylor, Thayer, Tinkler, Toole, Weeks, Willis, Bowers, Stavrinakis, Knight and Bales: A BILL TO AMEND SECTION 12-43-220, AS AMENDED, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO ASSESSMENT RATIOS, SO AS TO PROVIDE THAT WHEN AN OWNER RECEIVING THE FOUR PERCENT ASSESSMENT RATIO DIES, THE PROPERTY SHALL CONTINUE TO RECEIVE THE SPECIAL ASSESSMENT RATE UNTIL THE DECEASED'S ESTATE IS CLOSED, SO LONG AS THE PROPERTY IS NOT RENTED OR OCCUPIED. Read the first time and referred to the Committee on Finance. H. 4328 (Word version) -- Rep. White: A BILL TO AMEND SECTION 12-8-1530, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE QUARTERLY INCOME TAX WITHHOLDINGS, SO AS TO CHANGE THE DUE DATE OF THE FOURTH QUARTER RETURN FROM THE LAST DAY OF FEBRUARY TO THE LAST DAY OF JANUARY; AND TO AMEND SECTION 12-8-1550, RELATING TO THE DUE DATE FOR FILING STATEMENTS REGARDING INCOME TAX WITHHOLDINGS WITH THE DEPARTMENT OF REVENUE, SO AS TO CHANGE THE DUE DATE FROM THE LAST DAY OF FEBRUARY TO THE LAST DAY OF JANUARY. Read the first time and referred to the Committee on Finance. H. 4577 (Word version) -- Reps. White, Bales, Merrill, D. C. Moss, G. R. Smith and Cobb-Hunter: A BILL TO AMEND SECTION 12-37-2460, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE CREDITING OF AIRCRAFT PROPERTY TAXES, SO AS TO CREDIT THE PROCEEDS OF THE TAX TO THE STATE AVIATION FUND; AND TO AMEND SECTION 55-5-280, AS AMENDED, RELATING TO THE STATE AVIATION FUND, SO AS TO MAKE A CONFORMING CHANGE. Read the first time and referred to the Committee on Finance. H. 4960 (Word version) -- Rep. Delleney: A CONCURRENT RESOLUTION TO AUTHORIZE PALMETTO BOYS STATE TO USE THE CHAMBERS OF THE SOUTH CAROLINA HOUSE OF REPRESENTATIVES AND SENATE FOR ITS ANNUAL STATE HOUSE MEETING ON FRIDAY, JUNE 10, 2016, HOWEVER, THE CHAMBERS MAY NOT BE USED IF THE GENERAL ASSEMBLY IS IN SESSION OR THE CHAMBERS ARE OTHERWISE UNAVAILABLE. The Concurrent Resolution was introduced and referred to the Committee on Invitations. H. 4966 (Word version) -- Rep. G. M. Smith: A CONCURRENT RESOLUTION TO DESIGNATE THE MONTH OF MAY 2016 AS "MENTAL HEALTH MONTH" IN SOUTH CAROLINA AND TO RAISE COMMUNITY AWARENESS AND UNDERSTANDING OF MENTAL ILLNESS AND THE NEED FOR APPROPRIATE AND ACCESSIBLE SERVICES FOR ALL PEOPLE WITH MENTAL ILLNESSES. The Concurrent Resolution was introduced and referred to the Committee on Medical Affairs. H. 4974 (Word version) -- Rep. Pope: A CONCURRENT RESOLUTION TO DECLARE SATURDAY, MAY 21, 2016, AS "SOUTH CAROLINA DAY OF SERVICE" AND ENCOURAGE ALL SOUTH CAROLINIANS TO ROLL UP THEIR SLEEVES AND LEND A HAND TO MAKE A POSITIVE DIFFERENCE IN OUR GREAT STATE. The Concurrent Resolution was introduced and referred to the Committee on Invitations. Message from the House Columbia, S.C., February 24, 2016 Mr. President and Senators: The House respectfully informs your Honorable Body that it has confirmed the appointment: MASTER-IN-EQUITY Reappointment, Allendale Master-in-Equity, with term to commence December 31, 2014, and to expire December 31, 2020: Master-in-Equity The Honorable Walter H. Sanders, Jr., P. O. Box 840, Fairfax, South Carolina 29827 Very respectfully, Speaker of the House HOUSE CONCURRENCES S. 927 (Word version) -- Senator Bryant: A CONCURRENT RESOLUTION TO INVITE THE NATIONAL COMMANDER OF THE AMERICAN LEGION, THE HONORABLE DALE BARNETT, TO ADDRESS THE GENERAL ASSEMBLY IN JOINT SESSION IN THE CHAMBER OF THE SOUTH CAROLINA HOUSE OF REPRESENTATIVES AT 12:00 P.M. ON WEDNESDAY, MARCH 2, 2016. Returned with concurrence. S. 1080 (Word version) -- Senator Setzler: A CONCURRENT RESOLUTION TO RECOGNIZE AND CONGRATULATE WEST COLUMBIA CITY ADMINISTRATOR JENNIFER CUNNINGHAM UPON THE OCCASION OF HER RETIREMENT AND TO WISH HER MUCH SUCCESS AND HAPPINESS IN ALL HER FUTURE ENDEAVORS. Returned with concurrence. S. 1108 (Word version) -- Senators Setzler, Alexander, Allen, Bennett, Bright, Bryant, Campbell, Campsen, Cleary, Coleman, Corbin, Courson, Cromer, Davis, Fair, Gregory, Grooms, Hayes, Hembree, Hutto, Jackson, Johnson, Kimpson, Leatherman, Lourie, Malloy, L. Martin, S. Martin, Massey, J. Matthews, M.B. Matthews, McElveen, Nicholson, Peeler, Rankin, Reese, Sabb, Scott, Shealy, Sheheen, Thurmond, Turner, Verdin, Williams and Young: A CONCURRENT RESOLUTION TO HONOR MR. DAN EARL JONES, VICE PRESIDENT OF GOVERNMENT RELATIONS FOR TIME WARNER CABLE OF SOUTH CAROLINA, ON THE OCCASION OF HIS RETIREMENT, TO EXTEND DEEP APPRECIATION FOR HIS FIFTY YEARS OF DISTINGUISHED SERVICE, AND TO OFFER BEST WISHES FOR A SATISFYING AND REWARDING RETIREMENT. Returned with concurrence. THE SENATE PROCEEDED TO A CALL OF THE UNCONTESTED LOCAL AND STATEWIDE CALENDAR. HOUSE BILL RETURNED The following Bill was read the third time and ordered returned to the House with amendments. H. 3972 (Word version) -- Reps. Loftis, Burns, Hamilton, Willis, Collins, Clyburn, Robinson-Simpson, Bannister, Bedingfield, Gagnon, Henderson, Hosey, Nanney, G.R. Smith and Spires: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 6-29-1210 SO AS TO ESTABLISH THAT UNDEVELOPED PROPERTY MAY BE TRANSFERRED WITHOUT THE SUBMISSION OF A LAND DEVELOPMENT PLAN; AND TO AMEND SECTION 30-5-30, RELATING TO PREREQUISITES TO RECORDING, SO AS TO ESTABLISH THAT A LAND USE PLAN IS NOT REQUIRED TO EXECUTE A DEED OR OTHER INSTRUMENT. SENT TO THE HOUSE The following Bills were read the third time and ordered sent to the House of Representatives: S. 975 (Word version) -- Senators L. Martin and Hutto: A BILL TO AMEND SUBSECTION (B) OF SECTION 42-3-20 OF THE SOUTH CAROLINA CODE OF LAWS, 1976, SO AS TO PROVIDE THAT THE GOVERNOR MAY REAPPOINT A PERSON AS CHAIRMAN OF THE WORKERS' COMPENSATION COMMISSION, AND TO FURTHER PROVIDE THAT THE COMMISSION IS NOT REQUIRED TO ELECT A CHAIRMAN FROM AMONG ITS MEMBERS IN THE EVENT THE GOVERNOR DOES NOT APPOINT OR REAPPOINT A CHAIRMAN. S. 1002 (Word version) -- Senator Cleary: A BILL TO AMEND SECTION 4-23-10, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO THE BOUNDARIES OF THE MURRELL'S INLET-GARDEN CITY FIRE DISTRICT, SO AS TO REVISE THE BOUNDARIES; AND TO REPEAL SECTION 4-23-15 RELATING TO THE BOUNDARIES OF THE SAME DISTRICT. S. 853 (Word version) -- Senators Cleary, Fair, Campbell, Cromer, Johnson, Bryant, Nicholson, Hutto and Bright: A BILL TO AMEND CHAPTER 99, TITLE 44, CODE OF LAWS OF SOUTH CAROLINA, 1976, RELATING TO EMERGENCY TREATMENT FOR MEDICAL HAZARDS CAUSED BY INSECT STINGS, SO AS TO RENAME THE CHAPTER THE "EMERGENCY ANAPHYLAXIS TREATMENT ACT", TO ADD A DEFINITION FOR "EPINEPHRINE AUTO-INJECTOR", TO REQUIRE THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL TO DEVELOP A TRAINING AND CERTIFICATION PROGRAM FOR INDIVIDUALS WHO ADMINISTER EPINEPHRINE AUTO-INJECTORS, TO ALLOW CERTAIN ENTITIES TO OBTAIN A PRESCRIPTION FOR AN EPINEPHRINE AUTO-INJECTOR FROM PHYSICIANS, PHARMACISTS, AND OTHER AUTHORIZED INDIVIDUALS, TO ALLOW PHYSICIANS, PHARMACISTS, AND OTHER AUTHORIZED INDIVIDUALS TO PRESCRIBE OR SELL A PRESCRIPTION FOR AN EPINEPHRINE AUTO-INJECTOR TO CERTAIN ENTITIES, TO ALLOW APPROPRIATELY CERTIFIED EMPLOYEES OF CERTAIN ENTITIES TO USE AN EPINEPHRINE AUTO-INJECTOR, TO PROVIDE LIABILITY LIMITATIONS FOR CERTAIN INDIVIDUALS AND ENTITIES WHEN ADMINISTERING AN EPINEPHRINE AUTO-INJECTOR, AND FOR OTHER PURPOSES. The Senate proceeded to a consideration of the Bill. The Medical Affairs Committee proposed the following amendment (BH\853C002.BH.VR16), which was adopted: Amend the bill, as and if amended, by striking all after the enacting language and inserting: / SECTION 1. This act may be cited as the "Emergency Anaphylaxis Treatment Act". SECTION 2. Chapter 99, Title 44 of the 1976 Code is amended to read: "CHAPTER 99 Insect Sting Emergency Anaphylaxis Treatment Act Section 44-99-10. This chapter may be cited as the 'Insect Sting Emergency Treatment Act'. Section 44-99-20. As used in this chapter: (1) 'Certificate' means official acknowledgment by the department that an individual has completed the required training program pursuant to this chapter. (2) 'Department' means the Department of Health and Environmental Control. (3) 'Program' means the program established by the department for training and certifying individuals to administer treatment to persons suffering a severe adverse reaction to an insect sting which involves the administration of epinephrine. (4) Section 44-99-30. (A) The department is authorized to establish a program to provide for the training and certification of individuals to administer certain forms of emergency treatment for medical hazards caused by insect stings. The department shall develop standards, guidelines, and prescribe regulations for the implementation of the program. All administrative responsibility of the program is vested in the department. (B) In the development of the curriculum for training and certification under the program, the department shall include the following subjects: (1) techniques on how to recognize symptoms of systemic reactions to insect stings; (2) standards and procedures for administering a subcutaneous injection of epinephrine. (3) Section 44-99-40. (A) A person desiring certification for the administration of emergency treatment insect sting, pursuant to this chapter, shall apply to the department and complete the program established by the department for training and certification. (B) The department shall determine and establish the validation and expiration periods for certificates issued pursuant to this chapter and requirements and procedures for renewals if the department considers it necessary. (C) The department may suspend or revoke a certificate at any time it determines that the holder no longer meets the prescribed qualifications established by the department or has failed to provide services or treatment of a quality acceptable to the department pursuant to this chapter. (D) Section 44-99-50. (A) An applicant for certification shall meet the following requirements: (1) be eighteen years of age or older; (2) have, or reasonably expect to have, responsibility for at least one other person as a result of one's occupational or volunteer status, such as camp counselors, scout leaders, school teachers, forest rangers, tour guides, or chaperones; (3) successfully complete the training program established by the department. (B) A person, who meets the qualifications of this section and is certified by the department pursuant to this chapter, is authorized to administer in an emergency situation prescribed epinephrine to persons suffering adverse reaction to an insect sting. (C) A person, who is certified by the department to administer emergency services for insect stings as provided in this chapter, is authorized to obtain from a physician, pharmacist, or any other person or entity authorized to prescribe or sell prescribed medicines or drugs, a prescription for premeasured doses of epinephrine and the necessary supplies for the administration of the drug. (D) Section 44-99-60. Licensed, registered, and certified physicians, nurses, and other such certified professionals are not required to obtain certification for the administration of emergency treatment to persons suffering a severe adverse reaction to an insect sting as prescribed in this chapter. Section 44-99-70. The department may collect fees from applicants for the training program for administration of this chapter. Section 44-99-80. No cause of action may be brought against a certificate holder authorized by the department pursuant to this chapter for an act or omission of the certificate holder when acting in good faith while rendering emergency treatment pursuant to the authority granted by this chapter, except in cases of gross negligence. Section 44-99-10. As used in this chapter: (1) 'Administer' means the direct application of an epinephrine auto-injector to the body of an individual. (2) 'Authorized entity' means any entity or organization, other than a school described in Section 59-63-95, in connection with or at which allergens capable of causing anaphylaxis may be present including, but not limited to, recreation camps, colleges and universities, daycare facilities, places of worship, youth sports leagues, amusement parks, restaurants, places of employment, and sports arenas. (3) 'Department' means the South Carolina Department of Health and Environmental Control. (4) 'Epinephrine auto-injector' means a single-use device used for the automatic injection of a premeasured dose of epinephrine into the human body. (5) 'Health care practitioner' means a physician, an advanced practice registered nurse authorized to prescribe medication pursuant to Section 40-33-34, or a physician assistant authorized to prescribe medication pursuant to Sections (6) 40-47-955 through 40-47-965. (7) 'Physician' means a person authorized to practice medicine pursuant to Article 1, Chapter 47, Title 40. (8) 'Provide' means the supply of one or more epinephrine auto-injectors to an individual. (9) Section 44-99-20. Notwithstanding any other provision of law, a health care practitioner may prescribe epinephrine auto-injectors in the name of an authorized entity for use in accordance with this chapter. Notwithstanding any other provision of law, pharmacists and health care practitioners may dispense epinephrine auto-injectors pursuant to a prescription issued in the name of an authorized entity. A prescription issued pursuant to this chapter is valid for two years. For the purposes of administering and storing epinephrine auto-injectors, authorized entities are not subject to Chapter 43, Title 40 or Chapter 99 of the South Carolina Code of State Regulations. Section 44-99-30. Notwithstanding any other provision of law, an authorized entity may acquire and stock a supply of epinephrine auto-injectors pursuant to a prescription issued in accordance with this chapter. Epinephrine auto-injectors acquired pursuant to this chapter must be stored in a location readily accessible in an emergency and in accordance with the epinephrine auto-injector's instructions for use, requirements that may be established by the South Carolina Department of Health and Environmental Control, and recommendations included as part of an approved training. An authorized entity shall designate employees or agents who have completed the training required by Section 44-99-50 to be responsible for the storage, maintenance, control, and general oversight of epinephrine auto-injectors acquired by the authorized entity. Section 44-99-40. Notwithstanding any other provision of law, an employee, agent, or other individual associated with an authorized entity, who has completed the training required by Section 44-99-50, may use epinephrine auto-injectors prescribed pursuant to Section 44-99-20 to: (1) provide an epinephrine auto-injector to any individual who the employee, agent, or other individual believes in good faith is experiencing anaphylaxis, or the parent, guardian, or caregiver of that individual, for immediate administration, regardless of whether the individual has a prescription for an epinephrine auto-injector or has previously been diagnosed with an allergy; and (2) administer an epinephrine auto-injector to any individual who the employee, agent, or other individual believes in good faith is experiencing anaphylaxis, regardless of whether the individual has a prescription for an epinephrine auto-injector or has previously been diagnosed with an allergy. (3) Section 44-99-50. (A) An employee, agent, or other individual described in Section 44-99-30 or 44-99-40 before undertaking an act authorized by this chapter shall complete an anaphylaxis training program and must complete an anaphylaxis training program at least every two years following completion of the initial anaphylaxis training program. The training must be conducted by the South Carolina Department of Health and Environmental Control, a licensed medical provider, a nationally recognized organization experienced in training laypersons in emergency health treatment, the manufacturer of an epinephrine auto-injector, an organization with a training program that has been approved in at least three states, or an entity or individual approved by the department. The department also may approve specific entities or individuals or may approve classes of entities or individuals to conduct training. (B) Training may be conducted online or in person and, at a minimum, must address: (1)how to recognize signs and symptoms of severe allergic reactions, including anaphylaxis; (2) standards and procedures for the storage and administration of an epinephrine auto-injector; and (3) emergency follow-up procedures. (C) The entity that conducts the training shall issue a certificate to each person who successfully completes the anaphylaxis training program. The certificate, at a minimum, must include: (1)the name of the organization or individual conducting the training; (2)the name of the individual being trained; and (3)the date the training occurred. Section 44-99-60. (A) An authorized entity that possesses and makes available epinephrine auto-injectors, and its employees, agents, and other individuals, a health care practitioner that prescribes or dispenses epinephrine auto-injectors to an authorized entity, a pharmacist or health care practitioner that dispenses epinephrine auto-injectors to an authorized entity, a third party that facilitates the availability of epinephrine auto-injectors to an authorized entity, the department or other state agency engaged in approving training or in providing guidance to implement this chapter, and an individual or entity that conducts the training described in Section 44-99-50 are not liable for any injuries or related damages that result from any act or omission taken pursuant to this chapter; however, this immunity does not apply to acts or omissions constituting negligence, gross negligence, or wilful, wanton, or reckless disregard for the safety of others or for an act or omission that is performed while the individual is impaired by alcohol or drugs. (B) The administration of an epinephrine auto-injector in accordance with this chapter is not the practice of medicine or any other profession that otherwise requires licensure. (C) This chapter does not eliminate, limit, or reduce any other immunities or defenses that may be available pursuant to state law, including those available pursuant to Section 15-1-310 and Chapter 78, Title 15. (D) An entity located in this State is not liable for any injuries or related damages that result from the provision or administration of an epinephrine auto-injector outside of this State if the entity: (1)would not have been liable for the injuries or related damages had the provision or administration occurred within this State; or (2)is not liable for the injuries or related damages under the law of the state in which such provision or administration occurred." SECTION 3. This act takes effect upon approval by the Governor. / Renumber sections to conform. Amend title to conform. Senator CLEARY explained the amendment. The question then was second reading of the Bill. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 38; Nays 0 AYES Alexander Bright Bryant Campbell Cleary Coleman Corbin Courson Cromer Davis Fair Gregory Grooms Hayes Hembree Hutto Johnson Kimpson Leatherman Malloy Martin, Larry Martin, Shane Massey Matthews, Margie McElveen Nicholson Peeler Reese Sabb Scott Setzler Shealy Sheheen Thurmond Turner Verdin Williams Young Total--38 NAYS Total--0 There being no further amendments, the Bill was read the second time, passed and ordered to a third reading. S. 929 (Word version) -- Senators Campbell, Verdin, Cleary, Lourie, Hembree, Fair and Bright: A BILL TO AMEND TITLE 44 OF THE 1976 CODE, RELATING TO HEALTH, BY ADDING CHAPTER 137, TO ENACT THE RIGHT TO TRY ACT, TO PROVIDE FOR AN ELIGIBLE PATIENT'S RIGHT TO TRY INVESTIGATIONAL DRUGS, BIOLOGICAL PRODUCTS, OR DEVICES TO COMBAT A TERMINAL ILLNESS; TO PROVIDE FOR AN ELIGIBLE PATIENT'S REQUEST TO USE AN INVESTIGATIONAL DRUG, BIOLOGICAL PRODUCT, OR DEVICE; TO PROVIDE THAT AN ELIGIBLE PATIENT GIVE INFORMED CONSENT PRIOR TO USING AN INVESTIGATIONAL DRUG, BIOLOGICAL PRODUCT, OR DEVICE; TO PROVIDE PROTECTION FROM LIABILITY FOR DOCTORS PRESCRIBING AND MANUFACTURERS OF AN INVESTIGATIONAL DRUG, BIOLOGICAL PRODUCT, OR DEVICE; TO PROVIDE THAT STATE EMPLOYEES MAY NOT BLOCK THE PROPER USE OF AN INVESTIGATIONAL DRUG, BIOLOGICAL PRODUCT, OR DEVICE; AND TO DEFINE NECESSARY TERMS. The Senate proceeded to a consideration of the Bill. The Committee on Medical Affairs proposed the following amendment (S-929), which was adopted: Amend the bill, as and if amended, page 2, by striking lines 33-37 and inserting: / (4) 'Informed consent' means a written document that is signed by an eligible patient; or if the patient is a minor, by a parent or legal guardian; or if the patient is incapacitated or without sufficient mental capacity, by a designated health care agent pursuant to a health care power of attorney, that at a minimum includes: / Amend the bill further, page 3, by striking lines 18-22 and inserting: / (f) a statement that the eligible patient's health benefit plan or third-party administrator and provider are not obligated or required to pay for any cost of any investigational drug, biological product, or device or for any care or treatments consequent to the use of such investigational drug, biological product, or device; and / Amend the bill further, page 4, by striking lines 20-25 and inserting: / Section 44-137-50. No official, employee, or agent of this State shall block or attempt to block an eligible patient's lawful access to an investigational drug, biological product, or device. Counseling, advice, or a recommendation consistent with medical standards of care from a licensed health care provider does not constitute a violation of this section. / Renumber sections to conform. Amend title to conform. Senator CLEARY explained the amendment. The question then was second reading of the Bill. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 41; Nays 0 AYES Alexander Bright Bryant Campbell Campsen Cleary Coleman Corbin Courson Cromer Davis Fair Gregory Grooms Hayes Hembree Hutto Johnson Kimpson Leatherman Malloy Martin, Larry Martin, Shane Massey Matthews, John Matthews, Margie McElveen Nicholson Peeler Rankin Reese Sabb Scott Setzler Shealy Sheheen Thurmond Turner Verdin Williams Young Total--41 NAYS Total--0 There being no further amendments, the Bill was read the second time, passed and ordered to a third reading. S. 1036 (Word version) -- Senator Cleary: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 40-15-176 SO AS TO PROVIDE THE STATE BOARD OF DENTISTRY MAY ISSUE RESTRICTED DENTAL AUXILIARY INSTRUCTORS' LICENSES TO DENTISTS WHO MEET CERTAIN REQUIREMENTS, TO PROVIDE LICENSED DENTAL AUXILIARY INSTRUCTORS MAY PRACTICE DENTISTRY IN LIMITED CIRCUMSTANCES ASSOCIATED WITH CERTAIN ACCREDITED DENTAL AUXILIARY PROGRAMS OF TECHNICAL COLLEGES, AND TO PROVIDE FOR THE RENEWAL AND REVOCATION OF RESTRICTED DENTAL AUXILIARY LICENSES; AND TO AMEND SECTION 40-15-175, RELATING TO RESTRICTED INSTRUCTORS' LICENSES ISSUED BY THE BOARD, SO AS TO REVISE CRITERIA FOR LICENSURE AND REQUIRE RENEWAL BIENNIALLY INSTEAD OF ANNUALLY. The Senate proceeded to a consideration of the Bill. Senator CLEARY explained the Bill. The question being the second reading of the Bill. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 41; Nays 0 AYES Alexander Bright Bryant Campbell Campsen Cleary Coleman Corbin Courson Cromer Davis Fair Gregory Grooms Hayes Hembree Hutto Johnson Kimpson Leatherman Malloy Martin, Larry Martin, Shane Massey Matthews, John Matthews, Margie McElveen Nicholson Peeler Rankin Reese Sabb Scott Setzler Shealy Sheheen Thurmond Turner Verdin Williams Young Total--41 NAYS Total--0 The Bill was read the second time, passed and ordered to a third reading. H. 3251 (Word version) -- Reps. G.M. Smith, G.R. Smith and J.E. Smith: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING SECTION 44-1-310 SO AS TO REQUIRE THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL TO ESTABLISH THE MATERNAL MORBIDITY AND MORTALITY REVIEW COMMITTEE TO REVIEW AND STUDY MATERNAL DEATHS AND TO REPORT THE FINDINGS TO THE GENERAL ASSEMBLY. The Senate proceeded to a consideration of the Bill. THE MEDICAL AFFAIRS COMMITTEE proposed the following amendment (BH\3251C002.BH.VR16), which was adopted: Amend the bill, as and if amended, SECTION 2, page 3, by deleting Section 44-1-310(F) and inserting: / (F) Reports of aggregated nonindividually identifiable data for the previous calendar year must be compiled and disseminated by March first of the following year in an effort to further study the causes and problems associated with maternal deaths. Reports must be distributed to the General Assembly, the Director of the Department of Health and Environmental Control, health care providers and facilities, key governmental agencies, and others necessary to reduce the maternal death rate. / Amend the bill further, as and if amended, SECTION 2, page 4, by deleting Section 44-1-310(H). Renumber sections to conform. Amend title to conform. Senator CLEARY explained the amendment. The question then was second reading of the Bill. The "ayes" and "nays" were demanded and taken, resulting as follows: Ayes 39; Nays 0 AYES Alexander Allen Bright Bryant Campbell Campsen Cleary Coleman Corbin Courson Cromer Davis Fair Gregory Grooms Hayes Hembree Hutto Johnson Kimpson Leatherman Malloy Martin, Larry Martin, Shane Massey Matthews, Margie McElveen Peeler Rankin Sabb Scott Setzler Shealy Sheheen Thurmond Turner Verdin Williams Young Total--39 NAYS Total--0 There being no further amendments, the Bill was read the second time, passed and ordered to a third reading. CARRIED OVER S. 315 (Word version) -- Senator Grooms: A JOINT RESOLUTION TO REPEAL SECTION 6 OF ACT 114, RELATED TO THE TERMINATION OF THE GOVERNOR'S AUTHORITY TO APPOINT THE SECRETARY OF TRANSPORTATION; AND TO EXTEND THE GOVERNOR'S AUTHORITY UNTIL FURTHER ACTION BY THE GENERAL ASSEMBLY TO THE CONTRARY. On motion of Senator HUTTO, the Resolution was carried over. S. 267 (Word version) -- Senators Young, Campsen, Hembree, Bennett, Turner, Thurmond, Davis, Bright, Bryant, L. Martin, S. Martin and Hayes: A BILL TO AMEND SECTION 2-1-180 OF THE 1976 CODE, RELATING TO ADJOURNMENT OF THE GENERAL ASSEMBLY, TO CHANGE THE DATE FOR THE MANDATORY ADJOURNMENT OF THE GENERAL ASSEMBLY FROM THE FIRST THURSDAY IN JUNE TO THE FIRST THURSDAY IN MAY, AND PROVIDE THAT IN ANY YEAR THAT THE HOUSE OF REPRESENTATIVES FAILS TO GIVE THIRD READING TO THE APPROPRIATIONS BILL BY MARCH FIRST, RATHER THAN MARCH THIRTY-FIRST, THE DATE OF ADJOURNMENT IS EXTENDED BY ONE STATEWIDE DAY FOR EACH STATEWIDE DAY AFTER MARCH FIRST, THAT THE HOUSE FAILS TO GIVE THE BILL THIRD READING. On motion of Senator MALLOY, the Bill was carried over. H. 3682 (Word version) -- Reps. Finlay, Bannister, Newton, Cole, Delleney, Weeks, Whipper, Robinson-Simpson and Bingham: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING CHAPTER 4 TO TITLE 39 SO AS TO ENACT THE "BAD FAITH ASSERTION OF PATENT INFRINGEMENT ACT", TO PROVIDE THAT BAD FAITH ASSERTIONS OF PATENT INFRINGEMENTS ARE PROHIBITED, TO DEFINE TERMS, TO PROVIDE FOR A PRIVATE CAUSE OF ACTION IN STATE COURTS BY A RECIPIENT OF A BAD FAITH ASSERTION TO PATENT INFRINGEMENT, TO PROVIDE THAT ENFORCEMENT ACTIONS MAY BE BROUGHT BY THE ATTORNEY GENERAL AND WILFUL AND KNOWING VIOLATIONS MAY RESULT IN CIVIL PENALTIES OF NOT MORE THAN FIFTY THOUSAND DOLLARS FOR EACH VIOLATION, TO PROVIDE FOR THE FACTORS THAT A COURT MAY CONSIDER WHEN MAKING A BAD FAITH DETERMINATION, AND TO PROVIDE EXCEPTIONS. On motion of Senator MALLOY, the Bill was carried over. S. 868 (Word version) -- Senators Young, Massey, Setzler and Nicholson: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, BY ADDING ARTICLE 3 TO CHAPTER 7, TITLE 58 SO AS TO PROVIDE PROCEDURES FOR THE EXERCISE OF EMINENT DOMAIN BY PIPELINE COMPANIES, TO PROVIDE NECESSARY DEFINITIONS, TO PROVIDE CERTAIN RELATED CERTIFICATION OR PERMITTING FUNCTIONS AT THE PUBLIC SERVICE COMMISSION AND THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL, AND TO PROVIDE PROPERTY OWNER RIGHTS AND A CAUSE OF ACTION FOR DAMAGES SUSTAINED BY CERTAIN ADJACENT PROPERTY OF THE OWNER OF PROPERTY CONDEMNED UNDER THE PROVISIONS OF THIS ACT; AND TO DESIGNATE THE EXISTING PROVISIONS IN THE CHAPTER AS ARTICLE 1 ENTITLED "GAS AND WATER COMPANIES". On motion of Senator MALLOY, the Bill was carried over. S. 1065 (Word version) -- Senators Young, Massey, Setzler and Nicholson: A JOINT RESOLUTION TO CLARIFY THAT SECTION 58-7-10 OF THE 1976 CODE OF LAWS DOES NOT APPLY TO A PRIVATE, FOR-PROFIT PIPELINE COMPANY, INCLUDING A PUBLICLY-TRADED FOR-PROFIT COMPANY, THAT IS NOT A PUBLIC UTILITY AS DEFINED BY TITLE 58 OF THE 1976 SOUTH CAROLINA CODE OF LAWS; AND TO CREATE THE PETROLEUM PIPELINE STUDY COMMITTEE TO STUDY MATTERS RELATED TO THE PRESENCE OF PETROLEUM PIPELINES IN SOUTH CAROLINA, AND FOR THE STUDY COMMITTEE TO PROVIDE A REPORT TO THE GENERAL ASSEMBLY BY JANUARY 31, 2017, AND TO CONTINUE ITS WORK UNTIL JUNE 30, 2017, IF THE JANUARY REPORT DETERMINES FURTHER WORK IS NEEDED. On motion of Senator MALLOY, the Resolution was carried over. H. 4787 (Word version) -- Regulations and Administrative Procedures Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL, RELATING TO HORSE MEAT AND KANGAROO MEAT; FAIRS, CAMP MEETINGS, AND OTHER GATHERINGS; CAMPS; MOBILE/MANUFACTURED HOME PARKS; SANITATION OF SCHOOLS; AND NUISANCES, DESIGNATED AS REGULATION DOCUMENT NUMBER 4552, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE. Senator CLEARY explained the Resolution. On motion of Senator SCOTT, the Resolution was carried over. H. 4788 (Word version) -- Regulations and Administrative Procedures Committee: A JOINT RESOLUTION TO APPROVE REGULATIONS OF THE DEPARTMENT OF HEALTH AND ENVIRONMENTAL CONTROL, RELATING TO STANDARDS FOR LICENSING NURSING HOMES, DESIGNATED AS REGULATION DOCUMENT NUMBER 4543, PURSUANT TO THE PROVISIONS OF ARTICLE 1, CHAPTER 23, TITLE 1 OF THE 1976 CODE. Senator CLEARY explained the Resolution. On motion of Senator CLEARY, the Resolution was carried over. CARRIED OVER S. 1035 (Word version) -- Senators Cleary and Hutto: A BILL TO AMEND THE CODE OF LAWS OF SOUTH CAROLINA, 1976, TO ENACT THE "SOUTH CAROLINA TELEMEDICINE ACT" BY ADDING SECTION 40-47-37 SO AS TO FACILITATE THE USE OF TELEMEDICINE BY ESTABLISHING CERTAIN RECORDKEEPING REQUIREMENTS; TO AMEND SECTION 40-47-20, RELATING TO DEFINITIONS USED IN CHAPTER 47, TITLE 40, SO AS TO PROVIDE DEFINITIONS FOR "ASYNCHRONOUS STORE AND FORWARD TRANSFER" AND "TELEMEDICINE"; AND TO AMEND SECTION 40-47-113, RELATING TO THE REQUIREMENT OF A PHYSICIAN-PATIENT RELATIONSHIP BEFORE A PHYSICIAN MAY PRESCRIBE DRUGS FOR A PATIENT, SO AS TO ALLOW THE PRESCRIPTION OF DRUGS WHEN THE PHYSICIAN-PATIENT RELATIONSHIP IS ESTABLISHED BY TELEMEDICINE. The Senate proceeded to a consideration of the Bill. The Committee on Medical Affairs proposed the following amendment (S-1035), which was adopted: Amend the bill, as and if amended, by striking all after the enacting words and inserting: / SECTION 1. This act may be cited as the "South Carolina Telemedicine Act". SECTION 2. Article 1, Chapter 47, Title 40 of the 1976 Code is amended by adding: "Section 40-47-37. (A) A licensee who establishes a physician-patient relationship solely via telemedicine as defined in Section 40-47-20(52) shall adhere to the same standard of care as a licensee employing more traditional in-person medical care and be evaluated according to the standard of care applicable to the licensee's area of specialty. A licensee shall not establish a physician-patient relationship by telemedicine pursuant to Section 40-47-113(B) for the purpose of prescribing medication when an in-person physical examination is necessary for diagnosis. The failure to conform to the appropriate standard of care is considered unprofessional conduct under Section 40-47-110(B)(9). (B) A licensee who establishes a physician-patient relationship solely via telemedicine as defined in Section 40-47-20(52) shall generate and maintain medical records for each patient using such telemedicine services in compliance with any applicable state and federal laws, rules, and regulations, including this chapter, the Health Insurance Portability and Accountability Act (HIPAA), and the Health Information Technology for Economic and Clinical Health Act (HITECH). Such records shall be accessible to other practitioners and to the patient in a timely fashion when lawfully requested to do so by the patient or by a lawfully designated representative of the patient. (C) In addition to those requirements set forth in subsections (A) and (B), a licensee who establishes a physician-patient relationship solely via telemedicine as defined in Section 40-47-20(52) shall: (1) adhere to current standards for practice improvement and monitoring of outcomes and provide reports containing such information upon request of the board; (2) provide an appropriate evaluation prior to diagnosing and/or treating the patient, which need not be done in-person if the licensee employs technology sufficient to accurately diagnose and treat the patient in conformity with the applicable standard of care; provided, that evaluations in which a licensee is at a distance from the patient, but a practitioner is able to provide various physical findings the licensee needs to complete an adequate assessment, is permitted; further, provided, that a simple questionnaire without an appropriate evaluation is prohibited; (3) verify the identity and location of the patient and be prepared to inform the patient of the licensee's name, location, and professional credentials; (4) establish a diagnosis through the use of accepted medical practices, which may include patient history, mental status evaluation, physical examination, and appropriate diagnostic and laboratory testing in conformity with the applicable standard of care; (5) ensure the availability of appropriate follow-up care and maintain a complete medical record that is available to the patient and other treating health care practitioners, to be distributed to other treating health care practitioners only with patient consent and in accordance with applicable law and regulation; (6) prescribe within a practice setting fully in compliance with this section and during an encounter in which threshold information necessary to make an accurate diagnosis has been obtained in a medical history interview conducted by the prescribing licensee; provided, however, that Schedule II and Schedule III prescriptions are not permitted except for those Schedule II and Schedule III medications specifically authorized by the board, which may include, but not be limited to, Schedule II-nonnarcotic and Schedule III-nonnarcotic medications; further, provided, that licensees prescribing controlled substances by means of telemedicine must comply with all relevant federal and state laws including, but not limited to, participation in the South Carolina Prescription Monitoring Program set forth in Article 15, Chapter 53, Title 44 of the 1976 Code; further, provided, that prescribing of lifestyle medications including, but not limited to, hormone replacement therapies, birth control, or erectile dysfunction drugs are not permitted unless approved by the board; (7) maintain a complete record of the patient's care according to prevailing medical record standards that reflects an appropriate evaluation of the patient's presenting symptoms; provided that relevant components of the telemedicine interaction be documented as with any other encounter; (8) maintain the patient's record's confidentiality and disclose the records to the patient consistent with state and federal law; provided, that licensees practicing telemedicine shall be held to the same standards of professionalism concerning medical records transfer and communication with the primary care provider and medical home as licensees practicing via traditional means; further, provided, that if a patient has a primary care provider and a telemedicine provider for the same ailment, then the primary care provider's medical record and the telemedicine provider's record constitute one complete medical record; (9) be licensed to practice medicine in South Carolina; provided, however, a licensee need not reside in South Carolina so long as he or she has a valid, current South Carolina medical license; further, provided, that a licensee residing in South Carolina who intends to practice medicine via telemedicine to treat or diagnose patients outside of South Carolina shall comply with other state licensing boards; and (10) discuss with the patient the value of having a primary care medical home and, if the patient requests, provide assistance in identifying available options for a primary care medical home. (D) A licensee, practitioner, or any other person involved in a telemedicine encounter must be trained in the use of the telemedicine equipment and competent in its operation. (E) Notwithstanding any of the provisions of this section, the board shall retain all authority with respect to telemedicine practice as granted in Section 40-47-10(I) of this chapter." SECTION 3. Section 40-47-20(52) through (55) of the 1976 Code is amended to read: "(52) 'Telemedicine' means the practice of medicine using electronic communications, information technology, or other means between a licensee in one location and a patient in another location with or without an intervening practitioner. (52)(53) 'Temporary license' means a current, time-limited document that authorizes practice at the level for which one is seeking licensure. (53)(54) 'Unprofessional conduct' means acts or behavior that fail to meet the minimally acceptable standard expected of similarly situated professionals including, but not limited to, conduct that may be harmful to the health, safety, and welfare of the public, conduct that may reflect negatively on one's fitness to practice, or conduct that may violate any provision of the code of ethics adopted by the board or a specialty. (54)(55) 'Voluntary surrender' means forgoing the authorization to practice by the subject of an initial or formal complaint pending further order of the board. It anticipates other formal action by the board and allows any suspension subsequently imposed to include this time. (55)(56) 'Volunteer license' means authorization of a retired practitioner to provide medical services to others through an identified charitable organization without remuneration." SECTION 4. Section 40-47-113(B) of the 1976 Code is amended to read: "(B) Notwithstanding subsection (A), a licensee may prescribe for a patient whom the licensee has not personally examined under certain circumstances including, but not limited to, writing admission orders for a newly hospitalized patient, prescribing for a patient of another licensee for whom the prescriber is taking call, prescribing for a patient examined by a licensed advanced practice registered nurse, a physician assistant, or other physician extender authorized by law and supervised by the physician, or continuing medication on a short-term basis for a new patient prior to before the patient's first appointment, or prescribing for a patient for whom the licensee has established a physician-patient relationship solely via telemedicine so long as the licensee complies with Section 40-47-37 of this act." SECTION 5. This act takes effect upon approval by the Governor. / Renumber sections to conform. Amend title to conform. Senator CLEARY explained the amendment. On motion of Senator BRYANT, the Bill was carried over. S. 1024 (Word version) -- Senator Shealy: A CONCURRENT RESOLUTION TO EXPRESS THE SUPPORT OF THE SOUTH CAROLINA GENERAL ASSEMBLY AND THE STATE OF SOUTH CAROLINA FOR ORGAN, EYE, AND TISSUE DONATION AND TO DESIGNATE WEDNESDAY, APRIL 6, 2016, AS "ORGAN DONOR REGISTRATION DAY" IN SOUTH CAROLINA. The Resolution was adopted, ordered sent to the House. H. 4194 (Word version) -- Rep. Quinn: A CONCURRENT RESOLUTION TO REQUEST THAT THE DEPARTMENT OF CORRECTIONS NAME THE INMATE CEMETERY LOCATED ON ITS BROAD RIVER ROAD PROPERTY IN RICHLAND COUNTY "PAUL ISAIAH WELDON CEMETERY". The Resolution was adopted, ordered returned to the House. H. 4928 (Word version) -- Reps. Hiott, Clary, Collins, Alexander, Allison, Anderson, Anthony, Atwater, Bales, Ballentine, Bamberg, Bannister, Bedingfield, Bernstein, Bingham, Bowers, Bradley, Brannon, G.A. Brown, R.L. Brown, Burns, Chumley, Clemmons, Clyburn, Cobb-Hunter, Cole, Corley, H.A. Crawford, Crosby, Daning, Delleney, Dillard, Douglas, Duckworth, Erickson, Felder, Finlay, Forrester, Fry, Funderburk, Gagnon, Gambrell, George, Gilliard, Goldfinch, Govan, Hamilton, Hardee, Hart, Hayes, Henderson, Henegan, Herbkersman, Hicks, Hill, Hixon, Hodges, Horne, Hosey, Howard, Huggins, Jefferson, Johnson, Jordan, Kennedy, King, Kirby, Knight, Limehouse, Loftis, Long, Lowe, Lucas, Mack, McCoy, McEachern, McKnight, M.S. McLeod, W.J. McLeod, Merrill, Mitchell, D.C. Moss, V.S. Moss, Murphy, Nanney, Neal, Newton, Norman, Norrell, Ott, Parks, Pitts, Pope, Putnam, Quinn, Ridgeway, Riley, Rivers, Robinson-Simpson, Rutherford, Ryhal, Sandifer, Simrill, G.M. Smith, G.R. Smith, J.E. Smith, Sottile, Southard, Spires, Stavrinakis, Stringer, Tallon, Taylor, Thayer, Tinkler, Toole, Weeks, Wells, Whipper, White, Whitmire, Williams, Willis and Yow: A CONCURRENT RESOLUTION TO AFFIRM THE DEDICATION OF THE GENERAL ASSEMBLY TO THE FUTURE SUCCESS OF SOUTH CAROLINA'S YOUNG PEOPLE AND TO THE PREVENTION OF CHILD ABUSE AND NEGLECT AND TO DECLARE THE MONTH OF APRIL 2016 AS "CHILD ABUSE PREVENTION MONTH" IN THE STATE OF SOUTH CAROLINA. The Resolution was adopted, ordered returned to the House. H. 4930 (Word version) -- Reps. Clemmons, Yow, Fry, Hardee, Goldfinch, Duckworth, Alexander, Allison, Anderson, Anthony, Atwater, Bales, Ballentine, Bamberg, Bannister, Bedingfield, Bernstein, Bingham, Bowers, Bradley, Brannon, G.A. Brown, R.L. Brown, Burns, Chumley, Clary, Clyburn, Cobb-Hunter, Cole, Collins, Corley, H.A. Crawford, Crosby, Daning, Delleney, Dillard, Douglas, Erickson, Felder, Finlay, Forrester, Funderburk, Gagnon, Gambrell, George, Gilliard, Govan, Hamilton, Hart, Hayes, Henderson, Henegan, Herbkersman, Hicks, Hill, Hiott, Hixon, Hodges, Horne, Hosey, Howard, Huggins, Jefferson, Johnson, Jordan, Kennedy, King, Kirby, Knight, Limehouse, Loftis, Long, Lowe, Lucas, Mack, McCoy, McEachern, McKnight, M.S. McLeod, W.J. McLeod, Merrill, Mitchell, D.C. Moss, V.S. Moss, Murphy, Nanney, Neal, Newton, Norman, Norrell, Ott, Parks, Pitts, Pope, Putnam, Quinn, Ridgeway, Riley, Rivers, Robinson-Simpson, Rutherford, Ryhal, Sandifer, Simrill, G.M. Smith, G.R. Smith, J.E. Smith, Sottile, Southard, Spires, Stavrinakis, Stringer, Tallon, Taylor, Thayer, Tinkler, Toole, Weeks, Wells, Whipper, White, Whitmire, Williams and Willis: A CONCURRENT RESOLUTION TO DECLARE JULY 16, 2016, AS ATOMIC VETERANS DAY IN SOUTH CAROLINA. The Resolution was adopted, ordered returned to the House. THE CALL OF THE UNCONTESTED CALENDAR HAVING BEEN COMPLETED, THE SENATE PROCEEDED TO THE MOTION PERIOD. At 2:43 P.M., on motion of Senator LEATHERMAN, the Senate agreed to dispense with the balance of 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. 199 (Word version) -- Senators Grooms, Hembree, Bennett, Campbell, Verdin, Campsen, Gregory, Johnson, Setzler, Sabb, Nicholson and Scott: A BILL TO AMEND SECTION 56-5-1535 OF THE 1976 CODE, RELATING TO SPEEDING IN WORK ZONES AND PENALTIES ASSOCIATED WITH SPEEDING IN WORK ZONES, TO DELETE THIS PROVISION AND CREATE "PEANUT'S LAW", TO PROVIDE A DEFINITION FOR THE TERMS "HIGHWAY WORK ZONE" AND "HIGHWAY WORKER", TO CREATE THE OFFENSES OF "ENDANGERMENT OF A HIGHWAY WORKER", AND TO PROVIDE PENALTIES FOR THESE OFFENSES; TO AMEND SECTION 56-1-720, RELATING TO THE POINT SYSTEM ESTABLISHED FOR THE EVALUATION OF THE DRIVING RECORD OF PERSONS OPERATING MOTOR VEHICLES, TO PROVIDE THAT "ENDANGERMENT OF A HIGHWAY WORKER" VIOLATIONS RANGE BETWEEN TWO AND SIX POINTS; AND TO REPEAL SECTION 56-5-1536 RELATING TO DRIVING IN TEMPORARY WORK ZONES AND PENALTIES FOR UNLAWFUL DRIVING IN TEMPORARY WORK ZONES. On motion of Senator LEATHERMAN, the Bill was carried over. THE SENATE PROCEEDED TO THE INTERRUPTED DEBATE. DEBATE INTERRUPTED The Senate proceeded to a consideration of the Bill, the question being the second reading of the Bill. Amendment No. P1 Senators LOURIE and HUTTO proposed the following amendment (3579R007.KM.JL): Amend the committee amendment, as and if amended, page [3579-2], by striking lines 20-23 and inserting: / twelve cents. Fifteen percent of the funds raised by the increase in the motor fuel user fee imposed by this subsection shall be apportioned among the counties of the State in the manner provided in Section 12-28-2740. The remainder of the funds raised by the increase in / Amend the committee amendment further, as and if amended, page [3579-4], by striking lines 1-7 and inserting: / (C) The fees collected pursuant to this section must be credited to the Department of Transportation State Non-Federal Aid Highway Fund. Fifteen percent of the funds raised by the increase in the motor fuel user fee imposed by this subsection shall be apportioned among the counties of the State in the manner provided in Section 12-28-2740. The remaining fees collected pursuant to this section shall be credited to the State Highway Fund." / Amend the committee amendment further, as and if amended, page [3579-4], by striking lines 29-32 and inserting: / (G) From each biennial registration and license fee collected, sixteen dollars shall be credited as follows: fifteen percent of the funds raised by the increase in the motor fuel user fee imposed by this subsection shall be apportioned among the counties of the State in the manner provided in Section 12-28-2740 and the remainder credited to the State Highway Fund." / Amend the committee amendment further, as and if amended, page [3579-5], by striking lines 3-6 and inserting: / (B) Fifteen percent of the funds raised by the increase in the motor fuel user fee imposed by this subsection shall be apportioned among the counties of the State in the manner provided in Section 12-28-2740 and the remainder of the fees shall be credited to the State Highway Fund. / Amend the committee amendment further, as and if amended, page [3579-6], by striking lines 1-2 and inserting: / (i) fifteen percent shall be apportioned among the counties of the State in the manner provided in Section 12-28-2740. / Renumber sections to conform. Amend title to conform. Senator DAVIS spoke on the amendment. On motion of Senator FAIR, with unanimous consent, Senators HUTTO and FAIR were granted leave to attend a subcommittee meeting and were granted leave to vote from the balcony. Senator DAVIS resumed speaking on the amendment. Point of Quorum At 4:15 P.M., Senator BRIGHT made the point that a quorum was not present. It was ascertained that a quorum was not present. Call of the Senate Senator LEATHERMAN moved that a Call of the Senate be made. The following Senators answered the Call: Alexander Allen Bright Bryant Campbell Campsen Cleary Coleman Courson Cromer Davis Fair Hayes Hembree Hutto Jackson Johnson Leatherman Lourie Martin, Larry Martin, Shane Matthews, Margie McElveen Nicholson Peeler Rankin Reese Sabb Scott Setzler Shealy Sheheen Thurmond Turner Verdin Young A quorum being present, the Senate resumed. Senator DAVIS resumed speaking on the amendment. Point of Quorum At 6:38 P.M., Senator PEELER made the point that a quorum was not present. It was ascertained that a quorum was not present. Call of the Senate Senator PEELER moved that a Call of the Senate be made. The following Senators answered the Call: Alexander Bright Bryant Campbell Campsen Corbin Courson Cromer Davis Fair Grooms Hayes Hembree Jackson Johnson Leatherman Lourie Martin, Larry Martin, Shane Matthews, John Matthews, Margie McElveen Nicholson Peeler Rankin Sabb Scott Setzler Shealy Turner Verdin Young A quorum being present, the Senate resumed. Senator DAVIS resumed speaking on the amendment. Senator BRIGHT spoke on the amendment. On motion of Senator LEATHERMAN, with unanimous consent, the Senate agreed to stand adjourned with Senator BRIGHT retaining the floor on H. 3579. LOCAL APPOINTMENT Confirmation Having received a favorable report from the Senate, the following appointment was confirmed in open session: Reappointment, Allendale County Master-in-Equity, with the term to commence December 31, 2014, and to expire December 31, 2020 Walter H. Sanders, Jr., P. O. Box 840, Fairfax, SC 29827 On motion of Senators BRIGHT and SHANE MARTIN, with unanimous consent, the Senate stood adjourned out of respect to the memory of Mr. Michael H. Thompson of Spartanburg, S.C. Michael was a dear friend of Senator BRIGHT and Senator SHANE MARTIN and was dedicated to the community and children. He was a graduate of Clemson University and honorably served our country in the United States Army. He was a deacon at First Baptist Church and the retired owner of J.M. Solesbee Construction Company and co-owner of Carolina Traditions. Mike was a loving husband, devoted father and doting grandfather who will be dearly missed. and	2018-11-20T16:16:46	{"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": 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": 0.243909552693367, "perplexity": 9019.700658764667}, "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-2018-47/segments/1542039746465.88/warc/CC-MAIN-20181120150950-20181120172950-00098.warc.gz"}
http://trilinos.sandia.gov/packages/docs/dev/packages/didasko/doc/html/teuchos_ex4.html	// ********************************************************************* // // Didasko Tutorial Package // Copyright (2005) Sandia Corporation // // Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive // license for use of this work by or on behalf of the U.S. Government. // // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are // met: // // 1. Redistributions of source code must retain the above copyright // notice, this list of conditions and the following disclaimer. // // 2. Redistributions in binary form must reproduce the above copyright // notice, this list of conditions and the following disclaimer in the // documentation and/or other materials provided with the distribution. // // 3. Neither the name of the Corporation nor the names of the // contributors may be used to endorse or promote products derived from // this software without specific prior written permission. // // THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY // EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR // PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF // LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. // // Questions about Didasko? Contact Marzio Sala (marzio.sala _AT_ gmail.com) // // ********************************************************************* #ifdef HAVE_MPI #include "mpi.h" #endif #include "Teuchos_ParameterList.hpp" #include "Teuchos_ConfigDefs.hpp" int main(int argc, char* argv[]) { #ifdef HAVE_MPI MPI_Init(&argc,&argv); #endif // Creating an empty parameter list looks like: Teuchos::ParameterList My_List; // Setting parameters in this list can be easily done: My_List.set("Max Iters", 1550); My_List.set("Tolerance", 1e-10); My_List.set("Solver", "GMRES"); /* The templated set'' method should cast the input {\it value} to the correct data type. However, in the case where the compiler is not casting the input value to the expected data type, an explicit cast can be used with the set'' method: / My_List.set("Tolerance", (float)(1e-10)); / A hierarchy of parameter lists can be constructed using {\tt Teuchos::ParameterList}. This means another parameter list is a valid {\it value} in any parameter list. To create a sublist in a parameter list and obtain a reference to it: / Teuchos::ParameterList& Prec_List = My_List.sublist("Preconditioner"); // Now this parameter list can be filled with values: Prec_List.set("Type", "ILU"); Prec_List.set("Drop Tolerance", 1e-3); // The parameter list can be queried about the existance of a parameter, sublist, or type: // Has a solver been chosen? bool solver_defined, prec_defined, tol_double, dtol_double; solver_defined = My_List.isParameter("Solver"); // Has a preconditioner been chosen? prec_defined = My_List.isSublist("Preconditioner"); // Has a tolerance been chosen and is it a double-precision number? tol_double = My_List.INVALID_TEMPLATE_QUALIFIER isType<double>("Tolerance"); // Has a drop tolerance been chosen and is it a double-precision number? dtol_double = Teuchos::isParameterType<double>(Prec_List, "Drop Tolerance"); / The last two methods for checking the parameter type are equivalent. There is some question as to whether the syntax of the first type-checking method is acceptable to older compilers. Thus, the second type-checking method is offered as a portable alternative. / // Parameters can be retrieved from the parameter list in quite a few ways: // Get method that creates and sets the parameter if it doesn't exist. int its; its = My_List.get("Max Iters", 1200); // Get method that retrieves a parameter of a particular type. float tol; tol = My_List.INVALID_TEMPLATE_QUALIFIER get<float>("Tolerance"); / In the above example, the first get'' method is a safe way of obtaining a parameter when its existence is indefinite but required. The second get'' method should be used when the existense of the parameter is definite. This method will throw an exception if the parameter doesn't exist. The safest way to use the second get'' method is in a try/catch block: / try { tol = My_List.INVALID_TEMPLATE_QUALIFIER get<float>("Tolerance"); } catch (std::exception& e) { tol = 1e-6; } / The second get'' method uses a syntax that may not be acceptable to older compilers. Optionally, there is another portable templated get'' function that can be used in the place of the second get'' method: / try { tol = Teuchos::getParameter<float>(My_List, "Tolerance"); } catch (std::exception& e) { tol = 1e-6; } // A parameter list can be sent to the output stream: cout<< My_List << endl; / It is important to note that mispelled parameters (with additional space characters, capitalizations, etc.) may be ignored. Therefore, it is important to be aware that a given parameter has not been used. Unused parameters can be printed with method: / My_List.unused( cout ); #ifdef HAVE_MPI MPI_Finalize(); #endif return 0; } #else #include <stdlib.h> #include <stdio.h> int main(int argc, char argv[]) { #ifdef HAVE_MPI MPI_Init(&argc,&argv); #endif	2014-03-10T20:41:48	{"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": 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": 0.4946218729019165, "perplexity": 2099.3796679492752}, "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-2014-10/segments/1394011011190/warc/CC-MAIN-20140305091651-00055-ip-10-183-142-35.ec2.internal.warc.gz"}
https://mooseframework.inl.gov/syntax/BCs/index.html	BCs System Available Objects • Moose App • ConvectiveFluxBCDetermines boundary values via the initial and final values, flux, and exposure duration • DGFunctionDiffusionDirichletBC • DiffusionFluxBCComputes a boundary residual contribution consistent with the Diffusion Kernel. Does not impose a boundary condition; instead computes the boundary contribution corresponding to the current value of grad(u) and accumulates it in the residual vector. • DirichletBCImposes the essential boundary condition , where is a constant, controllable value. • EigenDirichletBCDirichlet BC for eigenvalue solvers • FunctionDirichletBCImposes the essential boundary condition , where is a (possibly) time and space-dependent MOOSE Function. • FunctionNeumannBCImposes the integrated boundary condition , where is a (possibly) time and space-dependent MOOSE Function. • FunctionPenaltyDirichletBC • FunctionPresetBCThe same as FunctionDirichletBC except the value is applied before the solve begins • LagrangeVecDirichletBCImposes the essential boundary condition , where are constant, controllable values. • LagrangeVecFunctionDirichletBCImposes the essential boundary condition , where components are calculated with functions. • MatchedValueBCImplements a NodalBC which equates two different Variables' values on a specified boundary. • NeumannBCImposes the integrated boundary condition , where is a constant, controllable value. • OneDEqualValueConstraintBC • PenaltyDirichletBCEnforces a Dirichlet boundary condition in a weak sense by penalizing differences between the current solution and the Dirichlet data. • PostprocessorDirichletBC • PostprocessorNeumannBC • PresetBCSimilar to DirichletBC except the value is applied before the solve begins • SinDirichletBCImposes a time-varying essential boundary condition , where varies from an given initial value at time to a given final value over a specified duration. • SinNeumannBCImposes a time-varying flux boundary condition , where varies from an given initial value at time to a given final value over a specified duration. • VacuumBC • VectorNeumannBCImposes the integrated boundary condition , where is a user-defined, constant vector. • WeakGradientBCComputes a boundary residual contribution consistent with the Diffusion Kernel. Does not impose a boundary condition; instead computes the boundary contribution corresponding to the current value of grad(u) and accumulates it in the residual vector. • Rdg App • AEFVBCA boundary condition kernel for the advection equation using a cell-centered finite volume method. • Functional Expansion Tools App • FXFluxBCSets a flux boundary condition, evaluated using a FunctionSeries instance. This does not fix the flux, but rather 'strongly encourages' flux agreement by penalizing the differences through contributions to the residual. • FXValueBCImposes a fixed value boundary condition, evaluated using a FunctionSeries instance. • FXValuePenaltyBCSets a value boundary condition, evaluated using a FunctionSeries instance. This does not fix the value, but rather 'strongly encourages' value agreement by penalizing the differences through contributions to the residual. • XFEMApp • CrackTipEnrichmentCutOffBCSimilar to DirichletBC except the value is applied before the solve begins • Heat Conduction App • ConvectiveFluxFunctionDetermines boundary value by fluid heat transfer coefficient and far-field temperature • CoupledConvectiveFlux • CoupledConvectiveHeatFluxBCConvective heat transfer boundary condition with temperature and heat transfer coefficent given by auxiliary variables. • GapHeatTransferTransfers heat across a gap between two surfaces dependant on the gap geometry specified. • HeatConductionBC • Richards App • Q2PPiecewiseLinearSinkSink of fluid, controlled by (pressure, bare_fluxes) interpolation. This is for use in Q2P models • RichardsExcavAllows the user to set variable values at the face of an excavation. You must have defined the excavation start time, start position, etc, through the excav_geom_function • RichardsHalfGaussianSink • RichardsPiecewiseLinearSink • Tensor Mechanics App • CoupledPressureBCApplies a pressure from a variable on a given boundary in a given direction • DashpotBC • DisplacementAboutAxisImplements a boundary condition that enforces rotationaldisplacement around an axis on a boundary • InteractionIntegralBenchmarkBC • PresetAccelerationPrescribe acceleration on a given boundary in a given direction • PresetDisplacementPrescribe the displacement on a given boundary in a given direction. • PresetVelocity • PressureApplies a pressure on a given boundary in a given direction • StickyBCImposes the boundary condition if exceeds the bounds provided • Navier Stokes App • EnergyFreeBC • INSMomentumNoBCBCLaplaceFormThis class implements the 'No BC' boundary condition based on the 'Laplace' form of the viscous stress tensor. • INSMomentumNoBCBCTractionFormThis class implements the 'No BC' boundary condition based on the 'traction' form of the viscous stress tensor. • INSTemperatureNoBCBCThis class implements the 'No BC' boundary condition discussed by Griffiths, Papanastiou, and others. • ImplicitNeumannBCThis class implements a form of the Neumann boundary condition in which the boundary term is treated 'implicitly'. • MassFreeBC • MomentumFreeBC • MomentumFreeSlipBC • NSEnergyInviscidSpecifiedBCThis class corresponds to the inviscid part of the 'natural' boundary condition for the energy equation. • NSEnergyInviscidSpecifiedDensityAndVelocityBCThis class corresponds to the inviscid part of the 'natural' boundary condition for the energy equation. • NSEnergyInviscidSpecifiedNormalFlowBCThis class corresponds to the inviscid part of the 'natural' boundary condition for the energy equation. • NSEnergyInviscidSpecifiedPressureBCThis class corresponds to the inviscid part of the 'natural' boundary condition for the energy equation. • NSEnergyInviscidUnspecifiedBCThis class corresponds to the inviscid part of the 'natural' boundary condition for the energy equation. • NSEnergyViscousBCThis class couples together all the variables for the compressible Navier-Stokes equations to allow them to be used in derived IntegratedBC classes. • NSEnergyWeakStagnationBCThe inviscid energy BC term with specified normal flow. • NSImposedVelocityBCImpose Velocity BC. • NSImposedVelocityDirectionBCThis class imposes a velocity direction component as a Dirichlet condition on the appropriate momentum equation. • NSInflowThermalBCThis class is used on a boundary where the incoming flow values (rho, u, v, T) are all completely specified. • NSMassSpecifiedNormalFlowBCThis class implements the mass equation boundary term with a specified value of rho(u.n) imposed weakly. • NSMassUnspecifiedNormalFlowBCThis class implements the mass equation boundary term with the rho(u.n) boundary integral computed implicitly. • NSMassWeakStagnationBCThe inviscid energy BC term with specified normal flow. • NSMomentumConvectiveWeakStagnationBCThe convective part (sans pressure term) of the momentum equation boundary integral evaluated at specified stagnation temperature, stagnation pressure, and flow direction values. • NSMomentumInviscidNoPressureImplicitFlowBCMomentum equation boundary condition used when pressure is not integrated by parts. • NSMomentumInviscidSpecifiedNormalFlowBCMomentum equation boundary condition in which pressure is specified (given) and the value of the convective part is allowed to vary (is computed implicitly). • NSMomentumInviscidSpecifiedPressureBCMomentum equation boundary condition in which pressure is specified (given) and the value of the convective part is allowed to vary (is computed implicitly). • NSMomentumPressureWeakStagnationBCThis class implements the pressure term of the momentum equation boundary integral for use in weak stagnation boundary conditions. • NSMomentumViscousBCThis class corresponds to the viscous part of the 'natural' boundary condition for the momentum equations. • NSPenalizedNormalFlowBCThis class penalizes the the value of u.n on the boundary so that it matches some desired value. • NSPressureNeumannBCThis kernel is appropriate for use with a 'zero normal flow' boundary condition in the context of the Euler equations. • NSStagnationPressureBCThis Dirichlet condition imposes the condition p_0 = p_0_desired. • NSStagnationTemperatureBCThis Dirichlet condition imposes the condition T_0 = T_0_desired. • NSThermalBCNS thermal BC. • Chemical Reactions App • ChemicalOutFlowBCChemical flux boundary condition • Porous Flow App • PorousFlowHalfCubicSinkApplies a flux sink to a boundary. The base flux defined by PorousFlowSink is multiplied by a cubic. • PorousFlowHalfGaussianSinkApplies a flux sink to a boundary. The base flux defined by PorousFlowSink is multiplied by a Gaussian. • PorousFlowPiecewiseLinearSinkApplies a flux sink to a boundary. The base flux defined by PorousFlowSink is multiplied by a piecewise linear function. • PorousFlowSinkApplies a flux sink to a boundary.	2018-12-10T15:43:04	{"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": 0.8804531693458557, "perplexity": 4320.505877530286}, "config": {"markdown_headings": false, "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-2018-51/segments/1544376823348.23/warc/CC-MAIN-20181210144632-20181210170132-00553.warc.gz"}
http://dlmf.nist.gov/10.43	# §10.43 Integrals ## §10.43(i) Indefinite Integrals Let be defined as in §10.25(ii). Then For the modified Struve function see §11.2(i). 10.43.3 , . ## §10.43(ii) Integrals over the Intervals and where and is Euler’s constant (§5.2). ## §10.43(iii) Fractional Integrals The Bickley function is defined by 10.43.11 when and , and by analytic continuation elsewhere. Equivalently, 10.43.12. ### ¶ Properties 10.43.13 10.43.14 10.43.16. 10.43.17 For further properties of the Bickley function, including asymptotic expansions and generalizations, see Amos (1983c, 1989) and Luke (1962, Chapter 8). ## §10.43(iv) Integrals over the Interval () When , For the second equation there is a cut in the -plane along the interval , and all quantities assume their principal values (§4.2(i)). For the Ferrers function and the associated Legendre function , see §§14.3(i) and 14.21(i). For the hypergeometric function see §15.2(i). For infinite integrals of triple products of modified and unmodified Bessel functions, see Gervois and Navelet (1984, 1985a, 1985b, 1986a, 1986b). ## §10.43(v) Kontorovich–Lebedev Transform The Kontorovich–Lebedev transform of a function is defined as 10.43.30 Then provided that either of the following sets of conditions is satisfied: • (a) On the interval , is continuously differentiable and each of and is absolutely integrable. • (b) is piecewise continuous and of bounded variation on every compact interval in , and each of the following integrals • converges. For asymptotic expansions of the direct transform (10.43.30) see Wong (1981), and for asymptotic expansions of the inverse transform (10.43.31) see Naylor (1990, 1996). For collections of the Kontorovich–Lebedev transform, see Erdélyi et al. (1954b, Chapter 12), Prudnikov et al. (1986b, pp. 404–412), and Oberhettinger (1972, Chapter 5). ## §10.43(vi) Compendia For collections of integrals of the functions and , including integrals with respect to the order, see Apelblat (1983, §12), Erdélyi et al. (1953b, §§7.7.1–7.7.7 and 7.14–7.14.2), Erdélyi et al. (1954a, b), Gradshteyn and Ryzhik (2000, §§5.5, 6.5–6.7), Gröbner and Hofreiter (1950, pp. 197–203), Luke (1962), Magnus et al. (1966, §3.8), Marichev (1983, pp. 191–216), Oberhettinger (1972), Oberhettinger (1974, §§1.11 and 2.7), Oberhettinger (1990, §§1.17–1.20 and 2.17–2.20), Oberhettinger and Badii (1973, §§1.15 and 2.13), Okui (1974, 1975), Prudnikov et al. (1986b, §§1.11–1.12, 2.15–2.16, 3.2.8–3.2.10, and 3.4.1), Prudnikov et al. (1992a, §§3.15, 3.16), Prudnikov et al. (1992b, §§3.15, 3.16), Watson (1944, Chapter 13), and Wheelon (1968).	2013-05-26T08:40:08	{"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": 0.9349974393844604, "perplexity": 8223.321539476}, "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/1368706762669/warc/CC-MAIN-20130516121922-00051-ip-10-60-113-184.ec2.internal.warc.gz"}
http://www.bnl.gov/events/	#### General Information April 2014 Sunday Monday Tuesday Wednesday Thursday Friday Saturday 1 1. 11 am, Small Seminar Room, Bldg. 510 Hosted by: Hui Wang RHIC science has entered an era where the goal is to make quantitative statements about the evolution and properties of the super-hadronic matter created in high-energy heavy-ion collisions. Given the heterogenous nature of the RHIC and LHC heavy-ion data sets, the significant uncertainties to the theoretical models, and the complex intertwined dependencies between model parameters and observables, stating conclusions with meaningful uncertainties represents a major challenge. I will present results from the MADAI collaboration, where we have constructed a statistical infrastructure for addressing exactly such problems and applied it to a subset of soft observables from 100A GeV + 100A GeV Au + Au collisions. The results from this pilot project are promising and the techniques should be extendable to larger data sets and to more flexible models with greater numbers of parameters. 2. 11 am, Bldg. 463B, John Dunn Seminar Room 157 Hosted by: Robert Harrison Plasma-Material Interface (PMI) mixes materials of the two worlds, creating a dynamical surface which is one of the most challenging areas of multidisciplinary science, with many fundamental processes and synergies. We present the experimentally validated atomistic theory and computation for studying the dynamics of the creation and evolution of the PMI under irradiation by atoms and molecules at carbon, lithiated carbon and tungsten, as well as the emerging elastic and inelastic processes, in particular retention and sputtering chemistry. Recent work with lithium coatings deposited on a variety of metallic and graphitic surfaces, in a number of tokamak fusion machines around the world, has provided evidence of the sensitive dependence plasma behavior has on these ultra-thin deposited films. Our computer simulations, done in collaboration with Japanese and French scientists, and validated by in-situ experiments at Purdue University and at NSTX of PPPL have elucidated roles of lithium in carbon walls to the recycling of the plasma hydrogen. We performed quantum-classical atomistic calculations on many thousands of random trajectories to clarify the interplay of lithium and oxygen in amorphous carbon. We show that the presence of oxygen in the surface plays the key role in the increased uptake chemistry and suppression of erosion, while lithium has a decisive role in achieving high concentrations of oxygen in the upper layers of the surface upon bombardment by deuterium. D atoms preferentially bind with O and C-O when there is a comparable amount of oxygen to Li at surface. This finding explains a number of previously puzzling laboratory and reactor-based experimental results obtained over the last decade, having ramifications that go well beyond fusion. 3. 1:30 pm, Bldg. 480 Conf Rm Hosted by: Ivan Bozovic The talk will review work at the division of quantum device physics at Chalmers. Quantum, limited dimensional devices can be used to study fundamental physical effect. At Chalmers, microwave pumped SQUID (Josephson inductance) terminated transmission lines have been used to study dynamical Casimir effects, i.e., vacuum fluctuations parametrically amplified to photons at half the pumping frequency. An imaginary component to the energy gap at node directions have been detected in YBCO by a single electron transistor. YBCO nanostructures can also be used to fabricate low noise SQUIDs. One use may be to study brain rhythms. Quantum Hall resistance normals have been realized in SiC based graphene. Their resolution is of the order of one part in ten-to-the-ten, and they promise to be the resistance standards in the future. 4. 3:30 pm, Large Seminar Room, Bldg. 510 Hosted by: Rob Pisarski After reviewing the basic properties of jets produced in elementary collisions, and how these can be understood from quantum chromodynamics (QCD), I shall show how the QCD cascade is modified by the presence of a quark-gluon plasma. Coherence effects that determine the most salient features of the QCD cascade in vacuum are suppressed, and the in-medium cascade exhibit turbulent behavior. Interestingly, the same self-similar behavior that characterizes this turbulent behavior shows up in the late stage of the "bottom-up" scenario for quark-gluon plasma thermalization. 2 1. 11 am, NSLS-II, Bldg. 745 Room 156 Hosted by: Ignace Jarrige Inelastic scattering measurements performed with resonance-tuned X-rays can provide a unique window into electron behavior at a femtosecond time scale and atomic length scale. Experiments of this type have a broad range of applications, granting key insight into the energetics of complex chemical environments (e.g. charging battery electrodes) and correlated electron systems (e.g. high temperature superconductors). I will discuss current efforts to turn the phase and energy profile of scattered light into a time-resolved picture of electron dynamics in quantum materials. The talk will review how many-body systems respond when impacted by resonant X-rays, and how scattered photons provide a fingerprint of important material properties such as atomic valence and spin states. Throughout the talk, I will touch on the long term trajectory of research, and ways in which the rapid ongoing development of spectrometers and X-ray light sources is opening exploration into new realms of fundamental physics. 2. 4:45 pm, Apartment Area & Dorms 3 1. No events scheduled 4 1. 12 pm, Bldg. 744 (LOB 4) Room: 4L 156 Hosted by: Klaus Attenkofer and Sanjit Ghose 2. 12 pm, Physics, Building 510, Room 2-160 Hosted by: Amarjit Soni 5 1. No events scheduled 6 1. No events scheduled 7 1. 3:30 pm, Bldg 911B, Large Conf. Rm., Rm. A202 Hosted by: Ilan Ben-Zvi "MaRIE stands for Matter-Radiation Interactions in Extremes. As ultimately envisioned, the MaRIE facility as a whole will be capable of applying several in situ diagnostics to observe transient phenomena at high resolution, in real time. These include both proton radiography from the existing LANSCE accelerator, and X-ray and electron radiography from the MaRIE 1.0 XFEL. MaRIE 1.0 will be the world's first very-hard (40 kV) x-ray free-electron laser. Designed to operate with a beam energy of 12 GeV, the MaRIE linac will require performance currently beyond state-of-the-art in most aspects of its design: beam source, linac structures, bunch compression, bunch train, and the diagnostics required to monitor all of the above. MaRIE presents challenges not only in terms of achieving the basic performance requirements, but also to the modeling and simulation tools we use to design such a machine. This talk will review the baseline MaRIE 1.0 requirements and present the current status of the baseline accelerator design. Approaches to addressing the design and modeling challenges will be presented, along with broader-ranging potential alternatives." 8 1. 8 am, Suffolk County Community College Michael J Grant C Hosted by: Suffolk County Office of Women's Services Panel Discussion with Christina Swinson of BWIS, Q & A, light breakfast served. Equal Pay Day The Annual Equal Pay Day Event is held to bring awareness statewide about the inequality in pay between men and women. Over fifty years ago the United States Congress passed the Equal Pay Act, yet women who work full time still earn just 77 cents for every dollar earned by a man. Every year EPW chapters plan an event that brings awareness to this inequality and participate in activities that make an impact on achieving change. Examples of Equal Pay Day and local projects. 2. 11 am, CFN, Building 735, Seminar Room, 2nd fl. Hosted by: Oleg Gang Coffee and cookies at 10:45 am Center for Functional Nanomaterials Colloquium Series Professor Paul V. Braun Department of Materials Science and Engineering University of Illinois at Urbana-Champaign Soft Matter Enhanced Electrochemical Energy Storage and 3D Photonic Crystals Tuesday, April 8, 2014 11:00 a.m. Seminar Room, 2nd Fl. Over the past decade, the sophistication of self and directed-assembly approaches for functional composite structures has increased dramatically, however, application of such structures in real-world systems has remained largely elusive, in part because such structures almost always contain finite defect densities. The storing, generating and harvesting of photons and electrons presents a unique opportunity for self-assembled composite materials. These applications are not only generally much more defect tolerant than for example self-assembled computational electronics, but also for these areas to make a substantive impact on the world energy situation, they must be produced in exceptionally large volume. In my talk, I will attempt to capture the state-of-the-art in highly functional self-assembled three-dimensional composites for energy harvesting and storage illustrated with examples from both my research and other groups with a particular focus on high charge and discharge rate nanostructured electrochemical energy storage systems (batteries and supercapacitors), and photonic crystals which exhibit unprecedented control over the absorption and emission of light (lasers, LEDs, and solar cells). Host: Oleg Gang 3. 12:15 pm, Large Conference Room, Bldg. 490 Hosted by: Michael Thorn Weight Watchers "Weight Watchers" Tuesday, March 4, 2014, Large Conference Room, Bldg. 490 Hosted by: michael Thorn On Site Weight Watchers Meetings!! Getting started with Weight Watchers is now Simpler then ever with Simple Start. Come on in and learn about our straight forward do-able 2 week started plan with delicious meal ideas and a great new app to get you started losing weight and on the path to long term success. Weight Watchers today at 12:15 in the Conference Room #490. If you are not already a member check out a meeting for free and hear all about Simple Start! Take advantage of the convenience of On-Site weekly meetings every Tuesday. Time for a new beginning. 4. 3:30 pm, Large Seminar Room, Bldg. 510 Hosted by: Bill Morse We all know that High Energy Physics research in the U.S. is funded almost entirely by the federal government. Our field competes for federal dollars with colleagues as close as Nuclear Physics, and as far removed as the National Park Service or School Lunch Program. Just how does our budget get put together, and by whom? What do we do, specifically as a User community, to advocate for our research program to the people who make the funding decisions for our field? Do we have any real, positive effect? And finally, how are the answers to these questions impacted by the current P5 process? 9 1. 10 am, Recreation Hall, Bldg. 317 To join Play Group, go to: meetup.com/BNL-playgroup Tours, snacks, information and general socializing! All are welcome! 2. 10 am, Room 300, Chemistry Bldg. 555 Water oxidation to oxygen in nature's photosynthesis is the source of most of the energy we use today. It is also anticipated to be (and it has to be) the source of most of the energy we use in the future through artificial photosynthesis. For the latter, one of the main challenges is the development of efficient and robust water oxidation catalysts. In this presentation, water oxidation catalysis by ruthenium complexes with two types of tetradentate ligands (2,2'-bipyridine-6,6'-dicarboxylic acid,bda and 2,2'-bipyridine-6,6'-diphosphonic acid, bpa) will be discussed. These catalysts oxidize water through seven-coordinate intermediates but follow different mechanisms. Water oxidation catalysts of the type [Ru(bda)(L)2] (L is 4-picoline (pic), or isoquinoline (isq)), as well as their mechanism for water oxidation, have been reported by Sun and coworkers. Nevertheless, unlikely 20- and 19-electron intermediates were proposed in the catalytic cycle. Here we revisit the mechanism for water oxidation by these catalysts based on electrochemistry, X-ray crystallography and well established inorganic and organometallic chemistry principles. In addition, a comparison between the two types of complexes in solution and bound to metal-oxide electrodes will be made with respect to catalytic performance. This comparison sheds light on the mechanism by which these complexes oxidize water in a true solar cell device configuration. 3. 12 pm, Berkner Hall, Room D Monthly meeting of the Brookhaven Women in Science (BWIS) board. All BWIS members and affiliates are welcome to attend. 4. 12 pm, Berkner Hall Auditorium Pianist Di Wu, praised in the Wall Street Journal as "most mature and sensitive," who charms audiences with her "charisma, steely technique, and keen musical intelligence" (Philadelphia Inquirer) and her "fire and authority" (Washington Post), will perform at the U.S. Department of Energy's Brookhaven National Laboratory on Wednesday, April 9, at noon in Berkner Hall. Sponsored by Brookhaven Science Associates, the concert is free and open to the public. All visitors to the Laboratory age 16 and older must bring a photo I.D. 5. 2 pm, Small Seminar Room, Bldg. 510 Hosted by: Hooman Davoudiasl "I will first analytically show a simple, yet subtle "invariance" of two-body decay kinematics for the case of a massless daughter and a mother particle which is unpolarized and has a generic boost distribution in the laboratory frame. Namely, the laboratory frame energy distribution of the massless decay product has a peak, whose location is identical to the (fixed) energy of that particle in the rest frame of the corresponding mother particle. As a proof of principle of the usefulness of this observation, I will then apply it for measuring the mass of the top quark at the LHC, using simulated data (including experimental effects). Finally, I will show how it can be used to measure all the superpartner masses in a cascade decay chain of the gluino." 6. 2:30 pm, Large Conference Room, Bldg. 535 Among the future hopes for high energy nuclear physics is the construction of an Electron-Ion Collider or EIC. BNL has developed detailed plans for the RHIC machine to evolve into the EIC (locally called eRHIC) by the addition of an electron ring. For the past several years, BNL has hosted an EIC R&D program targeted at addressing the technology needs for the EIC. I will report on the so-called "Tracking Consortium" work with particular emphasis on the compact RICH. The compact RICH uses CsI-coated Gas-Electron-Multipliers (GEMs) along with a specialized thin-coating mirror for good reflectivity into the deep UV. Results from test beam will be presented along with thoughts for further work. 10 1. 12 pm, Berkner Hall, Room B 2. 4 pm, Bldg 911B, Large Conf. Rm., Rm. A202 Hosted by: V. Litvinenko "eRHIC is an ongoing vibrant project under a full blown study. In this presentation, the author will show studies of several beam dynamic issues - Dynamic aperture, FEL amplifier in CeC and possible CSR issue in arcs and chicanes. The author also presents possible solutions/remedies for those issues. 3. 6:30 pm, Berkner Hall, Room B 11 1. 11 am, Seminar Room (201), Bldg. 734 Hosted by: Antonio Checco and Ernie Lewis Interfacial fluid mechanics, such as the dynamics of drops and bubbles, are important to problems in a variety of fields. For example, superhydrophobic surfaces can repel droplets, and bursting bubbles can disperse marine aerosols into the atmopshere. In this talk, I focus on two distinct phenomena: the reduction in contact time of a bouncing drop and the drainage of a viscous bubble prior to rupture. I will show both high-speed and time-lapse movies to highlight the phenomena, and I will discuss how experiments and mathematical modeling have given us insight into the underlying physics. 2. 12 pm, Bldg. 744 (LOB 4) Room: 4L 156 Hosted by: Klaus Attenkofer and Sanjit Ghose 12 1. No events scheduled 13 1. No events scheduled 14 1. 10 am, Research Library, Bldg. 477 2. 11 am, Bldg. 734, ISB Conf. Rm. 201 (upstairs) Hosted by: Jonathan Rameau In all known types of high-Tc superconductors - cuprate, Fe-based, and heavy fermion compounds - superconductivity emerges from the suppression of long range antiferromagnetic order. However, while superconductivity emerges from a Mott insulating state in the cuprates, the parent compounds of the Fe-based superconductors are metallic. Could a higher Tc be realized in compounds similar to the Fe-based superconductors if we start with a more correlated parent compound? We have synthesized single crystals of LaMnPO, which is isostructural to LaFeAsO, by the ux growth method. We find LaMnPO is an antiferromagnetic insulator that orders at TN = 375 K with a moment μ= 3.3 μB as T right arrow 0. I will present a combination of inelastic neutron scattering and optical transmission measurements and to show that antiferromagnetic exchange plays only a small role in formation of the charge gap. Instead, DFT+DMFT electronic structure calculations find Hunds coupling, thought to be responsible for correlations in the Fe-based compounds, is crucial for the formation of a charge gap in LaMnPO. Having identified LaMnPO as a more correlated version of the Fe-based superconductors, I will present our pressure and doping studies of LaMnPO. We find pressure drives LaMnPO toward a metallic and paramagnetic phase, but do not observe superconductivity. Doping studies are successful in reducing the activation gap in LaMnPO but the charge gap remains nearly unchanged. 3. 2:30 pm, Large Conference Room, Bldg. 535 We propose to place a stack of ultra thin transmission dynodes on top of a pixel chip, in vacuum. A single electron arriving at the first dynode will cause an electron avalanche on the pixel input pad. Due to the small source capacitance, a gain of 30 k of the dynode stack is sufficient to create a digital signal. The rise time of this signal could be ~ 2 ps. This single-electron sensitive device has therefore an excellent time resolution, and, due to the granularity of the pixel chip, a good 2D position resolution. When capped with a classical window + photocathode, a new photomultiplier is created. This Timed Photon Counter 'Tipsy' is single soft photon sensitive, has 2D position resolution defined by the granularity of the pixel chip, and a potential time resolution of ~ 2 ps per photon. Thanks to the granularity of the pixel chip, a high rate of multiple photon events results in an acceptable pixel occupancy. When capped with an electron emission membrane 'e-brane', the electron detector turns into Trixy: a tracker for charged particles (MIPs). The essential property of this membrane is the emission, with a high probability, of at least one electron after the passage of a MIP, at the crossing point of the MIPs' track and the membrane. We report on the progress in the development of the transmission dynode, and on theoretical aspects and simulations associated with the emission of (secondary) electrons. 15 1. 10 am, Berkner Hall, Room C Hosted by: Research Library introduction and tips & tricks for using CRC series including structure searching, draw & combine structures, use interactive tables, sort & filter search results. Learn how to keep your research organized with personalized bookshelves, export to citation managers and track your research with saved search results and histories http://www.crcnetbase.com/ 2. 12 pm, Berkner Hall, Room B Topics to be Covered: Warning Signs of Financial; Physical or Mental Elder Abuse; Importance of a Power of Attorney & Health Care Proxy; How you should title bank accounts for the best protection Joint Account, Power of Attorney,Payable on death designations; Legal Recourse: Guardianship and Criminal Proceedings 3. 1 pm, ISB Bldg. 734, Conf. Rm. 201 (upstairs) Hosted by: Genda Gu In this talk I will outline our groups efforts to generate and understand the high temperature superconducting proximity effect. Our focus is on interfaces between high Tc cuprates and topological insulators, in the hopes of observing and manipulating Majorana Fermions. I will also discuss the interest in these particles from both a fundamental and applied point of view. This has led us to develop the Mechanical Bonding processes that resulted in the first observation of high temperature superconductivity in Bi2Se3, Bi2Te3 and Graphite. I will also discuss recent efforts on the proximity effect in Bi2Te2Se where the fermi energy is in the gap. Interestingly in Bi2Te2Se/Bi2212 junctions we have observed a new zero bias conductance peak that does not couple to the orbital component, but only the spin. 4. 2 pm, Interdisciplinary Science Bldg. 734 (2nd floor) 5. 3:30 pm, Large Seminar Room, Bldg. 510 Hosted by: Peter Petreczky Despite the complexities of the nucleonic interactions in atomic nuclei, nuclei display remarkably simple patterns, and regularities as a function of neutron and proton number. Many of these patterns are associated with the emergence of collective behavior. Such behavior is largely the result of a competition between pairing interactions between like nucleons and proton-neutron (p-n) interactions. The Colloquium will survey the empirical behavior of nuclei and present ways to experimentally extract the strength of p-n interactions. The pivotal role of the latter in determining the former will then be discussed in terms of the correlations of p-n interaction strengths with the onset of collectivity and a newly recognized parallelism in the filling of proton and neutron orbits. 6. 5:30 pm, ASAP Lounge (Bldg 462) corner of Bell Av & Cen Hosted by: Association of Students and Postdocs Come and meet your peers from BNL and Stony Brook. Enjoy good food and board games. Sandwiches, snacks, and drinks will be available. 16 1. 10 am, Berkner Hall, Room B 2. 11 am, John Dunn Seminar Room, Bldg. 463 Hosted by: Reinhold Mann Understanding extreme events, such as hurricanes or forest fires, is of paramount importance because of their adverse impacts on human beings. Such events often propagate in space and time. Predicting��"even a few days in advance��"what locations will get affected by the event tracks and/or at what seasonal intensity these events are anticipated at those regions could benefit our society in many ways. Arguably, simulations from first principles, where underlying physics-based models are described by a system of equations, provide least reliable predictions for variables characterizing the dynamics of these extreme events. Data-driven model building has been recently emerging as a complementary approach that could learn the relationships between historically observed or simulated multiple, spatio-temporal ancillary variables and the dynamic behavior of extreme events of interest. While promising, the methodology for predictive learning from such complex data is still in its infancy. I will present a suit of dynamic networks-based methodologies for in-advance prediction of the dynamic tracks of emerging extreme events, for quantifying seasonal hurricane activity in North America, and for assessing rainfall activity in the Western Africa. These methods offer a superior predictive skill compared to any other methodology currently available in literature. In addition, various strategies for dealing with large-scale graphs will be presented. 3. 12 pm, Large Seminar Room, Bldg. 510 Hosted by: Research Library APS Publications - What's New with the Physical Review - Presented by Editors from the American Physical Society: Gene Sprouse, Editor in Chief; Daniel Kulp, Editorial Director; Ling Miao, Managing Editor, Physical Review X; and Julie Kim-Zajonz, Managing Editor, Physical Review Applied. A light lunch will be served. 4. 1:30 pm, Small Seminar Room, Bldg. 510 Hosted by: Ian Lewis 5. 2 pm, Physics Library, Bldg. 510 (2nd floor) 6. 3 pm, Large Seminar Room, Bldg. 510 Hosted by: Anze Slosar I will review the BICEP results and summarize potential concerns one might have about their validity. I will then discuss the implications of large tensor modes for Early Universe phenomenology. 7. 4 pm, Berkner Hall Auditorium Hosted by: Allen Orville 17 1. 10 am, Small Seminar Room, Bldg. 510 Hosted by: Research Library Ruth Wolfish from IEEE will share a sneak peek of what's new and what's coming this year. Her presentation will include IEEE content and features coming soon, 2014 IEEE journal titles and details, collaborations with other publishers, the new image applications, patent citations, and new library resources. For more information, please visit http://ieeexplore.ieee.org/Xplore/home.jsp 2. 11 am, Building 745, Conference Room 156 Hosted by: David P. Siddons In this seminar we will start with a brief overview of 3 X-ray lithography beamlines and the microfabrication facility at CAMD. This will follow with the examples showing the research work involving X-ray LIGA (German acronym for Lithography-Electroplating-Molding) based fabrication of high aspect ratio (HAR) microstructures for micro-electro-mechanical systems (MEMS), BioMEMS and/or microfluidic applications. These will include fabrication of X-ray mask using different type of substrates (carbon, silicon nitride & beryllium), precision alignment of pre-patterned substrate to mask & patterning of positive (PMMA) and negative resist (SU-8/ MRX/ SUEX), electroplating of patterned structures and molding using the electroplated mold insert. Here, we will also discuss the fabrication of multi-level structures using both positive and negative resist on silicon, polymer or printed circuit board substrates. Additionally, in brief we will discuss micromilling to produce rapidly high quality mold inserts for molding microfluidic chips for biomedical, biochemical as well as biological applications; and nanostructured &/or biocompatible thin films (Parylene & Diamond-like Carbon) deposition and characterization. 3. 12:30 pm, Physics, Bldg. 510, Room 2-160 Hosted by: Daniel Pitonyak I will discuss how multi-particle flow cumulants can help to distinguish between various models of p+A interactions. 4. 4 pm, Bldg. 911B, Large Conf. Rm., Rm. A202 "In a muon accelerator complex, a target is bombarded by a multi-MW proton beam to produce pions. The pion beam is captured by a high field tapered solenoid and later decay into muons. The captured muon beam has a large 6D emittance which requires reduction in order to fit within the muon accelerator acceptance and provide the required luminosity during collision in the collider ring. An optimization study of the muon beam production and capture will be presented including the impact of the capture solenoid field on the transverse and longitudinal phase-space of the muon beam. Additionally a design study of the muon collider final ionization cooling channel utilizing high field solenoids will be discussed." 18 1. 4 am, Bldg 911B, Large Conf. Rm., Rm. A202 Hosted by: V. Litvinenko "When a low energy electron beam crosses from top of a storage ring electron bunch, its coulomb force will kick a short slice from the core of the storage ring electron bunch. The separated slices, when passing through an undulator, will radiate ultra-short x-ray pulses at about 160fs. In the presentation, I will talk about the new approach to generate ultra-short x-ray pulses of the order of 100fs pulse length by electron beam slicing, and I will discuss our from start to end design of the electron beam slicing method in NSLS-II which includes the design of low energy bunch compressor, the design of the interaction of the linac bunch and the ring bunch and the separation design of the synchrotron radiation of the core and satellite." 2. 10 am, Research Library, Bldg. 477 3. 12 pm, Berkner Hall, Room D Hosted by: BERA AAAG 4. 2 pm, Small Seminar Room, Bldg. 510 Hosted by: Bjoern Schenke We introduce a "renormalized entanglement entropy" which is intrinsically UV finite and is most sensitive to the degrees of freedom at the scale of the size R of the entangled region. We illustrated the power of this construction by showing that the qualitative behavior of the entanglement entropy for a non-Fermi liquid can be obtained by simple dimensional analysis. The functional dependence of the "renormalized entanglement entropy" on R can be interpreted as describing the renormalization group flow of the entanglement entropy with distance scale. The corresponding quantity for a spherical region in the vacuum, has some particularly interesting properties. For example in three (spacetime) dimensions, it is always monotonic along RG flows, and provides a measure of the number of degrees of freedom of a system at scale R. 19 1. No events scheduled 20 1. No events scheduled 21 1. No events scheduled 22 1. APR 22 Tuesday 12 pm, Berkner Hall Lobby Tuesday, April 22, 2014, 12:00 pm 2. APR 22 Tuesday 3:30 pm, Large Seminar Room, Bldg. 510 Tuesday, April 22, 2014, 3:30 pm Hosted by: Peter Petreczky Hadron physics is unique at the forefront of science in tackling a problem whose fundamental degrees of freedom have never been directly observed. This presentation will describe some of the opportunities and challenges presented by the next decade — with an upgrade at Jefferson Lab, fixed target experiments at FermiLab and worldwide discussions about an electron ion collider. 3. APR 22 Tuesday 5 pm, Recreation Hall, Bldg. 317 Tuesday, April 22, 2014, 5:00 pm Hosted by: BERA African American Affinity Group Second Annual AAAG STEM Scholarship Reception. Five local high school students who plan to pursue STEM careers in college will be honored. Refreshments will be served. RSVP to Patrice Greenwood at [email protected]. 23 1. APR 23 Wednesday 10 am, Recreation Hall, Bldg. 317 Wednesday, April 23, 2014, 10:00 am Play group will sometimes schedule different types of play dates at various venues. To see the schedule and join, please use https://www.facebook.com/#!/groups/1438521623060022/ and open Brookhaven Lab Hospitality & Play Group and sign in. You do need an established Facebook account in order to do so. 2. APR 23 Wednesday 12 pm, Berkner Hall, Room B Wednesday, April 23, 2014, 12:00 pm Thinking of Buying or Selling? Join us for another workshop in the "Fiscally Fit" seminar series that focuses on buying, selling and financing real estate. Topics covered include: • Where to start - " A winning strategy for renters, buyers and owners. • How to reduce stress while saving time and money. • Qualifying - " How to get approval now. • Income tax savings/benefits. • R.I.C.E. - " Reserve, Income, Credit & Equity. • Understanding the closing process. Today's Real Estate Market - " Where the high and low-markets are headed and what this means for buyers, sellers and owners. 3. APR 23 Wednesday 2 pm, Small Seminar Room, Bldg. 510 Wednesday, April 23, 2014, 2:00 pm Hosted by: Taichi Kawanai 24 1. APR 24 Thursday 12:30 pm, Physics, Building 510, Room 2-160 Thursday, April 24, 2014, 12:30 pm Hosted by: Daniel Pitonyak I will show that the acoustic scaling patterns of anisotropic flow for different event shapes at a fixed collision centrality (shape-engineered events), provide robust constraints for the event-by-event fluctuations in the initial-state density distribution from ultrarelativistic heavy ion collisions. The empirical scaling parameters also provide a dual-path method for studying the temperature and baryon chemical potential (T, \mu_B) dependence of the specific shear viscosity (eta/s) of the quark-gluon plasma (QGP) produced in these collisions. An initial calibration of the scaling parameters via detailed viscous hydrodynamical model calculations, gives robust eta/s estimates for the plasma produced in Au+Au and Pb+Pb collisions at RHIC (Root_s =0.2 TeV) and the LHC (Root_s = 2.76 TeV) (respectively) which are insensitive to the initial-state geometry models considered. 2. APR 24 Thursday 3 pm, Small Seminar Room, Bldg. 510 Thursday, April 24, 2014, 3:00 pm Hosted by: Ketevi A. Assamagan In this talk, I will highlight some the latest searches for SUSY performed with the CMS detector at the LHC using the 8TeV dataset up to 20/fb. The results cover a broad range of signatures and final states, and probe a large range of the SUSY parameter space. The searches set stringent limits on the production of 1st and 2nd generation squarks and gluinos, 3rd generation squarks, EWK gauginos, sleptons, and include searches for R-parity violating SUSY. 3. APR 24 Thursday 4 pm, Large Seminar Room, Bldg. 510 Thursday, April 24, 2014, 4:00 pm Hosted by: Vivian Stojanoff Human epithelial cancers remain incurable, putting researchers on a constant quest to develop models and methods that will lead toward a deeper understanding of the disease. Bugallo, Electrical and Computer Engineering professor at Stony Brook University believes that it is possible to provide information on the evolution of cancer stem cells and tumors that are highly drug-resistant and do not respond to standard anti-cancer drugs through the development of models and methods that follow signal processing methods. These methods could provide fast, scalable, and expandable information filling in missing gaps, further enabling the fight against cancer 25 1. APR 25 Friday 11 am, Small Seminar Room, Bldg. 510 Friday, April 25, 2014, 11:00 am Hosted by: Ketevi Assamagan The measurement of the shape of the Z boson rapidity distribution for pp Z/�'*  e+e- + X events at a center-of-mass energy of 1.96 TeV is presented in this seminar. Data collected with the D0 detector during the whole RunII period of the Fermilab Tevatron pp collider are used. By using these data with an integrated luminosity of up to 9.86 fb-1, the uncertainties on the rapidity distribution in the forward region are significantly reduced compared with previous measurements. The measurement is made for events with electron-positron mass between 66 and 111 GeV. Predictions of Next-to-Leading-Order QCD theory with CTEQ and MSTW parton distribution functions are found to agree well with the data over the full rapidity range. 2. APR 25 Friday 2 pm, Small Seminar Room, Bldg. 510 Friday, April 25, 2014, 2:00 pm Hosted by: Bjoern Schenke At the highest possible transverse momenta at the LHC, quarkonia production should be dominated by fragmentation. I review recent developments in the calculation of quarkonium fragmentation functions using Non-Relativistic QCD (NRQCD) and SCET, including both single and double parton fragmentation functions. I then describe the recently developed fragmenting jet functions, which are applicable for calculating the cross section for an identified hadron produced within a jet. For a jet containing a quarkonium, these functions are calculable in terms of NRQCD production matrix elements. We show that measurement of the momentum distribution of quarkonium within a jet provides a novel means of extracting these matrix elements, thereby providing an interesting new test of NRQCD. 26 1. No events scheduled 27 1. No events scheduled 28 1. No events scheduled 29 1. APR 29 Tuesday 11 am, Small Seminar Room, Bldg. 510 Tuesday, April 29, 2014, 11:00 am Hosted by: Peter Steinberg The suppression of high transverse momentum charged particles is an important signature of the strongly interacting medium produced in central PbPb collisions. Both partonic energy loss and the initial state of the collision system may contribute to the nuclear modification factor. To further understand and distinguish these effects, the charged particle production in pPb collisions at a center-of-mass energy of 5.02 TeV per nucleon pair has been measured with the CMS detector. This measurement covers a broad transverse momentum range of 0.4 to 100 GeV/c, and several pseudorapidity ranges. The nuclear modification factor is determined at midrapidity by normalizing the measured pPb spectrum to an interpolated pp reference spectrum constructed from previous measurements, and is significantly enhanced for particles with a transverse momentum above 30 GeV/c. The asymmetry of the collision system provides an opportunity to study nuclear effects on the parton distribution function by considering the production of charged particles in different pseudorapdity ranges. To quantitatively measure these effects, the ratios of the charged particle yields between corresponding positive and negative pseudorapidity ranges have been determined. The evolution of these ratios with pseudorapidity will be discussed. 2. APR 29 Tuesday 3:30 pm, Large Seminar Room, Bldg. 510 Tuesday, April 29, 2014, 3:30 pm Hosted by: Rob Pisarski Advances at the intersection of quantum optics, nanoscience, gravitational wave interferometry and microwave technology are currently allowing experimentalists to extend the reach of quantum mechanics to large mechanical objects. As an emerging frontier in physics, macroscopic quantum mechanics is expected to yield fundamental insights as well as novel technologies. This talk will be centered around experiments on cryogenic electromechanical systems, optical resonator-cooled mechanics and levitated microparticles. Recent theoretical work on optomechanics in our group at RIT will also be discussed. 30 1. APR 30 Wednesday 10 am, Room 300, Chemistry Bldg. 555 Wednesday, April 30, 2014, 10:00 am Hosted by: James Muckerman Modern capabilities in computations and simulations in multi-scale approaches allow us to address successfully many of the complex chemistry and physics fundamentals of sun-to-fuel and electricity-to-fuel energy conversions. In this presentation we will highlight recent studies dealing with photo-electrodes, proton membranes, and molecular electro-catalysis, relevant to new energy technologies. In the context of photo conversions, efficient e/h polaron transport in single and multiphase oxide electrodes (such as TiO2 or Fe2O3) is essential. We successfully characterized the single-phase e/h transport properties of these materials using density functional theory DFT combined with Marcus/Holstein theory. Challenges remain for multi-phase materials. Our calculations led us also to formulate a universal role of excess electrons on the surface chemistry of oxides. In the context of proton membranes for fuel cells, understanding the factors affecting proton transport and molecular selectivity in polymeric and ionic liquid membranes is critical to the design of efficient low cost stable membranes. Ab initio and classical molecular dynamics MD combined with percolation theory provided a means to characterize successfully pore structure and proton transport properties. Water percolation is a key to efficient proton transport. Most recently, our focus has been on molecular electro-catalysis. DFT-based quantum QM and mixed QM/MM approaches coupled with accelerated MD simulations for free energy calculation, and micro-kinetic modeling have been combined to predict accurately the catalytic performance of novel proton relay-based molecular catalysts for H2 oxidation and evolution. These efforts have reached what is perhaps an unprecedented level of success that put us within grasp of design by computer. These studies underscore the power of computations and the impact of high performance computing in characterizing the fundamental chemistry in such complex mole 2. APR 30 Wednesday 10 am, Recreation Hall, Bldg. 317 Wednesday, April 30, 2014, 10:00 am Play group will sometimes schedule different types of play dates at various venues. To see the schedule and join, please use https://www.facebook.com/#!/groups/1438521623060022/ and open Brookhaven Lab Hospitality & Play Group and sign in. You do need an established Facebook account in order to do so. 3. APR 30 Wednesday 4 pm, Berkner Hall Auditorium Wednesday, April 30, 2014, 4:00 pm Hosted by: Peter Wanderer Synthetic biology is bringing together engineers, physicists and biologists to model, design and construct biological circuits out of proteins, genes and other bits of DNA, and to use these circuits to rewire and reprogram organisms. These re-engineered organisms are going to change our lives in the coming years, leading to cheaper drugs, rapid diagnostic tests, and targeted therapies to attack "superbugs". In this talk, we highlight recent efforts to create synthetic gene networks and programmable cells, and discuss a variety of synthetic biology applications in biocomputing, biotechnology and biomedicine. 1. APR 22 Tuesday Employee Lunch-time Tour "Tour NSERC" 12 pm, Berkner Hall Lobby Tuesday, April 22, 2014, 12:00 pm 2. APR 22 Tuesday Physics Colloquium "Prospects for the physics of cold, sparse hadrons" Presented by Craig Roberts, ANL 3:30 pm, Large Seminar Room, Bldg. 510 Tuesday, April 22, 2014, 3:30 pm Hosted by: Peter Petreczky Hadron physics is unique at the forefront of science in tackling a problem whose fundamental degrees of freedom have never been directly observed. This presentation will describe some of the opportunities and challenges presented by the next decade — with an upgrade at Jefferson Lab, fixed target experiments at FermiLab and worldwide discussions about an electron ion collider. 3. APR 22 Tuesday AAAG Scholarship Reception "2nd Annual AAAG STEM Scholarship Reception" 5 pm, Recreation Hall, Bldg. 317 Tuesday, April 22, 2014, 5:00 pm Hosted by: BERA African American Affinity Group Second Annual AAAG STEM Scholarship Reception. Five local high school students who plan to pursue STEM careers in college will be honored. Refreshments will be served. RSVP to Patrice Greenwood at [email protected]. 4. APR 23 Wednesday Hospitality Coffee & Playgroup Event "Hospitality Coffee & Play Group (10a-noon)" 10 am, Recreation Hall, Bldg. 317 Wednesday, April 23, 2014, 10:00 am Play group will sometimes schedule different types of play dates at various venues. To see the schedule and join, please use https://www.facebook.com/#!/groups/1438521623060022/ and open Brookhaven Lab Hospitality & Play Group and sign in. You do need an established Facebook account in order to do so. 5. APR 23 Wednesday Home Ownership & Financing "Presented by The Foundation for Personal Financial Education" Joe Jannace, Member, The Foundation for Personal Financial Education 12 pm, Berkner Hall, Room B Wednesday, April 23, 2014, 12:00 pm Thinking of Buying or Selling? Join us for another workshop in the "Fiscally Fit" seminar series that focuses on buying, selling and financing real estate. Topics covered include: • Where to start - " A winning strategy for renters, buyers and owners. • How to reduce stress while saving time and money. • Qualifying - " How to get approval now. • Income tax savings/benefits. • R.I.C.E. - " Reserve, Income, Credit & Equity. • Understanding the closing process. Today's Real Estate Market - " Where the high and low-markets are headed and what this means for buyers, sellers and owners. 6. APR 23 Wednesday High-Energy Physics & RIKEN Theory Seminar "Signal/noise enhancement strategies for stochastically estimated correlation functions" Presented by Michael G. Endres, Massachusetts Institute of Technology 2 pm, Small Seminar Room, Bldg. 510 Wednesday, April 23, 2014, 2:00 pm Hosted by: Taichi Kawanai 7. APR 24 Thursday RIKEN/BNL Lunch Time Talk "Acoustic scaling of anisotropic flow in shape-engineered events: implications for extraction of η/s(μB,T) of the QGP" Presented by Roy Lacey, Stony Brook University 12:30 pm, Physics, Building 510, Room 2-160 Thursday, April 24, 2014, 12:30 pm Hosted by: Daniel Pitonyak I will show that the acoustic scaling patterns of anisotropic flow for different event shapes at a fixed collision centrality (shape-engineered events), provide robust constraints for the event-by-event fluctuations in the initial-state density distribution from ultrarelativistic heavy ion collisions. The empirical scaling parameters also provide a dual-path method for studying the temperature and baryon chemical potential (T, \mu_B) dependence of the specific shear viscosity (eta/s) of the quark-gluon plasma (QGP) produced in these collisions. An initial calibration of the scaling parameters via detailed viscous hydrodynamical model calculations, gives robust eta/s estimates for the plasma produced in Au+Au and Pb+Pb collisions at RHIC (Root_s =0.2 TeV) and the LHC (Root_s = 2.76 TeV) (respectively) which are insensitive to the initial-state geometry models considered. 8. APR 24 Thursday Particle Physics Seminar "Latest results on SUSY searches from CMS" Presented by Eva Halkiadakis, Rutgers University 3 pm, Small Seminar Room, Bldg. 510 Thursday, April 24, 2014, 3:00 pm Hosted by: Ketevi A. Assamagan In this talk, I will highlight some the latest searches for SUSY performed with the CMS detector at the LHC using the 8TeV dataset up to 20/fb. The results cover a broad range of signatures and final states, and probe a large range of the SUSY parameter space. The searches set stringent limits on the production of 1st and 2nd generation squarks and gluinos, 3rd generation squarks, EWK gauginos, sleptons, and include searches for R-parity violating SUSY. 9. APR 24 Thursday Brookhaven Women In Science (BWIS) Event Monica F. Bugallo 4 pm, Large Seminar Room, Bldg. 510 Thursday, April 24, 2014, 4:00 pm Hosted by: Vivian Stojanoff Human epithelial cancers remain incurable, putting researchers on a constant quest to develop models and methods that will lead toward a deeper understanding of the disease. Bugallo, Electrical and Computer Engineering professor at Stony Brook University believes that it is possible to provide information on the evolution of cancer stem cells and tumors that are highly drug-resistant and do not respond to standard anti-cancer drugs through the development of models and methods that follow signal processing methods. These methods could provide fast, scalable, and expandable information filling in missing gaps, further enabling the fight against cancer 10. APR 25 Friday Particle Physics Seminar "Measurement of the shape of the boson rapidity distribution for pp Z/�'*  e+e- + X events produced at √s = 1.96 TeV" Presented by Pengfei Ding, The University of Manchester, UK 11 am, Small Seminar Room, Bldg. 510 Friday, April 25, 2014, 11:00 am Hosted by: Ketevi Assamagan The measurement of the shape of the Z boson rapidity distribution for pp Z/�'*  e+e- + X events at a center-of-mass energy of 1.96 TeV is presented in this seminar. Data collected with the D0 detector during the whole RunII period of the Fermilab Tevatron pp collider are used. By using these data with an integrated luminosity of up to 9.86 fb-1, the uncertainties on the rapidity distribution in the forward region are significantly reduced compared with previous measurements. The measurement is made for events with electron-positron mass between 66 and 111 GeV. Predictions of Next-to-Leading-Order QCD theory with CTEQ and MSTW parton distribution functions are found to agree well with the data over the full rapidity range. 11. APR 25 Friday Nuclear Physics & RIKEN Theory Seminar "Fragmentation and Fragmenting Jet functions in Quarkonium Production" Presented by Thomas Mehen, Duke University 2 pm, Small Seminar Room, Bldg. 510 Friday, April 25, 2014, 2:00 pm Hosted by: Bjoern Schenke At the highest possible transverse momenta at the LHC, quarkonia production should be dominated by fragmentation. I review recent developments in the calculation of quarkonium fragmentation functions using Non-Relativistic QCD (NRQCD) and SCET, including both single and double parton fragmentation functions. I then describe the recently developed fragmenting jet functions, which are applicable for calculating the cross section for an identified hadron produced within a jet. For a jet containing a quarkonium, these functions are calculable in terms of NRQCD production matrix elements. We show that measurement of the momentum distribution of quarkonium within a jet provides a novel means of extracting these matrix elements, thereby providing an interesting new test of NRQCD. 12. APR 29 Tuesday Nuclear Physics Seminar "Charged particle production in pPb collisions measured with CMS" Presented by Eric Appelt, Vanderbilt University 11 am, Small Seminar Room, Bldg. 510 Tuesday, April 29, 2014, 11:00 am Hosted by: Peter Steinberg The suppression of high transverse momentum charged particles is an important signature of the strongly interacting medium produced in central PbPb collisions. Both partonic energy loss and the initial state of the collision system may contribute to the nuclear modification factor. To further understand and distinguish these effects, the charged particle production in pPb collisions at a center-of-mass energy of 5.02 TeV per nucleon pair has been measured with the CMS detector. This measurement covers a broad transverse momentum range of 0.4 to 100 GeV/c, and several pseudorapidity ranges. The nuclear modification factor is determined at midrapidity by normalizing the measured pPb spectrum to an interpolated pp reference spectrum constructed from previous measurements, and is significantly enhanced for particles with a transverse momentum above 30 GeV/c. The asymmetry of the collision system provides an opportunity to study nuclear effects on the parton distribution function by considering the production of charged particles in different pseudorapdity ranges. To quantitatively measure these effects, the ratios of the charged particle yields between corresponding positive and negative pseudorapidity ranges have been determined. The evolution of these ratios with pseudorapidity will be discussed. 13. APR 29 Tuesday Physics Colloquium "Redrawing the boundary between classical and quantum mechanics" Presented by Mishkatul Bhattacharya, Rochester Institute of Technology 3:30 pm, Large Seminar Room, Bldg. 510 Tuesday, April 29, 2014, 3:30 pm Hosted by: Rob Pisarski Advances at the intersection of quantum optics, nanoscience, gravitational wave interferometry and microwave technology are currently allowing experimentalists to extend the reach of quantum mechanics to large mechanical objects. As an emerging frontier in physics, macroscopic quantum mechanics is expected to yield fundamental insights as well as novel technologies. This talk will be centered around experiments on cryogenic electromechanical systems, optical resonator-cooled mechanics and levitated microparticles. Recent theoretical work on optomechanics in our group at RIT will also be discussed. 14. APR 30 Wednesday Chemistry Department Seminar "The Power of Computing to Elaborate Fundamentals in New Energy Technologies" Presented by Michel Dupuis, Pacific Northwest National Laboratory 10 am, Room 300, Chemistry Bldg. 555 Wednesday, April 30, 2014, 10:00 am Hosted by: James Muckerman Modern capabilities in computations and simulations in multi-scale approaches allow us to address successfully many of the complex chemistry and physics fundamentals of sun-to-fuel and electricity-to-fuel energy conversions. In this presentation we will highlight recent studies dealing with photo-electrodes, proton membranes, and molecular electro-catalysis, relevant to new energy technologies. In the context of photo conversions, efficient e/h polaron transport in single and multiphase oxide electrodes (such as TiO2 or Fe2O3) is essential. We successfully characterized the single-phase e/h transport properties of these materials using density functional theory DFT combined with Marcus/Holstein theory. Challenges remain for multi-phase materials. Our calculations led us also to formulate a universal role of excess electrons on the surface chemistry of oxides. In the context of proton membranes for fuel cells, understanding the factors affecting proton transport and molecular selectivity in polymeric and ionic liquid membranes is critical to the design of efficient low cost stable membranes. Ab initio and classical molecular dynamics MD combined with percolation theory provided a means to characterize successfully pore structure and proton transport properties. Water percolation is a key to efficient proton transport. Most recently, our focus has been on molecular electro-catalysis. DFT-based quantum QM and mixed QM/MM approaches coupled with accelerated MD simulations for free energy calculation, and micro-kinetic modeling have been combined to predict accurately the catalytic performance of novel proton relay-based molecular catalysts for H2 oxidation and evolution. These efforts have reached what is perhaps an unprecedented level of success that put us within grasp of design by computer. These studies underscore the power of computations and the impact of high performance computing in characterizing the fundamental chemistry in such complex mole 15. APR 30 Wednesday Hospitality Coffee & Playgroup Event "Hospitality Coffee & Play Group (10am-noon)" 10 am, Recreation Hall, Bldg. 317 Wednesday, April 30, 2014, 10:00 am Play group will sometimes schedule different types of play dates at various venues. To see the schedule and join, please use https://www.facebook.com/#!/groups/1438521623060022/ and open Brookhaven Lab Hospitality & Play Group and sign in. You do need an established Facebook account in order to do so. 16. APR 30 Wednesday BSA Distinguished Lecture "Life Redesigned: The Emergence of Synthetic Biology" Presented by Professor James Collins, Howard Hughest Medical Institute, Boston University, Harvard University 4 pm, Berkner Hall Auditorium Wednesday, April 30, 2014, 4:00 pm Hosted by: Peter Wanderer Synthetic biology is bringing together engineers, physicists and biologists to model, design and construct biological circuits out of proteins, genes and other bits of DNA, and to use these circuits to rewire and reprogram organisms. These re-engineered organisms are going to change our lives in the coming years, leading to cheaper drugs, rapid diagnostic tests, and targeted therapies to attack "superbugs". In this talk, we highlight recent efforts to create synthetic gene networks and programmable cells, and discuss a variety of synthetic biology applications in biocomputing, biotechnology and biomedicine. 17. MAY 1 Thursday Particle Physics Seminar "Probing Light WIMPs with SuperCDMS" Presented by Adam Anderson, Massachusetts Institute of Technology 3 pm, Small Seminar Room, Bldg. 510 Thursday, May 1, 2014, 3:00 pm Hosted by: Elizabeth Worcester The SuperCDMS experiment at the Soudan Underground Laboratory is designed to detect dark matter directly by its interaction with nuclei in cryogenic germanium detectors. The improved detectors measure particle interactions using ionization and athermal phonon signals, whose topology allows for powerful rejection of radioactive backgrounds. In this talk, I will review recent SuperCDMS results focused on light WIMPs, including an analysis of 577 kg-d of low-energy data, and an analysis of specialized high-voltage data (CDMSlite). I will also discuss plans for a larger 100 kg germanium and silicon array planned for installation at SNOLAB. 18. MAY 1 Thursday Defensive Driving, Part 1 "Defensive Driving, Part 1" Edward Sierra, BNL 6 pm, Brookhaven Center, South Room Thursday, May 1, 2014, 6:00 pm 19. MAY 2 Friday New Employee Breakfast "New Employee Breakfast" 8:15 am, Brookhaven Center Friday, May 2, 2014, 8:15 am Hosted by: Robyn McKay New Employee breakfast for employees hired between 11/1/13 and 3/31/14. 20. MAY 2 Friday Particle Physics Seminar "Exploring three-flavor neutrino oscillations with MINOS" Presented by Joao Coelho, Tufts University 11 am, Small Seminar Room, Bldg. 510 Friday, May 2, 2014, 11:00 am Hosted by: Elizabeth Worcester Since the discovery of neutrino oscillations and through the combined efforts of many experiments we now know all of the neutrino mass splittings and mixing angles with reasonable precision. The remaining unknown quantity is perhaps the most relevant piece of the puzzle: the CP violating phase $\delta$. While a two-flavor approximation is usually applicable in measurements of mixing angles and mass splittings, CP violation is only present in a complete three-flavor description of neutrino oscillations. Additionally, two other discrete symmetries are broken by the inclusion of a third neutrino flavor: the mass ordering and the mixing angle octant. The determination of these extra discrete parameters is paramount to resolving degeneracies and enabling the precise measurement of $\delta$. In this seminar the latest oscillation results from the MINOS long-baseline neutrino experiment will be presented. The analysis performs a fit to three-flavor neutrino oscillations including the full data set of beam and atmospheric neutrinos and antineutrinos. It is the first combined analysis of $\nu_\mu$ disappearance and $nu_e$ appearance data by a long-baseline neutrino experiment. 21. MAY 2 Friday Nuclear Physics & RIKEN Theory Seminar "Aspects of functional renormalisation" Presented by Daniel Litim, University of Sussex 2 pm, Small Seminar Room, Bldg. 510 Friday, May 2, 2014, 2:00 pm Hosted by: Bjoern Schenke The past decade has seen substantial progress in the application of Wilson's ideas in modern quantum field theory. In this talk, I review the basics of functional renormalisation in the continuum, and illustrate its applications for a variety of strong coupling phenomena in quantum field theory and statistical physics. 22. MAY 3 Saturday Habitat for Humanity Build Day 8:45 am, Mastic Beach, NY Saturday, May 3, 2014, 8:45 am 23. MAY 3 Saturday Office of Educational Programs Event "Science Fair" 9 am, Berkner Hall Auditorium Saturday, May 3, 2014, 9:00 am 24. MAY 6 Tuesday Physics Colloquium "How Do Massive Stars Supernova?" Presented by Adam Burrows, Princeton University 3:30 pm, Large Seminar Room, Bldg. 510 Tuesday, May 6, 2014, 3:30 pm Hosted by: Peter Petreczky "Core-collapse supernovae have challenged theorists and computational science for half a century. Such explosions are the source of many of the heavy elements in the Universe and the birthplace of neutron stars and stellar-mass black holes. However, determining the mechanism of explosion remains the key goal of theory. Though the synergistic operation of turbulence and neutrino heating seems implicated, and multi-dimensional simulations with some physical fidelity that have provided insight, we have yet to reproduce the phenomenon theoretically. In this talk, I will review the goals of supernova theory, the state of the field, and the contending explosion models. In the process, I will highlight the computational astrophysics that has been applied to date, and that may be necessary in the future to credibly unravel this mystery." 25. MAY 6 Tuesday BNL Toastmasters "Guest Night" 5:30 pm, Biology (Bldg. 463, room 160) Tuesday, May 6, 2014, 5:30 pm Hosted by: Margaret Foster If you are worried about your next big presentation, Toastmasters can help. BNL Toastmasters Club will hold a special Guest Night on Tuesday, May 6, from 5:30 to 7:30 p.m. in Biology (Bldg.163), room 160. BNL Toastmasters will present a special demonstration during the meeting and light refreshments will be served. Contacts: Beth Lin [email protected] and Don Romard [email protected]. The Brookhaven National Laboratory Toastmasters club meets regularly on the first and third Tuesdays of the month to practice speaking and presentation skills. 26. MAY 7 Wednesday Hospitality Coffee & Playgroup Event "Hospitality Coffee & Play Group (10am-noon)" 10 am, Recreation Hall, Bldg. 317 Wednesday, May 7, 2014, 10:00 am Play group will sometimes schedule different types of play dates at various venues. To see the schedule and join, please use https://www.facebook.com/#!/groups/1438521623060022/ and open Brookhaven Lab Hospitality & Play Group and sign in. You do need an established Facebook account in order to do so. 27. MAY 7 Wednesday Physics Colloquium "The Economic Impact Of Particle Physics" Presented by Herman B. White, Fermi National Accelerator Laboratory 3 pm, Large Seminar Room, Bldg. 510 Wednesday, May 7, 2014, 3:00 pm Hosted by: Ketevi Assamagan Many metrics are not universally accepted in quantifying the impact of scientific research in general. The problem is more acute in the case of discovery science, where the motivation for pursuing the research was not necessarily to address or solve a specific economic problem, and therefore not readily tied to a return on investment for example. The topic to be presented in this colloquium focuses on the economic impact of particle physics research, and in general the impact of discovery science. The information is derived from one of our study groups, completed in the summer of 2013 at the University of Minnesota for the strategic planning exercise of the particle physics community of the United States. Making the case for supporting this science for DOE Laboratories occasionally includes a response to questions about the benefits to society of this research, including the economic benefits. If it were possible to better understand the broader impacts of the direction of this research, then hopefully this would contribute to making a clearer case for pursuing this research among decision makers. 28. MAY 7 Wednesday Defensive Driving, Part 2 "Defensive Driving, Part 2" Edward Sierra, BNL 6 pm, Brookhaven Center, South Room Wednesday, May 7, 2014, 6:00 pm 29. MAY 8 Thursday "Open to the Public" 6:30 pm, Berkner Hall, Room B Thursday, May 8, 2014, 6:30 pm 30. MAY 9 Friday HET/BNL Lunch Time Talk "TBA" Presented by Cen Zhang, UCL, Brussels 12 pm, Physics, Building 510, Room 2-95 Friday, May 9, 2014, 12:00 pm Hosted by: Amarjit Soni 31. MAY 9 Friday Nuclear Physics & RIKEN Theory Seminar "Quarks in strong magnetic fields" Presented by Toru Kojo 2 pm, Small Seminar Room, Bldg. 510 Friday, May 9, 2014, 2:00 pm Hosted by: Bjoern Schenke It has been known that magnetic fields enhance the chiral symmetry breaking (ChSB). According to studies of QED or models of the 4-fermi interactions, it was expected that the enhanced ChSB would resist the chiral restoration effects, increasing critical temperatures for the chiral restoration and deconfinement. Recent lattice calculations, however, showed the opposite behavior: the critical temperatures are reduced as a magnetic field increases. I will discuss how to resolve this apparent paradox, emphasizing which characteristic features of QCD make differences from other models. 32. MAY 13 Tuesday Physics Colloquium "Materials in 2-dimension and beyond" Presented by Philip Kim, Columbia University 3:30 pm, Large Seminar Room, Bldg. 510 Tuesday, May 13, 2014, 3:30 pm The recent advent of atomically thin 2-dimensional materials such as graphene, hexa boronitride, layered transition metal chalcogenide and many strongly correlated materials, where weak van der Waals (vdW) force holds the layers together, has provide a new opportunity of studying novel quantum phenomena in low dimensional systems. The vdW layered materials consist of covalently bonded atomic layers entities that weakly interact with other constituents. With a strong built-in anisotropy in their components, vdW materials often show a quasi-low dimensionality leading to strongly correlated electron behaviors. These materials in 2-d limits also allow us to apply new experimental techniques such as electrolyte gating, scanning potentiometry, and electromechanical magnetometry. Moreover, combination of different layered constituents may produce heterogeneous and functional materials. In this talk, we will discuss to develop the method of transferring two-dimensional atomic layers of van der Waals solids to build functional heterostacks. Novel electron transport and optoelectronic phenomena can occur across these hetero-interfaces of atomicallycontrolled quantum heterostructures. 33. MAY 14 Wednesday Hospitality Coffee & Playgroup Event "Hospitality Coffee & Play Group (10am-noon)" 10 am, Recreation Hall, Bldg. 317 Wednesday, May 14, 2014, 10:00 am Play group will sometimes schedule different types of play dates at various venues. To see the schedule and join, please use https://www.facebook.com/#!/groups/1438521623060022/ and open Brookhaven Lab Hospitality & Play Group and sign in. You do need an established Facebook account in order to do so. 34. MAY 14 Wednesday Brookhaven Women In Science (BWIS) Event "Board Meeting" 12 pm, Berkner Hall, Room D Wednesday, May 14, 2014, 12:00 pm Hosted by: Christina Swinson Monthly meeting of the Brookhaven Women in Science (BWIS) board. All BWIS members and affiliates are welcome to attend. 35. MAY 15 Thursday RIKEN/BNL Lunch Time Talk "TBA" Presented by Shu Lin, RBRC 12:30 pm, Physics, Bldg. 510, Room 2-160 Thursday, May 15, 2014, 12:30 pm Hosted by: Daniel Potonyak 36. MAY 16 Friday HET/BNL Lunch Time Talk "TBA" Presented by Tien-Tien Yu, YITP (SBU) 12 pm, Physics, Building 510, Room 2-160 Friday, May 16, 2014, 12:00 pm Hosted by: Amarjit Soni 37. MAY 18 Sunday Movie Screening & Discussion "Particle Fever" Documentary Screening & Panel Discussion" 2 pm, Cinema Arts Centre, 423 Park Ave., Huntington, NY Sunday, May 18, 2014, 2:00 pm "Particle Fever," a new documentary showcasing the hunt for the Higgs boson at CERN's Large Hadron Collider, will be hitting Long Island on Sunday, May 18, at 2 p.m. at the Cinema Arts Centre in Huntington. A panel discussion following the film will feature researchers from Brookhaven Lab and Stony Brook University who played a role in the Higgs search, along with a live video feed from CERN. After the panel discussion, the Centre will host a wine and cheese event to provide attendees with an opportunity to talk with the scientists about their work in an informal setting. Tickets for the event are not yet available as of March 10, but will be announced when they go on sale. 38. MAY 19 Monday Annual Users' Meeting "Joint NSLS/NSLS-II & CFN Users' Meeting" 8 am, Berkner Hall Auditorium Monday, May 19, 2014, 8:00 am Hosted by: Photon Sciences and CFN Useres' Executive Committees 39. MAY 20 Tuesday Annual Users' Meeting "Joint NSLS/NSLS-II & CFN Users' Meeting" 8 am, Berkner Hall Auditorium Tuesday, May 20, 2014, 8:00 am Hosted by: Photon Sciences and CFN Useres' Executive Committees 40. MAY 21 Wednesday Annual Users' Meeting "Joint NSLS/NSLS-II & CFN Users' Meeting" 8 am, Berkner Hall Auditorium Wednesday, May 21, 2014, 8:00 am Hosted by: Photon Sciences and CFN Useres' Executive Committees 41. MAY 21 Wednesday Hospitality Coffee & Playgroup Event "Hospitality Coffee & Play Group (10am-noon)" 10 am, Recreation Hall, Bldg. 317 Wednesday, May 21, 2014, 10:00 am Play group will sometimes schedule different types of play dates at various venues. To see the schedule and join, please use https://www.facebook.com/#!/groups/1438521623060022/ and open Brookhaven Lab Hospitality & Play Group and sign in. You do need an established Facebook account in order to do so. 42. MAY 22 Thursday Passport to Retirement "Presented by The Foundation for Personal Financial Education" Craig J. Ferrantino, NY Director, The Foundation for Personal Financial Education 12 pm, Berkner Hall, Room B Thursday, May 22, 2014, 12:00 pm Are You on Your Way to a First Class Retirement? Join the Foundation for Personal Financial Education for an introductory seminar on becoming fiscally fit through the process of proper investment planning. Learn how to: • Assess Your Investment Profile • Measure Risk in Your Portfolio • Develop Strategies to Minimize Risk • Discuss Taxes and Health Care Costs • Create Your Own Action Plan for Success 43. MAY 22 Thursday Passport to Retirement "Presented by The Foundation for Personal Financial Education" Craig J. Ferrantino, NY Director, The Foundation for Personal Financial Education 12 pm, Berkner Hall, Room B Thursday, May 22, 2014, 12:00 pm Are You on Your Way to a First Class Retirement? Join the Foundation for Personal Financial Education for an introductory seminar on becoming fiscally fit through the process of proper investment planning. Learn how to: • Assess Your Investment Profile • Measure Risk in Your Portfolio • Develop Strategies to Minimize Risk • Discuss Taxes and Health Care Costs • Create Your Own Action Plan for Success 44. MAY 22 Thursday Particle Physics Seminar "Selected topics in Higgs physics" Presented by Andrey Korytov, University of Florida 3 pm, Small Seminar Room, Bldg. 510 Thursday, May 22, 2014, 3:00 pm Hosted by: Ketevi A. Assamagan I will cover the most recent Higgs boson physics results from LHC with a special focus on precision measurements of properties of the recently discovered SM-like Higgs boson, which can potentially reveal signs for new physics. 45. MAY 28 Wednesday Hospitality Coffee & Playgroup Event "Hospitality Coffee & Play Group (10am-noon)" 10 am, Recreation Hall, Bldg. 317 Wednesday, May 28, 2014, 10:00 am Play group will sometimes schedule different types of play dates at various venues. To see the schedule and join, please use https://www.facebook.com/#!/groups/1438521623060022/ and open Brookhaven Lab Hospitality & Play Group and sign in. You do need an established Facebook account in order to do so. 46. MAY 30 Friday HET/BNL Lunch Time Talk "TBA" Presented by David Curtin, YITP, SBU 12 pm, Physics, Bldg. 510, Room 2-160 Friday, May 30, 2014, 12:00 pm Hosted by: Amarjit Soni 47. MAY 30 Friday NSLS-II Seminar "A metallic glass that grows from the melt like a crystal" Presented by Gabrielle Long, ANL, United States Minor Outlying Islands 2 pm, Bldg. 743 Rm 177 Friday, May 30, 2014, 2:00 pm Hosted by: Wah-Keat Lee Canceled Seminar scheduled for 2/13/14 due to snow and will be rescheduled. Exact date is unknown but selected 3/27/14 as an estimated dated (posted by em 2/12/14). When a molten material is cooled, it typically grows into orderly crystals. But if the cooling rate is too fast for the entire melt to crystallize, the remaining material ends up in a non-crystalline state known as a glass. This talk is about the discovery and characterization of a unique metallic glass that, during rapid cooling, forms a solid by means of nucleation followed by growth normal to a moving interface between the solid and melt, with partitioning of the chemical elements. We were able to show experimentally that this is not a polycrystalline composite with nanometer-sized grains, and conclude that this may be a new kind of structure: an atomically ordered, isotropic, non-crystalline solid, possessing no long-range translational symmetry. This novel structure��"isotropic with infinite rotational symmetry and no translational symmetry��"had been considered theoretically possible, but has never before been observed. 48. JUN 2 Monday Office of Educational Programs Event "DOE Summer Intern Program Begins" 8 am, Berkner Hall Auditorium Monday, June 2, 2014, 8:00 am 49. JUN 4 Wednesday Hospitality Coffee & Playgroup Event "Hospitality Coffee & Play Group (10am-noon)" 10 am, Recreation Hall, Bldg. 317 Wednesday, June 4, 2014, 10:00 am Play group will sometimes schedule different types of play dates at various venues. To see the schedule and join, please use https://www.facebook.com/#!/groups/1438521623060022/ and open Brookhaven Lab Hospitality & Play Group and sign in. You do need an established Facebook account in order to do so. 50. JUN 5 Thursday Office of Educational Programs Event "OSSP Celebration" 4:30 pm, Berkner Hall Auditorium Thursday, June 5, 2014, 4:30 pm Hosted by: Mel Morris 51. JUN 10 Tuesday Particle Physics Seminar "The JUNO Reactor Neutrino Experiment" Presented by Zeyuan Yu, Institute of High Energy Physics, Beijing, China, China 11 am, Small Seminar Room, Bldg. 510 Tuesday, June 10, 2014, 11:00 am Hosted by: Elizabeth Worcester Jiangmen Underground Neutrino Observatory (JUNO) is a medium baseline reactor neutrino experiment, to determine the neutrino mass hierarchy better than 3 sigma with 20kt liquid scintillator and six year data taking. The seminar will focus on the measurement of neutrino mass hierarchy with a short discussion on other possible physics topics, such as solar neutrino, supernova neutrino, etc. The progress of JUNO will also be reported, including project status, detector conceptual design, civil construction, electronics and offline software progress. 52. JUN 10 Tuesday Physics Colloquium "TBA" Presented by Chao-Lin Kuo, Stanford University 3:30 pm, Large Seminar Room, Bldg. 510 Tuesday, June 10, 2014, 3:30 pm Hosted by: Peter Petreczky 53. JUN 11 Wednesday Hospitality Coffee & Playgroup Event "Hospitality Coffee & Play Group (10am-noon)" 10 am, Recreation Hall, Bldg. 317 Wednesday, June 11, 2014, 10:00 am Play group will sometimes schedule different types of play dates at various venues. To see the schedule and join, please use https://www.facebook.com/#!/groups/1438521623060022/ and open Brookhaven Lab Hospitality & Play Group and sign in. You do need an established Facebook account in order to do so. 54. JUN 11 Wednesday Condensed-Matter Physics & Materials Science Seminar "Frustration-induced phase separation and magnetoelectric effects in a triangular spin lattice" Presented by Alexandros Lappas, Institute of Electronic Structure and Laser, Greece 1:30 pm, ISB Bldg. 734, Conf. Rm. 201 (upstairs) Wednesday, June 11, 2014, 1:30 pm Hosted by: Simon Billinge Chemically homogeneous, strongly correlated transition-metal oxides, with competing states, may display phase separation when the electron charge is coupled to spin or lattice degrees of freedom. Similar nanoscale inhomogeneities in insulating spin systems are rare and poorly understood, although they have been theoretically predicted to arise from geometrical frustration already in the doping-free limit. In this respect, the spatially-anisotropic triangular spin system NaMnO2 [1, 2], provides a paradigm where fingerprints of a unique magnetostructurally inhomogeneous ground state are identified. For this purpose we review our comprehensive structural synchrotron X-ray diffraction and HAADF-STEM investigations, which are complemented by local-probe NMR and muon-spin relaxation (μ+SR) measurements, incorporating also ab initio calculations [2]. We argue that the Néel order evolves as the outcome of symmetry-breaking pinning sites (e.g. interphases) due to the local-scale inhomogeneity which is endorsed by the inherent frustrated topology of the spin lattice. Remarkably, frustration-mediated structural complexity in this manganite goes beyond the limitations of the bulk symmetry and magnetoelectricity is unveiled in an otherwise collinear magnetic system. [1] M. Giot, L.C. Chapon, J. Androulakis, M.A. Green, P.G. Radaelli, and A. Lappas, Phys. Rev. Lett. 2007, 99, 247211. [2] C. Stock, L.C. Chapon, O. Adamopoulos, A. Lappas, M. Giot, J.W. Taylor, M.A. Green, C.M. Brown, and P.G. Radaelli, Phys. Rev. Lett. 2009, 103, 077202. [3] A. Zorko, O. Adamopoulos, M. Komelj, D. Arcon, and A. Lappas, Nat. Commun. 2014, 5:3222 doi: 10.1038/ncomms4222. 55. JUN 17 Tuesday RHIC/AGS Annual Users' Meeting "2014 RHIC/AGS Annual Users' Meeting" 9 am, Hamilton Seminar Room, Bldg. 555 Tuesday, June 17, 2014, 9:00 am 56. JUN 17 Tuesday Physics Colloquium "TBA" Presented by Alexander Kusenko, UCLA 3:30 pm, Large Seminar Room, Bldg. 510 Tuesday, June 17, 2014, 3:30 pm Hosted by: Peter Petreczky 57. JUN 18 Wednesday RHIC/AGS Annual Users' Meeting "2014 RHIC/AGS Annual Users' Meeting" 9 am, Hamilton Seminar Bldg.555/Physics Large Seminar Bl Wednesday, June 18, 2014, 9:00 am 58. JUN 18 Wednesday Hospitality Coffee & Playgroup Event "Hospitality Coffee & Play Group" 10 am, Recreation Hall, Bldg. 317 Wednesday, June 18, 2014, 10:00 am Play group will sometimes schedule different types of play dates at various venues. To see the schedule and join, please use https://www.facebook.com/#!/groups/1438521623060022/ and open Brookhaven Lab Hospitality & Play Group and sign in. You do need an established Facebook account in order to do so. 59. JUN 18 Wednesday High-Energy Physics & RIKEN Theory Seminar "TBA" Presented by Thomas Hamby, UCL, Brussel 2 pm, Physics, Building 510, Room 2-160 Wednesday, June 18, 2014, 2:00 pm Hosted by: Amarjit Soni 60. JUN 19 Thursday RHIC/AGS Annual Users' Meeting "2014 RHIC/AGS Annual Users' Meeting" 9 am, Berkner Hall Auditorium Thursday, June 19, 2014, 9:00 am 61. JUN 20 Friday RHIC/AGS Annual Users' Meeting "2014 RHIC/AGS Annual Users' Meeting" 9 am, Large Seminar Room, Bldg. 510 Friday, June 20, 2014, 9:00 am 62. AUG 6 Wednesday Office of Educational Programs Event "DOE Summer Intern Poster Session" 9 am, Berkner Hall Auditorium Wednesday, August 6, 2014, 9:00 am 63. 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http://itl.nist.gov/div898/software/dataplot/refman1/auxillar/oddschis.htm	Dataplot Vol 1 Vol 2 # ODDS RATIO CHI-SQUARE TEST Name: ODDS RATIO CHI-SQUARE TEST (LET) Type: Analysis Command Purpose: Perform an odds ratio chi-square test of a series of fourfold (2x2) tables. Description: Given two variables where each variable has exactly two possible outcomes (typically defined as success and failure), we define the odds ratio as: o = (N11/N12)/ (N21/N22) = (N11N22)/ (N12N21) where N11 = number of successes in sample 1 N21 = number of failures in sample 1 N12 = number of successes in sample 2 N22 = number of failures in sample 2 The first definition shows the meaning of the odds ratio clearly, although it is more commonly given in the literature with the second definition. The log odds ratio is the logarithm of the odds ratio: l(o) = LOG{(N11/N12)/ (N21/N22)} = LOG{(N11N22)/ (N12N21)} Alternatively, the log odds ratio can be given in terms of the proportions l(o) = LOG{(p11/p12)/ (p21/p22)} = LOG{(p11p22)/ (p12p21)} where p11 = N11/ (N11 + N21) = proportion of successes in sample 1 p21 = N21/ (N11 + N21) = proportion of failures in sample 1 p12 = N12/ (N12 + N22) = proportion of successes in sample 2 p22 = N22/ (N12 + N22) = proportion of failures in sample 2 Success and failure can denote any binary response. Dataplot expects "success" to be coded as "1" and "failure" to be coded as "0". The bias corrected version of the statistic is: l'(o) = LOG[{(N11+0.5) (N22+0.5)}/ {(N12+0.5) (N21+0.5)}] In addition to reducing bias, this statistic also has the advantage that the odds ratio is still defined even when N12 or N21 is zero (the uncorrected statistic will be undefined for these cases). Note that N11, N21, N12, and N22 defines a 2x2 contingency table. These types of contingency tables are also referred to as fourfold tables. The odds ratio chi-square test is applied in the situation where we have a series of fourfold tables. That is, the two variables for the fourfold tables are the same, but data is collected from different populations or groups with regards to these variables. Fleiss, Levin, and Paik (p. 234) list the following questions that are typically asked about these type of data: 1. Is there evidence that the degree of association, whatever its magnitude, is consistent from one group to another? 2. Assuming that the degree of association is found to be consistent, is the common degree of association statistically significant? 3. Assuming that the common degree of association is significant, what is the best estimate of the common value for the measure of association? What is its standard error? How does one construct a confidence interval for the common measure? The following description for this test is summarized from Chapter 10 of Fleiss, Levin, and Paik. Consult this reference for a more detailed discussion. Suppose we have g fourfold tables. Then yi = measure of association for table i syi = standard error of yi wi = $$1/s_{y_{i}}^{2}$$ g = number of groups (i.e., number of 2x2 tables) This test is based on decomposing the total chi-square in the following way: $$\begin{array}{lcl} \chi_{\mbox{total}}^{2} & = & \sum_{i=1}^{g}{w_{i} y_{i}^{2}} \\ & = & \chi_{\mbox{homogeneity}}^{2} + \chi_{\mbox{association}}^{2} \end{array}$$ The $$\chi_{\mbox{homogeneity}}^{2}$$ assesses the degree of homogeneity (i.e., equality) among the g measures of association. The $$\chi_{\mbox{association}}^{2}$$ assesses the significance of the average degree of association. The overall measure of association (across all groups) is the weighted average of the g individual measures: $$\bar{y} = \frac{\sum_{i=1}^{g}{w_{i} y_{i}}} {\sum_{i=1}^{g}{w_{i}}}$$ Under the hypothesis of zero overall association, $$\bar{Y}$$ has an average value of zero and a standard error of $$\bar{y} = \frac{\sum_{i=1}^{g}{w_{i} y_{i}}} {\sum_{i=1}^{g}{w_{i}}}$$ From this $$\frac{\bar{y}} {s_{\bar{y}}} = \frac{\sum_{i=1}^{g}{w_{i} y_{i}}} {\sqrt{\sum_{i=1}^{g}{w_{i}}}}$$ follows an approximately a standard normal distribution under the null hypothesis and $$\begin{array}{lcl} \chi_{\mbox{association}}^{2} & = & \bar{y}^{2} \sum_{i=1}^{g}{w_{i}} \\ & = & \frac{\left( \sum_{i=1}^{g}{w_{i} y_{i}} \right)^2} {\sum_{i=1}^{g}{w_{i}}} \end{array}$$ follows an approximately chi-square distribution with one degree of freedom. $$\begin{array}{lcl} \chi_{\mbox{homogeneity}}^{2} & = & \chi_{\mbox{total}}^{2} - \chi_{\mbox{association}}^{2} \\ & = & \sum_{i=1}^{g}{w_{i} y_{i}^2} - \bar{y}^{2} \sum_{i=1}^{g}{w_{i}} \\ & = & \sum_{i=1}^{g}{w_{i} (y_{i} - \bar{y})^2} \end{array}$$ follows an approximately chi-square distribution with g - 1 degrees of freedom. Note that $$\chi_{\mbox{association}}^{2}$$ and $$\chi_{\mbox{homogeneity}}^{2}$$ are uncorrelated. Based on the above formulas, we can answer the above questions as follows. 1. Consistency of association can be tested using the $$\chi_{\mbox{homogeneity}}^{2}$$ statistic. If this statistic is significant, this indicates that groups are different with respect to the measure of association. 2. If $$\chi_{\mbox{homogeneity}}^{2}$$ is not signficant (i.e., the groups can be considered equivalent), then the overall degree of association can be tested using the $$\chi_{\mbox{association}}^{2}$$ statistic. 3. The estimate of overall association is and a large sample confidence interval is $$\bar{y} \pm \Phi^{-1}(\alpha/2) s_{\bar{y}}$$ The above discussion is based on a generic statistic for the measure of association. For the odds ratio chi-square test, the specific measure of association is the bias corrected log odds ratio (given above). Note that the standard error of the bias corrected log odds ratio is: $$s_{l'(o)} = \sqrt{\frac{1}{N_{11}+0.5} + \frac{1}{N_{21}+0.5} + \frac{1}{N_{12}+0.5} + \frac{1}{N_{22}+0.5}}$$ The ODDS RATIO CHI-SQUARE TEST generates the following output: 1. A summary table of various statistics (odds ratio, log(odds ratio), standard error of log(odds ratio), wi and wilog(odds ratio)). 2. A table summarizing the combined log(odds ratio) and its standard error and the chi-square test statistics (total, association, and homogeneity). 3. A table for the chi-square test for homogeneity. 4. A table for the chi-square test for overall degree of association. 5. Estimates and large sample confidence intervals for the common log(odds ratio) and the common odds ratio. Syntax 1: ODDS RATIO CHI-SQUARE TEST <y1> <y2> <SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <y2> is the second response variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax is used for the case where <y1> and <y2> denote a series of 2x2 tables (i.e., rows 1 and 2 are group 1, rows 3 and 4 are group 2, and so on). Syntax 2: ODDS RATIO CHI-SQUARE TEST <y1> <y2> <groupid> <SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <y2> is the second response variable; <groupid> is a group id variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax is used for the case where you have raw data (i.e., the data has not yet been cross tabulated into a two-way table). In this case, the two response variables have an equal number of cases for each group. Syntax 3: ODDS RATIO CHI-SQUARE TEST <y1> <groupid1> <y2> <groupid2> <SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <groupid1> is a group id variable corresponding to <y1>; <y2> is the second response variable; <groupid2> is a group id variable corresponding to <y2>; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax is used for the case where you have raw data (i.e., the data has not yet been cross tabulated into a two-way table). In this case, the two response variables may have an unequal number of cases for each group, so <y1> and <y2> require different group id variables. Examples: ODDS RATIO CHI-SQUARE TEST Y1 Y2 ODDS RATIO CHI-SQUARE TEST Y1 Y2 X ODDS RATIO CHI-SQUARE TEST Y1 X1 Y2 X2 Note: This test is similar to the Mantel-Haenszel test. Fleiss, Levin, and Paik make the following recommendations in regard to these two tests (they include other tests in their comparison). 1. If the number of groups is small or moderate and the sample sizes within each group are large, the log(odds ratio) test performs well. 2. If the number of groups is large, but the sample sizes within the groups are small to moderate, then the Mantel-Haenszel test can be recommended. The log(odds ratio) test may perform poorly for this case. 3. If the number of groups and the sample sizes within the groups are both small, exact methods may be required. Dataplot does not currently support any exact methods for this problem. Note: The following information is written to the file dpst1f.dat (in the current directory): Column 1 = significance level Column 2 = lower confidence limit for common log(odds ratio) Column 3 = upper confidence limit for common log(odds ratio) Column 4 = lower confidence limit for common odds ratio Column 5 = upper confidence limit for common odds ratio To read this information into Dataplot, enter READ DPST1F.DAT SIGLEV LOGLOWCL LOGUPPCL ODDLOWCL ODDUPPCL Dataplot saves the following internal parameters: STATTOT = the "total" test statistic CDFTOTAL = the cdf for the "total" test statistic STATASSO = the "association" test statistic CDFASSOC = the cdf for the "association" test statistic STATHOMO = the "homogeneity" test statistic CDFHOMOG = the cdf for the "homogeneity" test statistic Default: None Synonyms: None Related Commands: MANTEL-HAENSZEL TEST = Perform a Mantel-Haenszel test. ODDS RATIO INDEPENDENCE TEST = Perform a log(odds ratio) independence test. CHI-SQUARE INDEPENDENCE TEST = Perform a chi-square independence test. FISHER EXACT TEST = Perform Fisher's exact test. ASSOCIATION PLOT = Generate an association plot. SIEVE PLOT = Generate a sieve plot. ROSE PLOT = Generate a Rose plot. BINARY TABULATION PLOT = Generate a binary tabulation plot. ROC CURVE = Generate a ROC curve. ODDS RATIO = Compute the bias corrected odds ratio. LOG ODDS RATIO = Compute the bias corrected log(odds ratio). Reference: Fleiss, Levin, and Paik (2003), Statistical Methods for Rates and Proportions, Third Edition, pp. 234-238. Applications: Categorical Data Analysis Implementation Date: 2007/5 Program: let n1 = 105 let n2 = 192 let n3 = 145 let n = n1 + n2 + n3 let x = 3 for i = 1 1 n let istop = n1 + n2 let x = 2 for i = 1 1 istop let x = 1 for i = 1 1 n1 . set statistic missing value -99 . . Group 1 values . let y1 = 0 for i = 1 1 n let y2 = 0 for i = 1 1 n let y1 = 1 for i = 1 1 81 let y2 = 1 for i = 1 1 34 . . Group 2 values (have unequal samples here, so fill . with missing values . let istrt = n1 + 1 let istop1 = istrt + 118 - 1 let istop2 = istrt + 69 - 1 let y1 = 1 for i = istrt 1 istop1 let y2 = 1 for i = istrt 1 istop2 let istrt2 = n1 + 174 + 1 let istop2 = n1 + n2 let y2 = -99 for i = istrt2 1 istop2 . . Group 3 values . let istrt = n1 + n2 + 1 let istop1 = istrt + 82 - 1 let istop2 = istrt + 52 - 1 let y1 = 1 for i = istrt 1 istop1 let y2 = 1 for i = istrt 1 istop2 . odds ratio chi-square test y1 y2 x The following output is generated. SUMMARY OF LOG(ODDS RATIO) \| LOG OF STANDARD \| ODDS RATIO ODDS RATIO ERROR 1/SE(L(i))2 w(i) GROUP \| O(i) L(i) SE(L(i)) w(i) L(i)**2 =============================================================================== 1. \| 6.894114 1.930668 0.3099319 10.41040 38.80455 2. \| 2.414514 0.8814980 0.2138429 21.86806 16.99233 3. \| 2.313836 0.8389067 0.2400251 17.35748 12.21558 =============================================================================== TOTAL \| 49.63593 68.01245 CHI-SQUARE ANALYSIS OF LOG(ODDS RATIO) NUMBER OF GROUPS = 3 ESTIMATE OF COMBINED LOG(ODDS RATIO) = 1.086652 STANDARD ERROR OF COMBINED LOG(ODDS RATIO) = 0.1419390 CHI-SQUARE TEST STATISTIC (TOTAL) = 68.01245 DEGRESS OF FREEDOM = 3 CDF OF TEST STATISTIC = 1.000000 CHI-SQUARE TEST STATISTIC (ASSOCIATION) = 58.61073 DEGRESS OF FREEDOM = 1 CDF OF TEST STATISTIC = 1.000000 CHI-SQUARE TEST STATISTIC (HOMOGENEITY) = 9.401718 DEGRESS OF FREEDOM = 2 CDF OF TEST STATISTIC = 0.9978321 CHI-SQUARE TEST FOR CONSISTENCY OF ASSOCIATION (HOMOGENEITY) NULL HYPOTHESIS NULL NULL CONFIDENCE CRITICAL ACCEPTANCE HYPOTHESIS HYPOTHESIS LEVEL VALUE INTERVAL CONCLUSION =================================================================== CONSISTENT 50.0% 1.39 (0,0.500) REJECT CONSISTENT 80.0% 3.22 (0,0.800) REJECT CONSISTENT 90.0% 4.61 (0,0.900) REJECT CONSISTENT 95.0% 5.99 (0,0.950) REJECT CONSISTENT 97.5% 7.38 (0,0.975) REJECT CONSISTENT 99.0% 9.21 (0,0.990) REJECT CHI-SQUARE TEST FOR OVERALL DEGREE OF ASSOCIATION NULL HYPOTHESIS NULL NULL CONFIDENCE CRITICAL ACCEPTANCE HYPOTHESIS HYPOTHESIS LEVEL VALUE INTERVAL CONCLUSION =================================================================== NO ASSOCIATION 50.0% 0.45 (0,0.500) REJECT NO ASSOCIATION 80.0% 1.64 (0,0.800) REJECT NO ASSOCIATION 90.0% 2.71 (0,0.900) REJECT NO ASSOCIATION 95.0% 3.84 (0,0.950) REJECT NO ASSOCIATION 97.5% 5.02 (0,0.975) REJECT NO ASSOCIATION 99.0% 6.63 (0,0.990) REJECT LARGE SAMPLE CONFIDENCE INTERVAL FOR LOG(ODDS RATIO) LOG(ODDS RATIO) ODDS RATIO ( 1.086652 ) ( 2.964333 ) CONFIDENCE LOWER UPPER LOWER UPPER VALUE (%) LIMIT LIMIT LIMIT LIMIT ----------------------------------------------------------------------- 50.000 0.990915 1.18239 2.69370 3.26216 80.000 0.904750 1.26855 2.47131 3.55571 90.000 0.853183 1.32012 2.34711 3.74387 95.000 0.808457 1.36485 2.24444 3.91513 97.500 0.768509 1.40479 2.15655 4.07469 99.000 0.721041 1.45226 2.05657 4.27277 NIST is an agency of the U.S. Commerce Department. Date created: 10/10/2008 Last updated: 11/04/2015	2016-07-30T09:12:13	{"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": 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": 0.8020607233047485, "perplexity": 3870.0178743708557}, "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-2016-30/segments/1469257836392.83/warc/CC-MAIN-20160723071036-00150-ip-10-185-27-174.ec2.internal.warc.gz"}
https://par.nsf.gov/biblio/10104829	High-redshift JWST predictions from IllustrisTNG: dust modelling and galaxy luminosity functions ABSTRACT The James Webb Space Telescope (JWST) promises to revolutionize our understanding of the early Universe, and contrasting its upcoming observations with predictions of the Λ cold dark matter model requires detailed theoretical forecasts. Here, we exploit the large dynamic range of the IllustrisTNG simulation suite, TNG50, TNG100, and TNG300, to derive multiband galaxy luminosity functions from z = 2 to z = 10. We put particular emphasis on the exploration of different dust attenuation models to determine galaxy luminosity functions for the rest-frame ultraviolet (UV), and apparent wide NIRCam bands. Our most detailed dust model is based on continuum Monte Carlo radiative transfer calculations employing observationally calibrated dust properties. This calibration results in constraints on the redshift evolution of the dust attenuation normalization and dust-to-metal ratios yielding a stronger redshift evolution of the attenuation normalization compared to most previous theoretical studies. Overall we find good agreement between the rest-frame UV luminosity functions and observational data for all redshifts, also beyond the regimes used for the dust model calibrations. Furthermore, we also recover the observed high-redshift (z = 4–6) UV luminosity versus stellar mass relation, the H α versus star formation rate relation, and the H α luminosity function at z = 2. The bright end more » Authors: ; ; ; ; ; ; ; ; ; ; Award ID(s): Publication Date: NSF-PAR ID: 10104829 Journal Name: Monthly Notices of the Royal Astronomical Society Volume: 492 Issue: 4 Page Range or eLocation-ID: 5167 to 5201 ISSN: 0035-8711 National Science Foundation ##### More Like this 1. ABSTRACT We present predictions for high redshift (z = 2−10) galaxy populations based on the IllustrisTNG simulation suite and a full Monte Carlo dust radiative transfer post-processing. Specifically, we discuss the H α and H β + $[\rm O \,{\small III}]$ luminosity functions up to z = 8. The predicted H β + $[\rm O \,{\small III}]$ luminosity functions are consistent with present observations at z ≲ 3 with ${\lesssim} 0.1\, {\rm dex}$ differences in luminosities. However, the predicted H α luminosity function is ${\sim }0.3\, {\rm dex}$ dimmer than the observed one at z ≃ 2. Furthermore, we explore continuum spectral indices, the Balmer break at 4000 Å; (D4000) and the UV continuum slope β. The median D4000 versus specific star formation rate relation predicted at z = 2 is in agreement with the local calibration despite a different distribution pattern of galaxies in this plane. In addition, we reproduce the observed AUV versus β relation and explore its dependence on galaxy stellar mass, providing an explanation for the observed complexity of this relation. We also find a deficiency in heavily attenuated, UV red galaxies in the simulations. Finally, we provide predictions for the dust attenuation curves of galaxies at z = 2−6 and investigate their dependence on galaxy colours andmore » 2. ABSTRACT 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 » 3. ABSTRACT The ionizing photon escape fraction [Lyman continuum (LyC) fesc] of star-forming galaxies is the single greatest unknown in the reionization budget. Stochastic sightline effects prohibit the direct separation of LyC leakers from non-leakers at significant redshifts. Here we circumvent this uncertainty by inferring fesc using resolved (R > 4000) Lyman α (Lyα) profiles from the X-SHOOTER Lyα survey at z = 2 (XLS-z2). With empirically motivated criteria, we use Lyα profiles to select leakers ($f_{\mathrm{ esc}} > 20{{\ \rm per\ cent}}$) and non-leakers ($f_{\mathrm{ esc}} < 5{{\ \rm per\ cent}}$) from a representative sample of >0.2L* Lyman α emitters (LAEs). We use median stacked spectra of these subsets over λrest ≈ 1000–8000 Å to investigate the conditions for LyC fesc. Our stacks show similar mass, metallicity, MUV, and βUV. We find the following differences between leakers versus non-leakers: (i) strong nebular C iv and He ii emission versus non-detections; (ii) [O iii]/[O ii] ≈ 8.5 versus ≈3; (iii) Hα/Hβ indicating no dust versus E(B − V) ≈ 0.3; (iv) Mg ii emission close to the systemic velocity versus redshifted, optically thick Mg ii; and (v) Lyα fesc of ${\approx} 50{{\ \rm per\ cent}}$ versus ${\approx} 10{{\ \rm per\ cent}}$. The extreme equivalent widths (EWs) in leakers ([O iii]+$\mathrm{ H}\beta \approx 1100$ Å rest frame)more » 4. Abstract We investigate the relationship between dust attenuation and stellar mass (M) in star-forming galaxies over cosmic time. For this analysis, we compare measurements from the MOSFIRE Deep Evolution Field survey atz∼ 2.3 and the Sloan Digital Sky Survey (SDSS) atz∼ 0, augmenting the latter optical data set with both UV Galaxy Evolution Explorer (GALEX) and mid-infrared Wide-field Infrared Survey Explorer (WISE) photometry from the GALEX-SDSS-WISE Catalog. We quantify dust attenuation using both spectroscopic measurements of Hαand Hβemission lines, and photometric measurements of the rest-UV stellar continuum. The Hα/Hβratio is used to determine the magnitude of attenuation at the wavelength of Hα,AHα. Rest-UV colors and spectral energy distribution fitting are used to estimateA1600, the magnitude of attenuation at a rest wavelength of 1600 Å. As in previous work, we find a lack of significant evolution in the relation between dust attenuation andMover the redshift rangez∼ 0 toz∼ 2.3. Folding in the latest estimates of the evolution ofMdust, (Mdust/Mgas), and gas surface density at fixedM*, we find that the expectedMdustand dust mass surface density are both significantly higher atz∼ 2.3 than atz∼ 0. These differences appear at odds with the lack of evolution in dust attenuation. To explain the striking constancymore » 5. Abstract We present Ly α and ultraviolet (UV)-continuum luminosity functions (LFs) of galaxies and active galactic nuclei (AGNs) at z = 2.0–3.5 determined by the untargeted optical spectroscopic survey of the Hobby–Eberly Telescope Dark Energy Experiment (HETDEX). We combine deep Subaru imaging with HETDEX spectra resulting in 11.4 deg 2 of fiber spectra sky coverage, obtaining 18,320 galaxies spectroscopically identified with Ly α emission, 2126 of which host type 1 AGNs showing broad (FWHM > 1000 km s −1 ) Ly α emission lines. We derive the Ly α (UV) LF over 2 orders of magnitude covering bright galaxies and AGNs in log L Ly α / [ erg s − 1 ] = 43.3 – 45.5 (−27 < M UV < −20) by the 1/ V max estimator. Our results reveal that the bright-end hump of the Ly α LF is composed of type 1 AGNs. In conjunction with previous spectroscopic results at the faint end, we measure a slope of the best-fit Schechter function to be α Sch = − 1.70 − 0.14 + 0.13 , which indicates that α Sch steepens from z = 2–3 toward high redshift. Our UV LF agrees well with previous AGN UVmore »	2022-11-28T22:21:32	{"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": 0.5596630573272705, "perplexity": 5751.9999093718325}, "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/1669446710662.60/warc/CC-MAIN-20221128203656-20221128233656-00214.warc.gz"}
https://pos.sissa.it/421/090/	Volume 421 - Neutrino Oscillation Workshop (NOW2022) - Session V. Particle Physics in the Cosmos Curing Sterile Neutrino Dark Matter with a Dark Force J. Kersten Full text: pdf Pre-published on: December 28, 2022 Published on: Abstract We propose a novel mechanism to generate sterile neutrinos $\nu_s$ in the early Universe, by converting ordinary neutrinos $\nu_a$ in scattering processes $\nu_s\nu_a\to\nu_s\nu_s$. After initial production by oscillations, this leads to an exponential growth in the $\nu_s$ abundance. We show that such a production regime naturally occurs for self-interacting $\nu_s$, and that this opens up significant new parameter space where $\nu_s$ make up all of the observed dark matter. DOI: https://doi.org/10.22323/1.421.0090 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.	2023-02-07T16:01:29	{"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": 0.26507002115249634, "perplexity": 3779.569415177171}, "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-2023-06/segments/1674764500619.96/warc/CC-MAIN-20230207134453-20230207164453-00363.warc.gz"}
https://mooseframework.inl.gov/syntax/BCs/CavityPressure/index.html	# Cavity Pressure Action ## Description The CavityPressure Action system is used to calculate the pressure from an ideal gas trapped within an internal volume. The pressure in the cavity is computed based on the ideal gas law, (1) where is the internal pressure, is the moles of gas, is the ideal gas constant, is the temperature, and is the volume of the cavity. The moles of gas, the temperature, and the cavity volume in Eq. (1) are free to change with time. The moles of gas at any time is the original amount of gas (computed based on original pressure, temperature, and volume) plus the amount in the cavity due to any gas injected during the simulation. ## Constructed MooseObjects The Cavity Pressure Action system consists of three separate actions, listed in the Associated Actions block below, which are all created within the same block. Table 1: Correspondence Among Action Functionality and MooseObjects for the CavityPressure Action FunctionalityReplaced ClassesAssociated Parameters Calculation of the initial moles quantityCavityPressureUserObjectvolume: the name of the internal volume postprocessor R: the universal gas constant temperature : the name of the average temperature postprocessor Store the value of the initial molesCavityPressurePostprocessoroutput_initial_moles: the postprocessor name to used to report the initial moles of gas Calculation of the current internal pressureCavityPressureUserObjectoutput: the name of the cavity pressure postprocessor Store the internal pressure valueCavityPressurePostprocessoroutput: the name of the cavity pressure postprocessor Apply the calculated internal pressure tractionPressureboundary: the list of boundary IDs to which the pressure should be applied displacements : a string of the displacement variables to which the Pressure BC should be applied ## Example Input Syntax [./CavityPressure] [./1] boundary = 100 initial_pressure = 100 material_input = materialInput R = 8.314472 temperature = aveTempInterior volume = internalVolume startup_time = 0.5 output = ppress save_in = 'pressure_residual_x pressure_residual_y pressure_residual_z' [../] [../] (modules/combined/test/tests/cavity_pressure/cavity_pressure.i) Postprocessors for both the average temperature and the internal volume are also required for the Cavity Pressure Action system. Note that the name of the postprocessors correspond to the arguments for the parameters temperature and internal_volume in the CavityPressure block. [./aveTempInterior] type = SideAverageValue boundary = 100 variable = temp execute_on = 'initial linear' [../] (modules/combined/test/tests/cavity_pressure/cavity_pressure.i) [./internalVolume] type = InternalVolume boundary = 100 execute_on = 'initial linear' [../] (modules/combined/test/tests/cavity_pressure/cavity_pressure.i) ## Input Parameters • boundaryThe list of boundary IDs from the mesh where the pressure will be applied C++ Type:std::vector Options: Description:The list of boundary IDs from the mesh where the pressure will be applied • displacementsThe nonlinear displacement variables C++ Type:std::vector Options: Description:The nonlinear displacement variables ### Required Parameters • active__all__ If specified only the blocks named will be visited and made active Default:__all__ C++ Type:std::vector Options: Description:If specified only the blocks named will be visited and made active • outputThe name to use for the cavity pressure value C++ Type:std::string Options: Description:The name to use for the cavity pressure value • inactiveIf specified blocks matching these identifiers will be skipped. C++ Type:std::vector Options: Description:If specified blocks matching these identifiers will be skipped. • save_inAuxiliary variables to save the displacement residuals C++ Type:std::vector Options: Description:Auxiliary variables to save the displacement residuals • use_displaced_meshTrueWhether to use displaced mesh in the boundary condition Default:True C++ Type:bool Options: Description:Whether to use displaced mesh in the boundary condition	2018-12-19T03:11:05	{"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": 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": 0.4820224642753601, "perplexity": 3533.400634941314}, "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-2018-51/segments/1544376830479.82/warc/CC-MAIN-20181219025453-20181219051453-00217.warc.gz"}
https://www.nist.gov/publications/erratum-collisions-room-temperature-helium-ultra-cold-lithium-and-van-der-waals-bound	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. # Erratum: Collisions of room temperature helium with ultra-cold lithium and the van-der-Waals bound state of HeLi [Phys. Rev. A 101, 012702 (2020)] Published ### Author(s) Constantinos Makrides, Daniel Barker, James A. Fedchak, Julia Scherschligt, Stephen Eckel, Eite Tiesinga ### Abstract We have found an error in the computation of the thermally-averaged total elastic rate coefficient for the collision of a room-temperature helium atom with an ultra-cold lithium atom presented. We omitted the factor $2/\sqrt\pi}$ in the normalization over the Boltzmann distribution. Our corrected prediction for the thermally-averaged rate coefficient for a 300 K helium gas and a 1 $\mu$K Li gas is $1.655(15) \times 10^-9}$ cm$^3}$/s for $^4$He+$^6$Li and $1.659(15) \times 10^-9}$ cm$^3}$/s for $^4$He+$^7$Li, where the numbers in parenthesis are the one-standard-deviation uncertainties in the last two significant digits. The temperature dependence of the rate coefficients must be corrected with the same factor. Citation Physical Review A (Atomic, Molecular and Optical Physics) Volume 105 ## Citation Makrides, C. , Barker, D. , Fedchak, J. , Scherschligt, J. , Eckel, S. and Tiesinga, E. (2022), Erratum: Collisions of room temperature helium with ultra-cold lithium and the van-der-Waals bound state of HeLi [Phys. Rev. A 101, 012702 (2020)], Physical Review A (Atomic, Molecular and Optical Physics), [online], https://doi.org/10.1103/PhysRevA.105.029902, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=934072 (Accessed November 30, 2022) Created February 28, 2022, Updated November 29, 2022	2022-11-30T20:53:01	{"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": 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": 0.506301999092102, "perplexity": 8062.836317667066}, "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/1669446710771.39/warc/CC-MAIN-20221130192708-20221130222708-00609.warc.gz"}
https://undergroundmathematics.org/sequences/achilles-and-the-tortoise	### Sequences Bigger picture The paradoxes of the ancient Greek philosopher Zeno, born approximately 490BC, have puzzled mathematicians and scientists for millennia. Perhaps the most famous paradox is that of the race between Achilles, the swift-footed warrior, and a lumbering tortoise. Sure of his superiority, Achilles gives the tortoise a head start. Zeno’s argument “proves” that Achilles will never overtake the tortoise. Suppose the tortoise starts at point $A$. By the time Achilles gets there the tortoise has moved on to $B$. By the time Achilles gets to $B$, the tortoise will have moved on to $C$. And so on. Whenever Achilles gets to where the tortoise was a moment ago, the tortoise will have moved on, so Achilles never catches up. To pick this apart, let’s assume that Achilles and the tortoise both move at constant speed. Achilles’ speed is $100$ metres per minute and the tortoise’s speed is $1$ metre per minute (the actual numbers don’t matter). Achilles is $100$ times faster than the tortoise, so let’s give the poor animal a very large head start: $100$m. Now by the time Achilles has travelled the $100$m to $A$ the tortoise has moved $1$m to point $B$ (because it’s $100$ times slower than Achilles). When Achilles gets to $B$, the tortoise has moved $0.01$m to $C$, etc. Adding up the infinitely many distances Achilles has to traverse before he catches up with the tortoise, we get $100+1+\frac{1}{100} + \frac{1}{10000} + \frac{1}{1000000} + \dotsb = 100 + 1 + \frac{1}{100} + \frac{1}{100^2} + \frac{1}{100^3} + \dotsb.$ This is a geometric series which sums to $101.010101\dots$ metres. Since he is travelling at constant speed Achilles can cover that finite distance in a finite amount of time ($1$ minute and $0.6$ seconds)—after that time he will have caught up with the tortoise. The flaw in Zeno’s argument was the unstated assumption that the infinite sum of distances (or equivalently the infinite sum of time periods needed to traverse each distance) cannot be finite. Below is a short animated video which tells this tale. Please use this video link if you require full screen. © The Open University 2011. Original available here. Licence under creative commons by-nc-sa.	2018-01-16T11:35:28	{"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": 2, "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": 0.7625637650489807, "perplexity": 1601.4056662283767}, "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-2018-05/segments/1516084886416.17/warc/CC-MAIN-20180116105522-20180116125522-00552.warc.gz"}
https://par.nsf.gov/biblio/10358404-low-luminosity-type-ii-supernovae-iv-sn-sn-edges-sub-luminous-supernovae-class	This content will become publicly available on May 24, 2023 Low luminosity Type II supernovae – IV. SN 2020cxd and SN 2021aai, at the edges of the sub-luminous supernovae class ABSTRACT Photometric and spectroscopic data for two Low Luminosity Type IIP Supernovae (LL SNe IIP) 2020cxd and 2021aai are presented. SN 2020cxd was discovered 2 d after explosion at an absolute magnitude of Mr = −14.02 ± 0.21 mag, subsequently settling on a plateau which lasts for ∼120 d. Through the luminosity of the late light curve tail, we infer a synthesized 56Ni mass of (1.8 ± 0.5) × 10−3 M⊙. During the early evolutionary phases, optical spectra show a blue continuum ($T\, \gt$8000 K) with broad Balmer lines displaying a P Cygni profile, while at later phases, Ca ii, Fe ii, Sc ii, and Ba ii lines dominate the spectra. Hydrodynamical modelling of the observables yields $R\, \simeq$ 575 R⊙ for the progenitor star, with Mej = 7.5 M⊙ and $E\, \simeq$ 0.097 foe emitted during the explosion. This low-energy event originating from a low-mass progenitor star is compatible with both the explosion of a red supergiant (RSG) star and with an Electron Capture Supernova arising from a super asymptotic giant branch star. SN 2021aai reaches a maximum luminosity of Mr = −16.57 ± 0.23 mag (correcting for AV = 1.92 mag), at the end of its remarkably long plateau (∼140 d). The estimated 56Ni mass is (1.4 ± 0.5) × 10−2 M⊙. The expansion velocities are compatible with those of other LL SNe IIP (few 103 km s−1). The physical more » Authors: ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more » Award ID(s): Publication Date: NSF-PAR ID: 10358404 Journal Name: Monthly Notices of the Royal Astronomical Society Volume: 513 Issue: 4 Page Range or eLocation-ID: 4983 to 4999 ISSN: 0035-8711 1. ABSTRACT Low-luminosity Type II supernovae (LL SNe II) make up the low explosion energy end of core-collapse SNe, but their study and physical understanding remain limited. We present SN 2016aqf, an LL SN II with extensive spectral and photometric coverage. We measure a V-band peak magnitude of −14.58 mag, a plateau duration of ∼100 d, and an inferred 56Ni mass of 0.008 ± 0.002 M⊙. The peak bolometric luminosity, Lbol ≈ 1041.4 erg s−1, and its spectral evolution are typical of other SNe in the class. Using our late-time spectra, we measure the [O i] λλ6300, 6364 lines, which we compare against SN II spectral synthesis models to constrain the progenitor zero-age main-sequence mass. We find this to be 12 ± 3 M⊙. Our extensive late-time spectral coverage of the [Fe ii] λ7155 and [Ni ii] λ7378 lines permits a measurement of the Ni/Fe abundance ratio, a parameter sensitive to the inner progenitor structure and explosion mechanism dynamics. We measure a constant abundance ratio evolution of $0.081^{+0.009}_{-0.010}$ and argue that the best epochs to measure the ratio are at ∼200–300 d after explosion. We place this measurement in the context of a large sample of SNe II and compare against various physical, light-curve, and spectral parameters, in search of trends that might allow indirect ways of constrainingmore » The ultraviolet (UV) and near-infrared (NIR) photometric and optical spectroscopic observations of SN 2020acat covering ∼250 d after explosion are presented here. Using the fast rising photometric observations, spanning from the UV to NIR wavelengths, a pseudo-bolometric light curve was constructed and compared to several other well-observed Type IIb supernovae (SNe IIb). SN 2020acat displayed a very short rise time reaching a peak luminosity of $\mathrm{{\rm Log}_{10}}(L) = 42.49 \pm 0.17 \, \mathrm{erg \, s^{-1}}$ in only ∼14.6 ± 0.3 d. From modelling of the pseudo-bolometric light curve, we estimated a total mass of 56Ni synthesized by SN 2020acat of MNi = 0.13 ± 0.03 M⊙, with an ejecta mass of Mej = 2.3 ± 0.4 M⊙ and a kinetic energy of Ek = 1.2 ± 0.3 × 1051 erg. The optical spectra of SN 2020acat display hydrogen signatures well into the transitional period (≳ 100 d), between the photospheric and the nebular phases. The spectra also display a strong feature around 4900 Å that cannot be solely accounted for by the presence of the Fe ii 5018 line. We suggest that the Fe ii feature was augmented by He i 5016 and possibly by the presence of N ii 5005. From both photometric and spectroscopic analysis, we inferred that the progenitor of SN 2020acat was an intermediate-mass compact star with an MZAMS of 15–20 M⊙.	2022-11-27T15:56:17	{"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": 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": 0.668452262878418, "perplexity": 3133.5411170436073}, "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/1669446710409.16/warc/CC-MAIN-20221127141808-20221127171808-00559.warc.gz"}
https://zbmath.org/authors/?q=ai%3Anagaev.alexander-v	# zbMATH — the first resource for mathematics ## Nagaev, Alexander Viktorovich Compute Distance To: Author ID: nagaev.alexander-v Published as: Nagaev, A.; Nagaev, A. V.; Nagaev, Aleksander V.; Nagaev, Alexander; Nagaev, Alexander V. External Links: MGP · Wikidata · GND Documents Indexed: 120 Publications since 1963, including 1 Book all top 5 #### Co-Authors 59 single-authored 6 Shkol’nik, S. M. 5 Mukhomor, T. P. 4 Davydov, Yu. A. 4 Kim, L. V. 4 Startsev, A. N. 3 Hodzabagjan, S. S. 3 Nagaev, S. A. 3 Rakhmanina, G. I. 3 Zaigraev, Alexander 2 Badal’baev, I. S. 2 Dzahangirova, F. A. 2 Jakubowski, Adam 2 Mikosch, Thomas 2 Steblovskaya, Victoria R. 2 Zajgraev, A. Yu. 1 Alama-Bućko, Magdalena 1 Anorina, L. A. 1 Czarnowska, A. 1 Dzhakhangirova, F. A. 1 Janaszewska, E. 1 Josephy, Norman H. 1 Juszczak, Dorota 1 Kagan, Abram Meerovich 1 Khamdamov, Isakjan Mamasalievich 1 Khrimpach, M. V. 1 Kimball, Lucia 1 Pasniewski, M. 1 Philippe, Anne 1 Sakoyan, S. K. 1 Sanginov, M. B. 1 Shcolnick, S. M. 1 Starcev, A. V. 1 Startsev, A. V. 1 Tkachuk, S. G. 1 Tsitsiashvili, Gurami G. 1 Zaigraev, A. Yu. 1 Zeigraev, Alexander Yu. all top 5 #### Serials 19 Theory of Probability and its Applications 8 Teoriya Veroyatnosteĭ i eë Primeneniya 7 Izvestiya Akademii Nauk UzSSR. Seriya Fiziko-Matematicheskikh Nauk 6 Mathematical Notes 6 Discrete Mathematics and Applications 6 Journal of Mathematical Sciences (New York) 5 Litovskiĭ Matematicheskiĭ Sbornik 4 Soviet Mathematics. Doklady 3 Applicationes Mathematicae 3 Obozrenie Prikladnoĭ i Promyshlennoĭ Matematiki 2 Matematicheskie Zametki 2 Journal of Applied Probability 2 Journal of Multivariate Analysis 2 Statistics & Probability Letters 2 Mathematical Methods of Statistics 2 Extremes 1 Advances in Applied Probability 1 Annals of the Institute of Statistical Mathematics 1 Doklady Akademii Nauk UzSSR 1 Èkonomika i Matematicheskie Metody 1 Mathematische Nachrichten 1 Selected Translations in Mathematical Statistics and Probability 1 Probability and Mathematical Statistics 1 Communications in Statistics. Stochastic Models 1 Diskretnaya Matematika 1 Bernoulli 1 Lithuanian Mathematical Transactions of the Academy of Sciences of the Lithuanian SSR all top 5 #### Fields 91 Probability theory and stochastic processes (60-XX) 21 Statistics (62-XX) 10 Biology and other natural sciences (92-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Numerical analysis (65-XX) 1 General and overarching topics; collections (00-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Approximations and expansions (41-XX) 1 Operations research, mathematical programming (90-XX) #### Citations contained in zbMATH 40 Publications have been cited 262 times in 198 Documents Cited by Year Large deviations of heavy-tailed sums with applications in insurance. Zbl 0927.60037 Mikosch, T.; Nagaev, A. V. 1998 Integral limit theorems taking deviations into account when Cramer’s condition does not hold. I. Zbl 0196.21002 Nagaev, A. V. 1969 Integral limit theorems taking large deviations into account when Cramer’s condition does not hold. II. Zbl 0196.21003 Nagaev, A. V. 1969 On the estimator for the mean value of the direct descendants of a particle in branching process. Zbl 0196.18804 Nagaev, A. V. 1967 Integral limit theorems taking into account large deviations when Cramer’s condition does not hold. I. Zbl 0172.21901 Nagaev, A. V. 1969 Rates in approximations to ruin probabilities for heavy-tailed distributions. Zbl 1003.60050 Mikosch, Thomas; Nagaev, Alexander 2001 Some properties of convex hulls generated by homogeneous Poisson point processes in an unbounded convex domain. Zbl 0829.60040 Nagaev, A. V. 1995 On a property of sums of independent random variables. Zbl 0376.60055 Nagaev, A. V. 1977 On two approaches to approximation of multidimensional stable laws. Zbl 1023.60022 Davydov, Yu.; Nagaev, A. V. 2002 Confidence regions of minimal area for the scale-location parameter and their applications. Zbl 1008.62567 Czarnowska, A.; Nagaev, A. V. 2001 Asymptotics of riskless profit under selling of discrete time call options. Zbl 1055.91031 Nagaev, A. V.; Nagaev, S. A. 2003 On the role of extreme summands in sums of independent random variables. Zbl 1036.60041 Khamdamov, I. M.; Nagaev, A. V. 2002 Renewal theorems in $$R^d$$. Zbl 0435.60085 Nagaev, A. V. 1980 On the asymmetrical problem of large deviations. Zbl 0346.60018 Kim, L. V.; Nagaev, A. V. 1975 The asymptotic analysis of a stochastic model of an epidemic. Zbl 0227.92003 Nagaev, A. V.; Startsev, A. N. 1970 An algorithmic approach to non-self-financing hedging in a discrete-time incomplete market. Zbl 1282.91111 Josephy, N.; Kimball, L.; Steblovskaya, V.; Nagaev, A.; Pasniewski, M. 2007 Asymptotic analysis of minimum volume confidence regions for location-scale families. Zbl 1102.62029 Alama-Bućko, M.; Nagaev, A. V.; Zaigraev, A. 2006 Cramer large deviations when the extreme conjugate distribution is heavy-tailed. Zbl 0954.60025 Nagaev, A. V. 1998 Multidimensional limit theorems allowing large deviations for densities of regular variation. Zbl 0929.60022 Nagaev, Alexander V.; Zeigraev, Alexander Yu. 1998 Renewal theorems in $$R^d$$. Zbl 0408.60088 Nagaev, A. V. 1979 A limit theorem for a supercritical branching process. Zbl 0226.60100 Nagaev, A. V. 1971 On the role played by extreme summands when a sum of independent and identically distributed random vectors is asymptotically $$\alpha$$-stable. Zbl 1055.60010 Davydov, Yu.; Nagaev, A. V. 2004 On nonparametric estimation of the Poisson spectral measure of a stable law. Zbl 1171.60343 Nagaev, A. V. 2001 On the joint distribution of the shorth height and length. Zbl 1103.62350 Janaszewska, E.; Nagaev, A. V. 1998 Large deviations for sums of lattice random variables under the Cramer conditions. Zbl 0976.60036 Nagaev, A. V. 1998 Some properties of symmetric stable distributions close to the normal distribution. Zbl 0676.60016 Nagaev, A. V.; Shkol’nik, S. M. 1988 On a method of calculating moments of ladder heights. Zbl 0595.60054 Nagaev, A. V. 1986 On a method of computing the moments of a ladder variables. Zbl 0575.60050 Nagaev, A. V. 1985 The local limit theorem for the number of renewals. Zbl 0213.19602 Nagaev, A. V. 1970 Integral limit theorems taking into account large deviations when Cramer’s condition does not hold. II. Zbl 0181.45004 Nagaev, A. V. 1969 Local limit theorems taking into account large deviations in the case when Cramér’s condition does not hold. Zbl 0211.49004 Nagaev, A. V. 1968 A Lemma on stochastic majorization and properties of the student distribution. Zbl 1147.60307 Kagan, A.; Nagaev, A. V. 2008 New large-deviation local theorems for sums of independent and identically distributed random vectors when the limit distribution is $$\alpha$$-stable. Zbl 1098.60031 Nagaev, Alexander; Zaigraev, Alexander 2005 Local large deviation theorem for sums of i.i.d. random vectors when the Cramér condition holds in the whole space. Zbl 1082.60016 Juszczak, Dorota; Nagaev, Aleksander V. 2004 Risk-free approach of the European-type vendor with a smooth payoff function. Zbl 1048.91045 Nagaev, A. V.; Nagaev, S. A. 2004 Limit theorems and testing hypotheses on Markov chains. Zbl 1052.62083 Nagaev, A. V. 2003 An asymptotic formula for the Bayes risk in discriminating between two Markov chains. Zbl 1008.62075 Nagaev, A. V. 2001 Large deviation probabilities for sums of lattice random vectors with heavy-tailed distribution. Zbl 0977.60031 Zajgraev, A. Yu.; Nagaev, A. V.; Jakubowski, A. 1997 Large deviation probabilities for sums of heavy-tailed dependent random vectors. Zbl 0899.60020 Jakubowski, Adam; Nagaev, Alexander V.; Zaigraev, Alexander 1997 Some properties of close to normal symmetric stable distributions. Zbl 0644.60014 Nagaev, A. V.; Shkolnik, S. M. 1988 A Lemma on stochastic majorization and properties of the student distribution. Zbl 1147.60307 Kagan, A.; Nagaev, A. V. 2008 An algorithmic approach to non-self-financing hedging in a discrete-time incomplete market. Zbl 1282.91111 Josephy, N.; Kimball, L.; Steblovskaya, V.; Nagaev, A.; Pasniewski, M. 2007 Asymptotic analysis of minimum volume confidence regions for location-scale families. Zbl 1102.62029 Alama-Bućko, M.; Nagaev, A. V.; Zaigraev, A. 2006 New large-deviation local theorems for sums of independent and identically distributed random vectors when the limit distribution is $$\alpha$$-stable. Zbl 1098.60031 Nagaev, Alexander; Zaigraev, Alexander 2005 On the role played by extreme summands when a sum of independent and identically distributed random vectors is asymptotically $$\alpha$$-stable. Zbl 1055.60010 Davydov, Yu.; Nagaev, A. V. 2004 Local large deviation theorem for sums of i.i.d. random vectors when the Cramér condition holds in the whole space. Zbl 1082.60016 Juszczak, Dorota; Nagaev, Aleksander V. 2004 Risk-free approach of the European-type vendor with a smooth payoff function. Zbl 1048.91045 Nagaev, A. V.; Nagaev, S. A. 2004 Asymptotics of riskless profit under selling of discrete time call options. Zbl 1055.91031 Nagaev, A. V.; Nagaev, S. A. 2003 Limit theorems and testing hypotheses on Markov chains. Zbl 1052.62083 Nagaev, A. V. 2003 On two approaches to approximation of multidimensional stable laws. Zbl 1023.60022 Davydov, Yu.; Nagaev, A. V. 2002 On the role of extreme summands in sums of independent random variables. Zbl 1036.60041 Khamdamov, I. M.; Nagaev, A. V. 2002 Rates in approximations to ruin probabilities for heavy-tailed distributions. Zbl 1003.60050 Mikosch, Thomas; Nagaev, Alexander 2001 Confidence regions of minimal area for the scale-location parameter and their applications. Zbl 1008.62567 Czarnowska, A.; Nagaev, A. V. 2001 On nonparametric estimation of the Poisson spectral measure of a stable law. Zbl 1171.60343 Nagaev, A. V. 2001 An asymptotic formula for the Bayes risk in discriminating between two Markov chains. Zbl 1008.62075 Nagaev, A. V. 2001 Large deviations of heavy-tailed sums with applications in insurance. Zbl 0927.60037 Mikosch, T.; Nagaev, A. V. 1998 Cramer large deviations when the extreme conjugate distribution is heavy-tailed. Zbl 0954.60025 Nagaev, A. V. 1998 Multidimensional limit theorems allowing large deviations for densities of regular variation. Zbl 0929.60022 Nagaev, Alexander V.; Zeigraev, Alexander Yu. 1998 On the joint distribution of the shorth height and length. Zbl 1103.62350 Janaszewska, E.; Nagaev, A. V. 1998 Large deviations for sums of lattice random variables under the Cramer conditions. Zbl 0976.60036 Nagaev, A. V. 1998 Large deviation probabilities for sums of lattice random vectors with heavy-tailed distribution. Zbl 0977.60031 Zajgraev, A. Yu.; Nagaev, A. V.; Jakubowski, A. 1997 Large deviation probabilities for sums of heavy-tailed dependent random vectors. Zbl 0899.60020 Jakubowski, Adam; Nagaev, Alexander V.; Zaigraev, Alexander 1997 Some properties of convex hulls generated by homogeneous Poisson point processes in an unbounded convex domain. Zbl 0829.60040 Nagaev, A. V. 1995 Some properties of symmetric stable distributions close to the normal distribution. Zbl 0676.60016 Nagaev, A. V.; Shkol’nik, S. M. 1988 Some properties of close to normal symmetric stable distributions. Zbl 0644.60014 Nagaev, A. V.; Shkolnik, S. M. 1988 On a method of calculating moments of ladder heights. Zbl 0595.60054 Nagaev, A. V. 1986 On a method of computing the moments of a ladder variables. Zbl 0575.60050 Nagaev, A. V. 1985 Renewal theorems in $$R^d$$. Zbl 0435.60085 Nagaev, A. V. 1980 Renewal theorems in $$R^d$$. Zbl 0408.60088 Nagaev, A. V. 1979 On a property of sums of independent random variables. Zbl 0376.60055 Nagaev, A. V. 1977 On the asymmetrical problem of large deviations. Zbl 0346.60018 Kim, L. V.; Nagaev, A. V. 1975 A limit theorem for a supercritical branching process. Zbl 0226.60100 Nagaev, A. V. 1971 The asymptotic analysis of a stochastic model of an epidemic. Zbl 0227.92003 Nagaev, A. V.; Startsev, A. N. 1970 The local limit theorem for the number of renewals. Zbl 0213.19602 Nagaev, A. V. 1970 Integral limit theorems taking deviations into account when Cramer’s condition does not hold. I. Zbl 0196.21002 Nagaev, A. V. 1969 Integral limit theorems taking large deviations into account when Cramer’s condition does not hold. II. Zbl 0196.21003 Nagaev, A. V. 1969 Integral limit theorems taking into account large deviations when Cramer’s condition does not hold. I. Zbl 0172.21901 Nagaev, A. V. 1969 Integral limit theorems taking into account large deviations when Cramer’s condition does not hold. II. Zbl 0181.45004 Nagaev, A. V. 1969 Local limit theorems taking into account large deviations in the case when Cramér’s condition does not hold. Zbl 0211.49004 Nagaev, A. V. 1968 On the estimator for the mean value of the direct descendants of a particle in branching process. Zbl 0196.18804 Nagaev, A. V. 1967 all top 5 #### Cited by 294 Authors 7 Nagaev, Alexander Viktorovich 7 Tang, Qihe 6 Mikosch, Thomas 5 Baltrūnas, Aleksandras 5 Leipus, Remigijus 5 Šiaulys, Jonas 4 Khamdamov, Isakjan Mamasalievich 4 Konstantinides, Dimitrios G. 4 Lu, Dawei 4 Song, Lixin 4 Wang, Kaiyong 4 Wang, Shijie 3 Alama-Bućko, Magdalena 3 Aleškevičienė, Aldona K. 3 Armendáriz, Inés 3 Blanchet, Jose H. 3 Borovkov, Aleksandr Alekseevich 3 Denisov, Denis E. 3 Josephy, Norman H. 3 Kimball, Lucia 3 Loukissas, Fotis 3 Loulakis, Michail 3 Majumdar, Satya N. 3 Ng, Kai Wang 3 Shen, Xinmei 3 Steblovskaya, Victoria R. 3 Su, Chun 3 Wang, Wensheng 3 Yang, Yang 3 Zaigraev, Alexander 3 Zhang, Yi 2 Albrecher, Hansjörg 2 Amosova, N. N. 2 Asmussen, Søren 2 Asselah, Amine 2 Barbe, Philippe 2 Bedbur, Stefan 2 Chakrabarty, Arijit 2 Daley, Daryl John 2 Davydov, Yu. A. 2 Duffy, Ken R. 2 Gao, Qingwu 2 Glynn, Peter W. 2 Jiang, Tao 2 Korshunov, Dmitry 2 Liao, Xin 2 Lin, Jianxi 2 Liu, Jingchen 2 Liu, Li 2 Liu, Xijun 2 Matsui, Muneya 2 McCormick, William P. 2 Mogul’skii, Anatolii Alfredovich 2 Monthus, Cécile 2 Nagaev, Sergey Victorovich 2 Olvera-Cravioto, Mariana 2 Paris, Richard Bruce 2 Peng, Zuoxiang 2 Rozovskiĭ, Leonid Viktorovich 2 Samorodnitsky, Gennady Pinkhosovich 2 Szewczak, Zbigniew Stanisław 2 Takemura, Akimichi 2 Tsitsiashvili, Gurami Sh. 2 Vinogradov, Vladimir V. 2 Wachtel, Vitali I. 2 Wang, Xuejun 2 Xu, Lihu 2 Yan, Jia-An 2 Yang, Hailiang 2 Yang, Yang 2 Zhang, Mei 1 Albers, Willem 1 Antoneli, Fernando jun. 1 Arcones, Miguel A. 1 Aurzada, Frank 1 Badal’baev, I. S. 1 Bai, Xiaodong 1 Barbour, Andrew D. 1 Barré, Julien 1 Bartkiewicz, Katarzyna 1 Bean, Nigel G. 1 Becker, Niels G. 1 Bee, Marco 1 Bérard, Jean 1 Berger, Quentin 1 Bloznelis, Mindaugas 1 Breuillard, Emmanuel 1 Broniatowski, Michel 1 Buchta, Christian 1 Buraczewski, Dariusz 1 Calka, Pierre 1 Cang, Yuquan 1 Cao, Zhansheng 1 Carlsson, Hasse 1 Castro, Diogo 1 Chai, Chunhong 1 Chan, Jennifer So Kuen 1 Chandra, K. Suresh 1 Chay, Zoya S. 1 Chen, Jinyuan ...and 194 more Authors all top 5 #### Cited in 71 Serials 21 Statistics & Probability Letters 11 Communications in Statistics. Theory and Methods 11 Stochastic Processes and their Applications 9 Lithuanian Mathematical Journal 7 Advances in Applied Probability 7 Journal of Applied Probability 6 Insurance Mathematics & Economics 6 The Annals of Applied Probability 5 The Annals of Probability 5 Journal of Statistical Mechanics: Theory and Experiment 4 Journal of Mathematical Analysis and Applications 4 Mathematical Notes 4 Siberian Mathematical Journal 4 Probability Theory and Related Fields 4 Journal of Theoretical Probability 4 Queueing Systems 4 Journal of Mathematical Sciences (New York) 3 Mathematical Biosciences 3 Journal of Multivariate Analysis 3 Journal of Soviet Mathematics 3 Journal of Statistical Planning and Inference 3 Journal of Inequalities and Applications 3 Extremes 3 Acta Mathematica Sinica. English Series 3 Methodology and Computing in Applied Probability 3 Scandinavian Actuarial Journal 3 Frontiers of Mathematics in China 2 Metrika 2 Rocky Mountain Journal of Mathematics 2 Annals of the Institute of Statistical Mathematics 2 Theoretical Population Biology 2 Bernoulli 2 Journal of Mathematical Inequalities 2 Journal of Statistical Theory and Practice 2 Journal of Siberian Federal University. Mathematics & Physics 1 Computers & Mathematics with Applications 1 Indian Journal of Pure & Applied Mathematics 1 Journal of the Franklin Institute 1 Journal of Mathematical Biology 1 Journal of Statistical Physics 1 Physica A 1 Bulletin of Mathematical Biology 1 Theory of Probability and its Applications 1 Applied Mathematics and Computation 1 Compositio Mathematica 1 Transactions of the American Mathematical Society 1 Stochastic Analysis and Applications 1 Science in China. Series A 1 Journal of Applied Mathematics and Stochastic Analysis 1 Siberian Advances in Mathematics 1 Communications in Statistics. Simulation and Computation 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Applied Mathematics. Series B (English Edition) 1 Electronic Journal of Probability 1 Electronic Communications in Probability 1 Finance and Stochastics 1 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 1 Abstract and Applied Analysis 1 Positivity 1 Mathematical Methods of Operations Research 1 International Journal of Theoretical and Applied Finance 1 International Game Theory Review 1 Stochastic Models 1 ASTIN Bulletin 1 Stochastics 1 Journal of Physics A: Mathematical and Theoretical 1 Electronic Journal of Statistics 1 Science China. Mathematics 1 Ufimskiĭ Matematicheskiĭ Zhurnal 1 Journal of Probability and Statistics 1 Journal of Statistical Distributions and Applications all top 5 #### Cited in 19 Fields 168 Probability theory and stochastic processes (60-XX) 49 Statistics (62-XX) 34 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 10 Statistical mechanics, structure of matter (82-XX) 7 Operations research, mathematical programming (90-XX) 6 Numerical analysis (65-XX) 6 Biology and other natural sciences (92-XX) 5 Convex and discrete geometry (52-XX) 3 Approximations and expansions (41-XX) 3 Computer science (68-XX) 1 Mathematical logic and foundations (03-XX) 1 Special functions (33-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Systems theory; control (93-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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http://www.faa.gov/nextgen/snapshots/guide/	# Performance Snapshots Reference Guide ## Access A global Air Traffic Management system should provide an operating environment that ensures all airspace users have right of access to the resources needed to meet their specific operational requirements and that the shared use of airspace by different users can be achieved safely. ### Percent of Qualified GA Airports with LPV or LP Access Reported as Cumulative Percent for NAS only Desired Trend: Increase Source: FAA Office of Airport Planning and Programming. Localizer Performance with Vertical guidance (LPV) & Localizer Performance (LP) data gathered from the FAA Global Navigation Satellite Systems Group. Airport information gathered from the General Aviation Airports: A National Asset study Webpage and the Airport Master Record Form 5010 data. The cumulative percent of qualified National, Regional, Local and Basic GA airports (as defined in the 2012 FAA GA Airports Study) with an LPV or LP procedure. The cumulative percent of qualified National, Regional, Local and Basic GA airports (as defined in the 2012 FAA GA Airports Study) with an LPV or LP procedure. Computations The cumulative percent of qualified airports within scope that have an LPV or LP procedure. Scope This metric only includes LPV and LP qualified National, Regional, Local and Basic General Aviation (GA) airports (as defined in the 2012 FAA General Aviation Airports Study). The yearly numbers of LPV and LP Procedures counted include those available at airports both with and without Instrument Landing System (ILS) Procedures. Statistical Issues This data is calculated based on the number of procedures published by the end of the Fiscal Year; within a year the value may vary due to the different charting dates. Procedures are counted per the original publishing date and do not account for procedure updates or changes. The list and categorization of non-primary airports is subject to change. Completeness LPV Data used to calculate metric was last updated on August 23 2012 The General Aviation Airports: A National Asset study was published in May 2012 To be qualified for an LP or LPV procedure an airport needs to have a paved runway of 3,200 feet or greater (terrain or obstacles around the airport may affect the ability to develop a procedure for an airport as well). LPV is similar to LNAV/VNAV except it is much more precise (40m lateral limit), enables descent to 200-250 feet above the runway, and can only be flown with a WAAS receiver. LPV approaches are operationally equivalent to the legacy ILS but are more economical because no navigation infrastructure (glideslope and localizer) has to be installed at the runway. All airports with a qualified runway should have an LP or LPV approach by 2018. ### LPV & LP Access at GA Airports without ILS Reported as Count of Airports for NAS only Desired Trend: Increase Source: FAA Office of Airport Planning and Programming. Localizer Performance with Vertical guidance (LPV) & Localizer Performance (LP) data gathered from the FAA Global Navigation Satellite Systems Group. Airport information gathered from the General Aviation Airports: A National Asset study. The count of National, Regional, Local and Basic GA airports (as defined in the 2012 FAA GA Airports Study) without an ILS that have an initial LPV or LP procedure published in the indicated year. Computations Sum of the count of airports within defined scope having an initial LPV or LP procedure published for a given fiscal year. Scope LPV and LP procedures were counted for airports that meet the following conditions: • Not be a primary airport as defined in the 2012 GA Airports Study, • Be listed as either a National, Regional, Local or Basic GA airport in the 2012 GA Airports Study, and • Not have any Instrument Landing System (ILS) Procedures Statistical Issues This data is calculated based on the number of procedures published by the end of the Fiscal Year; within the year the value may vary slightly due to different procedure publication dates. Procedures are counted per the original publishing date and do not account for procedure updates or changes. The list and categorization of non-primary airports is subject to change. Completeness LPV Data used to calculate the metric was last updated on August 23 2012. The General Aviation Airports: A National Asset study was published in May 2012. Outcome: LPV approaches provide reliable, precise access to airports during low visibility/ceiling weather conditions, particularly for general aviation aircraft operators. LPV is similar to LNAV/VNAV except it is much more precise (40m lateral limit), enables descent to 200-250 feet above the runway, and can only be flown with a WAAS receiver. LPV approaches are operationally equivalent to the legacy ILS but are more economical because no navigation infrastructure (glideslope and localizer) has to be installed at the runway. ## Environment The Air Traffic Management (ATM) should contribute to the protection of the environment by considering noise, gaseous emissions and other environmental issues in the implementation and operation of the global ATM system. ### Destination 2025 Targets (2018) NAS-Wide Energy Efficiency: 3.56kg/km Noise Exposure: 300,000 people ### Noise Exposure Reported as Number of People for NAS only Desired Trend: Decrease Source: FAA Office of Environment and Energy Number of persons exposed to significant aircraft noise (regardless of whether their houses or apartments have been sound-insulated). Significant aircraft noise levels are currently defined as values greater than or equal to 65 decibels (dB) Day Night Sound Level (DNL). Formula $∑ i = 1 n POP65 i - ∑ j = 1 9 POPREL j$ Where POP65i is the number of people residing in the DNL 65 dB contour at the ith "Noise Inventory" airport as of the current year projected from the 2000 Census, and n is the number of Noise Inventory airports. A Noise Inventory airport is defined as any airport that reported having at least 365 jet departures for the year being used in the analysis. POPRELj is the number of people relocated from the DNL 65 dB contour in the jth FAA region. This data is only available for the years 2000 - 2005. Beginning in 2006, the data is no longer collected by the FAA. Source: FAA Portfolio of Goals & FAA Office of Environment and Energy Computations POP65i is the number of people residing in the DNL 65 DB contour at the ith “Noise Inventory” airport as of the current year projected from the 2000 Census, and n is the number of Noise Inventory airports. A Noise Inventory airport is defined as any airport that reported having at least 365 jet departures for the year being used in the analysis. PROPRELj is the number of people relocated from the DNL 65 dB contour in the jth FAA region since the year 2000. Scope This metric tracks the residential population exposed to significant aircraft noise around U.S. airports. Significant aircraft noise is defined as aircraft noise above a Day-Night Average Sound Level (DNL) of 65 decibels (dB). DNL is the 24-hour average sound level, in dB, obtained from the accumulation of all events with the addition of 10 dB penalty to sound levels occurring at night (from 10 pm up to 7 am). The weighting of the nighttime events accounts for the increased interference effect of noise during the night when ambient levels are lower. Statistical Issues This metric is derived from model estimates that are subject to errors in model specification. Trends of U.S. noise exposure may change due to annual improvements to the noise exposure model. A major change to the model may result in a large change in the estimate of the number of people exposed to significant noise levels around US airports. Completeness No actual count is made of the number of people exposed to aircraft noise. Aircraft type and event level are current. However, some of the databases used to establish route and runway utilization were developed from 1990 to 1997. Changes in airport layout including expansions may not be reflected. The FAA continues to update these databases as they become available. The benefits of federally funded mitigation, such as buyout, are accounted for. Reliability The Integrated Noise Model (the core of the MAGENTA and AEDT tool) has been validated with actual acoustic measurements at airports. The population exposure methodology has been thoroughly reviewed by an ICAO task group and was most recently validated for a sample of airport-specific cases. The FAA migrated from the Model for Assessing Global Exposure to the Noise of Transport Aircraft (MAGENTA) to the Aviation Environmental Design Tool (AEDT) with the 2011 annual report. This KPI is calculated for calendar year (CY), and is rounded to three significant figures. ### CO2 Emissions Reported as Kilograms for NAS only Desired Trend: Decrease Source: FAA Office of Environment and Energy Estimated quantity of Carbon Dioxide (CO2) emitted by aircraft engines. Formula Fuel Burn (kg) × 3.155 (CO2 kg per kg of fuel burn) = CO2 in kilograms Computations As part of measuring and tracking NAS fuel efficiency from commercial aircraft operations, the FAA quantifies aircraft fuel burn using FAA’s Aviation Environmental Design Tool (AEDT). AEDT is a FAA-developed computer model that estimates aircraft fuel burn and emissions for variable year emissions inventories and for operational, policy, and technology-related scenarios. Statistical Issues Potential seasonal variability and variability from year-to-year can be expected when analyzing air traffic data and commercial operations. The extent to which enhancements are incorporated to improve model accuracy, for example via more robust aerodynamic performance modeling algorithms and database of aircraft/engine fuel burn information, will impact the overall results. This could create some statistical variability from year-to-year if not properly taken into account. In cases where such enhancements have the potential to create a significant shift in baseline, annual inventories may need to be re-processed and/or adjusted to ensure consistency and accuracy of results. The extent to which aircraft fleet improvements cannot be sufficiently modeled because of a lack of manufacturer proprietary data may also influence the performance target results. In this case, attempts will be made to characterize such aircraft with the best publicly available information, recognizing that newer aircraft types in the fleet will likely exist in significantly lesser numbers, thus minimizing the influence upon the results. Completeness Data used to measure aircraft performance are assessed for quality control purposes. Input data for the AEDT model are validated before proceeding with model runs. Radar data from the Traffic Flow Management System (TFMS) are assessed to remove any anomalies, check for completeness, and pre-processed for input to the AEDT model. TFMS data are verified against the Official Airline Guide (OAG) information in order to avoid any duplication of flights in the annual inventory. In some cases, TFMS data lack appropriate fields to conduct quality control and in these cases the data are removed. Data from the AEDT model are verified by comparing output from previous years and analyzing trends to ensure that they are consistent with expectations. In other cases monthly inventories may be analyzed to validate the results. Model output is subsequently post-processed through spreadsheets to perform the calculations for the performance target. Formulae and calculations are checked in order to ensure accuracy. Reliability The measuring procedure used is highly reliable. That is to say that the processing of data through the AEDT model including the performance of algorithms is not subject to random factors that could influence the results. However, this is potentially influenced by factors outside the control of FAA. We do not expect increases in fuel burn or decreases in distance traveled or both to degrade the fleet fuel efficiency significantly. We do expect that in the future, aircraft and engine technology improvements or air traffic management improvements or both may not be enough to offset traffic growth, congestion and delays. In addition, the current metric for measuring and tracking fuel efficiency may not adequately capture performance to the degree that would allow future decisions on technological and operational considerations. This KPI is calculated for calendar year (CY) ### NAS-Wide Energy Efficiency Reported as Kilograms per Kilometer for NAS only Desired Trend: Increase Source: FAA Office of Environment and Energy Estimated fuel Burn in kilograms per kilometer Formula $Fuel Burn (Tg) Distance (Billions of Kilometers)$ Computations Measuring and tracking fuel efficiency from commercial aircraft operations allows FAA to monitor improvements in aircraft/engine technology and operational procedures, as well as enhancements in the airspace transportation system. The FAA measures performance against this target using the Aviation Environmental Design Tool (AEDT). AEDT is a FAA-developed computer model that estimates aircraft fuel burn and emissions for variable year emissions inventories and for operational, policy, and technology-related scenarios. Scope This metric focuses on all U.S. commercial operations. Statistical Issues Potential seasonal variability and variability from year-to-year can be expected when analyzing air traffic data and commercial operations. The extent to which enhancements are incorporated to improve model accuracy, for example via more robust aerodynamic performance modeling algorithms and database of aircraft/engine fuel burn information, will impact the overall results. This could create some statistical variability from year-to-year if not properly taken into account. In cases where such enhancements have the potential to create a significant shift in baseline, annual inventories may need to be re-processed and/or adjusted to ensure consistency and accuracy of results. The extent to which aircraft fleet improvements cannot be sufficiently modeled because of a lack of manufacturer proprietary data may also influence the performance target results. In this case, attempts will be made to characterize such aircraft with the best publicly available information, recognizing that newer aircraft types in the fleet will likely exist in significantly lesser numbers, thus minimizing the influence upon the results. Completeness Data used to measure performance are assessed for quality control purposes. Input data for the AEDT model are validated before proceeding with model runs. Radar data from the Traffic Flow Management System (TFMS) are assessed to remove any anomalies, check for completeness, and pre-processed for input to the AEDT model. TFMS data are verified against the Official Airline Guide (OAG) information in order to avoid any duplication of flights in the annual inventory. In some cases, TFMS data lack appropriate fields to conduct quality control and in these cases the data are removed. Data from the AEDT model are verified by comparing output from previous years and analyzing trends to ensure that they are consistent with expectations. In other cases monthly inventories may be analyzed to validate the results. Model output is subsequently post-processed through spreadsheets to perform the calculations for the performance target. Formulae and calculations are checked in order to ensure accuracy. Reliability The measuring procedure used is highly reliable. That is to say that the processing of data through the AEDT model including the performance of algorithms is not subject to random factors that could influence the results. However this is potentially influenced by factors outside the control of FAA. We do not expect increases in fuel burn or decreases in distance traveled or both to degrade the fleet fuel efficiency significantly. We do expect that in the future, aircraft and engine technology improvements or air traffic management improvements or both may not be enough to offset traffic growth, congestion and delays. In addition, the current metric for measuring and tracking fuel efficiency may not adequately capture performance to the degree that would allow future decisions on technological and operational considerations. This KPI is calculated for calendar year (CY) ## Efficiency Efficiency addresses the operational and economic cost-effectiveness of gate-to-gate flight operations from a single-flight perspective. In all phases of flight, airspace users want to depart and arrive at the times they select and fly the trajectory they determine to be optimum. ### Taxi-Out Time Reported as Minutes per Flight for Core Airports during reportable hours Desired Trend: Decrease Source: MITRE/Airline Service Quality Performance System (ASQP) data derived from Aviation System Performance Metrics (ASPM) data During reportable hours, the yearly average of the difference between Gate-Out Time and Wheels-Off time for flights from the selected airport to any of the Aviation System Performance Metrics (ASPM) airports. Flights must depart during reportable hours, but may arrive outside them. The reportable hours vary by airport. Formula $∑ F TO n F$ where $TO = t off act - t out act$ The Taxi-Out Time metric is calculated as the average over all flights in the fiscal year defined within the Scope. The Taxi-Out Time for a flight (TO) is defined as the time the aircraft takes off ( $t off act$ ) minus the time the aircraft pushes back from the gate ( $t out act$ ). This value is added to all the other flights within scope (F) and divided by the number of F (nF). Computations The average of the difference between the Actual Gate-Out Time and Actual Wheels-Off Time over all departures for each group defined within the Scope. Scope Flights are restricted to domestic ASQP flights departing from the selected airport and traveling to an ASPM airport. To be included, a flight needs to depart within the reportable hours, but may arrive at the destination outside the reportable hours Statistical Issues The list of ASQP reporting carriers is subject to change yearly. Additionally, changes in carrier operations at an airport may impact data results over time. This calculation did not normalize the data for any changes in operator fleet mix. This calculation may include time an aircraft spends in a non-movement area (defined in the Aeronautical Information Manual as "Taxiways and apron (ramp) areas not under the control of air traffic"). Reporting carriers (operators) may use slightly different starting and/or ending points when gathering performance data. Completeness ASQP flights are those with data reported to the Department of Transportation (DOT). Reliability The metrics are derived directly from individual ASQP flight data obtained through the Aviation Performance Metrics (APM) website. In the original data set, the Official Airline Guide Aircraft Identification (OAG_ACID) column must equal “ASQP” in order for the flight to be considered an ASQP flight and used in the calculations. The Technical Directive outlining the ASQP reporting carriers is available on the Bureau of Transportation Statistics (BTS) webpage. Reportable hours vary by airport and are based on local time. Additional reportable hours information is included in the Airports section below. ### Taxi-In Time Reported as Minutes per Flight for Core Airports during reportable hours Desired Trend: Decrease Source: MITRE/Airline Service Quality Performance System (ASQP) data derived from Aviation System Performance Metrics (ASPM) data During reportable hours, the yearly average of the difference between Wheels-On Time and Gate-In Time for flights arriving at the selected airport from any of the Aviation System Performance Metrics (ASPM) airports. Flights may depart outside reportable hours, but must arrive during them. The reportable hours vary by airport. Formula $∑ F TI n F$ where $TI = t in act - t on act$ The Taxi-In Time metric is calculated as the average over all flights in the fiscal year defined within the Scope. The Taxi-In Time for a flight (TI) is defined as the time the aircraft pulls into the gate ( $t in act$ ) minus the time the aircraft wheels touch the ground ( $t on act$ ). This value is added to all the other flights within scope (F) and divided by the number of F (nF). Computations The average of the difference between the actual Gate-In Time and actual Wheels-On Time over all arrivals for each group defined within the Scope. Scope Flights are restricted to domestic ASQP flights departing from an ASPM airport and traveling to the selected airport by an ASQP reporting carrier. To be included, a flight needs to arrive within the reportable hours, but may depart the origin outside reportable hours. Statistical Issues The list of ASQP reporting carriers are subject to change yearly. Additionally, changes in carrier operations at an airport may impact data results over time. This calculation did not normalize the data for any changes in operator fleet mix. This calculation may include time an aircraft spends in a non-movement area (defined in the Aeronautical Information Manual as "Taxiways and apron (ramp) areas not under the control of air traffic"). Reporting carriers (operators) may use slightly different starting and/or ending points when gathering performance data. Completeness ASQP flights are those with actual data reported to the Department of Transportation (DOT). Reliability The metrics are derived directly from individual ASQP flight data obtained through the Aviation Performance Metrics (APM) website. In the original data set, the Official Airline Guide Aircraft Identification (OAG_ACID) column must equal “ASQP” in order for the flight to be considered an ASQP flight and used in the calculations. The Technical Directive outlining the ASQP reporting carriers is available on the Bureau of Transportation Statistics (BTS) webpage. Reportable hours vary by airport and are based on local time. Additional reportable hours information is included in the Airports Section below. ### Average Gate to Gate Time Reported as Minutes per Flight for Core Airports during reportable hours Desired Trend: Decrease Source: MITRE/Airline Service Quality Performance System (ASQP) data derived from Aviation System Performance Metrics (ASPM) data During reportable hours, the yearly average of the difference between the Actual Gate-In Time at the selected airport and the Actual Gate-Out time at the origin (any Aviation System Performance Metrics (ASPM) airport). Flights may depart outside reportable hours, but must arrive during them. Reportable hours vary by airport. Formula $∑ F BT act n F for each G$ where $BT act = ( t in act - t out act )$ and where G are the groups defined within Scope, BlockTime( $BT act$ ) is defined as $t in act$ (the actual Gate-In time at the selected (arrival) airport) minus $t out act$ (the actual Gate-Out time at the departure airport); F are all flights over the year within each group and nF is the number of F. Computations Average Gate-to-Gate Time over all flights in the fiscal year for each group defined within the Scope. Scope Flights are restricted to domestic ASQP flights departing from any ASPM airport and traveling to the selected airport by an ASQP reporting carrier. Additionally, to be included, a flight needs to arrive within the reportable hours (but may depart the origin outside reportable hours). Statistical Issues The list of ASQP reporting carriers is subject to change yearly. Additionally, changes in carrier operations at an airport may impact data results over time. This calculation did not normalize the data for any changes in operator fleet mix. This calculation may include time an aircraft spends in a non-movement area (defined in the Aeronautical Information Manual as "Taxiways and apron (ramp) areas not under the control of air traffic"). Reporting carriers (operators) may use slightly different starting and/or ending points when gathering performance data. Completeness ASQP flights are those with data reported to the Department of Transportation (DOT). Reliability The metric is derived directly from individual ASQP flight data obtained through the Aviation Performance Metrics (APM) website. In the original data set, the Official Airline Guide Aircraft Identification (OAG_ACID) column must equal “ASQP” in order for the flight to be considered an ASQP flight and used in the calculations. The Technical Directive outlining the ASQP reporting carriers is available on the Bureau of Transportation Statistics (BTS) webpage. Reportable hours vary by airport and are based on local time. Additional reportable hours information is included in the Airports section below. ### Average Gate Arrival Delay Reported as Minutes per Flight for Core Airports during reportable hours Desired Trend: Decrease Source: MITRE/Airline Service Quality Performance System (ASQP) data derived from Aviation System Performance Metrics (ASPM) data During reportable hours, the yearly average of the difference between the Actual Gate-In Time and the Scheduled Gate-In Time for flights to the selected airport from any of the Aviation System Performance Metrics (ASPM) airports. The delay for each fiscal year is calculated based on the 0.5 - 99.5 percentile of the distributions for the year. Flights may depart outside reportable hours, but must arrive during them. The reportable hours vary by airport. Formula $∑ F AD n F for each G$ where $AD = ( t in act - t in sch )$ and where G are the groups defined within Scope, Arrival Delay (AD) is equal to the actual time into the gate at the arrival airport ( $t in act$ ) minus the scheduled time in at the arrival airport ( $t in sch$ ); F are all flights over the year within each group and nF is the number of F. Computations Average Gate In Delay against schedule over all flights in the fiscal year for each group defined within the Scope. Scope Flights are restricted to domestic ASQP flights departing from an ASPM airport and traveling to the selected airport. To be included a flight needs to arrive within the reportable hours, but may depart the origin outside reportable hours. Statistical Issues The list of ASQP reporting carriers is subject to change yearly. Additionally, changes in carrier operations at an airport may impact data results over time. This calculation did not normalize the data for any changes in operator fleet mix. This calculation may include time an aircraft spends in a non-movement area (defined in the Aeronautical Information Manual as "Taxiways and apron (ramp) areas not under the control of air traffic"). Reporting carriers (operators) may use slightly different starting and/or ending points when gathering performance data. After the metric was calculated, the data was truncated to remove outliers. The information provided is based on the 0.5 — 99.5 percentile of the distributions by airport and year. Completeness ASQP flights are those with data reported to the Department of Transportation (DOT). Reliability The metrics are derived directly from individual ASQP flight data obtained through the Aviation Performance Metrics (APM) website. In the original data set, the Official Airline Guide Aircraft Identification (OAG_ACID) column must equal “ASQP” in order for the flight to be considered an ASQP flight and used in the calculations. Positive delays are considered any time beyond the scheduled arrival time (including delays less than 15 minutes). Due to the inclusion of flights arriving before schedule (negative delays), negative values are possible for this metric. The Technical Directive outlining the ASQP reporting carriers is available on the Bureau of Transportation Statistics (BTS) webpage. Reportable hours vary by airport and are based on local time. Additional reportable hours information is included in the Airports Section below. ### Distance in Level Flight from Top of Descent to Runway Threshold Reported as Nautical Miles per Flight for Core Airports Desired Trend: Decrease Source: MITRE/Performance Based Navigation Dashboard and Analysis System The distance flown in level flight as flights descend from cruise altitudes to the arrival airport, averaged for the fiscal year. Formula $= ∑ F D n F$ Where D D is the distance flown at level flight for each arrival in the Scope, F is the set of all flights in the Scope and nF is the number of F Computations The sum of the total distance flown at level flight for all flights within the Scope, divided by the count of all flights within the Scope. Scope Flights are restricted to jet arrivals at the designated airport from any origin airport. The distance in level flight is measured starting when each flight reaches Top-of-Descent (TOD) or 200 nautical miles from the airport, whichever is closer. An aircraft must be in level flight for at least 50 seconds and the change in altitude has to be less than 200 feet for a segment to be considered level. Statistical Issues When calculating this metric, flight trajectories are segmented into linear segments, and are classified as either ascending, descending or level. Vertical gradients are used to classify these segments. The threshold on the vertical climb gradient for descent and level segments is between 30 and 50 feet per nautical mile. This metric is calculated using all hours. ### Average Number of Level-offs Per Flight Reported as Count per Flight for Core Airports Desired Trend: Decrease Source: MITRE/Performance Based Navigation Dashboard and Analysis System The count of instances of level-offs as flights descend from cruise altitudes to the arrival airport, averaged for the fiscal year. Formula $= ∑ F LO n F$ LO is the count of level offs for each arrival in the Scope, F is the set of all flights in Scope and nF is the number of F Computations The sum of the count of level offs for each flight within Scope; divided by the total number of flights within the Scope. Scope Flights are restricted to jet arrivals at the designated airport from any origin airport. The level flight counts are measured starting when each flight reaches Top-of-Descent (TOD) or 200 nautical miles from the airport, whichever is closer. An aircraft must be in level flight for at least 50 seconds and the change in altitude has to be less than 200 feet for a segment to be considered level. Statistical Issues When calculating this metric, flight trajectories are segmented into linear segments, and are classified as either ascending, descending or level. Vertical gradients are used to classify these segments. The threshold on the vertical climb gradient for descent and level segments is between 30 and 50 feet per nautical mile. This metric is calculated using all hours. ## City Pairs When a traveler starts to plan a trip or when an airline operator starts to plan air service, they will look at pairs of cities or pairs of metropolitan areas. For airline operators, city-pair performance is the most direct way to connect two markets. ### Average Gate to Gate Time Reported as Minutes per Flight for Selected City Pairs during reportable hours (based on local time for the arrival airport) Desired Trend: Decrease Source: MITRE/Airline Service Quality Performance System (ASQP) derived from Aviation System Performance Metrics (ASPM) data During reportable hours at the destination airport, the yearly average of the difference between the Actual Gate-In Time at the destination airport and the Actual Gate-Out time at the origin airport. Flights may depart outside reportable hours, but must arrive during them. The reportable hours vary by airport. Formula $∑ F BT act n F for each G$ where $BT act = ( t in act - t out act )$ and where G are the groups defined within Scope, Block Time ( $BT act$) is defined as $t in act$ (the actual Gate-In time at the arrival airport) minus $t out act$ (the actual Gate-Out time at the departure airport); F are all flights over the year within each group and nF is the number of F. Computations Average Gate-to-Gate Time over all flights in the fiscal year for the selected City Pair within the Scope. Scope This KPI only measures ASQP reporting carriers operating domestic service between the selected airport pair in the direction indicated. Only flights arriving at the destination airport within the reportable hours are included in this measurement. Flights may depart the origin outside the reportable hours. Statistical Issues The list of ASQP reporting carriers is subject to change yearly. Additionally, changes in carrier operations at, or between the origin and destination may impact data results over time. This calculation did not normalize the data for any changes in operator fleet mix. This calculation may include time an aircraft spends in a non-movement area (defined in the Aeronautical Information Manual as "Taxiways and apron (ramp) areas not under the control of air traffic"). Reporting carriers may use slightly different starting and/or ending points when gathering performance data. Completeness ASQP flights are those with actual data reported to the Department of Transportation (DOT). No major carriers reported data between EWR and MDW until the third quarter of FY 2011; therefore data is only reported for FY 2012. Reliability The metric is derived directly from individual ASQP flight data obtained through the Aviation Performance Metrics (APM) website. In the original data set the Official Airline Guide Aircraft Identification (OAG_ACID) column must equal “ASQP” in order for the flight to be considered an ASQP flight and used in the calculations. The Technical Directive outlining the ASQP reporting carriers is available on the Bureau of Transportation Statistics (BTS) webpage. Reportable hours vary by airport and are based on local time. Additional reportable hours information is included in the Airports Section below. ## Airports Airports included on the NextGen Performance Snapshots (NPS) website are often identified by several characteristics, including airport code, name and city. Most of the airports are also listed as part of a Metroplex, a large geographic area covering many airports, serving major metropolitan areas and a diversity of aviation stakeholders. The locations detailed in the Airport Performance pages also include additional background information such as, operations and freight volume at the specified airport; this information is gathered from the 2012 Airports Council International, North American Airport Traffic Summary preliminary data. Several metrics on the NPS are measured during Reportable Hours. These hours, which are measured in local time, vary by airport and are selected to capture at least 90 percent of the total operations (arrivals and departures) at an airport. The entire percentage of total operations covered under these Reportable Hours may not be reflected in the NPS metrics due to the characteristics of the data sources used. Please see the individual metric definitions for additional data source information. In addition to general airport information, the table below includes the Reportable Hours for the airports measured on the NPS. Memphis International (MEM) is unique in this list as it is the only airport in which the Reportable Hours span a full 24-hour day due to its large number of freight operations during night hours. ### Airport Information Table City Airport Name Airport Code Metroplex Reportable Hours Atlanta Hartsfield-Jackson Atlanta International ATL Atlanta 07:00 - 22:59 Baltimore Baltimore/Washington International Thurgood Marshall BWI DC 06:00 - 22:59 Boston General Edward Lawrence Logan International BOS Boston 06:00 - 21:59 Charlotte Charlotte-Douglas International CLT Charlotte 07:00 - 22:59 Chicago Chicago O'Hare International ORD Chicago 06:00 - 21:59 Chicago Chicago Midway International MDW Chicago 07:00 - 20:59 Dallas-Fort Worth Dallas/Fort Worth International DFW North Texas 07:00 - 21:59 Denver Denver International DEN Denver 07:00 - 21:59 Fort Lauderdale Fort Lauderdale-Hollywood International FLL South Florida 07:00 - 22:59 Houston George Bush Intercontinental — Houston IAH Houston 07:00 - 21:59 Las Vegas McCarran International LAS Las Vegas 07:00 - 21:59 Los Angeles Los Angeles International LAX Southern California 06:00 - 22:59 Memphis Memphis International MEM Memphis 00:00 - 23:59 Miami Miami International MIA South Florida 07:00 - 22:59 Minneapolis Minneapolis-St Paul International/Wold-Chamberlain MSP Minneapolis 07:00 - 22:59 New York New York LaGuardia Airport LGA New York/Philadelphia 07:00 - 21:59 New York John F. Kennedy International JFK New York/Philadelphia 06:00 - 22:59 Newark Newark Liberty International EWR New York/Philadelphia 07:00 - 22:59 Orlando Orlando International MCO Orlando 07:00 - 21:59	2013-12-13T02:26:22	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 31, "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": 0.35434600710868835, "perplexity": 4437.096875333337}, "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-2013-48/segments/1386164819343/warc/CC-MAIN-20131204134659-00002-ip-10-33-133-15.ec2.internal.warc.gz"}
https://www.anl.gov/topic/pennsylvania	# Pennsylvania ## Filter Results • ### DOE awards funding to six Argonne battery manufacturing projects The projects will help bring technologies for safer, more robust batteries from the laboratory to commercial markets. • ### High-throughput X-ray diffraction instrument comes to Argonne’s Advanced Photon Source A consortium of institutions has joined with Argonne to build a new X-ray diffraction instrument for users of the APS, one that will enable materials research and clear the way for improvements in advance of the APS Upgrade. • ### Pennsylvania Argonne’s collaborations in Pennsylvania and across the United States have led to groundbreaking discoveries and development of new technologies that help meet the nation’s needs for sustainable energy, economic prosperity, and security. The laboratory’s research helped avoid $1 billion in potential costs for boiling water reactors in the wake of the Fukushima disaster, keeping power plants running while ensuring safety. • ### Big trucks, little emissions Researchers develop a new approach for converting ethanol using the latest advances in catalysis and process development. • ### Department of Energy awards$4.6 million to Argonne to support collaborations with industry Argonne National Laboratory received \$4.6 million to fund 12 projects across four research divisions. • ### Who’s using the User Facilities? Users come from academia and industry, the United States and abroad to access Argonne User Facility resources.	2020-12-05T00:26:26	{"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": 0.22468437254428864, "perplexity": 10883.257447414662}, "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-2020-50/segments/1606141745780.85/warc/CC-MAIN-20201204223450-20201205013450-00593.warc.gz"}
https://webgate.ec.europa.eu/devco-academy/course/index.php?categoryid=29	### Guidelines on the Integration of Environment and Climate Change in Development Cooperation Go to documentation These guidelines define a comprehensive reference framework for integrating the environment and climate change into the different stages of the cycle of operations for EC development cooperation covering the three aid delivery approaches. Tools and Methods Series, Guidelines N° 4 Version December, 2011 ### Integrating the environment and climate change into EU international cooperation and development Go to documentation These guidelines provide a framework for strengthening the contribution of European Union (EU) international cooperation and development policy to sustainable development by integrating, or mainstreaming, environmental and climate change considerations into the different phases of the EU programme and project cycle. Tools and Methods Series, Guidelines No 6 Version February, 2016	2019-02-23T15:10:11	{"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": 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": 0.3986423909664154, "perplexity": 4985.006677096383}, "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-2019-09/segments/1550249504746.91/warc/CC-MAIN-20190223142639-20190223164639-00323.warc.gz"}
https://dlmf.nist.gov/36.12	# §36.12 Uniform Approximation of Integrals ## §36.12(i) General Theory for Cuspoids The canonical integrals (36.2.4) provide a basis for uniform asymptotic approximations of oscillatory integrals. In the cuspoid case (one integration variable) 36.12.1 $I(\mathbf{y},k)=\int_{-\infty}^{\infty}\exp\left(ikf(u;\mathbf{y})\right)g(u,% \mathbf{y})\mathrm{d}u,$ ⓘ Defines: $I(\mathbf{y},k)$: oscillatory integral (locally) Symbols: $\mathrm{d}\NVar{x}$: differential of $x$, $\exp\NVar{z}$: exponential function, $\int$: integral, $k$: variable, $g(u,\mathbf{y})$: function, $f(u,\mathbf{y})$: function and $u(t;\mathbf{y})$: mapping Referenced by: §36.13 Permalink: http://dlmf.nist.gov/36.12.E1 Encodings: TeX, pMML, png See also: Annotations for §36.12(i), §36.12 and Ch.36 where $k$ is a large real parameter and $\mathbf{y}=\{y_{1},y_{2},\dots\}$ is a set of additional (nonasymptotic) parameters. As $\mathbf{y}$ varies as many as $K+1$ (real or complex) critical points of the smooth phase function $f$ can coalesce in clusters of two or more. The function $g$ has a smooth amplitude. Also, $f$ is real analytic, and $\ifrac{{\partial}^{K+2}f}{{\partial u}^{K+2}}>0$ for all $\mathbf{y}$ such that all $K+1$ critical points coincide. If $\ifrac{{\partial}^{K+2}f}{{\partial u}^{K+2}}<0$, then we may evaluate the complex conjugate of $I$ for real values of $\mathbf{y}$ and $g$, and obtain $I$ by conjugation and analytic continuation. The critical points $u_{j}(\mathbf{y})$, $1\leq j\leq K+1$, are defined by 36.12.2 $\frac{\partial}{\partial u}f(u_{j}(\mathbf{y});\mathbf{y})=0.$ The leading-order uniform asymptotic approximation is given by 36.12.3 $I(\mathbf{y},k)=\frac{\exp\left(ikA(\mathbf{y})\right)}{k^{1/(K+2)}}\sum% \limits_{m=0}^{K}\frac{a_{m}(\mathbf{y})}{k^{m/(K+2)}}\left(\delta_{m,0}-\left% (1-\delta_{m,0}\right)i\frac{\partial}{\partial z_{m}}\right)\Psi_{K}\left(% \mathbf{z}(\mathbf{y};k)\right)\left(1+O\left(\frac{1}{k}\right)\right),$ where $A(\mathbf{y})$, $\mathbf{z}(\mathbf{y},k)$, $a_{m}(\mathbf{y})$ are as follows. Define a mapping $u(t;\mathbf{y})$ by relating $f(u;\mathbf{y})$ to the normal form (36.2.1) of $\Phi_{K}\left(t;\mathbf{x}\right)$ in the following way: 36.12.4 $f(u(t,\mathbf{y});\mathbf{y})=A(\mathbf{y})+\Phi_{K}\left(t;\mathbf{x}(\mathbf% {y})\right),$ ⓘ Defines: $u(t;\mathbf{y})$: mapping (locally) Symbols: $\Phi_{\NVar{K}}\left(\NVar{t};\NVar{\mathbf{x}}\right)$: cuspoid catastrophe of codimension $K$, $t$: variable, $K$: codimension, $f(u,\mathbf{y})$: function and $A(\mathbf{y})$: function Permalink: http://dlmf.nist.gov/36.12.E4 Encodings: TeX, pMML, png See also: Annotations for §36.12(i), §36.12 and Ch.36 with the $K+1$ functions $A(\mathbf{y})$ and $\mathbf{x}(\mathbf{y})$ determined by correspondence of the $K+1$ critical points of $f$ and $\Phi_{K}$. Then 36.12.5 $f(u_{j}(\mathbf{y});\mathbf{y})=A(\mathbf{y})+\Phi_{K}\left(t_{j}(\mathbf{x}(% \mathbf{y}));\mathbf{x}(\mathbf{y})\right),$ where $t_{j}(\mathbf{x})$, $1\leq j\leq K+1$, are the critical points of $\Phi_{K}$, that is, the solutions (real and complex) of (36.4.1). Correspondence between the $u_{j}(\mathbf{y})$ and the $t_{j}(\mathbf{x})$ is established by the order of critical points along the real axis when $\mathbf{y}$ and $\mathbf{x}$ are such that these critical points are all real, and by continuation when some or all of the critical points are complex. The branch for $\mathbf{x}(\mathbf{y})$ is such that $\mathbf{x}$ is real when $\mathbf{y}$ is real. In consequence, 36.12.6 $A(\mathbf{y})=f(u(0,\mathbf{y});\mathbf{y}),$ ⓘ Defines: $A(\mathbf{y})$: function (locally) Symbols: $f(u,\mathbf{y})$: function and $u(t;\mathbf{y})$: mapping Permalink: http://dlmf.nist.gov/36.12.E6 Encodings: TeX, pMML, png See also: Annotations for §36.12(i), §36.12 and Ch.36 36.12.7 $\displaystyle\mathbf{z}(\mathbf{y};k)$ $\displaystyle=\{z_{1}(\mathbf{y};k),z_{2}(\mathbf{y};k),\dots,z_{K}(\mathbf{y}% ;k)\},$ $\displaystyle z_{m}(\mathbf{y};k)$ $\displaystyle=x_{m}(\mathbf{y})k^{1-(m/(K+2))},$ ⓘ Defines: $\mathbf{z}(\mathbf{y},k)$: function (locally) and $z_{m}(\mathbf{y},k)$: function (locally) Symbols: $n$: integer, $k$: variable, $K$: codimension and $\mathbf{x}(\mathbf{y})$: function Permalink: http://dlmf.nist.gov/36.12.E7 Encodings: TeX, TeX, pMML, pMML, png, png See also: Annotations for §36.12(i), §36.12 and Ch.36 36.12.8 $a_{m}(\mathbf{y})=\sum_{n=1}^{K+1}\frac{P_{mn}(\mathbf{y})G_{n}(\mathbf{y})}{(% t_{n}(\mathbf{x}(\mathbf{y})))^{m+1}\prod\limits_{\begin{subarray}{c}l=1\\ l\neq n\end{subarray}}^{K+1}(t_{n}(\mathbf{x}(\mathbf{y}))-t_{l}(\mathbf{x}(% \mathbf{y})))},$ ⓘ Defines: $a_{m}(\mathbf{y})$: function (locally) Symbols: $l$: integer, $n$: integer, $m$: integer, $K$: codimension and $t_{j}(\mathbf{x})$: solutions Permalink: http://dlmf.nist.gov/36.12.E8 Encodings: TeX, pMML, png See also: Annotations for §36.12(i), §36.12 and Ch.36 where 36.12.9 $P_{mn}(\mathbf{y})={(t_{n}(\mathbf{x}(\mathbf{y})))^{K+1}}+\sum_{l=m+2}^{K}% \frac{l}{K+2}x_{l}(\mathbf{y}){(t_{n}(\mathbf{x}(\mathbf{y})))^{l-1}},$ and 36.12.10 $G_{n}(\mathbf{y})=g(t_{n}(\mathbf{y}),\mathbf{y})\sqrt{\frac{\ifrac{{\partial}% ^{2}\Phi_{K}\left(t_{n}(\mathbf{x}(\mathbf{y}));\mathbf{x}(\mathbf{y})\right)}% {{\partial t}^{2}}}{\ifrac{{\partial}^{2}f(u_{n}(\mathbf{y}))}{{\partial u}^{2% }}}}.$ In (36.12.10), both second derivatives vanish when critical points coalesce, but their ratio remains finite. The square roots are real and positive when $\mathbf{y}$ is such that all the critical points are real, and are defined by analytic continuation elsewhere. The quantities $a_{m}(\mathbf{y})$ are real for real $\mathbf{y}$ when $g$ is real analytic. This technique can be applied to generate a hierarchy of approximations for the diffraction catastrophes $\Psi_{K}(\mathbf{x};k)$ in (36.2.10) away from $\mathbf{x}=\boldsymbol{{0}}$, in terms of canonical integrals $\Psi_{J}\left(\xi(\mathbf{x};k)\right)$ for $J. For example, the diffraction catastrophe $\Psi_{2}(x,y;k)$ defined by (36.2.10), and corresponding to the Pearcey integral (36.2.14), can be approximated by the Airy function $\Psi_{1}\left(\xi(x,y;k)\right)$ when $k$ is large, provided that $x$ and $y$ are not small. For details of this example, see Paris (1991). For further information see Berry and Howls (1993). ## §36.12(ii) Special Case For $K=1$, with a single parameter $y$, let the two critical points of $f(u;y)$ be denoted by $u_{\pm}(y)$, with $u_{+}>u_{-}$ for those values of $y$ for which these critical points are real. Then 36.12.11 $I(y,k)=\frac{\Delta^{1/4}\pi\sqrt{2}}{k^{1/3}}\exp\left(ik\widetilde{f}\right)% \left(\left(\frac{g_{+}}{\sqrt{f_{+}^{\prime\prime}}}+\frac{g_{-}}{\sqrt{-f_{-% }^{\prime\prime}}}\right)\mathrm{Ai}\left(-k^{2/3}\Delta\right)\left(1+O\left(% \frac{1}{k}\right)\right)-i\left(\frac{g_{+}}{\sqrt{f_{+}^{\prime\prime}}}-% \frac{g_{-}}{\sqrt{-f_{-}^{\prime\prime}}}\right)\frac{\mathrm{Ai}'\left(-k^{2% /3}\Delta\right)}{k^{1/3}\Delta^{1/2}}\left(1+O\left(\frac{1}{k}\right)\right)% \right),$ where 36.12.12 $\displaystyle\widetilde{f}$ $\displaystyle=\tfrac{1}{2}(f(u_{+}(y),y)+f(u_{-}(y),y)),$ $\displaystyle g_{\pm}$ $\displaystyle=g(u_{\pm}(y),y),$ $\displaystyle f_{\pm}^{\prime\prime}$ $\displaystyle=\frac{{\partial}^{2}}{{\partial u}^{2}}f(u_{\pm}(y),y),$ $\displaystyle\Delta$ $\displaystyle=\left(\tfrac{3}{4}(f(u_{-}(y),y)-f(u_{+}(y),y))\right)^{2/3}.$ For $\mathrm{Ai}$ and $\mathrm{Ai}'$ see §9.2. Branches are chosen so that $\Delta$ is real and positive if the critical points are real, or real and negative if they are complex. The coefficients of $\mathrm{Ai}$ and $\mathrm{Ai}'$ are real if $y$ is real and $g$ is real analytic. Also, $\Delta^{1/4}/\sqrt{f_{+}^{\prime\prime}}$ and $\Delta^{1/4}/\sqrt{-f_{-}^{\prime\prime}}$ are chosen to be positive real when $y$ is such that both critical points are real, and by analytic continuation otherwise.	2018-12-17T11:17:30	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 191, "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": 0.9511051774024963, "perplexity": 1831.1440618265756}, "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-2018-51/segments/1544376828501.85/warc/CC-MAIN-20181217091227-20181217113227-00086.warc.gz"}
http://legisquebec.gouv.qc.ca/en/showversion/cs/M-25.2?code=se:17_12_20&pointInTime=20201021	M-25.2 - Act respecting the Ministère des Ressources naturelles et de la Faune 17.12.20. The following sums are credited to the mining activity management component of the Fund: Not in force (1) the sums collected under section 61 of the Mining Act (chapter M-13.1) for the renewal of a claim, up to \$2,500,000 per fiscal year; (2) the sums collected in respect of the sale of property or services financed by the component; and (3) the income from the investment of the sums making up the mining activity management component. The surpluses accumulated in the mining activity management component are transferred to the general fund on the dates and to the extent determined by the Government. 2013, c. 16, s. 55.	2020-11-26T21:56:25	{"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": 0.8409279584884644, "perplexity": 7625.724644149094}, "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-2020-50/segments/1606141188947.19/warc/CC-MAIN-20201126200910-20201126230910-00719.warc.gz"}
https://pos.sissa.it/396/591/	Volume 396 - The 38th International Symposium on Lattice Field Theory (LATTICE2021) - Oral presentation Correlated Dirac eigenvalues around the transition temperature on $N_{\tau}=8$ lattices W.P. Huang*, H. Ding, M. Lin, S. Mukherjee, P. Petreczky and Y. Zhang Full text: pdf Pre-published on: May 16, 2022 Published on: Abstract We investigate the criticality of chiral phase transition manifested in the first and second order derivatives of Dirac eigenvalue spectrum with respect to light quark mass in (2+1)-flavor lattice QCD. Simulations are performed at temperatures from about 137 MeV to 176 MeV on $N_{\tau}=8$ lattices using the highly improved staggered quarks and the tree-level improved Symanzik gauge action. The strange quark mass is fixed to its physical value $m_s^{\text{phy}}$ and the light quark mass is set to $m_s^{\text{phy}}/40$ which corresponds to a Goldstone pion mass $m_{\pi}=110$ MeV. We find that in contrast to the case at $T\simeq 205$ MeV $m_l^{-1} \partial \rho(\lambda, m_l)/\partial m_l$ is no longer equal to $\partial ^2\rho(\lambda, m_l)/\partial m_l^2$ and $\partial ^2\rho(\lambda, m_l)/\partial m_l^2$ even becomes negative at certain low temperatures. This means that as temperature getting closer to $T_c$ $\rho(\lambda, m_l)$ is no longer proportional to $m_l^2$ and thus dilute instanton gas approximation is not valid for these temperatures. We demonstrate the temperature dependence can be factored out in $\partial \rho(\lambda, m_l)/ \partial m_l$ and $\partial^2 \rho(\lambda, m_l)/ \partial m_l^2$ at $T \in [137, 153]$ MeV, and then we propose a feasible method to estimate the power $c$ given $\rho \propto m_l^{c}$. DOI: https://doi.org/10.22323/1.396.0591 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.	2022-06-27T23:46:17	{"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": 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": 0.6282965540885925, "perplexity": 1055.485268967941}, "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-2022-27/segments/1656103344783.24/warc/CC-MAIN-20220627225823-20220628015823-00600.warc.gz"}
https://zbmath.org/authors/?q=rv%3A1228	## Neuman, Edward Compute Distance To: Author ID: neuman.edward Published as: Neuman, Edward; Neuman, E. Homepage: http://www.math.siu.edu/faculty-staff/emeritus/neuman.php External Links: MGP · Wikidata · Math-Net.Ru · dblp Documents Indexed: 129 Publications since 1969 1 Contribution as Editor Reviewing Activity: 65 Reviews Co-Authors: 18 Co-Authors with 27 Joint Publications 604 Co-Co-Authors all top 5 ### Co-Authors 103 single-authored 15 Sándor, József 3 Pečarić, Josip 2 Kazi, Haseeb 1 Árpád, Baricz 1 Baricz, Árpád 1 Bullen, Peter S. 1 Hajja, Mowaffaq 1 Klariǧić Bakula, M. 1 Łosiak, Janina 1 Matkowski, Janusz 1 Mettke, Holger 1 Nowak, Jolanta 1 Páles, Zsolt 1 Pearce, Charles Edward Miller 1 Pfeifer, Eckehard 1 Schmidt, Jochen Wilhelm 1 Simić, Slavko 1 Šimić, Vida all top 5 ### Serials 14 Journal of Mathematical Inequalities 11 Integral Transforms and Special Functions 10 Zastosowania Matematyki 8 Mathematical Inequalities & Applications 7 Journal of Mathematical Analysis and Applications 7 Journal of Approximation Theory 7 JIPAM. Journal of Inequalities in Pure & Applied Mathematics 6 Mathematica Pannonica 5 Applied Mathematics and Computation 5 Journal of Inequalities and Special Functions 4 International Journal of Mathematics and Mathematical Sciences 4 Aequationes Mathematicae 3 Journal of Computational and Applied Mathematics 3 Advanced Studies in Contemporary Mathematics (Kyungshang) 3 Bulletin of the International Mathematical Virtual Institute 3 Problemy Analiza. Issues of Analysis 2 Bulletin of the Australian Mathematical Society 2 BIT 1 IMA Journal of Numerical Analysis 1 International Journal of Mathematical Education in Science and Technology 1 Rocky Mountain Journal of Mathematics 1 Mathematics of Computation 1 Computing 1 Demonstratio Mathematica 1 Functiones et Approximatio. Commentarii Mathematici 1 Proceedings of the American Mathematical Society 1 Publikacije Elektrotehnickog Fakulteta. Univerzitat u Beogradu. Serija Matematika i Fizika 1 Results in Mathematics 1 Utilitas Mathematica 1 JCMCC. The Journal of Combinatorial Mathematics and Combinatorial Computing 1 Roczniki Polskiego Towarzystwa Matematycznego. Seria III. Matematyka Stosowana 1 SIAM Journal on Mathematical Analysis 1 Publikacije Elektrotehničkog Fakulteta. Serija: Matematika 1 International Journal of Mathematical and Statistical Sciences 1 Journal of Computational Analysis and Applications 1 The Australian Journal of Mathematical Analysis and Applications 1 Applicable Analysis and Discrete Mathematics 1 Bulletin of Mathematical Analysis and Applications 1 International Journal of Analysis all top 5 ### Fields 86 Real functions (26-XX) 51 Special functions (33-XX) 24 Approximations and expansions (41-XX) 20 Numerical analysis (65-XX) 6 Combinatorics (05-XX) 5 Number theory (11-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Computer science (68-XX) 1 Ordinary differential equations (34-XX) 1 Difference and functional equations (39-XX) ### Citations contained in zbMATH Open 102 Publications have been cited 867 times in 381 Documents Cited by Year On the Schwab-Borchardt mean. Zbl 1053.26015 Neuman, E.; Sándor, J. 2003 On the Schwab-Borchardt mean. II. Zbl 1100.26011 Neuman, Edward; Sándor, József 2006 On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa-Huygens, Wilker, and Huygens inequalities. Zbl 1204.26023 Neuman, Edward; Sándor, József 2010 A note on a certain bivariate mean. Zbl 1257.26013 Neuman, Edward 2012 Inequalities for the Schwab-Borchardt mean and their applications. Zbl 1252.26006 Neuman, Edward 2011 Inequalities and bounds for elliptic integrals. Zbl 1120.33020 Kazi, Haseeb; Neuman, Edward 2007 Inequalities and bounds for generalized complete elliptic integrals. Zbl 1206.33020 Neuman, Edward 2011 Inequalities involving modified Bessel functions of the first kind. Zbl 0769.33004 Neuman, Edward 1992 One- and two-sided inequalities for Jacobian elliptic functions and related results. Zbl 1193.33234 Neuman, Edward 2010 On certain means of two arguments and their extensions. Zbl 1040.26015 Neuman, Edward; Sándor, József 2003 Wilker and Huygens-type inequalities for the generalized trigonometric and for the generalized hyperbolic functions. Zbl 1410.33001 Neuman, Edward 2014 The weighted logarithmic mean. Zbl 0823.33002 Neuman, Edward 1994 Bounds for symmetric elliptic integrals. Zbl 1041.33015 Neuman, Edward 2003 Wilker- and Huygens-type inequalities for Jacobian elliptic and theta functions. Zbl 1283.26007 Neuman, Edward 2014 On some means derived from the Schwab-Borchardt mean. Zbl 1294.26033 Neuman, Edward 2014 Inequalities and bounds for the incomplete gamma function. Zbl 1275.33005 Neuman, Edward 2013 On Wilker and Huygens type inequalities. Zbl 1241.26011 Neuman, Edward 2012 Inequalities for Jacobian elliptic functions and Gauss lemniscate functions. Zbl 1241.33018 Neuman, Edward 2012 On some means derived from the Schwab-Borchardt mean. II. Zbl 1295.26032 Neuman, Edward 2014 Uniform approximation by some Hermite interpolating splines. Zbl 0388.41007 Neuman, Edward 1978 On Gauss lemniscate functions and lemniscatic mean. Zbl 1164.33007 Neuman, Edward 2007 Inequalities involving multivariate convex functions. II. Zbl 0699.26009 Neuman, Edward 1990 Moments and Fourier transforms of B-splines. Zbl 0452.42006 Neuman, Edward 1981 Inequalities involving modified Bessel functions of the first kind. II. Zbl 1114.33003 Baricz, Árpád; Neuman, Edward 2007 On lemniscate functions. Zbl 1273.26020 Neuman, Edward 2013 Inequalities and bounds for elliptic integrals. II. Zbl 1185.33025 Kazi, Haseeb; Neuman, Edward 2008 On a new bivariate mean. Zbl 1305.26060 Neuman, Edward 2014 Inequalities for weighted sums of powers and their applications. Zbl 1253.26041 Neuman, Edward 2012 On Gauss lemniscate functions and lemniscatic mean. II. Zbl 1289.33013 Neuman, Edward 2012 A one-parameter family of bivariate means. Zbl 1281.26026 Neuman, Edward 2013 On complete symmetric functions. Zbl 0654.26013 Neuman, Edward 1988 Companion inequalities for certain bivariate means. Zbl 1199.26087 Neuman, Edward; Sándor, József 2009 On comparison of Stolarsky and Gini means. Zbl 1021.26017 Neuman, Edward; Páles, Zsolt 2003 Inequalities for the generalized trigonometric, hyperbolic and Jacobian elliptic functions. Zbl 1333.26015 Neuman, Edward 2015 Quadratic splines and histospline projections. Zbl 0455.41005 Neuman, Edward 1980 Sharp inequalities involving Neuman-Sándor and logarithmic means. Zbl 1280.26051 Neuman, Edward 2013 On the Ky Fan inequality and related inequalities. II. Zbl 1086.26014 Neuman, Edward; Sándor, József 2005 On one-parameter family of bivariate means. Zbl 1238.33011 Neuman, Edward 2012 Some inequalities for the gamma function. Zbl 1242.33006 Neuman, Edward 2011 Product formulas and bounds for Jacobian elliptic functions with applications. Zbl 1253.33021 Neuman, Edward 2012 Inequalities involving multivariate convex functions. Zbl 0672.26010 Neuman, Edward; Pečarić, Josip 1989 Convex interpolating splines of arbitrary degree. II. Zbl 0559.41005 Neuman, Edward 1982 Inequalities involving generalized trigonometric and hyperbolic functions. Zbl 1305.26037 Neuman, Edward 2014 Inequalities involving generalized Jacobian elliptic functions. Zbl 1306.33026 Neuman, Edward 2014 Inequalities involving a logarithmically convex function and their applications to special functions. Zbl 1132.26337 Neuman, Edward 2006 On the $$p$$-version of the Schwab-Borchardt mean. Zbl 1308.26055 Neuman, Edward 2014 Two-sided inequalities for the lemniscate functions. Zbl 1312.33055 Neuman, Edward 2010 Optimal inequalities for hyperbolic and trigonometric functions. Zbl 1314.26019 Neuman, Edward; Sándor, József 2011 On the calculation of elliptic integrals of the second and third kinds. Zbl 0258.65017 Neuman, E. 1969 Inequalities involving generalized Bessel functions. Zbl 1080.33005 Árpád, Baricz; Neuman, Edward 2005 Quadratic spline interpolation with coinciding interpolation and spline grids. Zbl 0554.41017 Mettke, Holger; Pfeifer, Eckehard; Neuman, Edward 1982 Inequalities involving Bessel functions of the first kind. Zbl 1078.33003 Neuman, Edward 2004 On the inversion of certain band matrices. Zbl 0447.65009 Neuman, E. 1977 Inequalities involving Stolarsky and Gini means. Zbl 1026.26012 Neuman, Edward; Sándor, József 2003 Inequalities for the rations of certain bivariate means. Zbl 1214.26018 Neuman, Edward; Sándor, József 2008 On generalized symmetric means and Stirling numbers of the second kind. Zbl 0604.26015 Neuman, E. 1985 Inequalities involving Jacobian elliptic functions and their inverses. Zbl 1258.33012 Neuman, Edward; Sándor, József 2012 Inequalities for hyperbolic functions. Zbl 1245.26010 Neuman, Edward; Sándor, József 2012 On a new family of bivariate means. Zbl 1373.26036 Neuman, Edward 2017 Some properties of the generalized Jacobian elliptic functions. Zbl 1326.33028 Neuman, Edward 2015 Inequalities involving certain bivariate means. II. Zbl 1312.26057 Neuman, Edward 2013 On generalized Seiffert means. Zbl 1298.26095 Neuman, Edward 2014 Inequalities involving inverse circular and inverse hyperbolic functions. II. Zbl 1186.26010 Neuman, Edward 2010 Hermite-Hadamard’s inequalities for multivariate $$g$$-convex functions. Zbl 1071.26015 Klariǧić Bakula, M.; Neuman, E.; Pečarić, J.; Šimić, Vida 2005 Determination of a quadratic spline function with given values of the integrals in subintervals. Zbl 0447.41003 Neuman, Edward 1980 Inequalities involving generalized symmetric means. Zbl 0601.26013 Neuman, Edward 1986 On the $$p$$-version of the Schwab-Borchardt mean. II. Zbl 1473.26041 Neuman, Edward 2015 A note on the Jacobian elliptic sine function. Zbl 1279.33028 Neuman, Edward 2013 Optimal bounds for certain bivariate means. Zbl 1312.26051 Neuman, Edward 2014 Projections in uniform polynomial approximations. Zbl 0277.65005 Neuman, Edward 1974 Determination of an interpolating quadratic spline function. Zbl 0337.41001 Neuman, Edward 1976 On the convergence of quadratic spline interpolants. Zbl 0696.41003 Neuman, Edward; Schmidt, Jochen W. 1985 The inversion of cyclic tridiagonal matrices. Zbl 0697.65018 Łosiak, Janina; Neuman, E.; Nowak, Jolanta 1988 Properties of a class of polynomial splines. Zbl 0525.41013 Neuman, Edward 1983 Bounds for the norm of certain spline projections. Zbl 0425.41016 Neuman, Edward 1979 On the Ky Fan inequality and related inequalities. I. Zbl 1007.26015 Neuman, Edward; Sándor, József 2002 Generalized Heronian means. Zbl 1174.26018 Neuman, Edward; Sándor, József 2008 On Hahn polynomials and continuous dual Hahn polynomials. Zbl 1101.33008 Neuman, Edward 2006 On the inequalities for the generalized trigonometric functions. Zbl 1390.26028 Neuman, Edward 2014 Inequalities involving inverse circular and inverse hyperbolic functions. Zbl 1274.33004 Neuman, Edward 2007 Inequalities and bounds for a certain bivariate elliptic mean. Zbl 1353.26036 Neuman, Edward 2016 Some properties of the generalized Jacobian elliptic functions. III. Zbl 1414.33021 Neuman, Edward 2016 On two bivariate elliptic means. Zbl 1368.26032 Neuman, Edward 2017 On a new bivariate mean. II. Zbl 1321.26061 Neuman, Edward 2015 Some properties of the generalized Jacobian elliptic functions. II. Zbl 1336.33038 Neuman, Edward 2016 Inequalities involving hyperbolic functions and trigonometric functions. Zbl 1446.26013 Neuman, Edward 2012 Convex interpolating splines of odd degree. Zbl 0393.41005 Neuman, Edward 1978 A new formula for box splines on three-directional meshes. Zbl 0829.41008 Neuman, Edward 1994 Convex interpolating splines of arbitrary degree. III. Zbl 0653.41013 Neuman, Edward 1986 Computation of inner products of some multivariate splines. Zbl 0678.65013 Neuman, Edward 1989 Bounds for the norm of certain spline projections. II. Zbl 0519.41015 Neuman, Edward 1982 Dirichlet averages and their applications to Gegenbauer functions. Zbl 0915.33009 Neuman, E. 1996 Stolarsky means of several variables. Zbl 1078.26020 Neuman, Edward 2005 Optimal quadratures for a certain class of analytic functions. Zbl 0232.65017 Neuman, E. 1970 Convex interpolating splines of arbitrary degree. Zbl 0436.41001 Neuman, Edward 1980 Note on Stirling numbers of the first and second kinds. Zbl 0464.10007 Neuman, Edward 1980 Means and their inequalities. Zbl 1286.26002 2013 Inequalities involving multivariate convex functions. III. Zbl 1248.26036 Neuman, Edward 2012 Inequalities involving multivariate convex functions, IV. Zbl 1247.26036 Neuman, Edward 2012 Wilker and Huygens type inequalities for some elementary functions and Eulerian numbers. Zbl 1323.26020 Neuman, Edward 2015 On a new family of bivariate means. Zbl 1373.26036 Neuman, Edward 2017 On two bivariate elliptic means. Zbl 1368.26032 Neuman, Edward 2017 Wilker and Huygens-type inequalities involving Gudermannian and the inverse Gudermannian functions. Zbl 1384.26042 Neuman, E. 2017 Inequalities and bounds for a certain bivariate elliptic mean. Zbl 1353.26036 Neuman, Edward 2016 Some properties of the generalized Jacobian elliptic functions. III. Zbl 1414.33021 Neuman, Edward 2016 Some properties of the generalized Jacobian elliptic functions. II. Zbl 1336.33038 Neuman, Edward 2016 Inequalities for the generalized trigonometric, hyperbolic and Jacobian elliptic functions. Zbl 1333.26015 Neuman, Edward 2015 Some properties of the generalized Jacobian elliptic functions. Zbl 1326.33028 Neuman, Edward 2015 On the $$p$$-version of the Schwab-Borchardt mean. II. Zbl 1473.26041 Neuman, Edward 2015 On a new bivariate mean. II. Zbl 1321.26061 Neuman, Edward 2015 Wilker and Huygens type inequalities for some elementary functions and Eulerian numbers. Zbl 1323.26020 Neuman, Edward 2015 Wilker and Huygens-type inequalities for the generalized trigonometric and for the generalized hyperbolic functions. Zbl 1410.33001 Neuman, Edward 2014 Wilker- and Huygens-type inequalities for Jacobian elliptic and theta functions. Zbl 1283.26007 Neuman, Edward 2014 On some means derived from the Schwab-Borchardt mean. Zbl 1294.26033 Neuman, Edward 2014 On some means derived from the Schwab-Borchardt mean. II. Zbl 1295.26032 Neuman, Edward 2014 On a new bivariate mean. Zbl 1305.26060 Neuman, Edward 2014 Inequalities involving generalized trigonometric and hyperbolic functions. Zbl 1305.26037 Neuman, Edward 2014 Inequalities involving generalized Jacobian elliptic functions. Zbl 1306.33026 Neuman, Edward 2014 On the $$p$$-version of the Schwab-Borchardt mean. Zbl 1308.26055 Neuman, Edward 2014 On generalized Seiffert means. Zbl 1298.26095 Neuman, Edward 2014 Optimal bounds for certain bivariate means. Zbl 1312.26051 Neuman, Edward 2014 On the inequalities for the generalized trigonometric functions. Zbl 1390.26028 Neuman, Edward 2014 Inequalities and bounds for the incomplete gamma function. Zbl 1275.33005 Neuman, Edward 2013 On lemniscate functions. Zbl 1273.26020 Neuman, Edward 2013 A one-parameter family of bivariate means. Zbl 1281.26026 Neuman, Edward 2013 Sharp inequalities involving Neuman-Sándor and logarithmic means. Zbl 1280.26051 Neuman, Edward 2013 Inequalities involving certain bivariate means. II. Zbl 1312.26057 Neuman, Edward 2013 A note on the Jacobian elliptic sine function. Zbl 1279.33028 Neuman, Edward 2013 Means and their inequalities. Zbl 1286.26002 2013 A note on a certain bivariate mean. Zbl 1257.26013 Neuman, Edward 2012 On Wilker and Huygens type inequalities. Zbl 1241.26011 Neuman, Edward 2012 Inequalities for Jacobian elliptic functions and Gauss lemniscate functions. Zbl 1241.33018 Neuman, Edward 2012 Inequalities for weighted sums of powers and their applications. Zbl 1253.26041 Neuman, Edward 2012 On Gauss lemniscate functions and lemniscatic mean. II. Zbl 1289.33013 Neuman, Edward 2012 On one-parameter family of bivariate means. Zbl 1238.33011 Neuman, Edward 2012 Product formulas and bounds for Jacobian elliptic functions with applications. Zbl 1253.33021 Neuman, Edward 2012 Inequalities involving Jacobian elliptic functions and their inverses. Zbl 1258.33012 Neuman, Edward; Sándor, József 2012 Inequalities for hyperbolic functions. Zbl 1245.26010 Neuman, Edward; Sándor, József 2012 Inequalities involving hyperbolic functions and trigonometric functions. Zbl 1446.26013 Neuman, Edward 2012 Inequalities involving multivariate convex functions. III. Zbl 1248.26036 Neuman, Edward 2012 Inequalities involving multivariate convex functions, IV. Zbl 1247.26036 Neuman, Edward 2012 Inequalities involving Jacobian elliptic, trigonometric and hyperbolic functions. (Inequalities involving Jacobian elliptic, trigonomeric and hyperbolic functions.) Zbl 1312.33056 Neuman, Edward 2012 Inequalities for the Schwab-Borchardt mean and their applications. Zbl 1252.26006 Neuman, Edward 2011 Inequalities and bounds for generalized complete elliptic integrals. Zbl 1206.33020 Neuman, Edward 2011 Some inequalities for the gamma function. Zbl 1242.33006 Neuman, Edward 2011 Optimal inequalities for hyperbolic and trigonometric functions. Zbl 1314.26019 Neuman, Edward; Sándor, József 2011 On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa-Huygens, Wilker, and Huygens inequalities. Zbl 1204.26023 Neuman, Edward; Sándor, József 2010 One- and two-sided inequalities for Jacobian elliptic functions and related results. Zbl 1193.33234 Neuman, Edward 2010 Two-sided inequalities for the lemniscate functions. Zbl 1312.33055 Neuman, Edward 2010 Inequalities involving inverse circular and inverse hyperbolic functions. II. Zbl 1186.26010 Neuman, Edward 2010 Companion inequalities for certain bivariate means. Zbl 1199.26087 Neuman, Edward; Sándor, József 2009 Inequalities and bounds for elliptic integrals. II. Zbl 1185.33025 Kazi, Haseeb; Neuman, Edward 2008 Inequalities for the rations of certain bivariate means. Zbl 1214.26018 Neuman, Edward; Sándor, József 2008 Generalized Heronian means. Zbl 1174.26018 Neuman, Edward; Sándor, József 2008 Inequalities and bounds for elliptic integrals. Zbl 1120.33020 Kazi, Haseeb; Neuman, Edward 2007 On Gauss lemniscate functions and lemniscatic mean. Zbl 1164.33007 Neuman, Edward 2007 Inequalities involving modified Bessel functions of the first kind. II. Zbl 1114.33003 Baricz, Árpád; Neuman, Edward 2007 Inequalities involving inverse circular and inverse hyperbolic functions. Zbl 1274.33004 Neuman, Edward 2007 On the Schwab-Borchardt mean. II. Zbl 1100.26011 Neuman, Edward; Sándor, József 2006 Inequalities involving a logarithmically convex function and their applications to special functions. Zbl 1132.26337 Neuman, Edward 2006 On Hahn polynomials and continuous dual Hahn polynomials. Zbl 1101.33008 Neuman, Edward 2006 On the Ky Fan inequality and related inequalities. II. Zbl 1086.26014 Neuman, Edward; Sándor, József 2005 Inequalities involving generalized Bessel functions. Zbl 1080.33005 Árpád, Baricz; Neuman, Edward 2005 Hermite-Hadamard’s inequalities for multivariate $$g$$-convex functions. Zbl 1071.26015 Klariǧić Bakula, M.; Neuman, E.; Pečarić, J.; Šimić, Vida 2005 Stolarsky means of several variables. Zbl 1078.26020 Neuman, Edward 2005 Inequalities involving Bessel functions of the first kind. Zbl 1078.33003 Neuman, Edward 2004 On the Schwab-Borchardt mean. Zbl 1053.26015 Neuman, E.; Sándor, J. 2003 On certain means of two arguments and their extensions. Zbl 1040.26015 Neuman, Edward; Sándor, József 2003 Bounds for symmetric elliptic integrals. Zbl 1041.33015 Neuman, Edward 2003 On comparison of Stolarsky and Gini means. Zbl 1021.26017 Neuman, Edward; Páles, Zsolt 2003 Inequalities involving Stolarsky and Gini means. Zbl 1026.26012 Neuman, Edward; Sándor, József 2003 On the Ky Fan inequality and related inequalities. I. Zbl 1007.26015 Neuman, Edward; Sándor, József 2002 Dirichlet averages and their applications to Gegenbauer functions. Zbl 0915.33009 Neuman, E. 1996 The weighted logarithmic mean. Zbl 0823.33002 Neuman, Edward 1994 A new formula for box splines on three-directional meshes. Zbl 0829.41008 Neuman, Edward 1994 Inequalities involving modified Bessel functions of the first kind. Zbl 0769.33004 Neuman, Edward 1992 Inequalities involving multivariate convex functions. II. Zbl 0699.26009 Neuman, Edward 1990 Inequalities involving multivariate convex functions. Zbl 0672.26010 Neuman, Edward; Pečarić, Josip 1989 Computation of inner products of some multivariate splines. Zbl 0678.65013 Neuman, Edward 1989 On complete symmetric functions. Zbl 0654.26013 Neuman, Edward 1988 The inversion of cyclic tridiagonal matrices. Zbl 0697.65018 Łosiak, Janina; Neuman, E.; Nowak, Jolanta 1988 Inequalities involving generalized symmetric means. Zbl 0601.26013 Neuman, Edward 1986 Convex interpolating splines of arbitrary degree. III. Zbl 0653.41013 Neuman, Edward 1986 On generalized symmetric means and Stirling numbers of the second kind. Zbl 0604.26015 Neuman, E. 1985 On the convergence of quadratic spline interpolants. Zbl 0696.41003 Neuman, Edward; Schmidt, Jochen W. 1985 Properties of a class of polynomial splines. Zbl 0525.41013 Neuman, Edward 1983 Convex interpolating splines of arbitrary degree. II. Zbl 0559.41005 Neuman, Edward 1982 Quadratic spline interpolation with coinciding interpolation and spline grids. Zbl 0554.41017 Mettke, Holger; Pfeifer, Eckehard; Neuman, Edward 1982 Bounds for the norm of certain spline projections. II. Zbl 0519.41015 Neuman, Edward 1982 Moments and Fourier transforms of B-splines. Zbl 0452.42006 Neuman, Edward 1981 Quadratic splines and histospline projections. Zbl 0455.41005 Neuman, Edward 1980 Determination of a quadratic spline function with given values of the integrals in subintervals. Zbl 0447.41003 Neuman, Edward 1980 Convex interpolating splines of arbitrary degree. Zbl 0436.41001 Neuman, Edward 1980 Note on Stirling numbers of the first and second kinds. Zbl 0464.10007 Neuman, Edward 1980 Bounds for the norm of certain spline projections. Zbl 0425.41016 Neuman, Edward 1979 Uniform approximation by some Hermite interpolating splines. Zbl 0388.41007 Neuman, Edward 1978 Convex interpolating splines of odd degree. Zbl 0393.41005 Neuman, Edward 1978 On the inversion of certain band matrices. Zbl 0447.65009 Neuman, E. 1977 Determination of an interpolating quadratic spline function. Zbl 0337.41001 Neuman, Edward 1976 Projections in uniform polynomial approximations. Zbl 0277.65005 Neuman, Edward 1974 ...and 2 more Documents all top 5 ### Cited by 358 Authors 69 Chu, Yuming 43 Neuman, Edward 35 Yang, Zhenhang 31 Qian, Weimao 15 Song, Yingqing 15 Zhao, Tiehong 11 Zhang, Xiaohui 10 Sándor, József 10 Wang, Miaokun 9 Xu, Huizuo 9 Zhu, Ling 8 Baricz, Árpád 8 Raïssouli, Mustapha 8 Schmidt, Jochen Wilhelm 7 Qiu, Songliang 7 Wang, Gendi 7 Yin, Li 6 Alzer, Horst 6 Bhayo, Barkat Ali 6 Chen, Chaoping 6 Long, Boyong 6 Tian, Jingfeng 6 Zheng, Shenzhou 5 Chen, Xiaodiao 5 Dragomir, Sever Silvestru 5 Jiang, Yunliang 5 Páles, Zsolt 5 Pogány, Tibor K. 5 Vuorinen, Matti Keijo Kustaa 5 Zhang, Wen 4 Bagul, Yogesh J. 4 Chesneau, Christophe 4 Kwong, Man Kam 4 Lin, Xiuli 4 Malešević, Branko J. 4 Pečarić, Josip 4 Qi, Feng 3 Bercu, Gabriel 3 He, Zaiyin 3 Heß, Walter 3 Huang, Liguo 3 Huang, TiRen 3 Jiang, Weidong 3 Jiang, Yueping 3 Lv, Huilin 3 Ma, Xiaoyan 3 Mehrez, Khaled 3 Milovanović, Gradimir V. 3 Nowicka, Monika 3 Sablonnière, Paul 3 Sakai, Manabu 3 Wang, Yongli 3 Witkowski, Alfred 3 Yang, Yueying 2 Banjac, Bojan 2 Buescu, Jorge 2 Butzer, Paul Leo 2 Chen, Jingjing 2 Chu, Hong-Hu 2 Conde, Cristian M. 2 Daiya, Jitendra 2 Dubeau, François 2 Edelman, Alan Stuart 2 Fang, Shu-Cherng 2 Ha, Minghu 2 He, Jianhui 2 Kilgore, Theodore A. 2 Kostić, Marko 2 Lavery, John E. 2 Lei, Jianjun 2 Li, Junfeng 2 Li, Yongmin 2 Losonczi, László 2 Luo, Tianqi 2 Ma, Junyi 2 Mitroi-Symeonidis, Flavia-Corina 2 Moslehian, Mohammad Sal 2 Neumann, Edward 2 Paixão, A. C. 2 Paris, Richard Bruce 2 Pavić, Zlatko 2 Pearce, Charles Edward Miller 2 Qiu, Yefang 2 Richards, Kendall C. 2 Savoie, Jean 2 Shi, Huannan 2 Sun, Zhengjie 2 Takeuchi, Shingo 2 Tan, Shenyang 2 Tao, Xiao-Jing 2 Toader, Gheorghe 2 Usmani, Riaz A. 2 Van Fleet, Patrick J. 2 Verde-Star, Luis 2 Wang, Nan 2 Wu, Limin 2 Xing, Hongjie 2 Yang, Kang 2 Zhang, Yan 1 Agrawal, Om Prakash ...and 258 more Authors all top 5 ### Cited in 119 Serials 62 Journal of Inequalities and Applications 25 Journal of Mathematical Analysis and Applications 17 Integral Transforms and Special Functions 17 Abstract and Applied Analysis 17 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 16 Journal of Approximation Theory 16 Journal of Mathematical Inequalities 12 Applied Mathematics and Computation 8 BIT 8 Mathematical Inequalities & Applications 7 International Journal of Mathematics and Mathematical Sciences 7 Journal of Computational and Applied Mathematics 7 Results in Mathematics 6 Aequationes Mathematicae 5 Linear Algebra and its Applications 5 Applicable Analysis and Discrete Mathematics 5 Journal of Function Spaces 5 AIMS Mathematics 4 Computers & Mathematics with Applications 4 Rocky Mountain Journal of Mathematics 4 Computing 3 Bulletin of the Australian Mathematical Society 3 Expositiones Mathematicae 3 Journal of Applied Mathematics 3 Problemy Analiza. Issues of Analysis 2 Analysis Mathematica 2 Mathematical Notes 2 Journal of Number Theory 2 Mathematische Nachrichten 2 Mathematica Slovaca 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Acta Mathematica Hungarica 2 Numerical Algorithms 2 Journal of Mathematical Imaging and Vision 2 The Ramanujan Journal 2 Positivity 2 Communications of the Korean Mathematical Society 2 Acta Mathematica Scientia. Series B. (English Edition) 2 Mediterranean Journal of Mathematics 2 Journal of Nonlinear Science and Applications 2 Open Mathematics 1 American Mathematical Monthly 1 Artificial Intelligence 1 Discrete Mathematics 1 International Journal of Mathematical Education in Science and Technology 1 Indian Journal of Pure & Applied Mathematics 1 Journal of the Franklin Institute 1 Linear and Multilinear Algebra 1 Periodica Mathematica Hungarica 1 Mathematics of Computation 1 Chaos, Solitons and Fractals 1 Mathematics Magazine 1 Algebra and Logic 1 Algebra Universalis 1 Annals of the Institute of Statistical Mathematics 1 Calcolo 1 Information Sciences 1 Integral Equations and Operator Theory 1 Journal of Econometrics 1 Metron 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Numerical Functional Analysis and Optimization 1 Numerische Mathematik 1 Proceedings of the American Mathematical Society 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Rendiconti dell’Istituto di Matematica dell’Università di Trieste 1 Siberian Mathematical Journal 1 Studies in Applied Mathematics 1 Moscow University Computational Mathematics and Cybernetics 1 Applied Numerical Mathematics 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Applied Mathematics Letters 1 Mathematical and Computer Modelling 1 Journal of Scientific Computing 1 Science in China. Series A 1 Applications of Mathematics 1 Communications in Statistics. Simulation and Computation 1 SIAM Journal on Mathematical Analysis 1 Journal of Algebraic Combinatorics 1 Computational Optimization and Applications 1 Applied Mathematics. Series B (English Edition) 1 Journal of Mathematical Sciences (New York) 1 Filomat 1 Journal of Convex Analysis 1 Opuscula Mathematica 1 Monte Carlo Methods and Applications 1 Discrete and Continuous Dynamical Systems 1 Mathematical Problems in Engineering 1 Journal of Applied Analysis 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Journal of Mathematical Study 1 Annales Mathematicae Silesianae 1 Applied Mathematics E-Notes 1 Communications on Pure and Applied Analysis 1 Computational Methods and Function Theory 1 Journal of Applied Mathematics and Computing 1 Hacettepe Journal of Mathematics and Statistics 1 Analysis in Theory and Applications 1 Journal of Function Spaces and Applications 1 Advances in Difference Equations ...and 19 more Serials all top 5 ### Cited in 38 Fields 250 Real functions (26-XX) 140 Special functions (33-XX) 61 Approximations and expansions (41-XX) 41 Numerical analysis (65-XX) 13 Difference and functional equations (39-XX) 12 Harmonic analysis on Euclidean spaces (42-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 10 Combinatorics (05-XX) 10 Number theory (11-XX) 9 Functions of a complex variable (30-XX) 7 Ordinary differential equations (34-XX) 7 Operator theory (47-XX) 7 Probability theory and stochastic processes (60-XX) 7 Statistics (62-XX) 6 Computer science (68-XX) 5 Group theory and generalizations (20-XX) 5 Sequences, series, summability (40-XX) 4 Partial differential equations (35-XX) 3 General and overarching topics; collections (00-XX) 3 Convex and discrete geometry (52-XX) 3 Operations research, mathematical programming (90-XX) 3 Information and communication theory, circuits (94-XX) 2 History and biography (01-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Integral transforms, operational calculus (44-XX) 2 Functional analysis (46-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 General topology (54-XX) 2 Mechanics of deformable solids (74-XX) 2 Mathematics education (97-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 Topological groups, Lie groups (22-XX) 1 Abstract harmonic analysis (43-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Optics, electromagnetic theory (78-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-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.	2022-08-08T07:23:26	{"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": 0.4984912872314453, "perplexity": 4650.978291941258}, "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/1659882570767.11/warc/CC-MAIN-20220808061828-20220808091828-00459.warc.gz"}
https://zbmath.org/authors/?q=ai%3Adiamond.fred	## Diamond, Fred Compute Distance To: Author ID: diamond.fred Published as: Diamond, Fred; Diamond, F. Further Spellings: Diamond, Fred Irvin Homepage: https://www.kcl.ac.uk/nms/depts/mathematics/people/atoz/diamondf.aspx External Links: MGP · ORCID · Wikidata · Google Scholar · GND · IdRef Documents Indexed: 30 Publications since 1989, including 1 Book 3 Contributions as Editor Co-Authors: 26 Co-Authors with 24 Joint Publications 424 Co-Co-Authors all top 5 ### Co-Authors 9 single-authored 5 Taylor, Richard Lawrence 3 Kassaei, Payman L. 2 Breuil, Christophe 2 Conrad, Brian 2 Darmon, Henri René 2 Dembélé, Lassina 2 Flach, Matthias 2 Guo, Li 2 Kim, Minhyong 2 Kramer, Kenneth B. 1 Berger, Laurent 1 Bobylev, Nikolaĭ Antonovich 1 Böckle, Gebhard 1 Bulatov, Alexander V. 1 Buzzard, Kevin 1 Chang, Seunghwan 1 Dieulefait, Luis Victor 1 Dimitrov, Mladen 1 Dokchitser, Tim 1 Edixhoven, Bas 1 Im, John 1 Jarvis, Frazer 1 Matveenko, N. I. 1 Reduzzi, Davide A. 1 Ribet, Kenneth Alan 1 Roberts, David Peter 1 Rotger, Victor 1 Savitt, David 1 Shurman, Jerry 1 Voight, John Michael 1 Yumagulov, Marat Gayazovich all top 5 ### Serials 3 Compositio Mathematica 3 Mathematical Research Letters 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Duke Mathematical Journal 2 Inventiones Mathematicae 2 Journal of the American Mathematical Society 2 London Mathematical Society Lecture Note Series 1 Automation and Remote Control 1 Proceedings of the National Academy of Sciences of the United States of America 1 Doklady Mathematics 1 Annals of Mathematics. Second Series 1 Journal of the Institute of Mathematics of Jussieu 1 Graduate Texts in Mathematics 1 Forum of Mathematics, Sigma 1 Advanced Courses in Mathematics – CRM Barcelona all top 5 ### Fields 31 Number theory (11-XX) 6 Algebraic geometry (14-XX) 3 General and overarching topics; collections (00-XX) 3 Topological groups, Lie groups (22-XX) 1 Associative rings and algebras (16-XX) 1 $$K$$-theory (19-XX) 1 Group theory and generalizations (20-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Numerical analysis (65-XX) ### Citations contained in zbMATH Open 27 Publications have been cited 1,078 times in 813 Documents Cited by Year A first course in modular forms. Zbl 1062.11022 Diamond, Fred; Shurman, Jerry 2005 On the modularity of elliptic curves over $$\mathbb Q$$: wild 3-adic exercises. Zbl 0982.11033 Breuil, Christophe; Conrad, Brian; Diamond, Fred; Taylor, Richard 2001 On Serre’s conjecture for mod $$\ell$$ Galois representations over totally real fields. Zbl 1227.11070 Buzzard, Kevin; Diamond, Fred; Jarvis, Frazer 2010 Non-optimal levels of $$\text{mod }l$$ modular representations. Zbl 0847.11025 Diamond, Fred; Taylor, Richard 1994 Modularity of certain potentially Barsotti-Tate Galois representations. Zbl 0923.11085 Conrad, Brian; Diamond, Fred; Taylor, Richard 1999 Fermat’s Last Theorem. Zbl 0877.11035 Darmon, Henri; Diamond, Fred; Taylor, Richard 1995 Modular forms and modular curves. Zbl 0853.11032 Diamond, Fred; Im, John 1995 The Tamagawa number conjecture of adjoint motives of modular forms. Zbl 1121.11045 Diamond, Fred; Flach, Matthias; Guo, Li 2004 On deformation rings and Hecke rings. Zbl 0867.11032 Diamond, Fred 1996 The Taylor-Wiles construction and multiplicity one. Zbl 0916.11037 Diamond, Fred 1997 Hilbert modular forms modulo $$p$$ and values of extensions between Galois characters. (Formes modulaires de Hilbert modulo $$p$$ et valeurs d’extensions entre caractères galoisiens.) Zbl 1309.11046 Breuil, Christophe; Diamond, Fred 2014 Lifting modular mod $$l$$ representations. Zbl 0809.11025 Diamond, Fred; Taylor, Richard 1994 The refined conjecture of Serre. Zbl 0853.11031 Diamond, Fred 1995 A correspondence between representations of local Galois groups and Lie-type groups. Zbl 1230.11069 Diamond, Fred 2007 An extension of Wiles’ results. Zbl 0917.11021 Diamond, Fred 1997 Congruence primes for cusp forms of weight $$k\geq 2$$. Zbl 0783.11022 Diamond, Fred 1991 Extensions of rank one $$(\varphi ,\Gamma )$$-modules and crystalline representations. Zbl 1235.11105 Chang, Seunghwan; Diamond, Fred 2011 Modularity of a family of elliptic curves. Zbl 0867.11041 Diamond, Fred; Kramer, Kenneth 1995 On congruence modules associated to $$\Lambda$$-adic forms. Zbl 0686.10022 Diamond, Fred 1989 The Bloch-Kato conjecture for adjoint motives of modular forms. Zbl 1022.11023 Diamond, Fred; Flach, Matthias; Guo, Li 2001 $$\ell$$-adic modular deformations and Wiles’s “Main Conjecture”. Zbl 0919.11041 Diamond, Fred; Ribet, Kenneth A. 1997 Serre weights and wild ramification in two-dimensional Galois representations. Zbl 1417.11099 Dembélé, Lassina; Diamond, Fred; Roberts, David P. 2016 Serre weights for locally reducible two-dimensional Galois representations. Zbl 1396.11084 Diamond, Fred; Savitt, David 2015 Congruence between modular forms: Raising the level and dropping Euler factors. Zbl 0902.11018 Diamond, Fred 1997 On the Hecke action on the cohomology of Hilbert-Blumenthal surfaces. Zbl 0923.11074 Diamond, Fred 1998 Minimal weights of Hilbert modular forms in characteristic $$p$$. Zbl 1391.11073 Diamond, Fred; Kassaei, Payman L 2017 Crystalline lifts of two-dimensional $$\mod p$$ automorphic Galois representations. Zbl 1473.11115 Diamond, Fred; Reduzzi, Davide A. 2018 Crystalline lifts of two-dimensional $$\mod p$$ automorphic Galois representations. Zbl 1473.11115 Diamond, Fred; Reduzzi, Davide A. 2018 Minimal weights of Hilbert modular forms in characteristic $$p$$. Zbl 1391.11073 Diamond, Fred; Kassaei, Payman L 2017 Serre weights and wild ramification in two-dimensional Galois representations. Zbl 1417.11099 Dembélé, Lassina; Diamond, Fred; Roberts, David P. 2016 Serre weights for locally reducible two-dimensional Galois representations. Zbl 1396.11084 Diamond, Fred; Savitt, David 2015 Hilbert modular forms modulo $$p$$ and values of extensions between Galois characters. (Formes modulaires de Hilbert modulo $$p$$ et valeurs d’extensions entre caractères galoisiens.) Zbl 1309.11046 Breuil, Christophe; Diamond, Fred 2014 Extensions of rank one $$(\varphi ,\Gamma )$$-modules and crystalline representations. Zbl 1235.11105 Chang, Seunghwan; Diamond, Fred 2011 On Serre’s conjecture for mod $$\ell$$ Galois representations over totally real fields. Zbl 1227.11070 Buzzard, Kevin; Diamond, Fred; Jarvis, Frazer 2010 A correspondence between representations of local Galois groups and Lie-type groups. Zbl 1230.11069 Diamond, Fred 2007 A first course in modular forms. Zbl 1062.11022 Diamond, Fred; Shurman, Jerry 2005 The Tamagawa number conjecture of adjoint motives of modular forms. Zbl 1121.11045 Diamond, Fred; Flach, Matthias; Guo, Li 2004 On the modularity of elliptic curves over $$\mathbb Q$$: wild 3-adic exercises. Zbl 0982.11033 Breuil, Christophe; Conrad, Brian; Diamond, Fred; Taylor, Richard 2001 The Bloch-Kato conjecture for adjoint motives of modular forms. Zbl 1022.11023 Diamond, Fred; Flach, Matthias; Guo, Li 2001 Modularity of certain potentially Barsotti-Tate Galois representations. Zbl 0923.11085 Conrad, Brian; Diamond, Fred; Taylor, Richard 1999 On the Hecke action on the cohomology of Hilbert-Blumenthal surfaces. Zbl 0923.11074 Diamond, Fred 1998 The Taylor-Wiles construction and multiplicity one. Zbl 0916.11037 Diamond, Fred 1997 An extension of Wiles’ results. Zbl 0917.11021 Diamond, Fred 1997 $$\ell$$-adic modular deformations and Wiles’s “Main Conjecture”. Zbl 0919.11041 Diamond, Fred; Ribet, Kenneth A. 1997 Congruence between modular forms: Raising the level and dropping Euler factors. Zbl 0902.11018 Diamond, Fred 1997 On deformation rings and Hecke rings. Zbl 0867.11032 Diamond, Fred 1996 Fermat’s Last Theorem. Zbl 0877.11035 Darmon, Henri; Diamond, Fred; Taylor, Richard 1995 Modular forms and modular curves. Zbl 0853.11032 Diamond, Fred; Im, John 1995 The refined conjecture of Serre. Zbl 0853.11031 Diamond, Fred 1995 Modularity of a family of elliptic curves. Zbl 0867.11041 Diamond, Fred; Kramer, Kenneth 1995 Non-optimal levels of $$\text{mod }l$$ modular representations. Zbl 0847.11025 Diamond, Fred; Taylor, Richard 1994 Lifting modular mod $$l$$ representations. Zbl 0809.11025 Diamond, Fred; Taylor, Richard 1994 Congruence primes for cusp forms of weight $$k\geq 2$$. Zbl 0783.11022 Diamond, Fred 1991 On congruence modules associated to $$\Lambda$$-adic forms. Zbl 0686.10022 Diamond, Fred 1989 all top 5 ### Cited by 795 Authors 25 Gee, Toby 16 Dummigan, Neil 12 Khare, Chandrashekhar 11 Bleher, Frauke M. 11 Dieulefait, Luis Victor 11 Siksek, Samir 10 Bennett, Michael A. 10 Savitt, David 10 Schimmrigk, Rolf 9 Calegari, Frank 9 Klosin, Krzysztof 8 Diamond, Fred 8 Emerton, Matthew 8 Le, Daniel 7 Buium, Alexandru 7 Darmon, Henri René 7 Herzig, Florian 7 Hida, Haruzo 7 Liu, Tong 7 Morra, Stefano 7 Taylor, Richard Lawrence 6 Berger, Tobias 6 Choi, Dohoon 6 Freitas, Nuno 6 Geraghty, David 6 Harris, Michael Howard 6 Laurinčikas, Antanas 6 Lim, Subong 6 Newton, James 6 Skinner, Christopher M. 5 Bhattacharya, Soumya 5 Breuil, Christophe 5 Brown, Jim L. 5 Chen, Imin 5 Chinburg, Ted 5 Guitart, Xavier 5 Kisin, Mark 5 Le Hung, Bao V. 5 Levin, Brandon 5 Longo, Matteo 5 Murty, Maruti Ram 5 Pasten, Hector V. 5 Rotger, Victor 5 Rouse, Jeremy A. 5 Stein, William A. 5 Wiese, Gabor 5 Ye, Dongxi 4 Ahlgren, Scott D. 4 Bergström, Jonas 4 Bertolini, Massimo 4 Billerey, Nicolas 4 Böckle, Gebhard 4 Bruinier, Jan Hendrik 4 Buzzard, Kevin 4 Byeon, Dongho 4 Castella, Francesc 4 Chida, Masataka 4 Conrad, Brian 4 Delaunay, Christophe 4 Huber, Tim 4 Kim, Daeyeoul 4 Kiming, Ian 4 Koo, Jakyung 4 Long, Ling 4 Matar, Ahmed 4 Mazur, Barry 4 Poonen, Bjorn 4 Shin, Dong Hwa 4 Stoll, Michael 4 Thorne, Jack A. 4 Vatsal, Vinayak 4 Virdol, Cristian 4 Wiles, Andrew John 4 Wuthrich, Christian 3 Agarwal, Mahesh 3 Aygin, Zafer Selçuk 3 Banerjee, Debargha 3 Brunault, François 3 Caruso, Xavier 3 Cheng, Chuangxun 3 Cho, Bumkyu 3 Dąbrowski, Andrzej Bogdan 3 Dahmen, Sander R. 3 Dimitrov, Mladen 3 Garbaliauskienė, Virginija 3 Ghitza, Alexandru 3 González-Jiménez, Enrique 3 Grabner, Peter J. 3 Hsieh, Ming-Lun 3 Hu, Yongquan 3 Jarvis, Frazer 3 Jiménez-Urroz, Jorge 3 Kassaei, Payman L. 3 Kim, Byungchan 3 Kim, Chan-Ho 3 Kim, Chang Heon 3 Koutsianas, Angelos 3 Kumar, Narasimha 3 Lei, Antonio 3 Li, Wen-Ch’ing Winnie ...and 695 more Authors all top 5 ### Cited in 150 Serials 109 Journal of Number Theory 43 International Journal of Number Theory 34 Duke Mathematical Journal 31 Journal de Théorie des Nombres de Bordeaux 25 Transactions of the American Mathematical Society 24 Compositio Mathematica 23 Mathematics of Computation 23 The Ramanujan Journal 22 Proceedings of the American Mathematical Society 21 Research in Number Theory 17 Advances in Mathematics 17 Inventiones Mathematicae 15 Annales de l’Institut Fourier 15 Mathematische Annalen 15 Mathematische Zeitschrift 13 Bulletin of the American Mathematical Society. New Series 12 Journal of High Energy Physics 11 Israel Journal of Mathematics 11 Journal of Algebra 11 Journal of the American Mathematical Society 11 Experimental Mathematics 10 Journal für die Reine und Angewandte Mathematik 9 Journal of the Institute of Mathematics of Jussieu 8 Acta Arithmetica 8 Algebra & Number Theory 7 Functiones et Approximatio. Commentarii Mathematici 7 Research in the Mathematical Sciences 6 Mathematical Proceedings of the Cambridge Philosophical Society 6 Manuscripta Mathematica 6 Forum of Mathematics, Sigma 5 Communications in Mathematical Physics 5 Journal of Mathematical Analysis and Applications 5 Nuclear Physics. B 5 Publications Mathématiques 5 Annals of Mathematics. Second Series 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Glasgow Mathematical Journal 4 Journal of the London Mathematical Society. Second Series 4 Journal of the Mathematical Society of Japan 4 Journal of Mathematical Sciences (New York) 4 Finite Fields and their Applications 4 Selecta Mathematica. New Series 4 Documenta Mathematica 4 Forum of Mathematics, Pi 3 Indian Journal of Pure & Applied Mathematics 3 Mathematical Notes 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Journal of Pure and Applied Algebra 3 Memoirs of the American Mathematical Society 3 Nagoya Mathematical Journal 3 Tokyo Journal of Mathematics 3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 3 Journal of the European Mathematical Society (JEMS) 3 Journal of the Australian Mathematical Society 3 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 3 Annales Mathématiques du Québec 2 International Journal of Modern Physics A 2 American Mathematical Monthly 2 Bulletin of the Australian Mathematical Society 2 Lithuanian Mathematical Journal 2 Journal of Geometry and Physics 2 Archiv der Mathematik 2 Geometriae Dedicata 2 Mathematika 2 Michigan Mathematical Journal 2 Monatshefte für Mathematik 2 Pacific Journal of Mathematics 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Proceedings of the Japan Academy. Series A 2 Proceedings of the London Mathematical Society. Third Series 2 Advances in Applied Mathematics 2 Revista Matemática Iberoamericana 2 Journal of the Ramanujan Mathematical Society 2 International Journal of Mathematics 2 Elemente der Mathematik 2 Proceedings of the National Academy of Sciences of the United States of America 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Annales Mathématiques Blaise Pascal 2 Taiwanese Journal of Mathematics 2 Annals of Combinatorics 2 Acta Mathematica Sinica. English Series 2 Integers 2 Mathematical Modelling and Analysis 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Kyoto Journal of Mathematics 2 Journal de l’École Polytechnique – Mathématiques 1 Modern Physics Letters A 1 Communications in Algebra 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Physics 1 Letters in Mathematical Physics 1 Rocky Mountain Journal of Mathematics 1 Russian Mathematical Surveys 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Acta Mathematica 1 Bulletin de la Société Mathématique de France 1 Canadian Mathematical Bulletin 1 Colloquium Mathematicum 1 Journal of Approximation Theory ...and 50 more Serials all top 5 ### Cited in 39 Fields 747 Number theory (11-XX) 179 Algebraic geometry (14-XX) 29 Group theory and generalizations (20-XX) 29 Topological groups, Lie groups (22-XX) 23 Quantum theory (81-XX) 17 Relativity and gravitational theory (83-XX) 16 Special functions (33-XX) 11 Combinatorics (05-XX) 11 Associative rings and algebras (16-XX) 11 Several complex variables and analytic spaces (32-XX) 7 Information and communication theory, circuits (94-XX) 6 Category theory; homological algebra (18-XX) 6 Functions of a complex variable (30-XX) 5 Commutative algebra (13-XX) 5 Nonassociative rings and algebras (17-XX) 5 Differential geometry (53-XX) 5 Manifolds and cell complexes (57-XX) 4 General and overarching topics; collections (00-XX) 4 Field theory and polynomials (12-XX) 4 Geometry (51-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Ordinary differential equations (34-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Algebraic topology (55-XX) 3 Probability theory and stochastic processes (60-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 $$K$$-theory (19-XX) 2 Mathematics education (97-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Partial differential equations (35-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Abstract harmonic analysis (43-XX) 1 Functional analysis (46-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Computer science (68-XX) 1 Astronomy and astrophysics (85-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-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.	2022-07-02T11:59:56	{"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": 0.34489572048187256, "perplexity": 6709.754615415148}, "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/1656104054564.59/warc/CC-MAIN-20220702101738-20220702131738-00069.warc.gz"}
https://www.zbmath.org/authors/?q=ai%3Adana-picard.thierry-n	# zbMATH — the first resource for mathematics ## Dana-Picard, Thierry Noah Compute Distance To: Author ID: dana-picard.thierry-n Published as: Dana-Picard, Th.; Dana-Picard, Thierry; Dana-Picard, Thierry N. Homepage: http://ndp.jct.ac.il/ External Links: MGP · Wikidata · ORCID · ResearchGate · dblp Documents Indexed: 39 Publications since 1989 Reviewing Activity: 19 Reviews all top 5 #### Co-Authors 16 single-authored 7 Zeitoun, David G. 5 Schaps, Mary Elizabeth 3 Kotsireas, Ilias S. 3 Zehavi, Nurit 2 Kovács, Zoltán 2 Mozgawa, Witold 1 Beaudin, Michel 1 Bigatti, Anna Maria 1 Botana, Francisco 1 Cieślak, Waldemar 1 Cohen, Daniel E. 1 Gago, Felipe 1 Haenel, Arie 1 Koepf, Wolfram A. 1 Koutschan, Christoph 1 Ladra González, Manuel 1 Levin, Alexander Borisovich 1 Li, Wei 1 Mann, Giora 1 Naiman, Aharon 1 Prokopenya, Alexander N. 1 Robertz, Daniel 1 Seiler, Werner M. all top 5 #### Serials 15 International Journal of Mathematical Education in Science and Technology 7 Mathematics in Computer Science 2 Missouri Journal of Mathematical Sciences 1 Houston Journal of Mathematics 1 Rocky Mountain Journal of Mathematics 1 Journal of Geometry 1 Pacific Journal of Mathematics 1 Journal of Symbolic Computation 1 Journal of Interdisciplinary Mathematics 1 Journal of Integer Sequences 1 ACM Communications in Computer Algebra all top 5 #### Fields 10 Mathematics education (97-XX) 8 Associative rings and algebras (16-XX) 8 Real functions (26-XX) 8 Geometry (51-XX) 6 Numerical analysis (65-XX) 6 Computer science (68-XX) 5 Number theory (11-XX) 4 General and overarching topics; collections (00-XX) 3 Differential geometry (53-XX) 2 Commutative algebra (13-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Convex and discrete geometry (52-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) #### Citations contained in zbMATH 23 Publications have been cited 50 times in 26 Documents Cited by Year Bisoptic curves of hyperbolas. Zbl 1314.97005 Dana-Picard, Thierry; Mann, Giora; Zehavi, Nurit 2014 Integral presentations of Catalan numbers. Zbl 1292.97016 Dana-Picard, Thierry 2010 Explicit closed forms for parametric integrals. Zbl 1431.26004 Dana-Picard, Thierry 2004 Integral presentations of Catalan numbers and Wallis formula. Zbl 1273.97040 Dana-Picard, Thierry 2011 Classifying generic algebras. Zbl 0807.16022 Dana-Picard, Thierry; Schaps, Mary Elizabeth 1992 Automated study of envelopes of one-parameter families of surfaces. Zbl 1386.65088 Dana-Picard, Thierry; Zehavi, Nurit 2017 Parametric integrals and Catalan numbers. Zbl 1430.11038 Dana-Picard, Thierry 2005 An automated study of isoptic curves of an astroid. Zbl 1444.68302 Dana-Picard, Thierry 2020 Zooming algorithms for accurate plotting of functions of two real variables. Zbl 1386.65090 Zeitoun, David G.; Dana-Picard, Thierry 2017 Revival of a classical topic in differential geometry: the exploration of envelopes in a computerized environment. Zbl 1345.97009 Dana-Picard, Thierry; Zehavi, Nurit 2016 Parametric improper integrals, Wallis formula and Catalan numbers. Zbl 1241.97005 Dana-Picard, Thierry; Zeitoun, David G. 2012 Sequences of definite integrals, infinite series and Stirling numbers. Zbl 1273.97041 Dana-Picard, Thierry; Zeitoun, David G. 2012 Exploring the isoptics of Fermat curves in the affine plane using DGS and CAS. Zbl 07205385 Dana-Picard, Thierry; Naiman, Aharon; Mozgawa, Witold; Cieślak, Waldemar 2020 Automated determination of isoptics with dynamic geometry. Zbl 1417.68292 Dana-Picard, Thierry; Kovács, Zoltán 2018 Exploration of parametric integrals related to a question of soil mechanics. Zbl 1396.97020 Dana-Picard, Thierry; Zeitoun, David 2017 Closed forms for 4-parameter families of integrals. Zbl 1297.97023 Dana-Picard, Thierry; Zeitoun, David G. 2009 Plane transformations in a complex setting II: isometries. Zbl 1407.51009 Dana-Picard, Thierry 2007 Rays of light trapped by conics. Zbl 1019.51016 Dana-Picard, Thierry 2000 Some applications of barycentric computations. Zbl 1018.65026 Dana-Picard, Thierry 2000 Non reduced components of $$\text{Alg}_n$$. Zbl 0918.16023 Dana-Picard, Thierry; Schaps, M. 1998 Classifying generic algebras: The local case. Zbl 0877.16015 Dana-Picard, Th.; Schaps, M. 1996 Generic $$8$$-dimensional algebras with mixed basis-graph. Zbl 0799.16021 Dana-Picard, Thierry 1994 7-dimensional algebras with mixed basis-graph. Zbl 0772.16013 Dana-Picard, Thierry 1991 An automated study of isoptic curves of an astroid. Zbl 1444.68302 Dana-Picard, Thierry 2020 Exploring the isoptics of Fermat curves in the affine plane using DGS and CAS. Zbl 07205385 Dana-Picard, Thierry; Naiman, Aharon; Mozgawa, Witold; Cieślak, Waldemar 2020 Automated determination of isoptics with dynamic geometry. Zbl 1417.68292 Dana-Picard, Thierry; Kovács, Zoltán 2018 Automated study of envelopes of one-parameter families of surfaces. Zbl 1386.65088 Dana-Picard, Thierry; Zehavi, Nurit 2017 Zooming algorithms for accurate plotting of functions of two real variables. Zbl 1386.65090 Zeitoun, David G.; Dana-Picard, Thierry 2017 Exploration of parametric integrals related to a question of soil mechanics. Zbl 1396.97020 Dana-Picard, Thierry; Zeitoun, David 2017 Revival of a classical topic in differential geometry: the exploration of envelopes in a computerized environment. Zbl 1345.97009 Dana-Picard, Thierry; Zehavi, Nurit 2016 Bisoptic curves of hyperbolas. Zbl 1314.97005 Dana-Picard, Thierry; Mann, Giora; Zehavi, Nurit 2014 Parametric improper integrals, Wallis formula and Catalan numbers. Zbl 1241.97005 Dana-Picard, Thierry; Zeitoun, David G. 2012 Sequences of definite integrals, infinite series and Stirling numbers. Zbl 1273.97041 Dana-Picard, Thierry; Zeitoun, David G. 2012 Integral presentations of Catalan numbers and Wallis formula. Zbl 1273.97040 Dana-Picard, Thierry 2011 Integral presentations of Catalan numbers. Zbl 1292.97016 Dana-Picard, Thierry 2010 Closed forms for 4-parameter families of integrals. Zbl 1297.97023 Dana-Picard, Thierry; Zeitoun, David G. 2009 Plane transformations in a complex setting II: isometries. Zbl 1407.51009 Dana-Picard, Thierry 2007 Parametric integrals and Catalan numbers. Zbl 1430.11038 Dana-Picard, Thierry 2005 Explicit closed forms for parametric integrals. Zbl 1431.26004 Dana-Picard, Thierry 2004 Rays of light trapped by conics. Zbl 1019.51016 Dana-Picard, Thierry 2000 Some applications of barycentric computations. Zbl 1018.65026 Dana-Picard, Thierry 2000 Non reduced components of $$\text{Alg}_n$$. Zbl 0918.16023 Dana-Picard, Thierry; Schaps, M. 1998 Classifying generic algebras: The local case. Zbl 0877.16015 Dana-Picard, Th.; Schaps, M. 1996 Generic $$8$$-dimensional algebras with mixed basis-graph. Zbl 0799.16021 Dana-Picard, Thierry 1994 Classifying generic algebras. Zbl 0807.16022 Dana-Picard, Thierry; Schaps, Mary Elizabeth 1992 7-dimensional algebras with mixed basis-graph. Zbl 0772.16013 Dana-Picard, Thierry 1991 all top 5 #### Cited by 17 Authors 17 Dana-Picard, Thierry Noah 7 Zeitoun, David G. 2 Hajduk, Adam 2 Mozgawa, Witold 2 Qi, Feng 2 Zehavi, Nurit 1 Böttcher, Albrecht 1 Cieślak, Waldemar 1 Gun, Damla 1 Guo, Bai-Ni 1 Kaplan, Daniel T. 1 McCalla, Peter 1 Naiman, Aharon 1 Nkwanta, Asamoah 1 Schaps, Mary Elizabeth 1 Simsek, Yilmaz 1 Spitkovsky, Ilya Matvey all top 5 #### Cited in 13 Serials 8 International Journal of Mathematical Education in Science and Technology 4 Mathematics in Computer Science 1 Archiv der Mathematik 1 Journal of Algebra 1 Journal of Geometry 1 Journal of Symbolic Computation 1 Indagationes Mathematicae. New Series 1 Algebra Colloquium 1 Journal of Interdisciplinary Mathematics 1 Journal of Noncommutative Geometry 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Problemy Analiza. Issues of Analysis 1 Mathematics all top 5 #### Cited in 21 Fields 9 Real functions (26-XX) 9 Mathematics education (97-XX) 7 Number theory (11-XX) 5 Associative rings and algebras (16-XX) 4 Differential geometry (53-XX) 4 Numerical analysis (65-XX) 3 Combinatorics (05-XX) 3 Geometry (51-XX) 2 Commutative algebra (13-XX) 2 Special functions (33-XX) 2 Computer science (68-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Field theory and polynomials (12-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Category theory; homological algebra (18-XX) 1 Functions of a complex variable (30-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-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.	2021-04-17T00:37:13	{"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": 0.33829495310783386, "perplexity": 11006.365515467263}, "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-2021-17/segments/1618038092961.47/warc/CC-MAIN-20210416221552-20210417011552-00089.warc.gz"}
http://cci.lbl.gov/docs/cctbx/doc_maps_boxing/	## Boxing maps and models Learn how to work with a part of a map. In particular, this involves keeping track of coordinate shifts and symmetry. ### Cut out a box from a map It is often convenient to work with just a part of a map. For example, if your structure contains identical 24 copies of a molecule, you might want to work with just one copy and then duplicate it to create the other 23 later. In this section we are going to create a new map that represents part of the map_data map we have been working with. For this example, we are going to just look at the raw boxed map that results so that we can see how it works. In a real situation you would not only cut out the box but shift its origin using the map_model_manager (see further below). Cutting out part of a map is referred to here as boxing. The key step in cutting out a part of a map is specifying the part of the map to cut out. The grid point with the smallest indices in each direction in the cut-out map is called the “lower bounds” and the grid point with the highest indices is the “upper bounds”. If the lower_bounds is (la,lb,lc) and the upper_bounds is (ua,ub,uc) then the resulting box will have (1+ua-la, 1+ub-lb, 1+uc-lc) grid points along a, b and c. This is the value of all for the boxed map. The box will start at lower_bounds, which will be the value of origin for the boxed map. First, lets set up a map: from iotbx.map_model_manager import map_model_manager # load map_model_manager mmm=map_model_manager() # get initialized instance of the map_model_manager mmm.generate_map() # get a model and calculate a map for it map_data = mmm.map_data() # our 3D map object Let’s set some lower and upper bounds: lower_bounds = (10,10,10) # lower bounds for boxed map upper_bounds = (21,31,21) # upper bounds for boxed map Now let’s cut out a part of our map. In this example we are going to use maptbx.copy() to do this. Normally you will instead use the map_model_manager but using maptbx.copy() shows exactly what is happening: from cctbx import maptbx # import maptbx box_map_data = maptbx.copy(map_data, lower_bounds, upper_bounds) # box the map Let’s look at the origin and dimensions of this boxed map. We expect the origin to be at our lower_bounds (10,10,10) and the dimensions to be (12, 22, 12), and the last available point is (21,31,21): print( box_map_data.origin()) # prints (10, 10, 10) print( box_map_data.all()) # prints (12, 22, 12) print( box_map_data.last(False)) # prints (21, 31, 21) This boxed map is defined for any grid points from lower_bounds to upper_bounds, inclusive. We can get the value at grid point (11,12,13) just like we did before and we will get the same answer: print( box_map_data[11,12,13]) # prints 0.0416163499881 The boxed map is not defined at grid point (0,0,0) or any other points outside of the bounds. The boxed map is also a different size than the original (which had a size of 38400): print( box_map_data.size() ) # prints 3168 One final point: the boxed map is a copy, not a pointer to part of the original map. So if you change a value in your boxed map, the original map is unchanged. ### Shifting the origin of a boxed map Notice that indices of grid points in the boxed map we just created are still in the same reference frame as our original map (i.e., the grid point (11, 12, 13) has the same value in the original map as it has in the boxed map. However the origin of the boxed map (10,10,10) is different from the original origin (0,0,0). In cctbx, almost all work with maps is carried out after shifting the origin of the map to (0,0,0). If there is a model associated with a map, the coordinates of atoms in the model are also shifted. Normally this is done for you with the map_model_manager. In this section we are going to do an origin shift directly so that we can see how it works. Let’s shift the origin of our boxed map (box_map_data) to (0,0,0) with the shift_origin() function to see what happens: shifted_box_map_data = box_map_data.shift_origin() # shift origin to (0,0,0) Note that the shift_origin() function does not change the original object but rather returns a new object with shifted origin but the same data. Note also that if you change data in the shifted map you are changing the data in the unshifted map as well. Let’s look at the origin and dimensions of our boxed map after shifting the origin. The size should not change but the origin should be at (0,0,0) and the last available point should be (11,21,11) instead of (21,31,21): print(shifted_box_map_data.origin()) # prints (0, 0, 0) print(shifted_box_map_data.all()) # prints (12, 22, 12) print(shifted_box_map_data.last(False)) # prints (11, 21, 11) This shifted version of our boxed map data is defined from (0,0,0) to (11,21,11). There has been an origin shift of (10,10,10). If we want to see the value at the grid point that used to be called (11,12,13), we now have to look at the grid point (1,2,3): print(shifted_box_map_data[1,2,3]) # prints 0.0416163499881 ### Keeping track of shifts and crystal_symmetry The dimensions of our boxed map (12,22,12) in grid units and in Angstrom units are different from our original map. That means that the crystal_symmetry of our boxed map has changed. We need a way to keep track of several things: 1. any change in origins between original and boxed maps 2. the gridding of the original and boxed maps 3. crystal_symmetry of the original and boxed maps Here is the convention for keeping track of origins, gridding and dimensions: The number of grid points and crystal_symmetry corresponding to the full original map (the full map from cryo-EM or the crystallographic unit cell map for crystallography) are referred to as the unit_cell_grid and unit_cell_crystal_symmetry. Here unit_cell is intended to mean the full unit cell of the map. The origin shift between original and boxed maps is recorded in grid units as origin_shift_grid_units, where the origin shift is the shift needed to move the origin back to its original position. That means that if the origin of the boxed map was at (10,10,10) and it was moved to (0,0,0), the origin shift was (10,10,10). At the same time the origin shift is recorded as a shift in Cartesian coordinates called shift_cart. The value of shift_cart is the shift that has been applied to any coordinates. It has the opposite sign of origin_shift_grid_units. The crystal_symmetry of the boxed map is referred to as crystal_symmetry. This is the crystal_symmetry that is used for any calculations that are done with a boxed map and model. ### The map_model_manager keeps track of crystal_symmetry and origin shifts Now that we have seen how boxing and shifting origins works, we can appreciate how the map_model_manager (mmm) has methods to take care of everything for us. Let’s start from the beginning and box our original map and the model that goes with it using the map_model_manager. Let’s use the same lower and upper bounds we did before and create a new map_model_manager that is boxed and origin-shifted, but that knows all about how to put everything back where it was: boxed_mmm = mmm.extract_all_maps_with_bounds( # create box lower_bounds = lower_bounds, # lower bounds upper_bounds = upper_bounds) # upper bounds If we look at the map_data object from this boxed map_model_manager we will find that it looks just like the boxed, origin-shifted one we created a moment ago: new_shifted_box_map_data = boxed_mmm.map_manager().map_data() # print(new_shifted_box_map_data.origin()) # prints (0, 0, 0) print(new_shifted_box_map_data.all()) # prints (12, 22, 12) print(new_shifted_box_map_data.last(False)) # prints (11, 21, 11) print(new_shifted_box_map_data[1,2,3]) # prints 0.0416163499881 However the map_model_manager knows how to write out this boxed map so that it superimposes on the original: boxed_mmm.write_map('boxed_map.ccp4') # superimposes on orig Similarly, if you write out your map with the DataManager it will superimpose on the original. The map_model_manager shifts the origin of your map and it also shifts the origin of any model that is part of the map_model_manager. That means that the model in our new map_model_manager (boxed_mmm) matches the map in that map_model_manager. The way this happens is that the coordinates of atoms in the model were all shifted by the value of shift_cart() (calculated from the origin_shift_grid_units) that was set when the origin of the map was shifted. When you write out your model, the reverse shift is automatically applied by the DataManager. ### Working with maps and models extracted from a bigger map and model When your working map has been extracted from a larger map with a map_model_manager, the manager will shift the origin of all maps, models, and associated reconstruction symmetry (ncs_spec) objects to (0,0,0) before working with them. Then you do work with the origin at (0,0,0). You automatically get coordinates from your models that are relative to this origin if the model came from the map_model_manager where the origin was automatically shifted. For example you might say: working_sites_cart = boxed_mmm.model().get_sites_cart() # sites Note that when you are working with your boxed model, the values of coordinates that you get from your model with the function get_sites_cart() will not be the coordinates in the original reference frame of your model. They were shifted to match your boxed, shifted map. Finally when writing out maps, models, or ncs objects, the shift origin is shifted back. This shift back is automatic so you do not need to do anything. If you have created a map_model_manager with one map and model, and you have a new map that you want to match, just shift the origin of the new map with shift_origin(). If the maps are compatible, they will now match. You can check that with the is_similar() function. If for some reason you just create a map_manager and want to work with it and do not want to combine it with a model, you should shift the origin of your map_manager to (0,0,0) using the shift_origin() method before working with it. ### Extracting a box vs boxing in place The map_model_manager has two sets of methods for creating boxed versions of itself. One set extracts a new copy that is boxed, and the other changes itself by boxing. These two methods have different properties. The extracted version is a completely new object. In contrast, boxing a map_model_manager in place changes the map_model_manager itself. Its map is boxed,creating a new (differently-sized) map, but its model is changed in place, with new, shifted coordinates but keeping the same model object. To extract a boxed version of a map_model_manager, you use a method such as the extract_all_maps_with_bounds() method that we used above. boxed_mmm = mmm.extract_all_maps_with_bounds( # create box lower_bounds = lower_bounds, # lower bounds upper_bounds = upper_bounds) # upper bounds The extracted map and model are deep copies, not pointers to the originals. This means that if you change the extracted map or model, you do not change the original. Let’s do this just to see. Here are the current coordinates of a site in the model and a position in the map in the map_model_manager: print (mmm.model().get_sites_cart()[0]) # 14.476000000000003, 10.57, 8.342) print (mmm.map_manager().map_data()[11,12,13]) # prints 0.0416163499881 The coordinates for the extracted map_model_manager are shifted: print(boxed_mmm.model().get_sites_cart()[0])# (7.005666666666668, 3.339250000000002, 0.967625000000001) The indices of the map in the extracted map_model_manager are offset by (10,10,10) so now the index (1,2,3) corresponds to the index (11,12,13) in the original map: print (boxed_mmm.map_manager().map_data()[1,2,3]) # prints 0.0416163499881 Now we change the value of a coordinate or a value in the map for our extracted map_model_manager. (Note that the procedure for changing coordinates in a model has three steps: get the sites_cart, change something in sites_cart, set the sites cart in the model with the changed sites_cart): boxed_sites_cart = boxed_mmm.model().get_sites_cart() # get boxed sites boxed_sites_cart[0] = (10,10,10) # set value of one coordinate in boxed sites boxed_mmm.model().set_sites_cart(boxed_sites_cart) # set coordinates in model boxed_mmm.map_manager().map_data()[1,2,3] = 77. # change map value Nothing happens to the original because the extracted map_model_manager was a deep copy: print (mmm.model().get_sites_cart()[0]) # 14.476000000000003, 10.57, 8.342) print (mmm.map_manager().map_data()[11,12,13]) # prints 0.0416163499881 On the other hand, to box a map_model_manager in place, you use a method such as the box_all_maps_with_bounds_and_shift_origin method. Let’s make references to the model and map in our map_model_manager so that we can track what happens to them when we box the map_model_manager in place: mmm_model_ref = mmm.model() # reference to model in mmm mmm_map_manager_ref = mmm.map_manager() # reference to model in mmm Now let’s instead box the map_model_manager in place. This is going to produce a new map but will alter the model and it will not create a new model: mmm.box_all_maps_with_bounds_and_shift_origin( # change mmm in place lower_bounds = lower_bounds, # lower bounds upper_bounds = upper_bounds) # upper bounds The map_model_manager is changed in place( nothing is returned). The new map will be a new copy (its size has changed and changing it does not change the original), but the new model is the same model as the original, with shifted coordinates. If you change the model in this map_model_manager, any references to the original model also change. Let’s do this just to see. The current coordinates of the first site in the model are now shifted: print (mmm.model().get_sites_cart()[0]) # (7.005666666666668, 3.339250000000002, 0.967625000000001) and the indices of the map in the map_model_manager are offset by (10,10,10) so now the index (1,2,3) corresponds to the index (11,12,13) in the original map: print (mmm.map_manager().map_data()[1,2,3]) # prints 0.0416163499881 Now we change the value of a coordinate or a value in the map for our (now-shifted) map_model_manager: sites_cart = mmm.model().get_sites_cart() # get boxed sites sites_cart[0] = (20,20,20) # set value of one coordinate in sites_cart mmm.model().set_sites_cart(sites_cart) # set coordinates in model mmm.map_manager().map_data()[1,2,3] = 222. # change map value The value in our original model now changes because the model in our map_model_manager was shifted in place: print (mmm_model_ref.get_sites_cart()[0]) # (20.0, 20.000000000000004, 20.0) However nothing happens to the original map because the map_model_manager made a fresh copy of the map: print (mmm_map_manager_ref.map_data()[11,12,13]) # prints 0.0416163499881 ### Shifting a new model to match an existing map_manager with shift_model_to_match_map() If you have a map_manager and you have a new model that you want to match, use the function shift_model_to_match_map(new_model) which will shift the new model (in place, changing new_model) to match this map. ### Wrapping Crystallographic maps repeat indefinitely with a repeat unit of the unit cell. On the other hand, cryo-EM maps are only defined inside the region occupied by the original map. The parameter called wrapping is used to specify whether values at a grid point outside the boundaries of a map are to be calculated by wrapping the grid point back into the original map using unit cell translations. In general, crystallographic maps that are full size can be wrapped in this way, but cryo-EM maps and any parts of crystallographic maps cannot. Wrapping is normally guessed from the way a map is created, but it can be specified as part of the initialization of map_manager objects and map_model_manager objects. ### Ignoring symmetry conflicts The map_model_manager and tools that check to see whether the map and model are compatible by comparing their crystal_symmetry values, and if present, unit_cell_crystal_symmetry values. The crystal_symmetry values reflect the dimensions of the boxed map or model, and the unit_cell_crystal_symmetry values (if present) reflect the dimensions of the original map and model unit cells. In most cases, as long as the map_model_manager has been used to keep track of origin shifts and unit_cell_crystal_symmetry, a map and model that have gone through the same boxing steps will be compatible and nothing further needs to be done. However in some cases the crystal_symmetry of a model (for example) might be changed outside the map_model_manager, in which case an attempt to combine that model with a map that is otherwise compatible would fail with an error message that says that the symmetry of a map does not match that of a model and that they therefore cannot be combined successfully. If the model coordinates really are compatible with the map and the crystal symmetry of the model is incorrect, the map_model_manager can be instructed to ignore the symmetry of the model with the ignore_symmetry_conflicts=True keyword. ### Setting crystal_symmetry and unit_cell_crystal_symmetry for a model If you have a map_manager and a model that is in the same frame of reference as the map_manager but for some reason has a different crystal_symmetry or unit_cell_crystal_symmetry, you can match the symmetry of the map_manager (without changing any coordinates in the model) with the map_manager member function set_model_symmetries_and_shift_cart_to_match_map().	2021-10-18T21:02:20	{"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": 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": 0.6159378290176392, "perplexity": 1237.613384519444}, "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/1634323585209.43/warc/CC-MAIN-20211018190451-20211018220451-00145.warc.gz"}
https://vspu.larc.nasa.gov/training-content/chapter-2-modeling-and-designing-intent/subsurfaces/	# Subsurfaces ## Introduction Subsurfaces are lines, rectangles, or ellipses defined in the UW coordinates on an OpenVSP model surface. These features are honored by the CompGeom, CFD Mesh, and DegenGeom functions among others and may be used to model inlet/outlet boundary conditions, control surfaces, material properties, surface roughness, etc.	2023-01-31T03:19:39	{"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": 0.8020690083503723, "perplexity": 5647.164241648227}, "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/1674764499842.81/warc/CC-MAIN-20230131023947-20230131053947-00843.warc.gz"}
https://mfix.netl.doe.gov/doc/mfix/20.1.0/model_setup/regions.html	# 4.4. Regions¶ The Regions pane defines spatial regions (points, lines, planes, boxes, or STLs) of the geometry that are used for: • Initial Conditions • Boundary Conditions • Point Sources • Internal Surfaces • Monitors • Outputs The following buttons are at the top of the Regions pane: Icon Description create a new region delete the selected region duplicate the selected region create a region that encompasses the entire domain create a region on the left side of the domain create a region on the right side of the domain create a region on the top side of the domain create a region on the bottom side of the domain create a region on the front side of the domain create a region on the back side of the domain The (Add) button creates a new region. The region will be created with a generic name such as R_1; it is strongly recommended to rename the region to something more descriptive, so that it is easier to refer to it later. The Color button will change the color of the region in the model setup view. The table created with the “From” and “To” fields for the X, Y, and Z axes define the extents of the region. These widgets take special parameters, min and max, that reference the minimum and maximum values of the domain, as specified in the geometry section. These values will get automatically updated when the extents in the geometry section are updated. The region type will be inferred from the specified extents. If the region needs to be a collection of triangles from the STL file, select the Select Facets (STL) check-box. The selection shape can be changed between a box and an ellipsoid. Triangles that fall on the edge of the shape can be sliced by selecting the Slice Facets check-box. The triangles can be further filtered by the normal direction by specifying a vector and a deviation angle around that vector. Hint If a region is referenced by an item in the Used By column, the region can not be deleted and its type (STL vs non-STL) cannot be changed.	2022-05-18T15:12:18	{"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": 0.2888353765010834, "perplexity": 863.0105288854552}, "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-2022-21/segments/1652662522284.20/warc/CC-MAIN-20220518151003-20220518181003-00412.warc.gz"}
https://www.pnnl.gov/news?news%5B0%5D=research-topic%3ACoastal%20Science&news%5B1%5D=research-topic%3AComputational%20Mathematics%20%26%20Statistics&news%5B2%5D=research-topic%3AEmergency%20Response&news%5B3%5D=research-topic%3AEnergy%20Storage&news%5B4%5D=research-topic%3AGrid%20Architecture&news%5B5%5D=research-topic%3AHigh-Performance%20Computing&news%5B6%5D=research-topic%3AHuman%20Health&news%5B7%5D=research-topic%3APrecision%20Materials%20by%20Design&news%5B8%5D=research-topic%3ARadiological%20%26%20Nuclear%20Detection&news%5B9%5D=research-topic%3ASecure%20%26%20Adaptive%20Systems&news%5B10%5D=research-topic%3ASubsurface%20Energy%20Systems	# News & Media ## Featured Stories SUBSCRIBE TO PNNL NEWS ## Latest Stories 240 results found Filtered by Coastal Science, Computational Mathematics & Statistics, Emergency Response, Energy Storage, Grid Architecture, High-Performance Computing, Human Health, Precision Materials by Design, Radiological & Nuclear Detection, Secure & Adaptive Systems, and Subsurface Energy Systems JUNE 25, 2020 Web Feature ### Mapping the Molecular Health Benefits of Exercise Researchers from 25 institutions around the country, including PNNL, are working to find out how exercise changes the molecular makeup of our cells to generate health benefits. JUNE 10, 2020 Web Feature ### The Quest for a Viable Sodium Battery PNNL and WSU researchers have improved the performance and life cycle of sodium-ion battery technology to where it is comparable to some lithium-ion batteries. JUNE 9, 2020 Web Feature MAY 19, 2020 News Release ### New Study Confirms Important Clues to Fight Ovarian Cancer A new study using proteogenomics to compare cancerous tissue with normal fallopian tube samples advances insights about the molecular machinery that underlies ovarian cancer. MAY 15, 2020 Web Feature ### Staying Ahead of Antibiotic Resistance The recent coronavirus pandemic shows just how quickly a deadly pathogen can sweep across the globe, killing tens of thousands in the U.S. and disrupting daily life for millions more in the span of a few months. APRIL 28, 2020 News Release ### A Leap in Using Silicon for Battery Anodes Researchers at PNNL have come up with a novel way to use silicon as an energy storage ingredient, replacing the graphite in electrodes. Silicon can hold 10 times the electrical charge per gram, but it comes with problems of its own. APRIL 28, 2020 Web Feature ### The Quantum Gate Hack PNNL quantum algorithm theorist and developer Nathan Wiebe is applying ideas from data science and gaming hacks to quantum computing APRIL 17, 2020 Web Feature ### Identifying the Dark Matter of the Molecular World Artificial intelligence helps researchers identify metabolites, the small molecules that underlie life. APRIL 10, 2020 Web Feature ### How Lasers Can Help with Nuclear Nonproliferation Monitoring A team of researchers is working to expand our uranium chemistry understanding using a surprising tool: lasers. This capability gives never-before-seen insight into uranium gas-phase oxidation during nuclear explosions. MARCH 31, 2020 Web Feature ### Scientists Take Aim at the Coronavirus Toolkit A PNNL scientist is studying the structures of the proteins on the surface of the novel coronavirus, using NMR spectroscopy to reveal information about the molecular toolkit that holds the keys to a vaccine or treatment. MARCH 16, 2020 Web Feature ### Carving Out Quantum Space The race toward the first practical quantum computer is in full stride. Scientists at PNNL are bridging the gap between today’s fastest computers and tomorrow’s even faster quantum computers. MARCH 12, 2020 Web Feature ### Tracking Toxics in the Salish Sea With the help of a diagnostic tool called the Salish Sea Model, researchers found that toxic contaminant hotspots in the Puget Sound are tied to localized lack of water circulation and cumulative effects from multiple sources. MARCH 11, 2020 Web Feature ### Energy Storage Safety and Reliability Forum Convenes at PNNL The Energy Storage System Safety and Reliability Forum at PNNL brought together more than 120 energy storage experts from the U.S. Department of Energy, the national laboratories, utilities, industry and academia. MARCH 9, 2020 News Release ### PNNL, Verizon bring 5G to National Laboratory Verizon recently announced a partnership that will make Pacific Northwest National Laboratory the U.S. Department of Energy’s first national laboratory with Verizon 5G ultra wideband wireless technology.	2020-07-06T06:28:36	{"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": 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": 0.1816902905702591, "perplexity": 11029.468247541432}, "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/1593655890105.39/warc/CC-MAIN-20200706042111-20200706072111-00131.warc.gz"}
https://publications.drdo.gov.in/ojs/index.php/dsj/article/download/4007/4555	Differential Degradation Assessment of Helicopter Engines Operated in Marine Environment The helicopters used for marine operations encounter harsh environment laden with salt mist, sand and dust which could accelerate the deterioration of components. Assessment of the effect of operational environment on component degradation of such helicopter engines is crucial in scheduling their maintenance and ensuring flight safety. The objective of this study is to understand and assess the differential degradation pattern of aeroengines operated in marine environment in comparison to their counterparts operated in non-marine environment. In this study, a sample of 257 ex-service aeroengines of same type and make, operated in marine and non-marine environment were randomly selected and their degradation pattern observed. After obtaining the data on component degradation, further statistical analysis was carried out and the statistical significance of the observations were computed. Out of the ten major components considered in this study, five of them were found to have statistically significant differential degradation due to operation in marine environment. For the remaining components adequate evidence was not available to substantiate differential degradation due to operation in marine environment. These findings serve as valuable input for maintenance inventory planning as well as component improvement programme. Helicopters and small aircraft are extensively employed for commuting between sea bound installations, coastal patrolling and for Naval aviation. A significant portion of the operational cost in aviation activity is attributed to engine maintenance expenditure1,2. And hence assessment of the effect of marine environment on these aero engines is crucial in deciding their longevity and planning operational support. In marine environment, the sea winds carry several kilograms of salt per cubic kilometer of air which promotes corrosion in the engine components. Although the engine components are designed to withstand given stresses and to provide a specified factor of safety, erosion and corrosion changes the mechanical characteristics of the materials thus reducing the margin of safety and endangering the flight leading to aircraft accidents3,4. Unless the corrosion is detected and treated, it becomes a serious problem that hampers the flight safety of the aircraft5-7.Persistence of such issues despite extensive precautions taken by the designers and users indicate the need for further research. The menace of marine corrosion on aeroengines is far wider than the generally described aqueous corrosion observed in marine applications. It includes atmospheric corrosion of metals exposed in the marine environment and hot salt corrosion in engines operating at sea or taking in salt-laden air8-11. Further, the mechanism of corrosion that occurs on control equipment may be similar to that which occurs on the basic structure but a small amount of corrosion on avionics equipment can cause serious degradation or complete system failure. Thus the amount of corrosion that is detrimental varies from component to component and the corrosion tolerance of each component is an important factor while considering the overall system safety. As mentioned above, this study has been motivated by the fleet maintenance issues encountered during the operation of aeroengines in marine environment. The information on the differential degradation of engines exposed to marine environment serves as an important input for maintenance inventory planning. Hence a field study has been carried out on a large fleet of helicopter engines operated in temporal climatic region with a portion of the population exposed to marine environment. Based on the physical observations of these engines, a few components were identified for the detailed study regarding their differential degradation due to operation in marine environment. Data on the degradation level of these components were recorded for the entire sample of engines studied and the components were classified on the basis of their tolerance to marine environment. The field data collected during this exercise corresponds to approximately 3,00,000 h of cumulative flying spread over several calendar years. This prolonged duration of study involving a large sample of engines help to gather the aggregate average system response and to control the effect of any inadvertent heterogeneities in degradation arising out of seasonal variations, operational mission profiles, isolated maintenance issues, local climatic variations, etc. Though the accelerated degradation of the engines operated in marine environment is intuitively understandable, no systematic study has been reported on how the degradations in aeroengines operated in marine environment differs from their non-marine counterparts. One can observe a few general studies10,12-17 reported in the literature on the performance degradation of aero gas turbine engines due to various environmental effects. The most prominent among them is AGARD-CP-55817 which discusses the sand erosion issues encountered during the military operation in the deserts of Gulf region. Similar studies have been reported by Narayanamurthy18, et al. regarding the component deterioration of helicopter engines due to environmental effect mainly due to the sand erosion during desert operation by the Indian Armed Forces. These papers on the environmental effect on engine deterioration generally focuses on the material degradation mechanisms or atmost limit their scope of study to sub-system level such as compressor fouling and its effects due to sand ingestion during desert operation or flying in the vicinity of volcanic eruption16,18. Majority of them with the exception of a few19,20 do not distinguish between marine and non-marine environment while discussing the engine deterioration. Airworthiness authorities often intuitively assume the severity of marine environment and limit the operational life of aeroengines operated in marine environment at a level much lower than their non-marine counterparts. The published literature is sparse on this aspect and to the best of the author’s knowledge no article has been published on the comparative evaluation of the aeroengine degradation due to the operation in the marine and non-marine environments. This article fulfills the above literature gap and provides a methodology for comparative assessment of the degradation of aeroengines operated in marine environment vis-a-vis non-marine environment. An empirical field study has been chosen for analysing the differential degradation of aeroengines operated in marine environment. In addition to the operational environment, the extent of damage observed on the engine components depends on many factors such as material used, coatings applied, presence of degradation accelerating factors such as stress concentration, high temperature prevailing inside the aeroengine, presence of combustion products etc. In order to assess the marginal effect of marine environment, one needs to control all other influencing variables through appropriate research methodology. Therefore in the current study, instead of focusing on the ‘physics of failure’, a comparative evaluation of the engines operated in marine environment has been carried out with reference to those engines of same make and model having identical performance characteristics but operated in non-marine environment. The overall plan of research includes selection of a random sample of engines and classifying them into two mutually exclusive groups based on their operating environment for subsequent assessment of the degradation in its constituent components as shown in Fig. 1. Figure 1. The scheme of the proposed research. During this research, a large sample of aeroengines were selected and their degradation patterns observed after a predetermined duration of operation, i.e., each engine included in the sample needs to complete a minimum period of operation in the given environment so that the environmental effect if any could be visible on its components. This minimum operational duration specified as 1200 h in this study corresponds to the authorized time between overhauls of the given engine. In summary, the formal research approach identifies the degradation noticed on critical components of the aeroengine measured on a categorical scale as the variable and the operational environment as a factor. This leads to classification of the sample of engines into two mutually exclusive sets on the basis of their operational environment thus formulating the investigation as a typical two sample problem for differential comparison. Thus the research problem boils down to comparing the proportions of degradations in the marine sample with those of the non-marine sample as described in the following subsections. 2.1 Sampling Scheme and the Data The sample consists of helicopter engines drawn from various operating bases that includes marine as well as non-marine locations. Since it is extremely difficult to implement a probabilistic random sampling design in the actual military operational scenario, a non-probabilistic sampling design is adopted on an adhoc basis and subsequently the sample randomness has been verified using probabilistic methods as follows. To provide the statistical justification of the randomness of the sample selected, a runs test based on the theory of runs21 has been used. The identification number of the engine has been taken as the base reference and a run is defined based on the succession of the unit serial number in the order in which it has been included in the sample. The central idea is to ensure that there are no definite groupings or alternating patterns in the selection of engines as evidenced by too few runs or too many runs. Let n1 be the occurrences of type 1 sequences and n2 be the number of occurrences of type 2 sequences and r indicate the number of runs. Based on the sampling distributions of r, the mean µr and the standard deviation σr are given by (vide Eqns. 15.8 and 15.9 of Canavos22) ${\mu }_{r}=\frac{2{n}_{1}{n}_{2}}{\left({n}_{1}+{n}_{2}\right)}+1$ (1) ${\sigma }_{r}=\sqrt{2{n}_{1}{n}_{2}\frac{2{n}_{1}{n}_{2}-{n}_{1}-{n}_{2}}{{\left({n}_{1}+{n}_{2}\right)}^{2}\left({n}_{1}+{n}_{2}-1\right)}}$ (2) Now for testing the null hypothesis concerning the randomness of the field data, a two tailed test would be appropriate as too many or too few runs would indicate that the process of sample selection is not random. Also it is well known that for a sufficiently large number (say > 10) of n1 and n2 , the sampling distribution of r is closely approximated by Normal distribution. Therefore, based on the z- value for a significance level of 0.1, one can test the hypothesis on the randomness of the given sample. Once a random sample of engines is available, one needs to formulate the theoretical frame work for the differential degradation analysis. Even before that, one has to have clarity on the data needed and how to extract the data. The data extraction is proposed as per the scheme shown in Figure 2 for the entire sample of engines studied. Let each engine included in the sample fall into the Group {M} or {N} where {M} includes the engines operated in marine environment and {N} includes the engines operated in non-marine environment. Based on the operational practice, there is no exchange of engines between marine and non-marine operations and hence {M} and {N} are mutually exclusive. Figure 2.The data extraction scheme. 2.2 The Theoretical Framework Suppose the data on the degradation observed on the major components of a large number of engines is available, the next step is to evaluate the proportion of degradations in each sample. ie., for a given component, one is interested in comparing the proportions of degradations evident in the marine engines with that of non-marine engines. Let ${P}_{{M}_{J}}$ be the proportion of marine operated engines that had undergone degradation in j-th component and ${P}_{{N}_{J}}$ be the proportions of non-marine engines that had degradation in j-th component. Let NM and NN denote the sample sizes from marine and non-marine category respectively and let Xj and Yj be the observed number of degradations corresponding to marine and non-marine engines for a given part j. The sample proportions $\stackrel{̂}{{P}_{{M}_{j}}}={X}_{j}/{N}_{M}$ and $\stackrel{̂}{{P}_{{N}_{j}}}={Y}_{j}/{N}_{N}$ are the maximum likelihood estimators of ${P}_{{M}_{J}}$ and ${P}_{{N}_{J}}$ respectively. Once the sample proportions are known, the differential degradation of j-th component ${\Delta }_{j}$ which is defined as the difference in proportion of degradation between the marine and non-marine engines with respect to j-th component can be obtained as ${\Delta }_{j}={P}_{{M}_{J}}-{P}_{{N}_{J}}$ (3) Further to check whether the marine operations cause a differential degradation to part j, the following hypothesis testing is proposed.${H}_{o}:{P}_{{M}_{J}}={P}_{{N}_{J}}$ or ${P}_{{M}_{J}}-{P}_{{N}_{J}}=0$ against the alternative ${H}_{a}:{P}_{{M}_{J}}\ne {P}_{{N}_{J}}$ In order to test the above hypothesis, let us consider the statistic $\stackrel{̂}{{P}_{{M}_{j}}}-\stackrel{̂}{{P}_{{N}_{j}}}$ . Since by the assumption, Xj and Yj are binominal random variables, the variance estimators are given by $Var\left(\stackrel{̂}{{P}_{{M}_{j}}}\right)=Var\left(\frac{{X}_{j}}{{N}_{M}}\right)=\frac{\stackrel{̂}{{P}_{{M}_{j}}}\left(1-\stackrel{̂}{{P}_{{M}_{j}}}\right)}{{N}_{M}}$ (4) $\text{Var}\left(\stackrel{̂}{{P}_{{N}_{j}}}\right)=\text{Var}\left(\frac{{Y}_{j}}{{N}_{N}}\right)=\frac{\stackrel{̂}{{P}_{{N}_{j}}}\left(1-\stackrel{̂}{{P}_{{N}_{j}}}\right)}{{N}_{N}}$ (5) Under Ho, the two proportions are assumed to be equal. ie., let the common proportions be ${P}_{{M}_{j}}={P}_{{N}_{j}}={P}_{{O}_{j}}$ where ${P}_{{O}_{j}}$ is the pooled estimate of the proportion of degradations. Then, if null hypothesis is true, for sufficiently large number of samples, the statistic $\stackrel{̂}{{P}_{{M}_{j}}}-\stackrel{̂}{{P}_{{N}_{j}}}$ is approximately normally distributed with mean $E\left(\stackrel{̂}{{P}_{{M}_{j}}}-\stackrel{̂}{{P}_{{N}_{j}}}\right)=0$ (6) and Variance, $Var\left(\stackrel{̂}{{P}_{{M}_{j}}}-\stackrel{̂}{{P}_{{N}_{j}}}\right)=\frac{{P}_{{O}_{j}}{\left(1-{P}_{{O}_{j}}\right)}_{}}{{N}_{M}}+\frac{{P}_{{O}_{j}}{\left(1-{P}_{{O}_{j}}\right)}_{}}{{N}_{N}}$ (7) Therefore the standard deviation (SD) follows as, $SD\left(\stackrel{̂}{{P}_{{M}_{j}}}–\stackrel{̂}{{P}_{{N}_{j}}}\right)=\sqrt{{P}_{{O}_{j}}{\left(1-{P}_{{O}_{j}}\right)}_{}\left(\frac{1}{{N}_{M}}+\frac{1}{{N}_{N}}\right)}$ (8) Since ${P}_{{O}_{j}}$ is unknown, let us try to get the best estimator of ${P}_{{O}_{j}}$ as $\stackrel{̂}{{P}_{{O}_{j}}}$ by pooling the information from both samples from the marine and non-marine operating environment to determine the pooled estimates, i.e., $\stackrel{̂}{{P}_{{O}_{j}}}=\frac{{X}_{j}+{Y}_{j}}{{N}_{M}+{N}_{N}}$ (9) where Xj and Yj are the number of degradations in sample of marine and non-marine engines respectively for the j-th component. Therefore standard deviation $SD\left(\stackrel{̂}{{P}_{{M}_{j}}}–\stackrel{̂}{{P}_{{N}_{j}}}\right)=\sqrt{\stackrel{̂}{{P}_{{O}_{j}}}{\left(1-\stackrel{̂}{{P}_{{O}_{j}}}\right)}_{}\left(\frac{1}{{N}_{M}}+\frac{1}{{N}_{N}}\right)}$ (10) Under Ho, for large NM and NN, the distribution of the static $\stackrel{̂}{{P}_{{M}_{j}}}–\stackrel{̂}{{P}_{{N}_{j}}}$ is approximately normal, i.e., $\frac{\left(\stackrel{̂}{{P}_{{M}_{j}}}–\stackrel{̂}{{P}_{{N}_{j}}}\right)}{\text{SD}\left(\stackrel{̂}{{P}_{{M}_{j}}}–\stackrel{̂}{{P}_{{N}_{j}}}\right)}\text{\hspace{0.17em}}\sim N\left(0,1\right)$ therefore, $z=\frac{\stackrel{̂}{{P}_{{M}_{j}}}–\stackrel{̂}{{P}_{{N}_{j}}}}{\sqrt{\stackrel{̂}{{P}_{{O}_{j}}}{\left(1-\stackrel{̂}{{P}_{{O}_{j}}}\right)}_{}\left(\frac{1}{{N}_{M}}+\frac{1}{{N}_{N}}\right)}}$ (11) and the p-value is given by $P\left(z>{z}_{obs}\right)=1-P\left(z\le {z}_{obs}\right)$ (12) When the p-value is high, we have no adequate evidence to reject the null, i.e., As far as Ho is concerned, the analyst does not have adequate evidence to say that the degradation of this component is affected solely by the marine operations. On the corollary; we can infer that marine environment operations has no significant effect on the life of the component in comparison with operations in non-marine environment. One might further be interested in examining the confidence interval (CI) for the differential degradation. The statistic of interest is the difference between the two sample proportions $\left(\stackrel{̂}{{P}_{{M}_{j}}}-\stackrel{̂}{{P}_{{N}_{j}}}\right)$ . Since $E\left(\stackrel{̂}{{P}_{{M}_{j}}}\right)={P}_{{M}_{j}}$ and $E\left(\stackrel{̂}{{P}_{{N}_{j}}}\right)={P}_{{N}_{j}}$ , it could be shown that $E\left(\stackrel{̂}{{P}_{{M}_{j}}}-\stackrel{̂}{{P}_{{N}_{j}}}\right)={P}_{{M}_{j}}-{P}_{{N}_{j}}$ and $Var\left(\stackrel{̂}{{P}_{{M}_{j}}}-\stackrel{̂}{{P}_{{N}_{j}}}\right)=Var\left({P}_{{M}_{j}}\right)+Var\left({P}_{{N}_{j}}\right)$ . It implies that $Var\left(\stackrel{̂}{{P}_{{M}_{j}}}-\stackrel{̂}{{P}_{{N}_{j}}}\right)=\frac{{P}_{{M}_{j}}{\left(1-{P}_{{M}_{j}}\right)}_{}}{{N}_{M}}+\frac{{P}_{{N}_{j}}{\left(1-{P}_{{N}_{j}}\right)}_{}}{{N}_{N}}$ (13) For sufficiently large number of samples, the distribution of the statistic $\left(\stackrel{̂}{{P}_{{M}_{j}}}-\stackrel{̂}{{P}_{{N}_{j}}}\right)$ is approximately normal with mean and variance as shown above. Then the distribution of z is obtained as follows. $z=\frac{\left(\stackrel{̂}{{P}_{{M}_{j}}}-\stackrel{̂}{{P}_{{N}_{j}}}\right)-\left({P}_{{M}_{j}}-{P}_{{N}_{j}}\right)}{\sqrt{\frac{{P}_{{M}_{j}}{\left(1-{P}_{{M}_{j}}\right)}_{}}{{N}_{M}}+\frac{{P}_{{N}_{j}}{\left(1-{P}_{{N}_{j}}\right)}_{}}{{N}_{N}}}}$ (14) Therefore the probability of the random interval $\stackrel{̂}{\left({P}_{{M}_{j}}}-\stackrel{̂}{{P}_{{N}_{j}}}\right)±{\Phi }_{1-\alpha /2}^{-1}SD\left(\stackrel{̂}{{P}_{{M}_{j}}}-\stackrel{̂}{{P}_{{N}_{j}}}\right)=\left(1-\alpha \right)$ where $\Phi \left(.\right)$ is the standard Normal cumulative density function and hence the $100\left(1-\alpha \right)%$ confidence interval of the differential degradation of the j-th component due to operation in marine environment is given by $\left(\stackrel{̂}{{P}_{{M}_{j}}}-\stackrel{̂}{{P}_{{N}_{j}}}\right)±{\Phi }_{1-\alpha /2}^{-1}×\sqrt{\frac{{P}_{{M}_{j}}\left(1-{P}_{{M}_{j}}\right)}{{N}_{M}}+\frac{{P}_{{N}_{j}}\left(1-{P}_{{N}_{j}}\right)}{{N}_{N}}}$ (15) As described above, one can obtain the sample proportions and other statistical properties of the differential degradation of the engines operated in the marine environment. These quantities provide the theoretical basis for the differential degradation assessment of engines presented in this article. Now let us move on to the assessment of differential degradations of a fleet of helicopter engines based on the field observations. It covers a large fleet of engines out of which a portion is exclusively used for marine aviation and hence provides an opportunity to study the effect of marine environment on the degradation of engine components. For large samples of data collected over a period of time, one need not be very pessimistic on the randomness of the sample due to the non-probabilistic sampling technique adopted. The total number of engines and the environment wise break-up are given in Table 1. Here the sample sizes of both marine operated and non-marine operated engines are large enough to approximate the sampling distribution of the ‘number of runs’ (r) by Normal distribution. The number of runs is counted based on the order in which the engines are withdrawn from service and the run test result with p-value = 0.36249 indicate that there is no evidence against the randomness of the selected sample. Table 1. Number of engines sampled. While the randomness of the sample selection has been ensured using statistical test, the identicalness of the units considered in the sample is ensured by means of engineering analysis. Due to their similarity in both construction as well as functional characteristics, the assumption of identical systems forming a homogeneous sample is implicitly tenable. The engineering details such as the standard of preparation, constructional aspects, embodiment of modifications etc. of each engine included in the sample have been verified from the records available with the engine manufacturer. On observing the physical condition of the ex-service components, the criteria for assessing the degradation has been adopted from the engine manufacturer as indicated in the overhaul manual. Domain expertise has been extensively involved in the above decision process. Based on the physical observations made during the pilot study, ten components have been identified for further investigation. Let us denote these components as C1, C2 , …., C10 without getting into the engineering details. Let the degradation level of each ex-service component be indicated in a nominal scale as follows. If the component is physically degraded (component rejected in industrial terms prescribed by the engine manufacturer) denote the observation as 1’ or else denote it as 0’. A snapshot of the data base generated on this basis is shown in Table 2. Table 2. A snapshot of the database. The physical condition of components C1, C2 , …., C10 have been observed for all the ex-service engines included in the study. Different components exhibited varying levels of degradation after prolonged exposure to the operating environment. A summary of the number of degradations observed in each component is presented in Table 3. One important feature observed is the high number of degradations for some engine components (eg. component C4) irrespective of the operating environment. If one looks at the marine operated engines alone, it may lead to wrong conclusion. For instance, in 42 cases out of 48 marine engines, component C4 has been degraded giving a prima facie impression that degradation of component C4 is due to its exposure to marine environment. However if one closely examines the case of engines operated in non-marine environment, component C4 has the maximum number of degradations (163 cases out of 209 engines) and one may not find any statistical support for the argument for differential degradation on component C4. Similarly for component C5, degradation during non-marine operation seems to be more severe than the marine operation. Table 3. Number of degradations observed in each component C1, C2 , …., C10. Having obtained the data on the differential degradation due to the operational environment, further statistical analysis has been carried out. The point estimates of the proportion of degradation in different environments, the point and interval estimates of the differential degradation and the Statistical significance of the observations were computed and tabulated as shown in Table 4. Out of the ten major components considered in this study, five of them were found to have statistically significant differential degradation due to operation in marine environment. For the remaining components adequate evidence is not available to substantiate differential degradation due to operation in marine environment. Table 4. Significance (p-value) of the differential degradation ($\Delta$ j) noticed on different components . Motivated by the maintenance issues of helicopter engines that are used in marine as well as non-marine environments, a systematic study on the differential degradation assessment of aeroengine has been carried out as illustrated in this article. The severity of marine environment is often taken as a basic premise and many airworthiness engineers believe that the aeroengines operated in marine environment have very limited life potential compared to engines operated in non-marine environment. This intuitive assumption needs a formal verification and hence a hypothesis test has been proposed. Under the null hypothesis it is assumed that $\Delta$ j =0. It implies that under null, the marine operating environment has no marginal effect on the component deterioration. The above hypothesis has been tested based on the data collected from a random sample of engines to confirm the differential degradation if any. Statistically significant differential degradation due to operation in marine environment has been observed in five components C2, C6, C8,C9 and C10 with p-values 2.58141 × 10-06 , 7.17953 × 10-36, 1.09585 × 10-04, 2.70403 × 10-14 and 3.46773 × 10-04 respectively as shown in Table 4. However, for components C1, C3, C4 and C7 the p- values obtained are 0.38492, 0.34456, 0.32181 and 0.39008 respectively indicating that there is no adequate evidence available to prove the differential degradation due to marine environment. However for component C5 non-marine degradation seems to be more predominant than degradation induced by marine environment. Figure 3 depicts the 95% confidence intervals of the differential degradation for the components C1, C2, …., C10 in a lucid manner and provides a bird’s eye view of the results obtained. Figure 3. 95% Confidence interval for differential degradation of components C1, C2 , …., C10. This study reveals varying response of different components to the differential degradation while operating in marine environment. Marine environment surely affects the degradation of certain components, but this statement needs to be interpreted carefully. As revealed in this study, operation in marine environment cannot be solely responsible for the component degradation as many components degraded during non-marine operation as well. This probably negates the conventional wisdom of imposing arbitrary life restrictions on marine engines under the pretext of harsh marine environment. This result opens up a large area of research in life management of critical components of complex systems operated in marine environment. As mentioned above, this study emphasizes the need for detailed material analysis and institution of degradation mitigation plans leading to judicious life management of aeroengines. Some components are susceptible for higher rate of degradation in marine environment such as C2, C6, C8, C9 and C10 and these may be identified for further study under component improvement programme. Similarly component C5 needs some re-look from the engineering perspective related to the non-marine operation, probably issues related to operation at high altitudes or hot desert conditions and so on. The remaining components C1, C3, C4 and C7 have degradation as a result of operational exploitation but one cannot attribute it on the harshness of marine environment. These components are affected by some degradation mechanisms prevailing both at marine and non-marine environments. These aspects offer new venues of research and can be explored further as an extension to this work. Further, the component rejections during engine overhaul is directly linked to the extent of degradation and thus the outcome of this study provides an essential input for maintenance planning and inventory management. The demand rate of these high value inventory and their differential consumption pattern for marine vis-a-vis non marine application is an indispensable information for the maintenance-repair-overhaul (MRO) supply chain management. An assessment of the differential degradation of a typical helicopter engine operated in marine environment has been carried out. While discussing the practical issues, methodological issues were also addressed. Data analysis revealed that five out of the ten selected components of the given aeroengine do exhibit statistically significant differential degradation due to operation in marine environment. This study brings out the need for systematic assessment of the environmental degradation on critical components of complex systems. Through the analysis of operational feedback collected from a large fleet of engines, this article highlights the methodology to assess equipment degradation due to operation in marine environment through a field survey. The author wishes to thank Dr K. Tamilmani, DS & Chief Executive, CEMILAC for granting permission to publish this article. The technical association with Dr. Suresh Srivastava is acknowledged with thanks. The constructive criticism and the contribution by the referees are also greatly appreciated. 1. Orupp. Maintenance cost forecast for civil aircraft gas turbine engines. In Proceedings of the XIV International Symposium on Air breathing Engines (ISABE), Florence, Italy, 1999. 2. Singnori, B. Engine fleet management Alitalia experience on engine maintenance. In Proceedings of the XIV International Symposium on Air breathing Engines (ISABE), Florence, Italy, 1999. 3. Campbell, G.S. & Lahey, R. A survey of serious aircraft accidents involving fatigue fracture. Int. J. Fatigue, 1984,6(1), 25-30. 4. Esaklul, K.A. Handbook of case histories in failure analysis. ASM International, USA, 1993, Vol. 2. 5. Cole, I.S. & Paterson, D.A. Modeling aerosol deposition rates on aircraft and implications for pollutant accumulation and corrosion. Corros. Eng. Sci. Technol., 2009,44(5), 332-39. 6. Steensma, D.K. Audit report on U.S. navy aircraft corrosion prevention and control program. US Navy Report No.97-181, 1997. 7. James, M.N. Crashing aircraft, sinking ships - fractographic and SEM support for unusual failure hypothesis. Eng. Fail. Anal., 2002, 9(3), 313-28. 8. Knight, S.P.; Salagaras, M. & Trueman, A.R. The study of intergranular corrosion in aircraft aluminum alloys using X-ray tomography. Corrosion Science, 2011, 53(2), 727-34. 9. Richardson, Tony J.A. Ed., Shreir’s corrosion. Vol. 4. Elsevier, 2010, 3175-97. 10. Carter, T.J. Common failures in gas turbine blades. Eng. Fail. Anal., 2005, 12(2), 237-47. 11. Ren, X.; Wang, F. & Wang, X. High temperature oxidation and hot corrosion behavior of the NiCr-CrAl coating on a nickel based super alloy. Surf. Coat. Technol., 2005, 198(1-3), 425-31. 12. Turan, D. & Karci, A. Failure analysis of aircraft piston engine components. Eng. Fail. Anal., 2009, 16(4), 1339-45. 13. Scala, S.M.; Konrad, M. & Mason, R.B. Predicting the performance of a gas turbine engine undergoing compressor blade erosion. In Proceedings of 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, AIAA 2003-5259, Huntsville, Alabama, 2003. 14. Sirs, R.C. The operation of gas turbine engines in hot and sandy condition. In Proceedings of the Conference of the Advisory Group for Aerospace Research and Development, AGARD-CP-558, Rotterdam, Netherland, 25-28April, 1994. 15. Edmard, V.R. & Rouse, P.L. U.S. Army rotorcraft turboshaft engines with environmental ingestion effects. In Proceedings of the Conference of the Advisory Group for Aerospace Research and Development- AGARD-CP-558, Rotterdam, Netherland, 25-28April, 1994. 16. Webley, P.W. Virtual globe visualisation of ash-aviation encounters with the special case of the 1989 Redoubt-KLM incident. Computers Geosciences, 2011, 37(1), 25-37. 17. AGARD CP 558: Erosion corrosion and foreign object damage effects on gas turbines. In the Proceedings of the Conference of the Advisory Group for Aerospace Research and Development. Rotterdam, Netherland, 25-28 April, 1994. 18. Narayanamurthy, R.V.; Unnikrishnan, V.; Amarnath, B.G. & Srinivasa, K. Erosion problem of axial compressor blades of a turboshaft engine. In Proceedings of the VIII International Symposium on Air breathing Engines (ISABE), Cincinnati, Ohio,USA,1987. 19. Samuel, M.P.; Rao, V.S. & Unnikrishnan, V. Problems associated with operation of aeroengines in marine environment. In Proceedings of NRB Seminar on Naval Materials: Present and Futuristic Trends, NMRL, Mumbai, India, 2000. 19. Hoffman, M.E. & Hoffman, P.C. Corrosion and fatigue research-structural issues and relevance to naval aviation. Int. J. Fatigue, 2001, 23(1), 1-10. 20. Mood, A.M. The distribution theory of runs. Ann. Math. Stat., 1940, 11, 367-92. 21. Canavos, G.C. Applied probability and statistical methods. Little Brown & Co. Ltd., USA, 1984. Dr Mathews P. Samuel Dr Mathews P. Samuel received BTech in the 1993 and MS (Mechanical Engg) from IIT, Madras in 1996. In 2010 he got PhD from Indian Institute of Science (IISc), Bangalore. Currently he is a scientist at RCMA(Engines), Center for Military Airworthiness and Certification, Bangalore, India.	2019-10-14T03:16:34	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 45, "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": 0.6374019384384155, "perplexity": 1694.4481595842037}, "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-2019-43/segments/1570986649035.4/warc/CC-MAIN-20191014025508-20191014052508-00489.warc.gz"}
https://www.anl.gov/argonne-scientific-publications/pub/127521	Publication # Engineering of hydrogenated two-dimensional h-BN/C superlattices as electrostatic substrates. ### Authors Liu, Zhun; Zhong, Xiaoliang; Yan, Hui; Wang, Ru-Zhi ### Abstract Hybridized two-dimensional materials incorporating domains from the hexagonal boron nitride (h-BN) and graphene is an interesting branch of materials science due to their highly tunable electronic properties. In the present study, we investigate the hydrogenated two-dimensional (2D) h-BN/C superlattices (SLs) with zigzag edges using first-principles calculations. We found that the domain width, the phase ratio, and the vertical dipole orientation all have significant influence on the stability of SLs. The electronic reconstruction is associated with the lateral polar discontinuities at the zigzag edges and the vertically polarized (B2N2H4)(m) domains, which modifies the electronic structures and the spatial potential of the SLs significantly. Furthermore, we demonstrate that the hydrogenated 2D h-BN/C SLs can be applied in engineering the electronic structure of graphene: laterally-varying doping can be achieved by taking advantage of the spatial variation of the surface potential of the SLs. By applying an external vertical electric field on these novel bidirectional heterostructures, graphene doping levels and band offsets can be tuned to a wide range, such that the graphene doping profile can be switched from the bipolar (p-n junction) to unipolar (n(+)-n junction) mode. It is expected that such bidirectional heterostructures provide an effective approach for developing novel nanoscale electronic devices and improving our understanding of the fundamentals of low-dimensional materials. MSD 2016 Article	2019-02-17T20:13:38	{"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": 0.8050615191459656, "perplexity": 3148.2407121915}, "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-2019-09/segments/1550247482478.14/warc/CC-MAIN-20190217192932-20190217214932-00140.warc.gz"}
http://dlmf.nist.gov/20.13	# §20.13 Physical Applications The functions , , provide periodic solutions of the partial differential equation with . For , with real, (20.13.1) takes the form of a real-time diffusion equation with diffusion constant . Let . Then the nonperiodic Gaussian is also a solution of (20.13.2), and it approaches a Dirac delta (§1.17) at . These two apparently different solutions differ only in their normalization and boundary conditions. From (20.2.3), (20.2.4), (20.7.32), and (20.7.33), and Thus the classical theta functions are “periodized”, or “anti-periodized”, Gaussians; see Bellman (1961, pp. 18, 19). Theta-function solutions to the heat diffusion equation with simple boundary conditions are discussed in Lawden (1989, pp. 1–3), and with more general boundary conditions in Körner (1989, pp. 274–281). In the singular limit , the functions , , become integral kernels of Feynman path integrals (distribution-valued Green’s functions); see Schulman (1981, pp. 194–195). This allows analytic time propagation of quantum wave-packets in a box, or on a ring, as closed-form solutions of the time-dependent Schrödinger equation.	2014-03-10T11:33:15	{"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": 0.9525039196014404, "perplexity": 2178.938689705157}, "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-2014-10/segments/1394010765401/warc/CC-MAIN-20140305091245-00079-ip-10-183-142-35.ec2.internal.warc.gz"}
https://www.zbmath.org/authors/?q=ai%3Aaskey.richard-a	# zbMATH — the first resource for mathematics ## Askey, Richard Allen Compute Distance To: Author ID: askey.richard-a Published as: Askey, Richard; Askey, R.; Askey, Richard A.; Askey, R. A.; Askey, Richard A. (Dick); Askey, Richard Allen; Askey, Dick Homepage: http://www.math.wisc.edu/~askey/ External Links: MGP · Math-Net.Ru · Wikidata · dblp · GND · MacTutor Documents Indexed: 157 Publications since 1959, including 10 Books Reviewing Activity: 188 Reviews Biographic References: 8 Publications all top 5 #### Co-Authors 89 single-authored 11 Ismail, Mourad El-Houssieny 8 Gasper, George Jun 7 Andrews, George Eyre 7 Wainger, Stephen 4 Fitch, James 4 Koornwinder, Tom H. 4 Suslov, Sergei K. 4 Wilson, James A. 3 Al-Salam, Waleed A. 3 Allaway, William R. 3 Roy, Ranjan 2 Boas, Ralph Philip jun. 2 Hirschman, Isidore Isaac jun. 2 Rahman, Mizan 2 Steinig, John 2 Tepper Haimo, Deborah 1 Atakishiev, Natig M. 1 Berndt, Bruce Carl 1 Bingham, Nicholas Hugh 1 de Boor, Carl 1 Harris, Lawrence A. 1 Karlin, Samuel 1 Koelink, Erik 1 Nevai, Paul G. 1 Pollard, Harry 1 Ramanathan, Kollagunta G. 1 Rankin, Robert Alexander 1 Rashed, Thanaa M. 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Indagationes Mathematicae all top 5 #### Fields 104 Special functions (33-XX) 29 Harmonic analysis on Euclidean spaces (42-XX) 12 History and biography (01-XX) 9 Combinatorics (05-XX) 9 Sequences, series, summability (40-XX) 7 Number theory (11-XX) 7 Real functions (26-XX) 6 General and overarching topics; collections (00-XX) 4 Functions of a complex variable (30-XX) 4 Approximations and expansions (41-XX) 4 Integral transforms, operational calculus (44-XX) 4 Numerical analysis (65-XX) 3 Computer science (68-XX) 3 Quantum theory (81-XX) 2 Difference and functional equations (39-XX) 2 Abstract harmonic analysis (43-XX) 2 Probability theory and stochastic processes (60-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Geometry (51-XX) #### Citations contained in zbMATH Open 130 Publications have been cited 2,999 times in 2,319 Documents Cited by Year Special functions. Zbl 0920.33001 Andrews, George E.; Askey, Richard; Roy, Ranjan 1999 Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Zbl 0572.33012 Askey, Richard; Wilson, James 1985 Oethogonal polynomials and special functions. Zbl 0298.33008 1975 A set of orthogonal polynomials that generalize the Racah coefficients or 6-j symbols. Zbl 0437.33014 Askey, Richard; Wilson, James 1979 Recurrence relations, continued fractions and orthogonal polynomials. Zbl 0548.33001 1984 Mean convergence of expansions in Laguerre und Hermite series. Zbl 0125.31301 Askey, R.; Wainger, S. 1965 The q-gamma and q-beta functions. Zbl 0398.33001 1978 Special functions. Paperback ed. Zbl 1075.33500 Andrews, George E.; Askey, Richard; Roy, Ranjan 2000 Some absolutely monotonic functions. Zbl 0298.26010 1975 Some basic hypergeometric extensions of integrals of Selberg and Andrews. Zbl 0458.33002 1980 Integral representations for Jacobi polynomials and some applications. Zbl 0172.08803 Askey, R.; Fitch, J. 1969 Ramanujan’s extensions of the gamma and beta functions. Zbl 0437.33001 1980 Associated Laguerre and Hermite polynomials. Zbl 0547.33006 Askey, Richard; Wimp, Jet 1984 A generalization of ultraspherical polynomials. Zbl 0532.33006 1983 Mean convergence of orthogonal series and Lagrange interpolation. Zbl 0253.41003 1972 Orthogonal polynomials and positivity. Zbl 0188.12402 1969 A convolution structure for Jacobi series. Zbl 0186.12303 Askey, R.; Wainger, S. 1969 Another q-extension of the beta function. Zbl 0471.33001 Andrews, George E.; Askey, Richard 1981 Sieved ultraspherical polynomials. Zbl 0547.33005 Al-Salam, Waleed; Allaway, W. R.; Askey, Richard 1984 Some positive trigonometric sums. Zbl 0244.42002 Askey, Richard; Steinig, John 1974 Integrability theorems for Fourier series. Zbl 0136.36501 Askey, R.; Wainger, S. 1966 A set of hypergeometric orthogonal polynomials. Zbl 0496.33007 Askey, Richard; Wilson, James 1982 Positive Jacobi polynomial sum. II. Zbl 0355.33005 Askey, Richard; Gasper, George 1976 Continuous Hahn polynomials. Zbl 0582.33007 1985 Convolution structures for Laguerre polynomials. Zbl 0347.33006 Askey, Richard; Gasper, George 1977 On the behavior of special classes of ultraspherical expansions. I, II. Zbl 0132.29403 Askey, R.; Wainger, S. 1965 Mean summability for ultraspherical polynomials. Zbl 0132.29501 Askey, R.; Hirschman, I. I. jun. 1963 Summability of Jacobi series. Zbl 0268.33015 1973 On a general $$q$$-Fourier transformation with nonsymmetric kernels. Zbl 0871.33008 Askey, Richard A.; Rahman, Mizan; Suslov, Sergej K. 1996 Grünbaum’s inequality for Bessel functions. Zbl 0253.33009 1973 Linearization of the product of Jacobi polynomials. III. Zbl 0212.40904 Askey, R.; Gasper, G. 1971 Classical orthogonal polynomials. Zbl 0596.33016 Andrews, George E.; Askey, Richard 1985 Enumeration of partitions: the role of Eulerian series and $$q$$-orthogonal polynomials. Zbl 0381.10008 Andrews, George E.; Askey, Richard 1977 A simple proof of Ramanujan’s summation of the $$_1\Psi_1$$. Zbl 0401.33002 Andrews, George E.; Askey, Richard 1978 Permutation problems and special functions. Zbl 0313.05005 1976 More q-beta integrals. Zbl 0599.33002 Askey, Richard; Roy, Ranjan 1986 The $$q$$-harmonic oscillator and the Al-Salam and Carlitz polynomials. Zbl 0919.33010 Askey, R.; Suslov, S. K. 1993 Jacobi polynomial expansions of Jacobi polynomials with non-negative coefficients. Zbl 0217.11402 Askey, R.; Gasper, G. 1971 Gaussian processes on compact symmetric spaces. Zbl 0329.60019 Askey, R.; Bingham, N. H. 1976 A transplantation theorem between ultraspherical series. Zbl 0135.27603 Askey, R.; Wainger, S. 1966 A transplantation theorem for Jacobi series. Zbl 0174.35303 1969 Ramanujan and hypergeometric and basic hypergeometric series. Zbl 0722.33009 1990 Certain rational functions whose power series have positive coefficients. Zbl 0242.33023 Askey, Richard; Gasper, George 1972 A transplantation theorem for ultraspherical coefficients. Zbl 0136.37201 Askey, R.; Wainger, S. 1966 Evaluation of Sylvester type determinants using orthogonal polynomials. Zbl 1090.15007 2005 Orthogonal expansions with positive coefficients. Zbl 0136.05103 1965 Positivity of the Cotes numbers for some ultraspherical abscissas. Zbl 0169.08301 Askey, R.; Fitch, J. 1968 Some absolutely monotonic and completely monotonic functions. Zbl 0239.26010 Askey, Richard; Pollard, Harry 1974 A q-extension of Cauchy’s form of the beta integral. Zbl 0463.33003 1981 Hausdorff’s moment problem and expansions in Legendre polynomials. Zbl 0483.44012 Askey, R.; Schoenberg, I. J.; Sharma, A. 1982 A q-beta integral associated with $$BC_ 1$$. Zbl 0501.33002 1982 An elementary evaluation of a beta type integral. Zbl 0523.33001 1983 Jacobi polynomial expansions with positive coefficients and imbeddings of projective spaces. Zbl 0167.35003 1968 Weighted permutation problems and Laguerre polynomials. Zbl 0405.05008 Askey, Richard; Ismail, Mourad E. H.; Koornwinder, Tom 1978 The very well-poised Psi(6,6). Zbl 0412.33005 1979 Positivity of the Cotes numbers for some Jacobi abscissas. Zbl 0237.65012 1972 An integral of Ramanujan and orthogonal polynomials. Zbl 0665.33001 1987 Divided difference operators and classical orthogonal polynomials. Zbl 0696.33008 1989 Norm inequalities for some orthogonal series. Zbl 0173.06703 1966 A dual convolution structure for Jacobi polynomials. Zbl 0174.36305 Askey, R.; Wainger, S. 1968 Special functions: Group theoretical aspects and applications. Zbl 0543.00007 Askey, R. A. (ed.); Koornwinder, T. H. (ed.); Schempp, Walter (ed.) 1984 Problems which interest and/or annoy me. Zbl 0797.33006 1993 Jacobi polynomials. I: New proofs of Koornwinder’s Laplace type integral representation and Bateman’s bilinear sum. Zbl 0242.33019 1974 The very well-poised $$_6\Psi_6$$. Zbl 0387.33002 Askey, R. A.; Ismail, Mourad E. H. 1979 Vietoris’s inequalities and hypergeometric series. Zbl 0899.33002 1998 Finite differences and orthogonal polynomials. Zbl 0801.33005 1994 Continuous q-Hermite polynomials when $$q>1$$. Zbl 0694.33006 1989 A transplantation theorem for Jacobi coefficients. Zbl 0172.08601 1967 Dual equations and classical orthogonal polynomials. Zbl 0185.12601 1968 Jacobi’s generating function for Jacobi polynomials. Zbl 0393.33010 1978 Limits of some q-Laguerre polynomials. Zbl 0641.33018 1986 Similarities between Fourier and power series. Zbl 0854.33005 Askey, Richard; Haimo, Deborah Tepper 1996 Two integrals of Ramanujan. Zbl 0503.33001 1982 Linearization of the product of orthogonal polynomials. Zbl 0212.41001 1970 Orthogonal polynomials and theta functions. Zbl 0675.33006 1989 Positivity of the cotes numbers for some Jacobi abscissas. II. Zbl 0416.65016 1979 An intergral of products of ultraspherical functions and a q-extension. Zbl 0564.33008 Askey, Richard; Koornwinder, Tom H.; Rahman, Mizan 1986 An analog of the Fourier transformation for a $$q$$-harmonic oscillator. Zbl 0863.33020 Askey, R.; Atakishiyev, N. M.; Suslov, S. K. 1993 The $$q$$-harmonic oscillator and an analogue of the Charlier polynomials. Zbl 0859.33021 Askey, R.; Suslov, S. K. 1993 Positive Jacobi polynomial sums. Zbl 0237.33010 1972 A positive sum from summability theory. Zbl 0295.40008 Askey, Richard; Gasper, George; Ismail, Mourad E.-H. 1975 An integral for Jacobi polynomials. Zbl 0308.33006 1973 Smoothness conditions for Fourier series with monotone coefficients. Zbl 0172.34701 1967 On a positive trigonometric sum. Zbl 0174.35704 Askey, R.; Fitch, J.; Gasper, G. 1968 Orthogonal expansions with positive coefficients. II. Zbl 0202.35302 1971 Maximal degrees for Young diagrams in a strip. Zbl 0555.05009 Askey, Richard; Regev, Amitai 1984 Some elementary integrability theorems for special transforms. Zbl 0212.41402 Askey, R.; Karlin, S. 1970 Beta integrals and q-extensions. Zbl 0697.33002 1988 Certain rational functions whose power series have positive coefficients. II. Zbl 0291.33010 1974 Some characteristic functions of unimodal distributions. Zbl 0308.60016 1975 Weighted quadratic norms and ultra-spherical polynomials. I. Zbl 0199.46701 Askey, R.; Hirschman, I. jun. 1959 Beta integrals in Ramanujan’s papers, his unpublished work and further examples. Zbl 0648.33001 1988 A recurrence relation generalizing those of Apéry. Zbl 0558.33003 Askey, Richard; Wilson, J. A. 1984 The work of George Andrews: a Madison perspective. Zbl 1041.01505 1999 Ted Chihara and his work on orthogonal polynomials. Zbl 0999.01023 Askey, R.; Ismail, M. E. H.; Van Assche, W. 2001 A look at the Bateman project. Zbl 0837.33001 1994 The Rogers q-ultraspherical polynomials. Zbl 0479.33013 Askey, Richard A.; Ismail, Mourad E. H. 1980 The very well poised $$_6\psi_6$$. II. Zbl 0509.33001 1983 Some integrability theorems for power series with positive coefficients. Zbl 0212.41401 Askey, R.; Boas, R. P. jun. 1970 An integral of products of Legendre functions and a Clebsch-Gordan sum. Zbl 0524.33004 1982 Completing Brahmagupta’s extension of Ptolemy’s theorem. Zbl 1322.01005 2010 Evaluation of Sylvester type determinants using orthogonal polynomials. Zbl 1090.15007 2005 The 1839 paper of permutations: its relation to the Rodrigues formula and further developments. Zbl 1130.01006 2005 Ted Chihara and his work on orthogonal polynomials. Zbl 0999.01023 Askey, R.; Ismail, M. E. H.; Van Assche, W. 2001 Special functions. Paperback ed. Zbl 1075.33500 Andrews, George E.; Askey, Richard; Roy, Ranjan 2000 Special functions. Zbl 0920.33001 Andrews, George E.; Askey, Richard; Roy, Ranjan 1999 The work of George Andrews: a Madison perspective. Zbl 1041.01505 1999 Vietoris’s inequalities and hypergeometric series. Zbl 0899.33002 1998 On a general $$q$$-Fourier transformation with nonsymmetric kernels. Zbl 0871.33008 Askey, Richard A.; Rahman, Mizan; Suslov, Sergej K. 1996 Similarities between Fourier and power series. Zbl 0854.33005 Askey, Richard; Haimo, Deborah Tepper 1996 Dedication: Remembering Paul Turán. Zbl 0856.01047 1996 Gabor Szegö: 1895–1985. Zbl 0873.01030 Askey, Richard; Nevai, Paul 1996 Finite differences and orthogonal polynomials. Zbl 0801.33005 1994 A look at the Bateman project. Zbl 0837.33001 1994 Gaussian quadrature in Ramanujan’s second notebook. Zbl 0794.41022 1994 The $$q$$-harmonic oscillator and the Al-Salam and Carlitz polynomials. Zbl 0919.33010 Askey, R.; Suslov, S. K. 1993 Problems which interest and/or annoy me. Zbl 0797.33006 1993 An analog of the Fourier transformation for a $$q$$-harmonic oscillator. Zbl 0863.33020 Askey, R.; Atakishiyev, N. M.; Suslov, S. K. 1993 The $$q$$-harmonic oscillator and an analogue of the Charlier polynomials. Zbl 0859.33021 Askey, R.; Suslov, S. K. 1993 Ramanujan and hypergeometric and basic hypergeometric series. Zbl 0722.33009 1990 Graphs as an aid to understanding special functions. Zbl 0694.33002 1990 Relative extrema of Legendre functions of the second kind. Zbl 0698.33006 1990 Divided difference operators and classical orthogonal polynomials. Zbl 0696.33008 1989 Continuous q-Hermite polynomials when $$q>1$$. Zbl 0694.33006 1989 Orthogonal polynomials and theta functions. Zbl 0675.33006 1989 Variants of Clausen’s formula for the square of a special $$_ 2F_ 1$$. Zbl 0756.33002 1989 Selberg’s second beta integral and an integral of Mehta. Zbl 0683.33001 Askey, Richard; Richards, Donald 1989 Beta integrals and the associated orthogonal polynomials. Zbl 0683.33002 1989 Beta integrals and q-extensions. Zbl 0697.33002 1988 Beta integrals in Ramanujan’s papers, his unpublished work and further examples. Zbl 0648.33001 1988 Ramanujan revisited. Proceedings of the centenary conference, University of Illinois at Urbana-Champaign, June 1–5, 1987. Zbl 0635.00003 Andrews, George E.; Askey, Richard A.; Berndt, Bruce C.; Ramanathan, K. G.; Rankin, Robert A. 1988 An integral of Ramanujan and orthogonal polynomials. Zbl 0665.33001 1987 More q-beta integrals. Zbl 0599.33002 Askey, Richard; Roy, Ranjan 1986 Limits of some q-Laguerre polynomials. Zbl 0641.33018 1986 An intergral of products of ultraspherical functions and a q-extension. Zbl 0564.33008 Askey, Richard; Koornwinder, Tom H.; Rahman, Mizan 1986 Positive quadrature methods and positive polynomial sums. Zbl 0613.41027 1986 Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Zbl 0572.33012 Askey, Richard; Wilson, James 1985 Continuous Hahn polynomials. Zbl 0582.33007 1985 Classical orthogonal polynomials. Zbl 0596.33016 Andrews, George E.; Askey, Richard 1985 Appendix. Zbl 0589.33003 1985 Some problems about special functions and computations. Zbl 0596.33001 1985 Recurrence relations, continued fractions and orthogonal polynomials. Zbl 0548.33001 1984 Associated Laguerre and Hermite polynomials. Zbl 0547.33006 Askey, Richard; Wimp, Jet 1984 Sieved ultraspherical polynomials. Zbl 0547.33005 Al-Salam, Waleed; Allaway, W. R.; Askey, Richard 1984 Special functions: Group theoretical aspects and applications. Zbl 0543.00007 Askey, R. A.; Koornwinder, T. H.; Schempp, Walter 1984 Maximal degrees for Young diagrams in a strip. Zbl 0555.05009 Askey, Richard; Regev, Amitai 1984 A recurrence relation generalizing those of Apéry. Zbl 0558.33003 Askey, Richard; Wilson, J. A. 1984 A characterization of the continuous q-ultraspherical polynomials. Zbl 0537.33004 Al-Salam, Walleed; Allaway, W. R.; Askey, Richard 1984 Remarks on the preceding paper by Gavin Brown and Edwin Hewitt. Zbl 0553.42001 1984 Orthogonal polynomials and some definite integrals. Zbl 0562.33007 1984 A generalization of ultraspherical polynomials. Zbl 0532.33006 1983 An elementary evaluation of a beta type integral. Zbl 0523.33001 1983 The very well poised $$_6\psi_6$$. II. Zbl 0509.33001 1983 A set of hypergeometric orthogonal polynomials. Zbl 0496.33007 Askey, Richard; Wilson, James 1982 Hausdorff’s moment problem and expansions in Legendre polynomials. Zbl 0483.44012 Askey, R.; Schoenberg, I. J.; Sharma, A. 1982 A q-beta integral associated with $$BC_ 1$$. Zbl 0501.33002 1982 Two integrals of Ramanujan. Zbl 0503.33001 1982 An integral of products of Legendre functions and a Clebsch-Gordan sum. Zbl 0524.33004 1982 Another q-extension of the beta function. Zbl 0471.33001 Andrews, George E.; Askey, Richard 1981 A q-extension of Cauchy’s form of the beta integral. Zbl 0463.33003 1981 Some basic hypergeometric extensions of integrals of Selberg and Andrews. Zbl 0458.33002 1980 Ramanujan’s extensions of the gamma and beta functions. Zbl 0437.33001 1980 The Rogers q-ultraspherical polynomials. Zbl 0479.33013 Askey, Richard A.; Ismail, Mourad E. H. 1980 A set of orthogonal polynomials that generalize the Racah coefficients or 6-j symbols. Zbl 0437.33014 Askey, Richard; Wilson, James 1979 The very well-poised Psi(6,6). Zbl 0412.33005 1979 The very well-poised $$_6\Psi_6$$. Zbl 0387.33002 Askey, R. A.; Ismail, Mourad E. H. 1979 Positivity of the cotes numbers for some Jacobi abscissas. II. Zbl 0416.65016 1979 Some absolutely monotonic functions. Zbl 0391.33009 1979 The q-gamma and q-beta functions. Zbl 0398.33001 1978 A simple proof of Ramanujan’s summation of the $$_1\Psi_1$$. Zbl 0401.33002 Andrews, George E.; Askey, Richard 1978 Weighted permutation problems and Laguerre polynomials. Zbl 0405.05008 Askey, Richard; Ismail, Mourad E. H.; Koornwinder, Tom 1978 Jacobi’s generating function for Jacobi polynomials. Zbl 0393.33010 1978 Convolution structures for Laguerre polynomials. Zbl 0347.33006 Askey, Richard; Gasper, George 1977 Enumeration of partitions: the role of Eulerian series and $$q$$-orthogonal polynomials. Zbl 0381.10008 Andrews, George E.; Askey, Richard 1977 Positive Jacobi polynomial sum. II. Zbl 0355.33005 Askey, Richard; Gasper, George 1976 Permutation problems and special functions. Zbl 0313.05005 1976 Gaussian processes on compact symmetric spaces. Zbl 0329.60019 Askey, R.; Bingham, N. H. 1976 A monotonic trigonometric sum. Zbl 0334.42003 Askey, Richard; Steinig, John 1976 Oethogonal polynomials and special functions. Zbl 0298.33008 1975 Some absolutely monotonic functions. Zbl 0298.26010 1975 A positive sum from summability theory. Zbl 0295.40008 Askey, Richard; Gasper, George; Ismail, Mourad E.-H. 1975 Some characteristic functions of unimodal distributions. Zbl 0308.60016 1975 Inequalities via fractional integration. Zbl 0307.26014 1975 A derangement problem. Zbl 0337.05011 Askey, Richard; Ismail, Mourad E. H.; Rashed, Thanaa M. T. 1975 Some positive trigonometric sums. Zbl 0244.42002 Askey, Richard; Steinig, John 1974 Some absolutely monotonic and completely monotonic functions. Zbl 0239.26010 Askey, Richard; Pollard, Harry 1974 Jacobi polynomials. I: New proofs of Koornwinder’s Laplace type integral representation and Bateman’s bilinear sum. Zbl 0242.33019 1974 Certain rational functions whose power series have positive coefficients. II. Zbl 0291.33010 1974 Positive Cesaro means of numerical series. Zbl 0288.40010 1974 Summability of Jacobi series. Zbl 0268.33015 1973 Grünbaum’s inequality for Bessel functions. Zbl 0253.33009 1973 An integral for Jacobi polynomials. Zbl 0308.33006 1973 Refinements of Abel summability for Jacobi series. Zbl 0282.43008 1973 Mean convergence of orthogonal series and Lagrange interpolation. Zbl 0253.41003 1972 Certain rational functions whose power series have positive coefficients. Zbl 0242.33023 Askey, Richard; Gasper, George 1972 Positivity of the Cotes numbers for some Jacobi abscissas. Zbl 0237.65012 1972 Positive Jacobi polynomial sums. Zbl 0237.33010 1972 Jacobi summability. Zbl 0234.40016 1972 Linearization of the product of Jacobi polynomials. III. Zbl 0212.40904 Askey, R.; Gasper, G. 1971 Jacobi polynomial expansions of Jacobi polynomials with non-negative coefficients. Zbl 0217.11402 Askey, R.; Gasper, G. 1971 ...and 30 more Documents all top 5 #### Cited by 2,200 Authors 71 Ismail, Mourad El-Houssieny 29 Askey, Richard Allen 22 Rahman, Mizan 20 Alzer, Horst 19 Stanton, Dennis W. 17 Chu, Wenchang 17 Koelink, Erik 17 Koepf, Wolfram A. 17 Spiridonov, Vyacheslav Pavlovich 17 Suslov, Sergei K. 17 Terwilliger, Paul M. 16 Area, Iván 16 Godoy, Eduardo Paciência 16 Koornwinder, Tom H. 16 Nevai, Paul G. 16 Van Assche, Walter 15 Koumandos, Stamatis 14 Cao, Jian 14 Ito, Masahiko 14 Srivastava, Hari Mohan 14 Zhedanov, Alexei S. 13 Marcellán Español, Francisco 12 Atakishiev, Natig M. 12 Gasper, George Jun 12 Karniadakis, George Em 12 Stokman, Jasper V. 12 van Diejen, Jan Felipe 11 Kilic, Emrah 11 Kwong, Man Kam 11 Tikhonov, Sergey Yur’evich 11 Vinet, Luc 11 Zhang, Ruiming 10 Abd-Elhameed, Waleed Mohamed 10 Bryc, Włodzimierz 10 Milne, Stephen C. 10 Mimachi, Katsuhisa 10 Ronveaux, André 10 Voit, Michael 10 Wang, Mingjin 10 Warnaar, S. Ole 9 Coffey, Mark William 9 Doha, Eid H. 9 Karp, Dmitriĭ Borisovich 9 Markett, Clemens 9 Mhaskar, Hrushikesh N. 9 Ostrovska, Sofiya 9 Xu, Yuan 9 Zeilberger, Doron 9 Zeng, Jiang 8 Álvarez-Nodarse, Renato 8 Bouzeffour, Fethi 8 Dai, Feng 8 Jordaan, Kerstin 8 Klimyk, Anatoliy Ul’yanovich 8 Masjed-Jamei, Mohammad 8 McCoy, Peter A. 8 Noumi, Masatoshi 8 Thangavelu, Sundaram 8 Wang, Lilian 7 Brown, Gavin 7 Chen, William Yong-Chuan 7 Chihara, Theodore Seio 7 Gupta, Vijay 7 Iliev, Plamen 7 Ito, Tatsuro 7 Lewanowicz, Stanisław 7 Li, Zhongkai 7 Ma, Chunsheng 7 Masson, David R. 7 Porcu, Emilio 7 Shen, Jie 7 Simeonov, Plamen C. 7 Stempak, Krzysztof 7 Tratnik, M. V. 7 Vuorinen, Matti Keijo Kustaa 7 Zarzo, Alejandro 6 Aomoto, Kazuhiko 6 Barnard, Roger W. 6 Berg, Christian 6 Bringmann, Kathrin 6 Cohl, Howard Saul 6 Dehesa, Jesús S. 6 Demni, Nizar 6 Dimitrov, Dimitar K. 6 Forrester, Peter J. 6 Foupouagnigni, Mama 6 Geronimo, Jeffrey S. 6 Groenevelt, Wolter G. M. 6 Kanjin, Yuichi 6 Kim, Taekyun 6 Krattenthaler, Christian Friedrich 6 Lasser, Rupert 6 Liu, Zhi-Guo 6 Long, Ling 6 Lubinsky, Doron S. 6 Ol’shanskiĭ, Grigoriĭ Iosifovich 6 Petronilho, José C. 6 Rains, Eric M. 6 Rivoal, Tanguy 6 Schlosser, Michael J. ...and 2,100 more Authors all top 5 #### Cited in 384 Serials 136 Journal of Mathematical Analysis and Applications 115 Journal of Computational and Applied Mathematics 109 The Ramanujan Journal 106 Proceedings of the American Mathematical Society 102 Journal of Approximation Theory 76 Transactions of the American Mathematical Society 46 Journal of Mathematical Physics 43 Constructive Approximation 41 Mathematics of Computation 37 Advances in Mathematics 36 Integral Transforms and Special Functions 30 Applied Mathematics and Computation 29 Advances in Applied Mathematics 29 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 25 Communications in Mathematical Physics 24 Rocky Mountain Journal of Mathematics 24 Journal of Combinatorial Theory. Series A 23 Results in Mathematics 21 Journal of Computational Physics 21 Advances in Difference Equations 20 Letters in Mathematical Physics 19 Linear Algebra and its Applications 17 Duke Mathematical Journal 17 Journal of Functional Analysis 17 The Journal of Fourier Analysis and Applications 17 Journal of High Energy Physics 16 Journal d’Analyse Mathématique 16 Acta Mathematica Hungarica 15 Tohoku Mathematical Journal. 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Académie des Sciences, Paris 6 Mediterranean Journal of Mathematics 6 International Journal of Number Theory 6 Journal of Pseudo-Differential Operators and Applications 5 Acta Mathematica Academiae Scientiarum Hungaricae 5 Computing 5 Journal of the Mathematical Society of Japan 5 Statistics & Probability Letters 5 Journal of Symbolic Computation 5 Indagationes Mathematicae. New Series 5 Journal of Algebraic Combinatorics 5 Turkish Journal of Mathematics 5 Bulletin des Sciences Mathématiques 5 Infinite Dimensional Analysis, Quantum Probability and Related Topics 5 Central European Journal of Mathematics 5 Analysis and Applications (Singapore) 5 Journal of Applied Mathematics & Informatics 5 Analysis and Mathematical Physics 5 Problemy Analiza. Issues of Analysis 4 Applicable Analysis 4 Israel Journal of Mathematics 4 The Mathematical Intelligencer ...and 284 more Serials all top 5 #### Cited in 61 Fields 1,198 Special functions (33-XX) 491 Harmonic analysis on Euclidean spaces (42-XX) 269 Combinatorics (05-XX) 237 Number theory (11-XX) 227 Approximations and expansions (41-XX) 215 Numerical analysis (65-XX) 181 Probability theory and stochastic processes (60-XX) 152 Real functions (26-XX) 137 Functions of a complex variable (30-XX) 129 Quantum theory (81-XX) 113 Partial differential equations (35-XX) 101 Difference and functional equations (39-XX) 90 Operator theory (47-XX) 88 Ordinary differential equations (34-XX) 85 Nonassociative rings and algebras (17-XX) 83 Abstract harmonic analysis (43-XX) 79 Functional analysis (46-XX) 74 Integral transforms, operational calculus (44-XX) 73 Linear and multilinear algebra; matrix theory (15-XX) 69 Statistics (62-XX) 58 Statistical mechanics, structure of matter (82-XX) 43 Topological groups, Lie groups (22-XX) 42 Sequences, series, summability (40-XX) 35 Group theory and generalizations (20-XX) 27 Computer science (68-XX) 25 Several complex variables and analytic spaces (32-XX) 25 Fluid mechanics (76-XX) 24 Potential theory (31-XX) 21 Algebraic geometry (14-XX) 19 Dynamical systems and ergodic theory (37-XX) 19 Global analysis, analysis on manifolds (58-XX) 17 History and biography (01-XX) 17 Integral equations (45-XX) 16 Associative rings and algebras (16-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 14 Differential geometry (53-XX) 13 Mechanics of deformable solids (74-XX) 13 Operations research, mathematical programming (90-XX) 13 Biology and other natural sciences (92-XX) 11 Relativity and gravitational theory (83-XX) 10 Systems theory; control (93-XX) 9 Information and communication theory, circuits (94-XX) 8 Manifolds and cell complexes (57-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Commutative algebra (13-XX) 7 Convex and discrete geometry (52-XX) 5 Order, lattices, ordered algebraic structures (06-XX) 5 Measure and integration (28-XX) 5 Geometry (51-XX) 5 Mechanics of particles and systems (70-XX) 4 Field theory and polynomials (12-XX) 3 Optics, electromagnetic theory (78-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Geophysics (86-XX) 2 General and overarching topics; collections (00-XX) 2 Mathematical logic and foundations (03-XX) 2 Category theory; homological algebra (18-XX) 1 $$K$$-theory (19-XX) 1 General topology (54-XX) 1 Astronomy and astrophysics (85-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.	2021-08-04T13:33:26	{"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": 0.6589441299438477, "perplexity": 5217.338282435351}, "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-2021-31/segments/1627046154805.72/warc/CC-MAIN-20210804111738-20210804141738-00209.warc.gz"}
https://ftp.mcs.anl.gov/pub/fathom/moab-docs/mbex4_8cpp.html	MOAB: Mesh Oriented datABase (version 5.3.0) mbex4.cpp File Reference beginner tutorial, example 4: Create a 2D structured mesh and set some tag data on it More... #include "moab/Core.hpp" #include "moab/ScdInterface.hpp" #include <iostream> #include <cmath> Include dependency graph for mbex4.cpp: Go to the source code of this file. int main () ## Detailed Description beginner tutorial, example 4: Create a 2D structured mesh and set some tag data on it In this example, we create a 2D structured mesh (actually a 3D mesh made of quads) and then we will actually set data on the mesh. Tags represent data that is attached to entities. In this example, we will create two tags: 1. A "temperature" tag that is a single double precision number attached to each quad. 2. A "velocity" tag that is an array of 2 double precision numbers attached to each vertex. We will write the mesh out to a file, and you can visualize the data using your favorite tool. In this example, I am demonstrating these operations in the clearest possible way - not using the most efficient method. MOAB has been designed so that users do not need to sacrifice performance - future examples will demonstrate how to access/manipulate the mesh using the fastest methods possible. Definition in file mbex4.cpp. ## Function Documentation int main ( ) Definition at line 42 of file mbex4.cpp. { moab::ErrorCode rval; moab::Core mbint; // *********************** // * Create the Mesh * // *********************** // First, lets make the mesh. It will be a 100 by 100 uniform grid // (there will be 100x100 quads, 101x101 vertexes) with dx = dy = // 0.1. Unlike the previous example, we will first make the mesh, // then set the coordinates one at a time. const unsigned NI = 100; const unsigned NJ = 100; // moab::ScdInterface is the structured mesh interface class for // MOAB. moab::ScdInterface* scdint; // Tell MOAB that our mesh is structured: rval = mbint.query_interface( scdint );MB_CHK_SET_ERR( rval, "mbint.query_interface failed" ); // Create the mesh: moab::ScdBox* scdbox = NULL; rval = scdint->construct_box( moab::HomCoord( 0, 0, 0 ), moab::HomCoord( NI, NJ, 0 ), NULL, 0, scdbox );MB_CHK_SET_ERR( rval, "scdint->construct_box failed" ); // MOAB knows to make quads instead of hexes because the last start // and end indexes are the same (0). Note that it is still a "3D" // mesh because each vertex coordinate is still defined using three // numbers although every element in the mesh is a quadrilateral. // ****************************** // * Set Vertex Coordinates * // ****************************** // The "NULL" and "0" arguments in the call to construct_box are // where we could specify the vertex coordinates. Since we didn't // give any coordinates, every vertex is given a position of 0,0,0 // by default. Now we will set the vertex coordinates... const double DX = 0.1; const double DY = 0.1; for( unsigned i = 0; i < NI + 1; i++ ) for( unsigned j = 0; j < NJ + 1; j++ ) { // First, get the entity handle: moab::EntityHandle handle = scdbox->get_vertex( i, j ); // Compute the coordinate: double coord[3] = { DX * i, DY * j, 0.0 }; // Change the coordinate of the vertex: mbint.set_coords( &handle, 1, coord ); } // ******************* // * Attach Tags * // ******************* // The vertex coordinates have been defined, now let's attach some // data to the mesh. In MOAB this is done using "tags". Tags are // little bits of information that can be attached to any mesh // entity. In our example, we want to create two tags. The // "temperature" tag will be attached to each quad and will be 1 // double. The "velocity" tag will be attached to each vertex and // will be an array of two doubles. // zero and twozeros represent the initial tag // Create the tags: moab::Tag temp_tag; double temp_default_value = 0.0; rval = mbint.tag_get_handle( "temperature", 1, moab::MB_TYPE_DOUBLE, temp_tag, moab::MB_TAG_DENSE \| moab::MB_TAG_CREAT, &temp_default_value );MB_CHK_SET_ERR( rval, "mbint.tag_get_handle(temperature) failed" ); moab::Tag vel_tag; double vel_default_value[2] = { 0.0, 0.0 }; rval = mbint.tag_get_handle( "velocity", 2, moab::MB_TYPE_DOUBLE, vel_tag, moab::MB_TAG_DENSE \| moab::MB_TAG_CREAT, vel_default_value );MB_CHK_SET_ERR( rval, "mbint.tag_get_handle(velocity) failed" ); // Note that when we created each tag, we specified two flags: // // The moab::MB_TAG_DENSE flag tells MOAB that this is a dense // tag. Dense tags will get automatically assigned to entities which // have continuous handles. For this example, this means that once // we set a tag on one vertex, memory will be allocated for // assigning the tag to all vertexes. The same is true of // quads. Dense tags are much more efficient when assigning tags to // lots of entities. If you only want to assign a tag to a few // entities, it is more efficient to use sparse tags // (moab::MB_TAG_SPARSE). // // The moab::MB_TAG_CREAT flag tells MOAB to create the tag if it // The tags have now been created, now we have to attach them to // entities and set their values. NOTE: I am going to do this in a // manner which emphasizes clarity - this is not the most efficient // approach - that will be saved for later tutorial examples. // Loop through each quad and set the temperature: for( unsigned i = 0; i < NI; i++ ) for( unsigned j = 0; j < NJ; j++ ) { // Get the handle for this quad: moab::EntityHandle handle = scdbox->get_element( i, j ); // Compute the temperature... double xc = DX * ( i + 0.5 ); double yc = DY * ( j + 0.5 ); double r = std::sqrt( xc * xc + yc * yc ); double temperature = std::exp( -0.5 * r ); // Set the temperature on a single quad: rval = mbint.tag_set_data( temp_tag, &handle, 1, &temperature );MB_CHK_SET_ERR( rval, "mbint.tag_set_data(temp_tag) failed" ); } // Loop through each vertex and set the velocity: for( unsigned i = 0; i < NI + 1; i++ ) for( unsigned j = 0; j < NJ + 1; j++ ) { // Get the handle for this vertex: moab::EntityHandle handle = scdbox->get_vertex( i, j ); double velocity[2] = { i, j }; // Set the velocity on a vertex: rval = mbint.tag_set_data( vel_tag, &handle, 1, velocity );MB_CHK_SET_ERR( rval, "mbint.tag_set_data(vel_tag) failed" ); } // *************************** // * Write Mesh to Files * // *************************** // NOTE: Some visualization software (such as VisIt) may not // interpret the velocity tag as a vector and you may not be able to // plot it. But you should be able to plot the temperature on top of // the mesh. rval = mbint.write_file( "mbex4.vtk" );MB_CHK_SET_ERR( rval, "write_file(mbex4.vtk) failed" ); return 0; }	2021-10-27T16:09:14	{"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": 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": 0.3214819133281708, "perplexity": 7213.756601836742}, "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/1634323588216.48/warc/CC-MAIN-20211027150823-20211027180823-00494.warc.gz"}
http://semantic-domain.blogspot.com/	## Friday, March 7, 2014 University of Nottingham, 22-26 April 2014 The Midlands Graduate School (MGS) in the Foundations of Computing Science is a collaboration between researchers at the Universities of Birmingham, Leicester, Nottingham and Sheffield. It was established in 1999. The MGS has two main goals: to provide PhD students with a sound basis for research in the mathematical and practical foundations of computing and to give PhD students the opportunity to make contact with established researchers in the field and their peers who are at a similar stage in their research careers. This year, the MGS is at the University of Nottingham. It will start on 22 April and finish on 26 April. # Program MGS2014 consists of ten courses, each with five hours of lectures plus exercise sessions. One third of the programme offers introductory (or core) courses which all participants attend. The remainder provides advanced (or specialised) courses from which each participant selects a subset depending upon his or her interests and one course given by an invited lecturer (Conor McBride). ## Core Courses Course TitleAcronymLecturerAffiliation Category TheoryCATRoy CroleLeicester Denotational Semantics DENAchim JungBirmingham Typed Lambda CalculusLAMPaul Blain LevyBirmingham Course TitleAcronymLecturerAffiliation Concurrency, Causality, ReversibilityCCRIrek UlidowskiLeicester Theory of Randomised Search HeuristicsHEUDirk Sudholt, Per Kristian Lehre, Pietro S. Oliveto, Christine ZargesBirmingham, Nottingham, Sheffield Homotopy Type TheoryHOTThorsten AltenkirchNottingham Infinite Data StructuresINFVenanzio CaprettaNottingham Logical relations and parametricityPARUday ReddyBirmingham Higher-Order Functional Reactive ProgrammingREANeelakantan KrishnaswamiBirmingham # Invited Lecturer In addition to the standard programme, Conor McBride from the University of Strathclyde will give an invited course on Dependently Typed Programming (DTP). # Registration The deadline for registration for MGS 2014 is Friday, 21 March. The registration fee is £440. This includes 5 nights of accommodation (from Monday 21 evening to Saturday 26 April morning), catering for lunches and coffee breaks and the conference dinner. Accommodation is at the University's Newark Hall of Residence and includes breakfast. To register for MGS 2014, you need to book this via the University of Nottingham online store. The site will ask you to register, if this is the first time to use it. You can pay using a credit or debit card. We recommend to register as early as possible because places will be allocated on a first-come first-serve base and it is quite possible that we run out of space before 21 March. ## Contact For any additional information, contact the local organiser, Thorsten Altenkirch, at the address [email protected]. ## Monday, February 3, 2014 ### Retiring a joke I just saw that Andy Pitts has a new draft out, An Equivalent Presentation of the Bezem-Coquand-Huber Category of Cubical Sets, with the following abstract: Staton has shown that there is an equivalence between the category of presheaves on (the opposite of) finite sets and partial bijections and the category of nominal restriction sets: see [2, Exercise 9.7]. The aim here is to see that this extends to an equivalence between the category of cubical sets introduced in [1] and a category of nominal sets equipped with a "01-substitution" operation. It seems to me that presenting the topos in question equivalently as 01-substitution sets rather than cubical sets will make it easier (and more elegant) to carry out the constructions and calculations needed to build the intended univalent model of intentional constructive type theory. Nominal methods have been an active area of research in PL theory for a while now, and have achieved a rather considerable level of sophistication. I have occasionally joked that it seems like we had to aim an awful lot of technical machinery at the problem of alpha-equivalence -- so what happens when we realize that there are other equivalence relations in mathematics? But with this note, it looks like the last laugh is on me! Pitts shows that you can use nominal techniques to give a simpler presentation of the cubical sets model of univalent type theory. Since HoTT gives us a clean constructive account of quotient types and higher inductive types, all the technical machinery invented to handle alpha-equivalence scales smoothly up to handle any equivalence relation you like. ## Saturday, January 25, 2014 ### OBT 2014 I just attended the Off the Beaten Track workshop, which is a POPL workshop where people gather to offer their new, untested, and (ideally) radical ideas. Here are some quick and incomplete reactions. Chris Martens gave a talk, Languages for Actions in Simulated Worlds, in which she described some of her ideas for using linear logic programming to model interactive fiction. The idea behind this is that you can view the state of a game (say, an interactive fiction) as a set of hypotheses in linear logic, and the valid state transitions as hypotheses of the form $A \multimap B$. So if your game state is $$\Gamma = \{ A, X, Y, Z \}$$ Then matching the rule $A \multimap B$ against the context and applying the $\multimap{}L$ rule will give you the modified context $$\Gamma = \{ \mathbf{B}, X, Y, Z \}$$ Then, a story is a proof that the end of the story is derivable • A story is actually a linearization of a proof term. The proof term just records the dependencies in the state transitions, and there is no intrinsic order beyond that. There are many possible linearizations for each proof term, and different linearizations yield different stories. So one question is whether various literary effects (like plot structure) can be seen to arise as properties of the linearization. There has been a lot of work on linearizing proof nets, and I wonder if that has some applications to this. • Can control operators be used to model flashbacks? That is, not all stories occur in a linear chronological order. Sometimes narratives jump forwards and backwards in time. Can we somehow use control operators to model time travel? Call/cc is often explained intuitively in terms of time travel, and it would be cool if that could be turned into a literal explanation of what was happening. • In Martens's account, proof search is used by the computer to work out the consequences of user actions. Is there any way we can make the player do some deduction? For example, some stories gradually reveal information to the reader until the reader has a flash of insight about what has really happening. So is there any way to "make the player do proof search", in order to achieve game effects related to hidden information? (I'm not even sure what I mean, honestly.) • Can we use theorem proving to model fate and prophecies in games? So, if you have a Lincoln simulator in which John Wilkes Booth kills Abraham Lincoln at the end of the game, then you might want to let the player do anything which does not make this impossible. In current games, this might be done by giving Booth rules-breaking defenses or simply forbidding players from aiming at Booth. But this lacks elegance, not to mention literary value! It would be better if the available actions to the player to only be those that don't rule out this event -- not just immediately, but eventually into the future. We might imagine that the game could use linear theorem proving, and then forbid an actions if there is any path along which Booth dies $n$ steps in the future. It's still removing choice, but perhaps if we are subtle enough about it, it will seem a bit more natural, as if coincidence is worked subtly to ensure the outcome rather than a game hack. Note that all of these ideas were spurred by just the very first section of her talk -- she gave me a lot to think about! Bret Victor gave the keynote talk. On the internet, he has a reputation as a bomb-throwing radical interaction designer, but his in-person persona is very mild. He opened his talk with a paean to the virtues of direct manipulation, and then he moved on to demo some sample pieces of software which worked more like the way he wanted. His argument, loosely paraphrased, was that people write programs to create interactive behaviors, and that it would be easier to do in a direct manipulation style. By this, he meant that you want a programming environment in which the behavior and the means for creating and modifying them "lived together" -- that is, you use the same conceptual framework for both the relevant behaviors and the operators on them. So if you want to create a visual program, he thought it would be better to offer visual operators to modify pictures rather than code. He illustrated this with a pair of demo programs. The first of these was a program that let you build interactive animations with timelines and some vector graphics primitives, and the second was a data visualization program that worked similarly, but which replaced the timeline with a miniature spreadsheet. Both of these programs seemed like extremely mild and conservative designs to me. The basic vocabulary he worked with --- grids, vectors, timelines, spreadsheets --- were all familiar primitives from drawing, animation and data-manipulation programs, and then he augmented it all by letting you parameterize these things with variables, to get you procedural abstractions. He was careful to make variables visualizable using sliders, a la Conal Elliot's tangible values, but beyond that he really seemed to hook things together in the most direct way possible. Something I was really curious about was how Victor might design an interface that was not visual --- e.g., how would you apply his design principles for a blind user? What does it mean for sounds, rather than pictures? ## Friday, December 20, 2013 ### PhD Opportunities at the University of Birmingham My university, the University of Birmingham, is looking for applicants to the CS PhD program. I'm putting our advertisement on my blog, in case you (or your students, if you're a professor) are looking for a graduate program -- well, we're looking for students! Let me just say that my colleagues are a terrific bunch, who know and do work on all kinds of fantastic things. I am very happy to able to work with them, and can confirm that this is a very exciting group to be a part of. We invite applications for PhD study at the University of Birmingham. We are a group of (mostly) theoretical computer scientists who explore fundamental concepts in computation and programming language semantics. This often involves profound and surprising connections between different areas of computer science and mathematics. From category theory to lambda-calculus and computational effects, from topology to constructive mathematics, from game semantics to program compilation, this is a diverse field of research that continues to provide new insight and underlying structure. • See our webpage, with links to individual researchers, here: • Information about PhD applications may be found here: • If you are considering applying, please contact any of us. We will be very happy to discuss the opportunities available. • Martin Escardo (topology, computation with infinite objects, constructive mathematics, intuitionistic type theory) • Dan Ghica (game semantics, heterogeneous computing, model checking) • Achim Jung (mathematical structures in the foundations of computing: logic, topology, order) • Neel Krishnaswami (type theory, verification, substructural logic, interactive computation) • Paul Levy (denotational semantics, lambda-calculus with effects, nondeterminism, category theory, game semantics) • Uday Reddy (semantics of state, separation logic) • Eike Ritter (security protocol verification) • Hayo Thielecke (abstract machines, concurrent and functional programming, software security) • Steve Vickers (constructive mathematics and topology, category theory and toposes) ## Thursday, November 7, 2013 ### Antimirov Derivatives for Regular Expressions Brzozowski derivatives are one of the shibboleths of functional programming: if you ask someone about implementing regular expressions, and you get back an answer involving derivatives of regular expressions, then you have almost surely identified a functional programmer. The reason that functional programmers like derivatives so much is that they offer an elegantly algebraic and inductive approach to string matching. The derivative function $\delta_c$ takes a character $c$ and a regular expression $r$, and returns a new regular expression $r'$, which accepts a string $s$ if and only if $r$ accepts $c\cdot s$. This function can be defined as follows: $$\begin{array}{lcl} \delta_c(c) & = & \epsilon \\ \delta_c(c') & = & \bot \\ \delta_c(\epsilon) & = & \bot \\ \delta_c(r_1 \cdot r_2) & = & \left\{ \begin{array}{ll} \delta_c(r_1) \cdot r_2 \vee \delta_c(r_2) & \mbox{if } r_1 \mbox{ nullable} \\ \delta_c(r_1) \cdot r_2 & \mbox{otherwise} \end{array} \right. \\ \delta_c(\bot) & = & \bot \\ \delta_c(r_1 \vee r_2) & = & \delta_c(r_1) \vee \delta_c(r_2) \\ \delta_c(r\ast) & = & \delta_c(r)\cdot r\ast \end{array}$$ Now we can turn the 1-character derivative into a word derivative as follows: $$\begin{array}{lcl} \delta_\epsilon(r) & = & r \\ \delta_{c\cdot w}(r) & = & \delta_w(\delta_c(r)) \end{array}$$ Again, this is a simple inductive definition. So to match a string we just call the 1-character derivative for each character, and then check to see if the final regular expression is nullable. However, there's a catch! As you can see from the definition of $\delta_c$, there is no guarantee that the size of the derivative is bounded. So matching a long string can potentially lead to the construction of very large derivatives. This is especially unfortunate, since it is possible (using DFAs) to match strings using regular expressions in constant space. In his 1962 paper, Brzozowski showed that the number of derivatives of a regular expression is finite, if you quotient by the associativity, commutativity, and idempotence axioms for for union $r_1 \vee r_2$. That is, suppose we consider regular expressions modulo an equivalence relation $\equiv$ such that: $$\begin{array}{lcl} r \vee r & \equiv & r \\ r \vee \bot & \equiv & r \\ r \vee r' & \equiv & r' \vee r \\ r_1 \vee (r_2 \vee r_3) & \equiv & (r_1 \vee r_2) \vee r_3 \\ \end{array}$$ Then his theorem guarantees that the set of derivatives is finite. However, computing with derivatives up to equivalence is rather painful. Even computing equality and ordering is tricky, since union can occur anywhere in a regular expression, and without that it's difficult to implement higher-level data structures such as sets of regular expressions. So for the most part, derivatives have remained a minor piece of functional programming folklore: they are cute, but a good implementation of derivatives is not really simple enough to displace the usual Dragon Book automata constructions. However, in 1995 Valentin Antimirov introduced the notion of a partial derivative of a regular expression. The idea is that if you have a regular expression $r$ and a character $c$, then a partial derivative is a regular expression $r'$ such that if $r'$ accepts a word $s$, then $r$ accepts $c \cdot s$. Unlike a derivative, this is only a if-then relationship, and not an if-and-only-if relationship. Then, rather than taking regular expressions modulo the ACUI equations, we can construct sets of partial derivatives, which collectively accept the same strings as the Brzozowski derivative. The idea is that we can use the algebraic properties of sets to model the effect of the ACUI equations. Below, I give the partial derivative function: $$\begin{array}{lcl} \alpha_c(c) & = & \setof{\epsilon} \\ \alpha_c(c') & = & \emptyset \\ \alpha_c(\epsilon) & = & \emptyset \\ \alpha_c(r_1 \cdot r_2) & = & \left\{ \begin{array}{ll} \comprehend{r \cdot r_2}{ r \in \alpha_c(r_1)} \cup \alpha_c(r_2) & \mbox{if } r_1 \mbox{ nullable} \\ \comprehend{r \cdot r_2}{ r \in \alpha_c(r_1)} & \mbox{otherwise} \end{array} \right. \\ \alpha_c(\bot) & = & \emptyset \\ \alpha_c(r_1 \vee r_2) & = & \alpha_c(r_1) \cup \alpha_c(r_2) \\ \alpha_c(r\ast) & = & \comprehend{ r' \cdot r\ast }{ r' \in \alpha_c(r) } \end{array}$$ Partial derivatives can be lifted to words just as ordinary derivatives can be, and it is relatively easy to prove that the set of partial word derivatives of a regular expression is finite. We can show this even without taking a quotient, and so partial derivatives lend themselves even more neatly to an efficient implementation than Brzozowski derivatives do. I'll illustrate this point by using Antimirov derivatives to construct a DFA-based regular expression matcher in ~50 lines of code. You can find the Ocaml source code here. First, let's define a datatype for regular expressions. type re = C of char \| Nil \| Seq of re * re \| Bot \| Alt of re * re \| Star of re So C is the constructor for single-character strings, Nil and Seq correspond to $\epsilon$ and $r\cdot r'$, and Bot and Alt correspond to $\bot$ and $r \vee r'$. Next, we'll define the nullability function, which returns true if the regular expression accepts the empty string, and false if it doesn't. It's the obvious recursive definition. let rec null = function \| C _ \| Bot -> false \| Nil \| Star _ -> true \| Alt(r1, r2) -> null r1 \|\| null r2 \| Seq(r1, r2) -> null r1 && null r2 Now come some scaffolding code. The R module is the type of finite sets of regular expressions, the M module are finite maps keyed by sets of regexps, and I is the type of finite sets of ints. The rmap function maps a function over a set of regexps, building a new regexp. (I don't know why this is not in the standard Set signature.) module R = Set.Make(struct type t = re let compare = compare end) let rmap f rs = R.fold (fun r -> R.add (f r)) rs R.empty module M = Map.Make(R) module I = Set.Make(struct type t = int let compare = compare end) The aderiv function implements the Antimirov derivative function $\alpha_c$ described above. It's basically just a direct transcription of the mathematical definition into Ocaml. The deriv function applies the derivative to a whole set of regular expressions and takes the union. let rec aderiv c = function \| C c' when c = c' -> R.singleton Nil \| C _ \| Nil \| Bot -> R.empty \| Seq(r1, r2) -> R.union (rmap (fun r1' -> Seq(r1', r2)) (aderiv c r1)) (if null r1 then aderiv c r2 else R.empty) \| Star r -> rmap (fun r' -> Seq(r', Star r)) (aderiv c r) let deriv c rs = R.fold (fun r acc -> R.union (aderiv c r) acc) rs R.empty Since the set of partial derivatives is finite, this means that the powerset of this set is also finite, and so by treating sets of partial derivatives as states, we can construct a deterministic finite-state automaton for matching regular expressions. Let's define an Ocaml type for DFAs: type dfa = {size : int; fail : int; trans : (int * char * int) list; final : int list} Here, size is the number of states, and we'll use integers in the range [0,size) to label the states. We'll use fail to label the sink state for non-matching strings, and take trans to be the list of transitions. The final field is a list of accepting states for the DFA. Now, we'll need a little more scaffolding. The enum function is a "functional for-loop" looping from i to max. We use this to write charfold, which lets us fold over all of the ASCII characters. let rec enum f v i max = if i < max then enum f (f i v) (i+1) max else v let charfold f init = enum (fun i -> f (Char.chr i)) init 0 256 We use this to define the dfa function, which constructs a DFA from a regular expression: let find rs (n,m) = try M.find rs m, (n,m) with _ -> n, (n+1, M.add rs n m) let dfa r = let rec loop s v t f rs = let (x, s) = find rs s in if I.mem x v then (s, v, t, f) else charfold (fun c (s, v, t, f) -> let rs' = deriv c rs in let (y, s) = find rs' s in loop s v ((x,c,y) :: t) f rs') (s, I.add x v, t, if R.exists null rs then x :: f else f) in let (s, v, t, f) = loop (0, M.empty) I.empty [] [] (R.singleton r) in let (fail, (n, m)) = find R.empty s in { size = n; fail = fail; trans = t; final = f } The find function takes a set of regular expression and returns a numeric index for it. To do this, it uses a state (n, m), where n is a counter for a gensym, and m is the map we use to map sets of regular expressions to their indices. The main work happens in the loop function. The s parameter is the state parameter for find, and v is the visited set storing the set of states we have previously visited. The t parameter is the list of transitions built to date, and f are the final states generated so far. The rs parameter is the current set of regular expressions. We first look up its index x, and if we have visited it, we return. Otherwise, we add the current state to the visited set (and to the final set if any of its elements are nullable), and iterate over the ASCII characters. For each character c, we can take the derivative of rs, and find its index y. Then, we can add the transition (x, c, y) to t, and loop on the derivative. Essentially, this does a depth-first search of the spanning tree. We then kick things off with empty states and the singleton set of the argument regexp r, and build a DFA from the return value. Note that the failure state is simply the index corresponding to the empty set of partial derivatives. The initial state will always be 0, since the first state we find will be the singleton set r. Since we have labelled states by integers from 0 to size, we can easily build a table-based matcher from our dfa type. type table = { m : int array array; accept : bool array; error : int } let table d = { error = d.fail; accept = Array.init d.size (fun i -> List.mem i d.final); m = (let a = Array.init d.size (fun _ -> Array.make 256 0) in List.iter (fun (x, c, y) -> a.(x).(Char.code c) <- y) d.trans; a) } Here, the table type has a field m for the transition table, an array of booleans indicating whether the state accepts or not, and the error state. We build the table in the obvious way in the table function, by building an array of array of integers and initializing it using the list of transitions. Then, we can give the matching function. The matches' function takes a table t, a string s, an index i, and a current state x. It will just trundle along updating its state, as long as we have not yet reached the end of the string (or hit the error state), and then it will report whether it ends in an accepting state or not. The re_match function just calls matches' at index 0, in state 0. let rec matches' t s i x = if i < String.length s && x != t.error then matches' t s (i+1) t.m.(x).(Char.code s.[i]) else t.accept.(x) let re_match t s = matches' t s 0 0 And that's it! Obviously more work is needed to make this a real regexp implementation, but the heart of the story is here. It's also possible to improve this implementation a bit further by adding a DFA minimization step, but that's a tale for another day. (DFA minimization is a very pretty little coinductive algorithm, and so makes a nice companion to the inductive story here.) ## Tuesday, July 23, 2013 ### What Declarative Languages Are On his blog, Bob Harper asks what, if anything, a declarative language is. He notes that "declarative" is often used to mean "logic or functional programming", and is (justly) skeptical that this is a useful pairing. However, there's actually a surprisingly simple and useful definition of declarative language: a declarative language is any language with a semantics has some nontrivial existential quantifiers in it. To illustrate this definition, let's begin by looking at some examples of declarative languages: • Regular expressions • Context-free grammars • Database query languages based on relational algebra (eg, SQL) • Logic programming languages (eg, Prolog) • Constraint-based languages for layout (eg, CSS) The common factor is that all of these languages have a semantics which relies on some existential quantifiers which it is not immediately obvious how to discharge. For example, the semantics of regular expressions can be explained in terms of string membership, by giving a judgement $w \in r$ meaning that the string $w$ is an inhabitant of the regular expression $r$. $$\begin{array}{c} \frac{} {\epsilon \in \cdot} \\[1em] \frac{} { c \in c} \\[1em] \frac{ w \in r_i \qquad i \in \{1,2\} } { w \in r_1 \vee r_2} \\[1em] \mbox{(no rule for w \in \bot)} \\[1em] \frac{\exists w_1, w_2.\; w = w_1 \cdot w_2 \qquad w_1 \in r_1 \qquad w_2 \in r_2 } {w \in r_1 \cdot r_2} \\[1em] \frac{\exists w_1, w_2.\; w = w_1 \cdot w_2 \qquad w_1 \in r \qquad w_2 \in r* } {w \in r*} \end{array}$$ In particular, note the appearance of an existential quantifier in the premises of the sequential composition and Kleene star cases, and note the nondeterministic choice of a branch in the alternation case. So read as a logic program, this semantics is not well-moded. Of course, to implement a regular expression matcher, you need an operational semantics which is well-moded and functional, which we get by constructing a finite state machine from the regular expression. But now we have a proof obligation to show that the operational semantics agrees with the declarative semantics. We can make a similar distinction for each of the examples above. Context-free languages also have a declarative membership relation, but are recognized with parsing algorithms such as CYK and Earley parsing. Query languages have a declarative semantics in terms of the relational algebra, where relational composition is hiding an existential, but are implemented in terms of nested loops and indices. Logic programming has a declarative semantics in terms of the model theory of first-order logic, and an implementation in terms of backtracking and unification. Constraint languages have a declarative semantics in terms of simultaneous satisfaction of a collection of equations, with the existentials lurking in the values assigned to the free variables, but are implemented in terms of simplification and propagation through imperative graphs. This also lets us make the prediction that the least-loved features of any declarative language will be the ones that expose the operational model, and break the declarative semantics. So we can predict that people will dislike (a) backreferences in regular expressions, (b) ordered choice in grammars, (c) row IDs in query languages, (d) cut in Prolog, (e) constraint priorities in constraint languages. And lo and behold, these are indeed the features which programmers are encouraged to avoid as much as possible! This definition also lets say that functional programming is not a declarative language -- the reduction relation of the lambda calculus is well-moded, in that we do not need to guess any part of a term to figure out how to reduce it. (And if you fix an evaluation order, the reduction relation is even deterministic.) The same is true for imperative languages like ML or Haskell: now we're just additionally threading a store through the reduction relation. ## Wednesday, June 19, 2013 ### Internalizing Parametricity at CSL 2013 My paper with Derek Dreyer, Internalizing Relational Parametricity in the Extensional Calculus of Constructions, has been accepted to CSL 2013! I've never been to Torino before, nor published at CSL. I especially like the fact that the CSL proceedings are Creative Commons-licensed.	2014-03-08T06:54:07	{"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": 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": 0.44916975498199463, "perplexity": 1427.045830651423}, "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-2014-10/segments/1393999653833/warc/CC-MAIN-20140305060733-00060-ip-10-183-142-35.ec2.internal.warc.gz"}
https://www.genderequalitycommission.vic.gov.au/about-commission-gender-equality-public-sector	# About the Commission for Gender Equality in the Public Sector We are driving gender equality in the Victorian public sector and wider community. The Commission for Gender Equality in the Public Sector was established after the Gender Equality Bill 2019 (Vic) passed in February 2020. The Commission supports the Public Sector Gender Equality Commissioner to oversee the implementation of the Gender Equality Act 2020 and promote gender equality in the public sector workforce and the broader Victorian community. Reviewed 22 August 2022	2023-02-02T13:46:27	{"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": 0.8882520794868469, "perplexity": 6044.715775507798}, "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/1674764500028.12/warc/CC-MAIN-20230202133541-20230202163541-00621.warc.gz"}
http://www-theory.lbl.gov/wordpress/?page_id=6745	Christian Bauer Email: [email protected] Tel: 510-486-7773 Fax: 510-486-6808 Office: 50A-5123 # Biography Christian Bauer received his undergraduate education in Karlsruhe, Germany, and his PhD from the University of Toronto under Michael Luke. After graduating in 2000, he took a postdoc position at UC San Diego. In 2003 he moved to Caltech as a McCone senior research fellow and joined the LBNL theory group in 2005 as a Divisional Fellow to LBNL. Since 2006 he has been Senior Staff Scientist. In 2005 he received an Outstanding Junior Investigator award, and in 2010 an Early Career Award from the Department of Energy. In 2010 he was the recipient of the Presidential Early Career Award. # Research interests Much of my research in the past has focused on the development of novel calculational techniques to increase our ability to make precise predictions in the standard model.Effective field theories are a wonderful tool to work in realistic situations, where widely separated scales make perturbation theory slowly converging, or where non-perturbative effects become important. One of my major accomplishments is the development of Soft-collinear effective theory (SCET), which has been widely used in B physics in the past, and is now applied with great success in the LHC era. Much of the development in the Monte Carlo community over the past decade has been to improve the accuracy of event generators at fixed order. This has led to fully exclusive simulations, which for inclusive enough distributions make predictions at next-to-leading order (NLO). These programs are used extensively by the LHC experiments. One of the main differences of the GENEVA Monte Carlo compared to any other event generators currently on the market or under development, is that GENEVA does not only include higher fixed order accuracy, but higher logarithmic accuracy as well. Many high profile analyses such as $H \to WW$ require jet vetoes to control the backgrounds, and higher logarithmic resummation has been shown to be of crucial importance to reduce theoretical uncertainties to a level comparable with experimental uncertainties. GENEVA will therefore be of vital importance to provide fully exclusive predictions in such restricted regions of phase space. An automatic by-product of this higher logarithmic resummation is NLO accuracy of different multiplicities, and even NNLO accuracy, something many groups strive to achieve in a general setting. A major feature of GENEVA is that it completely separates the perturbative calculation from the algorithmic parton shower. This allows all theoretical improvements to be handled directly using perturbative QCD, without having to take into account constraints from the parton shower algorithms. This will in the future allow groups with no knowledge in parton showers to contribute perturbative calculations to GENEVA, similar in spirit to the Powheg Box~(\href{http://arxiv.org/abs/arXiv:1002.2581}{1002.2581}). By clearly separating the perturbative from the nonpeturbative physics also allows to set state of the art perturbative from both resummation and fixed order perturbation theory. In GENEVA, uncertainties are provided on an event-by-event basis.	2018-08-19T17:13:58	{"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": 0.4594481885433197, "perplexity": 1353.7453213612575}, "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-2018-34/segments/1534221215261.83/warc/CC-MAIN-20180819165038-20180819185038-00674.warc.gz"}
https://www.oshrc.gov/assets/1/18/21-0240_Decision_and_Order_-_redacted.html?12018	Some personal identifiers have been redacted for privacy purposes. UNITED STATES OF AMERICA OCCUPATIONAL SAFETY AND HEALTH REVIEW COMMISSION SECRETARY OF LABOR, Complainant, v. OSHRC Docket No. 21-0240 DARLING INGREDIENTS, INC.,Respondent. DECISION AND ORDER Attorneys and Law firms Matt Shepherd, Attorney, Office of the Solicitor, U.S. Department of Labor, Nashville, TN, for Complainant. Kristina T. Brooks, Attorney, Jackson Lewis P.C., Albuquerque, NM, for Respondent. Juliana C. Gaige, Attorney, Jackson Lewis P.C., Houston, TX, for Respondent. JUDGE: John B. Gatto, United States Administrative Law Judge. I. INTRODUCTION This case involves a tragic accident that occurred at Darling Ingredients, Inc.’s chicken-rendering facility in Byram, Mississippi, which resulted in the death of two of its employees. The United States Department of Labor, through its Occupational Safety and Health Administration (OSHA), conducted an investigation and ultimately issued1 a citation on February 9, 2021, alleging repeated2 violations of 29 C.F.R. §1910.147(c)(4)(ii) and 29 C.F.R. §1910.147(c)(4)(ii)(B), the control of hazardous energy (lockout/tagout or LOTO) standard under the Occupational Safety and Health Act of 1970 (the Act), 29 U.S.C. § 651-78. These regulations address the types of steps that must be included in an employer’s LOTO procedures. The parties stipulated the Commission has jurisdiction over this action, Darling is a covered employer under the Act, and Darling’s principal place of business is in Irving, Texas (Jt. Pretrial Order, Attach. C.; Joint Preliminary Report and Discovery Plan $¶$ 12). Based on the stipulations and the record evidence, the court concludes the Commission has jurisdiction over this proceeding under section 10(c) of the Act, and Darling is a covered employer under section 3(5) of the Act. 29 U.S.C. §§ 659(c), 652(5). The court held a trial on February 2, 2022, and the parties filed post-trial briefs on April 22, 2022. Pursuant to Commission Rule 90, after hearing and carefully considering all the evidence and the arguments of counsel, the court issues this Decision and Order, which constitutes its final disposition of the proceedings under section 12(j) of the Act. 29 U.S.C. § 661(j).3 For the reasons indicated infra, the court holds the Secretary has proven his prima facie case with regard to the cited items and therefore, the court AFFIRMS Items 1a and 1b of Citation 1 and ASSESSES a group penalty of \$75,092.00. II. BACKGROUND Darling is in the animal-rendering industry. (Tr. 71:10-13). In 2010, Darling bought the Byram chicken-rendering facility (the “worksite”) from Griffin Industries. (Tr. 70:20-21). Each of Darling’s facilities maintains its own operations group management. (Tr. 74:22 – 75:1). At the Mississippi facility, the general manager, Scott Brown, oversees the management of the plant; the operations manager, Sam Badalucco, oversees daily operations and its personnel; and the maintenance manager, Mike Jennings, oversees maintenance and its personnel. (Tr. 74:22 – 75:8, 76:16-23). Plant management then reports up the corporate chain through either the eastern or western division. (Tr. 75:9-15). The Mississippi plant reports through the eastern division. (Tr. 74:8-21). Hydrolizer4 A breaks down chicken feathers using pressurized steam similar to a pressure cooker. (Tr. 26:21-25, 82:17 – 83:3). Periodically, material will start to collect and adhere itself within the Hydrolizer, creating a blockage. (Tr. 77:21 – 78:15). When a blockage occurs, the pressure is unable to release through the inlet side of the Hydrolizer, causing the whole process to stop. (Tr. 78:3-15). When this occurs, the process operator will attempt to relieve the pressure by “shuttling the gates” and/or opening the pressure relief valve on the Hydrolizer itself. (Tr. 77:2-7, 80:14-21, 86:4-10). On August 10, 2020, David Abston, a Process Operator, was operating Hydrolizer A at the worksite. (Ex. R-11, 1:1; Ex. R-6, 9). The Hydrolizer A apparently became clogged, and the pressure was not releasing inside the Hydrolizer. (Tr. 28:11-14; Tr. 77:2-5; Ex. R-11, 1:1, 2). As part of the normal operating procedures, Abston tried “shuttling” the gates to release the pressure. (Tr. 77:2-7). “Shuttling the gates” refers to when an operator opens one gate (in a series of gates) to let part of the material come out, then closes that gate, and then opens another gate to let the material out. (Tr. 78:16-25). Unsuccessful in his attempts to release the pressure, Abston called his supervisor, Sam Badalucco, operations manager, to notify him of the issue with Hydrolizer A. (Tr. 77:8; Ex. R-11, 1:1). Badalucco in turn contacted the maintenance team. (Tr. 77:9, 81:9-13; Ex. R-11, 1:3). The maintenance department sent a team of three maintenance workers – [redacted], [redacted], and [redacted] – to address the issue at Hydrolizer A. (Tr. Ex. R-11, 1:2). The maintenance team double-checked the normal procedures followed by the process operator. (Ex. R-11, 1:3). First, the team opened the shuttle gate, with no decrease in pressure, and then opened the manual pressure relief valve, and there was still no decrease in pressure. (Ex. R-11, 1:3). Through his discussions with plant personnel, Corporate Safety Director Wayne Stanberry determined that the team then de-energized the electrical circuits and isolated the steam valve feeding into Hydrolizer A. (Tr. 87:5-9; Ex. R-6; Ex. R-11, 2:14b). At this point, because normal procedures did not clear the pressure in the Hydrolizer, the team should have waited for the Hydrolizer to cool down. Stanberry explained that you always do it the same way. (Tr. 86:18). He stated, You always wait until it cools down. When the equipment cools down the steam condenses, the pressure goes away and you end up with zero pressure and then you take the bolts out of that flange and that allows you to get in and actually dig out the material that’s inside there and clear whatever blockage there was. (Tr. 86:18-24). While the Hydrolizer is cooling down, maintenance can re-route the material to Hydrolizer B or vice versa. (Tr. 81:14 – 82:13). The Mississippi plant installed a duplicate Hydrolizer as a back-up system to continue to process the material if one is taken offline. (Tr. 81:20 – 82:13). However, even if both Hydrolizers are down, the product can sit for days because feathers do not go bad. (Tr. 83:4-7). Stanberry explained, “We still have some plants that only have one Hydrolizer. And that’s exactly what they do, they just stop processing and wait till it cools down and they fix it and get back into running.” (Tr. 83:13-18). Unfortunately, one of the employees decided to loosen the bolts attached to a 4” flange on the side of the hydrolyzer to let the trapped steam escape. As the employees loosened the bolts, steam would flow out of the machine. This process continued for 10-15 minutes until the flange blew off, and steam and hot material from inside the hydrolyzer spewed out of the machine, covering the three maintenance employees. [redacted] and [redacted] were killed as a result of the injuries they sustained.5 (Ex. R-11). No manager was aware that [redacted] and his crew were removing bolts from the flange on August 10, 2020. (Tr. 55:12-16, 84:4-8). At no time did the employees stop work and insist that the proper procedures be utilized as taught in Darling’s training. (Ex. R-11, 4:2). III. ANALYSIS The fundamental objective of the Act is to prevent occupational deaths and serious injuries. Whirlpool Corp. v. Marshall, 445 U.S. 1, 11 (1980). The Act “establishes a comprehensive regulatory scheme designed ‘to assure so far as possible safe and healthful working conditions’ for ‘every working man and woman in the Nation.’” Martin v. Occupational Safety and Health Review Comm'n (CF&I Steel Corp.), 499 U.S. 144, 147 (1991) (quoting 29 U.S.C. § 651(b)). “The Act imposes a general duty on employers to furnish employees a workplace ‘free from recognized hazards that are causing or are likely to cause death or serious physical harm.’” Houston Aquarium, Inc. v. Occupational Safety & Health Rev. Comm'n, 965 F.3d 433, 439–40 (5th Cir. 2020) (quoting 29 U.S.C. § 654(a)(1)). “It delegates authority to promulgate specific safety standards to the Secretary of Labor.” Id. (citing id. § 655). “[T]he Commission is responsible for the adjudicatory functions under the OSH Act” StarTran, Inc. v. Occupational Safety & Health Rev. Comm'n, 290 F. App'x 656, 670 (5th Cir. 2008), and serves “as a neutral arbiter and determine whether the Secretary's citations should be enforced over employee or union objections.” Cuyahoga Valley Ry. Co. v. United Transp. Union, 474 U.S. 3, 7 (1985) (per curiam). Thus, Congress vested the Commission with the “adjudicatory powers typically exercised by a court in the agency-review context.” CF&I Steel Corp., 499 U.S. at 151. When there has been a violation of any specific OSHA regulation, such as the alleged violations in the instant case, such violation constitutes violation of the “special duty clause” of the Act, 29 U.S.C. § 654(a)(2). Sw. Bell Tel. Co. v. Chao, 277 F.3d 1374 (5th Cir. 2001).6 Under the law of the Fifth Circuit where this case arose,7 “[t]o establish an employer has violated a regulation, the Secretary has the burden to prove (1) ‘that the cited standard applies’; (2) that the employer has not complied with the cited standard; (3) that employees have ‘access or exposure to the violative conditions’; and (4) ‘that the employer had actual or constructive knowledge of the conditions,’ i.e., that it actually knew of the conditions or, with the exercise of reasonable diligence, should have known.” Southern Hens, Inc. v. Occupational Safety & Health Rev. Comm'n, 930 F.3d 667, 675 (5th Cir. 2019) (quoting Sanderson Farms, Inc. v. Perez, 811 F.3d 730, 735 (5th Cir. 2016)). Grouped Items 1a and 1b: Alleged Serious Violations of §1910.147(c)(4)(ii) and §1910.147(c)(4)(ii)(B) Grouped Item 1a alleges that on or about August 10, 2020, Darling violated 29 CFR 1910.147(c)(4)(ii), OSHA’s lockout-tagout (LOTO) standard, when “employees removing a clog were exposed to a serious burn hazard from trapped steam and condensation, in that the procedures did not clearly and specifically address appropriate lockout, tagout procedures for steam trapped in [Hydrolizer] during clog removal.” (Compl. Ex. A.) This provision of the LOTO standard mandates in relevant part that Darling’s “procedures shall clearly and specifically outline the scope, purpose, authorization, rules, and techniques to be utilized for the control of hazardous energy[.]” 29 C.F.R. §1910.147(c)(4)(ii). Grouped Item 1b alleges that on or about August 10, 2020, Darling violated 29 CFR 1910.147(c)(4)(ii)(B), when its LOTO “procedures did not clearly and specifically outline the steps for shutting down, isolating, blocking and securing machines or equipment to control hazardous energy. (Compl. Ex. A.) This provision of the LOTO standard mandates, more specifically, that Darling’s LOTO procedures shall include “[s]pecific procedural steps for shutting down, isolating, blocking and securing machines or equipment to control hazardous energy[.]” 29 C.F.R. §1910.147(c)(4)(ii)(B). (1) The Cited Standards Apply Section 147 “covers the servicing and maintenance of machines and equipment in which the unexpected energization or start up of the machines or equipment, or release of stored energy could cause injury to employees.” 29 C.F.R. § 1910.147(a)(1). “This standard applies to the control of energy during servicing and/or maintenance of machines and equipment.” 29 C.F.R. §1910.147(a)(2)(i). “Normal production operations are not covered by this standard.” 29 C.F.R. §1910.147(a)(2)(ii). Darling admits that the procedure its employees subsequently undertook-- taking the cover off the flange by removing its bolts-- was service and/or maintenance work on Hydrolizer A. (Tr. 85.) Therefore, the Secretary has established the cited standards applied to the cited conditions. (2) Darling Has Not Complied With Cited Standards There is no dispute that Darling had a LOTO policy in place as well as a separate LOTO procedure specific to the Hydrolizer. The question is whether Darling’s LOTO procedure met Section 147’s requirements that it clearly and specifically outline the scope, purpose, authorization, rules, and techniques to be utilized for the control of hazardous energy,” including “[s]pecific procedural steps for shutting down, isolating, blocking and securing machines or equipment to control hazardous energy[.]” The Secretary asserts that it did not. Darling argues that its “LOTO Policy and Procedure must be read in conjunction with the hydrol[i]zer manual and the training provided on how to isolate the thermal energy.” (Resp’t’s Br. p. 9.) The court finds no merit in Darling’s position. As indicated supra, the LOTO standard mandates that Darling’s “procedures shall clearly and specifically outline the scope, purpose, authorization, rules, and techniques to be utilized for the control of hazardous energy[,]” including “[s]pecific procedural steps for shutting down, isolating, blocking and securing machines or equipment to control hazardous energy[.]” 29 C.F.R. §1910.147(c)(4)(ii), (B) (emphasis added). Darling also argues its LOTO Procedures “actual[ly] provide all needed information to safely and effectively lockout the Hydrol[i]zer A.” (Resp’t’s Br. 17.) Again, the court does not agree. Darling’s LOTO procedure specific to the Hydrolizer A contained the following relevant Step: 1. 6.Make all of the following sources of stored energy (capacitors, flywheels, springs, pressure lines of hydraulics/steam/air/water/grease) safe by relieving pressure, restraining, disconnecting, or discharging: a. Relieve internal pressure (Ex. R-4, p. 2) (emphasis in original). Stanberry explained: (Tr. 102.) By Darling’s own admission, step 6 is erroneous since, if there is still internal pressure when the employee gets to step 6, the employee cannot “relieve [the] internal pressure.” Darling’s LOTO procedures must say more. The LOTO standard requires the employer's LOTO procedure to "clearly and specifically outline the . . . techniques to be utilized." Step 6 of Darling's LOTO procedure instructs employees to relieve the internal pressure of Hydrolizer A. Darling's employees cannot accomplish this step, however, if the usual methods of pressure relief have not been successful and internal pressure remains. Therefore, at a minimum, Darling could have, and should have, simply instructed employees at step 6 to stop and wait for Hydrolizer A to cool down until the pressure dissipates to a nonhazardous level before moving to the next step. Thus, the Secretary has established Darling did not comply with cited standard’s requirement that its LOTO “procedures shall clearly and specifically outline the scope, purpose, authorization, rules, and techniques to be utilized for the control of hazardous energy[,]” including “[s]pecific procedural steps for shutting down, isolating, blocking and securing machines or equipment to control hazardous energy[.]” (3) Darling Employees were Exposed to a Hazard There is no question that at a minimum, the two employees that died as a result of the accident were exposed to a serious burn hazard. Therefore, the Secretary has established Darling employees had access or exposure to the violative conditions. (4) Darling had Actual or Constructive Knowledge of the Conditions To prove a serious violation of the Act, § 666(k) “imposes liability on the employer only if the employer knew, or ‘with the exercise of reasonable diligence, [should have known] of the presence of the violation.’ 29 U.S.C. § 666(k).” W.G. Yates & Sons Const. Co. Inc. v. Occupational Safety & Health Rev. Comm'n, 459 F.3d 604, 607 (5th Cir. 2006). Therefore, “to impart liability to an employer for a violation of the special duty clause, the Secretary must prove that an employer had knowledge of the violation as part of its prima facie case.” Sw. Bell, 277 F.3d at 1378. The Fifth Circuit has “dealt with employer knowledge as a fact-specific, practical inquiry, looking to company practice, the details of specific incidents, knowledge of supervisors imputable to the company, and commonsense inferences about what a company and its supervisors should know and do.” W.G. Yates, 459 F.3d at 607. “To prove the knowledge element, ‘the Secretary must show that the employer knew of, or with exercise of reasonable diligence could have known of the non-complying condition.’” Sw. Bell, 277 F.3d at 1378 (quoting Trinity Indus. v. Occupational Safety and Health Review Comm'n, 206 F.3d 539, 542 (5th Cir.2000)). Thus, in this case, the Secretary must show that Darling knew or should have known that its LOTO procedures did not “clearly and specifically outline the scope, purpose, authorization, rules, and techniques to be utilized for the control of hazardous energy, and the means to enforce compliance including, but not limited to, the following: (B) Specific procedural steps for shutting down, isolating, blocking and securing machines or equipment to control hazardous energy[.]” Darling asserts that it did not know the maintenance workers were going to remove the flange while the Hydrolyzer A was under pressure, nor would it have known so through the exercise of reasonable due diligence. (Resp’t’s Br. 18.) Darling’s assertion is a red herring. What is relevant is that Darling knew or, with the exercise of reasonable diligence, should have known of the conditions constituting the violation, i.e., its failure to implement a LOTO procedure that met the requirements of the LOTO standard. Darling knew of the contents of its own LOTO procedure, and also knew it had recently been cited for a similar LOTO violation, i.e., its failure to implement a LOTO procedure that met the requirements of the LOTO standard. Thus, Darling knew or should have known that its procedure was deficient. Therefore, the Secretary has established Darling had actual or constructive knowledge of the violation. Characterization of the Violations The Secretary characterized the violations as “serious” and “repeat” violations. A violation is a “serious” one “if there is a substantial probability that death or serious physical harm could result from” the violative condition. 29 U.S.C. § 666(k). “This means that the Secretary must show that death or serious physical harm is a probable consequence if an accident results from the violative condition—he is not required to show that an accident is itself likely.” Home Rubber Co., LP, No. 17-0138, 2021 WL 3929735, at *5 (OSHRC Aug. 26, 2021) (emphasis in original) (citations omitted). Here, there is no questions the violations were serious—death did occur and it was a probable consequence if an accident resulted from the violative condition. Item 1a and 1b were appropriately characterized as serious. As to the “repeated” characterization, in the Fifth Circuit, a “violation is repeated if, at the time it occurred, ‘there was a Commission final order against the same employer for a substantially similar violation.’” Deep S. Crane & Rigging Co. v. Harris, 535 F. App'x 386, 390 (5th Cir. 2013) (quoting Bunge Corp. v. Sec'y of Labor, 638 F.2d 831, 837 (5th Cir.1981)). “The employer … would then have the burden of disproving the substantial similarity of the conditions, or proving any affirmative defenses such as impossibility of complying with the prior citation, lack of notice of the prior violation, or lack of a reasonable time to comply with the prior citation.” Bunge, 638 F.2d at 838. “For violations of the same specific standard, ‘rebuttal may be difficult since the two violations almost have to be substantially similar in nature in order to constitute violations of the specific standard.’” Id. at 837. Here, the Secretary asserts the violations were properly characterized as repeated violations since Darling was previously cited for violations of the same provisions of the LOTO standard, § 1910.147(c)(4)(ii) and § 1910.147(c)(4)(ii)(B), regarding OSHA Inspection Number 1471984, Citation 1, Item 1a and Item 1b, which were affirmed as a final order on June 18, 2020, with respect to a workplace located in Idaho. See Ex C-5. On its face the court concludes the two violations appear to be substantially similar in nature since they both deal with Darling’s failure to implement a LOTO procedure that met the requirements of § 1910.147(c)(4)(ii) and § 1910.147(c)(4)(ii)(B). Therefore, the burden shifts to Darling to disprove the substantial similarity of the conditions, or prove any affirmative defenses. Darling argues that in the present case, “the equipment-specific procedures for a highly specialized hydrolyzer that breaks down chicken feathers is very different from the equipment-specific procedures that applied in the [previous] case[,]” which dealt “with pneumatic air-powered equipment that pushes cow carcasses.” (Resp’t’s Br. 1.) While it is true the equipment may have been different, the violations were substantially similar in nature— both violations were caused by the same hazard, i.e., Darling’s failure to implement LOTO procedures that met the requirements of § 1910.147(c)(4)(ii) and § 1910.147(c)(4)(ii)(B). See Deep S. Crane, 535 F. App'x at 390 (even when prior violation involved a different type of equipment that caused a different injury, the violations were substantially similar in nature because “both violations were caused by the same hazard.”) Therefore, the Secretary has established the violations were properly characterized as repeated violations. Affirmative Defenses IV. PENALTY DETERMINATION The Act provides that an employer who commits a “repeated” violation may be assessed a civil penalty in an amount not to exceed \$70,000. See 29 U.S.C. § 666(a). However, the Federal Civil Penalties Inflation Adjustment Act of 1990, as amended by the Federal Civil Penalties Inflation Adjustment Act Improvements Act of 2015, requires the Department of Labor to annually adjust its civil money penalty levels for inflation no later than January 15 of each year. Therefore, at the time of the issuance of the citation, the maximum penalty for a repeated violation was \$136,532.00. See 29 CFR § 1903.15(d)(2) (2021); see also 86 FR 2969, Jan. 14, 2021. The Secretary proposed a group penalty of \$75,092.00 for Item 1a and 1b. The Commission is empowered to “assess all civil penalties” provided in this section, “giving due consideration to the appropriateness of the penalty with respect to the size of the business of the employer being charged, the gravity of the violation, the good faith of the employer, and the history of previous violations.” 29 U.S.C. § 666(j). “[G]enerally speaking, the gravity of a violation is the primary element in the penalty assessment.” J.A. Jones Constr., 15 BNA OSHC 2201, 2216 (No. 87-2059, 1993) (citing Trinity Indus., Inc., 15 BNA OSHC 1481, 1483 (No. 88-2691, 1992)). “Moreover, while gravity is normally the primary factor in assessing appropriate penalties, an employer's substantial history of prior violations may skew the importance of gravity in the final penalty determination.” Quality Stamping Prods. Co., 16 BNA OSHC 1927, 1929 (No. 91-414, 1994). The gravity of the violations was high. Darling employs more than 250 people and is therefore not entitled to a reduction in the penalties based upon its size. Darling is also not entitled to a reduction in the penalties based upon a lack of history, or a good faith reduction since it has a repeated violation of the same cited standards. Giving due consideration to the appropriateness of the penalty with respect to the size of the business of the employer being charged, the gravity of the violation, the good faith of the employer, and the history of previous violations, for grouped Item 1a and 1b, the court finds a penalty of \$75,092.00 is appropriate. Accordingly, V. ORDER IT IS HEREBY ORDERED THAT Items 1a and 1b of the Citation are AFFIRMED and a group penalty of \$75,092.00 is ASSESSED. SO ORDERED. /s/___________________________ JOHN B. GATTO, Judge Dated: May 17, 2022 Atlanta, GA 1 The Secretary of Labor has assigned responsibility for enforcement of the Act to OSHA and has delegated his authority under the Act to the Assistant Secretary for Occupational Safety and Health, who heads OSHA. See Order No. 1–2012, Delegation of Authority and Assignment of Responsibility to the Assistant Secretary for Occupational Safety and Health, 77 Fed. Reg. 3912 (Jan. 25, 2012). The Assistant Secretary has redelegated his authority to OSHA’s Area Directors to issue citations and proposed penalties. See 29 C.F.R. §§ 1903.14(a) and 1903.15(a). The terms “Secretary” and “OSHA” are used interchangeably herein. 2 The Act contemplates various grades of violations of the statute and its attendant regulations—“willful”; “repeated”; “serious”; and those “determined not to be of a serious nature” (the Commission refers to the latter as “other-than-serious”). 29 U.S.C. § 666. 3 All arguments not expressly addressed have nevertheless been considered and rejected. If any finding is in truth a conclusion of law, or if any stated conclusion is in truth a finding of fact, it shall be deemed so. 4 Although OSHA referred to the machine as a “Hydrolyzer” in its citation, the company in its LOTO procedure referred to it as a “Hydrolizer.” The court adopts the company’s spelling. 5 [redacted] is the only surviving witness to the accident and these facts are based upon OSHA’s investigation and Stanberry’s investigation and interviews with [redacted]. 6 “To implement its statutory purpose, Congress imposed dual obligations on employers. They must first comply with the ‘general duty’ to free the workplace of all recognized hazards.” ComTran Grp., Inc. v. U.S. Dep't of Labor, 722 F.3d 1304, 1307 (11th Cir. 2013). “They also have a ‘special duty’ to comply with all mandatory health and safety standards.” (Id.) 7 The employer or the Secretary may appeal a final decision and order to the federal court of appeals for the circuit in which the violation allegedly occurred or where the employer has its principal office, and the employer also may appeal to the D.C. Circuit. See 29 U.S.C. §§ 660(a) and (b). Here, the violation occurred in Mississippi, and Darling’s principal place of business is located in Texas, both in the Fifth Circuit. The Commission has held that where it is highly probable that a case will be appealed to a particular circuit, it generally has applied the precedent of that circuit in deciding the case— even though it may differ from the Commission’s precedent. Kerns Bros. Tree Serv., 18 BNA OSHC 2064, 2067 (No. 96-1719, 2000). The court therefore applies the precedent of the Fifth Circuit in deciding the case where it is highly probable the case would be appealed. 8 Darling failed to offer any evidence in support of any of the other affirmative defenses raised in its answer, which the court concludes are also waived by Darling.	2022-11-26T08:22:15	{"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": 0.3591722548007965, "perplexity": 9565.279741757757}, "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/1669446706285.92/warc/CC-MAIN-20221126080725-20221126110725-00068.warc.gz"}
https://www.nist.gov/publications/benefits-and-costs-research-case-study-improved-service-life-prediction	# Benefits and Costs of Research: A Case Study of Improved Service Life Prediction Published: October 15, 2009 ### Author(s) Robert E. Chapman, David T. Butry, Allison L. Huang, Douglas S. Thomas ### Abstract This report focuses on a critical analysis of the economic impacts of research conducted by BFRL s Service Life Prediction (SLP) Program for High-Performance Polymeric Construction Materials. The SLP Program is an interdisciplinary research effort within BFRL in collaboration with the private sector, other federal agencies, and other laboratories within NIST to develop key enabling technologies and advanced measurement technologies needed to deliver high-performance polymeric construction materials to the construction industry. This case study of BFRL s SLP-related research, development, and deployment effort illustrates how to apply in practice a series of standardized methods to evaluate and compare the economic impacts of alternative research investments. It is presented in sufficient detail to understand the basis for the economic impact assessment and to reproduce the results. It is based on past research efforts. The results of this study demonstrate that the use of high-performance polymeric construction materials will generate substantial cost savings to materials manufacturers, the owners and managers of commercial buildings, and to other key construction industry stakeholders. The present value of savings nationwide expected from the use of improved SLP products and services is nearly $190 million (measured in 2008 dollars). Furthermore, because of BFRL s involvement, improved SLP products and services are expected to be commercially available on a more-timely basis and in greater quantity. The present value of these cost savings attributable to BFRL is approximately$48 million. These cost savings measure the value of BFRL s contribution for its SLP-related investment costs of approximately $38.5 million. Stated in present value terms, every public dollar invested in BFRL s SLP-related research, development, and deployment effort is expected to generate$1.23 in cost savings to the public. Citation: Technical Note (NIST TN) - 1650 Report Number: 1650 NIST Pub Series: Technical Note (NIST TN) Pub Type: NIST Pubs	2019-11-15T21:17:09	{"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": 0.2673877775669098, "perplexity": 4555.109287428175}, "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/1573496668712.57/warc/CC-MAIN-20191115195132-20191115223132-00488.warc.gz"}
https://www.bnl.gov/event.php?q=14675	# Nuclear Physics Seminar ## "Measurements and Calculations of $\hat{q}L$ via transverse momentum broadening in RHIC collisions using di-hadron correlations" #### Presented by Michael Tannenbaum, BNL Tuesday, January 29, 2019, 11:00 am — Small Seminar Room, Bldg. 510 The renewed interest in analyzing RHIC data on di-hadron correlations as probes of final state transverse broadening as shown at Quark Matter 2018 by Miklos Gyulassy citing theoretical calculations compared to experimental measurements which didn't look right on Miklos' figure led me to take a closer look at this issue using published PHENIX data . The measured values of $\hat{q}L$ show the interesting effect of being consistent with zero for values of the associated particle transverse momentum pTa >3 GeV/c. This is shown to be related to the well-known effect of the variable IAA, the ratio of the Au+Au to p+p pTa distributions for a given trigger pTt. Hosted by: Jin Huang 14675 \| INT/EXT \| Events Calendar	2021-11-28T12:24:14	{"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": 0.6272847652435303, "perplexity": 3131.59348483101}, "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/1637964358520.50/warc/CC-MAIN-20211128103924-20211128133924-00052.warc.gz"}
https://warrobots.fandom.com/wiki/User_blog:Piisfun/How_DPS_is_calculated_for_various_weapons	## FANDOM 263 Pages NOTE: BLOG MAY TAKE UP TO THIRTY SECONDS TO FULLY LOAD! When calculating DPS, we start by dividing weapons into a number of categories: • Constant weapons • Normal or "Simple" weapons • Accelerated weapons • Burst weapons • Charge weapons These categories take into account the widely varied firing and reloading mechanics in War Robots. Constant Weapons can be fired continuously, with negligible reload time. I will begin with these, as they are the simplest to calculate, and in fact form the base for every other classification: ${\color{Orchid}DPS}=\frac{\color{Red}damage}{\color{Green}time}$ ### Weapons in this class Normal weapons are simple. They fire until they are empty, and then they reload. The main difference here is that we need to know the DPS both with and without the reload time included: ${\color{Orchid} DPS_{burst}}=\frac{{\color{Red} damage}{\color{Yellow}rounds}}{\color{Cyan}time_{unload}}$ ${\color{Orchid} DPS_{burst}}=\frac{{\color{Red} damage}{\color{Yellow}rounds}}{{\color{Cyan}time_{unload}}+{\color{Green}time_{reload}}}$ ### Weapons in this class Accelerated weapons fire at at set speed for a certain duration, and then, once they have warmed up, fire faster. The trouble here is that due to the change in speed, the rate of fire must be found BEFORE the DPS can be calculated. Also, this change in speed means that there is no true cycle DPS, as it will vary depending on the way you use the weapon. ${\color{Orchid} DPS_{Low}}={\color{Red} damage}{\color{Orange} rate_{\color{Purple}low}}$ ${\color{Orchid} DPS_{High}}={\color{Red} damage}{\color{Orange} rate_{\color{Magenta}high}}$ ### Weapons in this class RWF weapons can be continuously reloaded, even while they are being fired. Because rounds are constantly being reloaded here, a full burst is has more rounds than a full clip, and this must be accounted for to find the burst DPS. ${\color{Orchid} DPS_{burst}}=\frac{{\color{Red}damage}{\color{Orange}rounds_{burst}}}{\color{Pink} time_{burst}}$ The constant DPS has two meanings here: it is both the DPS when firing on an empty clip AND the true cycle DPS of an RWF weapon. ${\color{Orchid} DPS_{constant}}=\frac{{\color{Red}damage}{\color{Yellow}rounds}}{\color{Green}time_{reload}}$ ### Weapons in this class Burst Weapons fire everything they have at one time. As there is no unload time for these weapons, they only have a cycle DPS. ${\color{Orchid}DPS}=\frac{{\color{Red}damage}{\color{Yellow}rounds}}{\color{Green}time_{reload}}$ ### Weapons in this class Charge weapons fire everything they have at one time, but can be fired before they are fully recharged, albeit with reduced output. Like, burst weapons, these have no unload time, and thus only have a cycle DPS. However, this cycle DPS is a range, as they can be fired early. The full DPS is the cycle DPS of a fully charged shot, which is generally the maximum DPS. ${\color{Orchid}DPS_{full}}=\frac{{\color{Red}damage}{\color{Yellow}rounds}}{{\color{Green}time_{reload}}+{\color{Pink}time_{charge}}}$ The rapid cycle DPS is the other end of the range, when the weapon is cycled as fast as possible. ${\color{Orchid}DPS_{rapid}}=\frac{\color{Red}damage}{\color{Green}time_{reload}}$ # Other Considerations Note that these calculation do not take into the account Damage-Over-Time effects of Sting, Wasp, or Viper. In reality, these effects are difficult at best to add to the calculation. Likewise, the Close-combat increase in the damage of Spark and Scourge are not included, but can be easily found by multiplying the DPS by the range modifier percentages found on these weapons pages. And finally, these numbers, somewhat optimistically, assume that every round finds its mark. for weapons with bullet spread, simply multiplying by the typical accuracy at a given range will give a DPS for that range. Community content is available under CC-BY-SA unless otherwise noted.	2019-12-10T11:37:09	{"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": 0.5035010576248169, "perplexity": 2517.7211622016425}, "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-2019-51/segments/1575540527205.81/warc/CC-MAIN-20191210095118-20191210123118-00356.warc.gz"}
https://control.com/textbook/wireless-instrumentation/wirelesshart/	# WirelessHART Radio Communication Standard ## Chapter 14 - Wireless Field Instruments and Long-range Wireless Data Links An exciting development in industrial instrumentation is the WirelessHART radio communication standard, specifically designed for field instrument use (e.g. transmitters, valve positioners) as opposed to general data communication. The IEC (International Electrotechnical Commission) has codified the WirelessHART standard as IEC 62591. ### Introduction to WirelessHART WirelessHART is a subset of the HART industrial instrument communication standard as of version 7, communicating process data over 2.4 GHz radio waves. Individual instruments communicate with a common “gateway” device serving as an interface between the wireless network and a wired network or a host control system. In addition to this, though, individual WirelessHART devices also form links with one another, so that the network data routes look like a “mesh” with all nearby nodes interconnected in addition to connecting with the gateway: In a mesh network, devices (nodes) perform double-duty as repeaters to relay data from other instruments to the gateway as needed. In other words, data transmitted from one WirelessHART instrument may not be directly received by the gateway device if that path is blocked or too far away. Instead, the data may “hop” from one device to another nearby, which then re-broadcasts that information to the gateway via a clearer path. The purpose of a mesh network is to provide redundant data pathways in case of device failure or changes in the environment interrupting radio communication between devices. In this way, data packets may be re-routed to the gateway if the shortest route fails, in a manner similar to how Terminal Control Protocol (TCP) and Internet Protocol (IP) work together to route data segments from source to destination over the “mesh” of the Internet. This feature is often referred to in WirelessHART technical literature as the self-healing property of the mesh network. According to the HART Foundation, reliability for a well-designed WirelessHART mesh network is 99.7300204% minimum, and typically greater than 99.9999998%. With each WirelessHART field instrument capable of functioning as a radio repeater, the potential exists to form wireless networks larger in size than the maximum broadcast/reception range of any one device. This illustration shows what is possible: An important consideration when planning a WirelessHART network is battery life. With the main purpose of wireless field instruments being the elimination of wired connections to the host system, the field instruments cannot rely on a host system for their electrical power needs. Lithium-based batteries currently fulfill this role as primary power source, with life expectancies of several years. Interestingly, the amount of energy required by a WirelessHART device to transmit radio-frequency data is small compared to the energy required to power its essential instrument functions (e.g. pressure measurement, temperature measurement). This means a WirelessHART device operating as a radio repeater (in addition to being a measurement device) adds little burden to its battery. Perhaps the greatest challenge in sustaining any wireless field instrument network is ensuring network integrity despite unending changes in the physical environment around the instruments. Remember that this is an industrial, field-instrument wireless network designed to be installed in less-than-ideal physical environments. These wireless devices must somehow reliably communicate with each other despite interference from high-power electrical devices (e.g. variable-frequency motor drive units), while mounted on or near metal objects such as girders, pipes, pipe racks, large vessels, motors, enclosures, shelters, and electrical conduits. Even the ground of an industrial environment can be an impediment to robust radio communication: steel-reinforced concrete and electrical grounding grids form what is essentially a solid “ground plane” that will interfere with WirelessHART devices mounted too close to ground level. Added to all this spatial complexity is the continual presence of large vehicles and other moving machines (cranes, forklifts, manlifts, etc.). It is not uncommon for scaffolding to be temporarily erected for maintenance work in industrial areas, presenting yet one more obstacle for RF signals. In answer to these challenges is an integral and essential component of a WirelessHART network called the Network Manager: an advanced digital algorithm usually executed by the network gateway’s microprocessor. The purpose of the Network Manager is to manage the details of the network automatically, “tuning” various parameters for optimum reliability and data throughput. Among other tasks, the Network Manager assigns “timeslots” for individual devices to transmit, determines the frequency-hopping schedule, detects and authenticates new devices added to the network, dynamically adjusts device transmission power, and selects alternative routes between devices. In a sense, the Network Manager in a WirelessHART network continually audits and tunes the RF system in an attempt to maximize reliability. The Network Manager’s functionality does not substitute for good planning during the design phase of the WirelessHART network, but it does eliminate the need for a human technician or engineer to continuously monitor the network’s performance and make the small adjustments necessary to compensate for changing conditions. When changes occur in a WirelessHART network that cannot be compensated by the Network Manager, the real-time statistics provided by the Network Manager are invaluable to the technician or engineer assigned to update the network. ### WirelessHART network protocol The OSI reference model will be used here to identify and describe various features of the WirelessHART protocol. #### Physical Layer • 2.4 GHz to 2.5 GHz (“ISM” – Industrial, Scientific, Medical) signal band • O-QPSK modulation (offset quadrature phase-shift keying) • 250 kbps data rate • Direct-sequence spread-spectrum (DSSS) with frequency-hopping between 15 channels within that band for security and interference reduction • Variable transmit power, with 10 dBm (10 milliwatts) being default WirelessHART uses 2.4 GHz (nominal) as its transmission frequency and low power levels (10 dBm nominal) because meeting these criteria allows WirelessHART devices to be unlicensed according to FCC (Federal Communications Commission) standards. If WirelessHART fell outside of these limits, the FCC would require end-users to obtain and maintain licenses for the use of these devices and licenses for maintenance personnel installing and maintaining the devices. Such requirements would make WirelessHART prohibitively expensive for all but the most challenging applications and thereby limit its marketability. The purpose of variable transmit power (as scheduled by the Network Manager) is to conserve battery life: an important priority for instruments whose main (or even sole) source of energy is a battery with a finite life. A secondary benefit of this power-limiting feature is that the interference potential of a WirelessHART network on other wireless devices sharing the same 2.4 GHz band is further minimized. #### Data Link Layer • TDMA (Time-Division Multiple Access) bus arbitration, with 10-millisecond timeslots allocated for device transmission • Network ID number uniquely identifies each WirelessHART network, allowing multiple networks to overlap the same physical area • Channel “blacklisting” – automatically avoids hopping to noisy channels TDMA bus arbitration means that the Network Manager plans and schedules the transmission times of all field devices, giving each one its own dedicated time to “speak.” With these non-overlapping timeslots scheduled and broadcast to all the field devices, collisions are prevented while at the same time ensuring determinism (the guarantee that data packets will reach their destination within a certain specified time) barring any physical interruption of the data path. #### Network Layer • “Mesh” networking – devices automatically establish links with any other nearby WirelessHART devices • Signal repeating – devices may act as “repeaters” for other devices too far away from the master unit • A Network Manager device determines communication routes between field devices, as well as timing schedules • Four levels of data message priority (listed from highest to lowest): Command: network management messages Process data: PV values Normal: all messages other than Command, Process, or Alarm Alarm: messages reporting device alarms and events The Network Manager in a WirelessHART network plays a role similar to the Link Active Scheduler (LAS) in a FOUNDATION Fieldbus network segment. The Network Manager assigns time-slots for individual devices to communicate, determines alternative communication routes (i.e. it designs and continually updates the mesh), and continually adjusts device transmit power in order to ensure optimal operation. This dynamic management of the wireless network is critically important in order to maintain low data latency times and high reliability in the face of changing environment variables such as objects coming into and out of the radio pathways (e.g. cranes, trucks, forklifts, man-lifts, scaffolding, and any other large metal structures which may temporarily alter the RF environment in an industrial setting.). Like FOUNDATION Fieldbus LAS devices, multiple (redundant) Network Managers are possible within a WirelessHART network with only one being active at any time. #### Application Layer • 128-bit encryption of data • Backward-compatibility with wired-HART command structure and DDL (Device Description Language) The backward compatibility of WirelessHART with wired-HART field instruments is an incredibly valuable feature of this standard, as it opens the door to wireless integration of legacy HART instruments. All that is needed to make a wired-HART instrument part of a functioning WirelessHART network is to attach the appropriate adapter, such as Emerson’s THUM. Essentially, this step adds an antenna (and associated network interface electronics) on any legacy HART instrument, enabling it to communicate with native WirelessHART instruments and with the wireless gateway. This backward compatibility also improves integration of WirelessHART instruments, as they may communicate with legacy HART software application just as easily as wired-HART devices can. This means programs such as Emerson’s AMS are able to interrogate Wireless HART instruments just as easily as they can wired-HART instruments, with no changes to the program code. Other wireless networking protocols exist which are similar but not identical to WirelessHART. A few are listed here in contrast for better understanding. #### WirelessHART versus Bluetooth Bluetooth is a popular wireless communication standard used in personal computing and other personal electronic devices such as cell phone headsets. Like WirelessHART, Bluetooth supports channel-hopping and uses TDMA arbitration. However, Bluetooth uses a much simpler star network topology: up to seven Bluetooth slave devices may communicate with one Bluetooth master device. By contrast, WirelessHART allows for a greater number of field devices communicating with one Network Manager device, and the network topology is mesh, where any device may transmit data to any other device on the same network and have that other device “repeat” the data to the Network Manager. #### WirelessHART versus ZigBee ZigBee is a mesh-networking wireless communication standard which has found application in building automation systems. It applies the IEEE 802.15.4-2006 standard for both Physical and Data Link layers, whereas WirelessHART employs its own unique Data Link layer including features such as channel “blacklisting” and time-slot synchronization to avoid collisions. A major difference between ZigBee and WirelessHART is the methods of channel arbitration used: ZigBee uses CSMA/CA while WirelessHART uses TDMA. Time Division arbitration tends to be more time-efficient (and certainly more deterministic) when large numbers of devices are within range of each other. #### WirelessHART versus Wi-Fi Wi-Fi (IEEE 802.11) is a wireless communication standard that is extremely popular for personal computer Internet access. Unlike WirelessHART, Wi-Fi does not support channel-hopping for security and interference reduction. Wi-Fi, like ZigBee, also uses CSMA/CA channel arbitration, while WirelessHART uses TDMA channel arbitration to achieve determinism. ### WirelessHART network gateway device The Network Gateway is a critically important component in a WirelessHART system. It is the sole channel through which all field device data funnels to the host control system. Physically, a network gateway is nothing more than a box with an antenna on it, and connections within for electrical power and wired networks (e.g. Ethernet, EIA/TIA-485). Shown here is an Emerson model 1420 “Smart Wireless Gateway”: Electrically, these devices are quite complex. They are microprocessor-controlled, and often serve as the physical host for the Network Manager algorithm: orchestrating and tuning the wireless network communications. Since WirelessHART is a purely digital communication standard, all data points from the field devices are stored in the gateway in digital form, and must be accessed digitally. In the case of Emerson’s Smart Wireless Gateway, the data may be accessed by any host system via Modbus query commands, communicated either serially (EIA/TIA-485, Modbus RTU format) or encapsulated in Ethernet packets (Modbus TCP). Screw terminal connections exist on the Emerson gateway for an EIA/TIA-485 (RS-485) cable to connect, as well as multiple RJ-45 Ethernet ports for connection to a hub or switch where other Ethernet-based computers and systems may connect as well: Like so many other industrial Ethernet-ready devices, the Emerson Smart Wireless Gateway has a built-in web server, allowing password-protected access to configuration pages using nothing more than a personal computer with Ethernet connectivity and a web (Internet) browser program. Simply type the IP address of the gateway port into the browser’s URL field, and the personal computer will connect to the gateway. Individual device data points are custom-mapped by the user to specific Modbus registers inside the gateway’s memory, as shown on this configuration page: In this screenshot we see the primary variables (PV) of two Rosemount model 648 WirelessHART temperature transmitters mapped to Modbus registers 30001 and 30002. It should be noted that all WirelessHART field instruments are multi-variable devices, and as such are capable of reporting more than one variable to the gateway. If anyone were interested, it would have been possible in this example to assign battery voltage as a secondary variable (SV), tertiary variable (TV), or quaternary variable (QV) inside one or both temperature transmitters, then map those data points to their own Modbus registers in the gateway so that a host system could access and monitor battery voltage for the field instruments. Just as in wired-HART communication, multi-variable data communication from each transmitter is possible. This is not often done as a regular course of action with wired-HART instruments due to the very slow data rate of wired HART (1200 bps). However, with the much faster data rate of WirelessHART (250 kbps), the extra time required for a field instrument to transmit three or four variables instead of just one variable is insignificant with respect to the needs of process measurement and control. The next screenshot shows a portion of a simple PLC program written to query these two Modbus registers inside the Emerson gateway. The PLC in this example happens to be an Automation Direct “CLICK” model with a built-in EIA/TIA-485 data port, which connects directly to the gateway’s Modbus RTU network screw terminals. Here, the “Receive” instruction in the PLC sends a Modbus function code 04 to read two analog input registers inside the slave device, that slave device being the Emerson Smart Wireless Gateway (Modbus address 10 on this particular EIA/TIA-485 network). The result of this Modbus query is shown in the next screenshot, where the “Data View” window of the PLC is configured to display the two integer values obtained from the Modbus 04 command. These integer values (stored to registers DS1 and DS2 inside the PLC’s memory) happen to be 60 and 61, representing 60 degrees Fahrenheit and 61 degrees Fahrenheit, respectively. The two temperature transmitters happened to be measuring outdoor ambient temperature at the time this screenshot was taken: Now that the temperature data resides in the PLC registers, the PLC may be programmed to take action on this data. For example, the PLC may be programmed to turn on cooling fans when the temperatures exceed pre-set limits. Many modern HMI (Human-Machine Interface) display panels are also capable of serving as Modbus master devices, and may directly read from and write to the network gateway without the need of a PLC. For WirelessHART systems requiring no automatic control (i.e. monitoring and/or manual control functions only) interfacing an HMI panel to the gateway is a simple and practical solution. ### WirelessHART device commissioning and configuration WirelessHART field instruments look much like their wired counterparts, with the obvious addition of an antenna. A WirelessHART Rosemount model 648 temperature transmitter appears in this photograph: Removing the large cover on this transmitter reveals the lithium battery: A pair of metal terminals marked “Comm” on the transmitter where the battery plugs in provide a place to connect a standard HART communicator device, such as an Emerson model 475. Remember that WirelessHART instruments are fully HART-compliant devices, and may be configured identically to a wired-HART device using the same tools. Two parameters unique to WirelessHART devices, essential to specify in each field device (WirelessHART instrument) for establishing communication with the network gateway, are the Network ID and Device Join Key. These two parameters are contrasted in the following table: Parameter Format Scope Network ID Integer between 0 and 36863 Shared by gateway and its field devices Device Join Key Four 4-byte fields (128 bits) May be unique to each field device The purpose of the Network ID is to simply associate each field device with one network gateway. Each WirelessHART gateway is programmed with one unique Network ID number, which is shared by all field devices communicating with that gateway. The purpose of the Device Join Key is altogether different: this is to provide data security by ensuring that only permitted devices can become a part of a particular gateway’s wireless mesh network. This essential difference explains why the Join Key is a much larger digital data field than the Network ID: the larger the “passcode” to join a network, the less likely any unauthorized agent will be able to randomly guess that passcode and establish a connection with that network. An analogy to help understand the distinction between the Network ID and the Device Join Key is a street address versus a door key of a house, respectively. Each person living in a house must know where to find the house (thus the purpose for memorizing the street address), but access is granted only by possessing a key that unlocks the house door. In the simplest WirelessHART systems, all devices on a particular mesh network share the same Join Key, just as they (must) share the same Network ID. This is analogous to all residents of a house carrying identical keys to unlock the same door. Although it is possible to configure a network gateway to have one “common” Join Key shared by all associated devices in that network, stronger security will be realized by assigning a unique Join Key to each device. In the latter case, the network gateway will maintain a list of all Join Keys and their associated devices, to ensure a device cannot become part of the wireless mesh network unless its programmed Join Key matches the one stored inside the gateway. Returning to our house analogy, this would be the equivalent of each resident having their own unique key to fit their own door on the house, with each door guarded by a security agent checking the name of the person trying to enter: in order to enter the house, your name would have to be on the resident list and you would have to be carrying the matching key for your name! For even stronger security, the gateway may be configured to generate random Join Keys (instead of the technician having to create their own 128-bit numbers), and may even be configurable to rotate the Device Join Keys on a periodic basis so that the Join Key for any particular device will not remain the same over time. Once a WirelessHART device has been powered, configured with the proper Network ID and Join Key parameters, and placed within range of a WirelessHART mesh network, it should be automatically detected by the Network Manager in time. Once detected, the device will appear in a list of network devices active in that WirelessHART network. Here are some tips to aid the commissioning process: • Be sure to configure the device’s HART long tag with the HART communicator prior to commissioning on the wireless network. This way the device will appear on the list of active devices with its proper tagname already configured, rather than as a cryptic MAC address. In the case of a WirelessHART adapter for a wired-HART device (e.g. an Emerson THUM connected to a legacy HART field instrument), you will need to place the instrument tagname in the wired HART device’s “message” field. This tagname will become the leading portion of each variable name within the device: for example, the primary variable (PV) within a WirelessHART temperature transmitter with the tagname TT-35 will be addressed as TT-35.PV on the gateway’s list of device variables once commissioned. • Ensure a strong radio communication pathway between the WirelessHART field device and the gateway. This includes maintaining proper antenna orientation (either vertical up or down) and not too close to ground level, minimal obstructions between the device and the gateway, and not too far away from the gateway. • Keep the field device powered down (i.e. its battery unplugged) until you have it in position and ready to commission. The default setting of WirelessHART devices is to request to join the network when powered up, so the act of plugging in the battery to a field device is the initiating event for commissioning on the wireless network. • Turn the “Active Advertising” mode of the gateway on. This prompts the entire network (including all field devices) to actively search for uncommissioned devices and thereby expedites the joining process. • Turn the “Rotate Network Key” feature of the gateway off. You do not want the Join Key randomly changing on you as you try to commission new devices! • When commissioning several field devices in one area, begin with the device closest to the gateway antenna and proceed to the farthest device. This will exploit the ability of all WirelessHART field devices to act as repeaters for devices located far from the gateway. • Refresh your web browser screen when checking device statuses on the gateway, because not all web browser software responds reliably to new data “pushed” from the gateway’s HTTP server. • If a field device is slow to join the wireless network, you may connect a HART communicator to the device’s “COMM” terminals and monitor its join status directly. This will reveal any problems with the join process. • Initially set the Update Rate to the fastest (i.e. shortest update time) possible in the field device. This does not affect the device’s join time, but once joined it decreases the amount of time you must wait to monitor variables within the device. You may always re-set the update time to a slower value after commissioning, through the gateway. • Be patient. Even when you have done everything correctly, the commissioning may take several minutes. Have other work ready to do (e.g. update instrument documentation, Modbus configuration in the gateway) while you are waiting for devices to join the wireless network. Having all field device tagnames pre-configured helps, because it allows you to populate the Modbus mapping table with proper variable names before the device has joined the wireless network. Network gateways provide some basic statistical information on connected devices, which may be useful for diagnosing problems. Some of these statistics may be seen in the following computer screenshot taken from an Emerson model 1420 gateway: “RSSI” refers to Received Signal Strength Indication, and is a measure of each device’s received RF signal strength, in units of dBm. Problems related to antennas, path loss, fade loss, and interference will result in decreased RSSI for that device. This same page shows the battery voltage for each field device. The “neighbors” parameter tells us how many WirelessHART devices are within range of each field device (the network gateway is counted among them). Thus, in this simple WirelessHART network consisting of two field devices and one gateway, all within range of each other, each field device reports having two neighbors. • Share Published under the terms and conditions of the Creative Commons Attribution 4.0 International Public License	2020-07-04T21:21:42	{"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": 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": 0.2202422320842743, "perplexity": 3253.665487561964}, "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-2020-29/segments/1593655886706.29/warc/CC-MAIN-20200704201650-20200704231650-00064.warc.gz"}
https://par.nsf.gov/biblio/10354701-direct-serendipity-mixed-finite-elements-convex-quadrilaterals	This content will become publicly available on April 1, 2023 Direct serendipity and mixed finite elements on convex quadrilaterals Abstract The classical serendipity and mixed finite element spaces suffer from poor approximation on nondegenerate, convex quadrilaterals. In this paper, we develop families of direct serendipity and direct mixed finite element spaces, which achieve optimal approximation properties and have minimal local dimension. The set of local shape functions for either the serendipity or mixed elements contains the full set of scalar or vector polynomials of degree r , respectively, defined directly on each element (i.e., not mapped from a reference element). Because there are not enough degrees of freedom for global $$H^1$$ H 1 or $$H(\text {div})$$ H ( div ) conformity, exactly two supplemental shape functions must be added to each element when $$r\ge 2$$ r ≥ 2 , and only one when $$r=1$$ r = 1 . The specific choice of supplemental functions gives rise to different families of direct elements. These new spaces are related through a de Rham complex. For index $$r\ge 1$$ r ≥ 1 , the new families of serendipity spaces $${\mathscr {DS}}_{r+1}$$ DS r + 1 are the precursors under the curl operator of our direct mixed finite element spaces, which can be constructed to have reduced or full $$H(\text {div})$$ H ( more » Authors: ; ; Award ID(s): Publication Date: NSF-PAR ID: 10354701 Journal Name: Numerische Mathematik Volume: 150 Issue: 4 Page Range or eLocation-ID: 929 to 974 ISSN: 0029-599X We consider the problem of covering multiple submodular constraints. Given a finite ground setN, a weight function$$w: N \rightarrow \mathbb {R}_+$$$w:N\to {R}_{+}$,rmonotone submodular functions$$f_1,f_2,\ldots ,f_r$$${f}_{1},{f}_{2},\dots ,{f}_{r}$overNand requirements$$k_1,k_2,\ldots ,k_r$$${k}_{1},{k}_{2},\dots ,{k}_{r}$the goal is to find a minimum weight subset$$S \subseteq N$$$S\subseteq N$such that$$f_i(S) \ge k_i$$${f}_{i}\left(S\right)\ge {k}_{i}$for$$1 \le i \le r$$$1\le i\le r$. We refer to this problem asMulti-Submod-Coverand it was recently considered by Har-Peled and Jones (Few cuts meet many point sets. CoRR.arxiv:abs1808.03260Har-Peled and Jones 2018) who were motivated by an application in geometry. Even with$$r=1$$$r=1$Multi-Submod-Covergeneralizes the well-known Submodular Set Cover problem (Submod-SC), and it can also be easily reduced toSubmod-SC. A simple greedy algorithm gives an$$O(\log (kr))$$$O\left(log\left(kr\right)\right)$approximation where$$k = \sum _i k_i$$$k={\sum }_{i}{k}_{i}$and this ratio cannot be improved in the general case. In this paper, motivated by several concrete applications, we consider two ways to improve upon the approximation given by the greedy algorithm. First, we give a bicriteria approximation algorithm forMulti-Submod-Coverthat covers each constraint to within a factor of$$(1-1/e-\varepsilon )$$$\left(1-1/e-\epsilon \right)$while incurring an approximation of$$O(\frac{1}{\epsilon }\log r)$$$O\left(\frac{1}{ϵ}logr\right)$in the cost. Second, we consider the special case when each$$f_i$$${f}_{i}$is a obtained from a truncated coverage function and obtain an algorithm that generalizes previous work on partial set cover (Partial-SC), covering integer programs (CIPs) and multiple vertex cover constraintsmore »	2023-01-28T16:55:17	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 12, "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": 0.6135367155075073, "perplexity": 917.6879039931748}, "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/1674764499646.23/warc/CC-MAIN-20230128153513-20230128183513-00092.warc.gz"}

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