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http://mathhelpforum.com/advanced-algebra/200900-isomorphism.html | # Math Help - Isomorphism
1. ## Isomorphism
Let U & V be n-dimensional vector spaces, and f:U-->V is a linear transformation. Prove that if dimension of f:U-->V is equal to n and dimension of image of f is equal to n, then f is an isomorphism.
Thanks.
2. ## Re: Isomorphism
traditionally, we like people to show some of their work, and not just solve the problems for them. where are you having trouble? | {"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": 0.8831992149353027, "perplexity": 850.43062227687}, "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-2015-06/segments/1422122191023.37/warc/CC-MAIN-20150124175631-00178-ip-10-180-212-252.ec2.internal.warc.gz"} |
http://cvgmt.sns.it/paper/3594/ | # Ricci tensor on smooth metric measure space with boundary
created by han1 on 27 Sep 2017
modified on 28 Sep 2017
[BibTeX]
Submitted Paper
Inserted: 27 sep 2017
Last Updated: 28 sep 2017
Year: 2017
Notes:
This is my preliminary attempt to study metric measure space with boundary.
Abstract:
The aim of this note is to study the measure-valued Ricci tensor on smooth metric measure space with boundary, which is a generalization of Bakry-Emery's modified Ricci tensor on weighted Riemannian manifold. As an application, we offer a new approach to study curvature-dimension condition of smooth metric measure space with boundary. | {"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": 0.9878163933753967, "perplexity": 701.5875635469341}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824894.98/warc/CC-MAIN-20171021190701-20171021210701-00829.warc.gz"} |
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CHARM2: An updated Catalog of High Angular Resolution MeasurementsWe present an update of the Catalog of High Angular ResolutionMeasurements (CHARM, Richichi & Percheron \cite{CHARM}, A&A,386, 492), which includes results available until July 2004. CHARM2 is acompilation of direct measurements by high angular resolution methods,as well as indirect estimates of stellar diameters. Its main goal is toprovide a reference list of sources which can be used for calibrationand verification observations with long-baseline optical and near-IRinterferometers. Single and binary stars are included, as are complexobjects from circumstellar shells to extragalactic sources. The presentupdate provides an increase of almost a factor of two over the previousedition. Additionally, it includes several corrections and improvements,as well as a cross-check with the valuable public release observationsof the ESO Very Large Telescope Interferometer (VLTI). A total of 8231entries for 3238 unique sources are now present in CHARM2. Thisrepresents an increase of a factor of 3.4 and 2.0, respectively, overthe contents of the previous version of CHARM.The catalog is only available in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/431/773 J - K DENIS photometry of a VLTI-selected sample of bright southern starsWe present a photometric survey of bright southern stars carried outusing the DENIS instrument equipped with attenuating filters. Theobservations were carried out not using the survey mode of DENIS, butwith individual target pointings. This project was stimulated by theneed to obtain near-infrared photometry of stars to be used in earlycommissioning observations of the ESO Very Large TelescopeInterferometer, and in particular to establish a network of brightcalibrator sources.We stress that near-infrared photometry is peculiarly lacking for manybright stars. These stars are saturated in 2MASS as well as in regularDENIS observations. The only other observations available for brightinfrared stars are those of the Two Micron Sky Survey dating from overthirty years ago. These were restricted to declinations above≈-30°, and thus cover only about half of the sky accessible fromthe VLTI site.We note that the final 2MASS data release includes photometry of brightstars, obtained by means of point-spread function fitting. However, thismethod only achieves about 30% accuracy, which is not sufficient formost applications.In this work, we present photometry for over 600 stars, each with atleast one and up to eight measurements, in the J and K filters. Typicalaccuracy is at the level of 0\fm05 and 0\fm04 in the J and K_s bands,respectively.Based on observations collected at the European Southern Observatory, LaSilla.Tables 1 and 2 are only available in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/413/1037 Hipparcos red stars in the HpV_T2 and V I_C systemsFor Hipparcos M, S, and C spectral type stars, we provide calibratedinstantaneous (epoch) Cousins V - I color indices using newly derivedHpV_T2 photometry. Three new sets of ground-based Cousins V I data havebeen obtained for more than 170 carbon and red M giants. These datasetsin combination with the published sources of V I photometry served toobtain the calibration curves linking Hipparcos/Tycho Hp-V_T2 with theCousins V - I index. In total, 321 carbon stars and 4464 M- and S-typestars have new V - I indices. The standard error of the mean V - I isabout 0.1 mag or better down to Hp~9 although it deteriorates rapidly atfainter magnitudes. These V - I indices can be used to verify thepublished Hipparcos V - I color indices. Thus, we have identified ahandful of new cases where, instead of the real target, a random fieldstar has been observed. A considerable fraction of the DMSA/C and DMSA/Vsolutions for red stars appear not to be warranted. Most likely suchspurious solutions may originate from usage of a heavily biased color inthe astrometric processing.Based on observations from the Hipparcos astrometric satellite operatedby the European Space Agency (ESA 1997).}\fnmsep\thanks{Table 7 is onlyavailable in electronic form at the CDS via anonymous ftp tocdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/397/997 CHARM: A Catalog of High Angular Resolution MeasurementsThe Catalog of High Angular Resolution Measurements (CHARM) includesmost of the measurements obtained by the techniques of lunaroccultations and long-baseline interferometry at visual and infraredwavelengths, which have appeared in the literature or have otherwisebeen made public until mid-2001. A total of 2432 measurements of 1625sources are included, along with extensive auxiliary information. Inparticular, visual and infrared photometry is included for almost allthe sources. This has been partly extracted from currently availablecatalogs, and partly obtained specifically for CHARM. The main aim is toprovide a compilation of sources which could be used as calibrators orfor science verification purposes by the new generation of largeground-based facilities such as the ESO Very Large Interferometer andthe Keck Interferometer. The Catalog is available in electronic form atthe CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/386/492, and from theauthors on CD-Rom. Speckle Interferometry of New and Problem Hipparcos Binaries. II. Observations Obtained in 1998-1999 from McDonald ObservatoryThe Hipparcos satellite made measurements of over 9734 known doublestars, 3406 new double stars, and 11,687 unresolved but possible doublestars. The high angular resolution afforded by speckle interferometrymakes it an efficient means to confirm these systems from the ground,which were first discovered from space. Because of its coverage of adifferent region of angular separation-magnitude difference(ρ-Δm) space, speckle interferometry also holds promise toascertain the duplicity of the unresolved Hipparcos ``problem'' stars.Presented are observations of 116 new Hipparcos double stars and 469Hipparcos ``problem stars,'' as well as 238 measures of other doublestars and 246 other high-quality nondetections. Included in these areobservations of double stars listed in the Tycho-2 Catalogue andpossible grid stars for the Space Interferometry Mission. Long period variable stars: galactic populations and infrared luminosity calibrationsIn this paper HIPPARCOS astrometric and kinematic data are used tocalibrate both infrared luminosities and kinematical parameters of LongPeriod Variable stars (LPVs). Individual absolute K and IRAS 12 and 25luminosities of 800 LPVs are determined and made available in electronicform. The estimated mean kinematics is analyzed in terms of galacticpopulations. LPVs are found to belong to galactic populations rangingfrom the thin disk to the extended disk. An age range and a lower limitof the initial mass is given for stars of each population. A differenceof 1.3 mag in K for the upper limit of the Asymptotic Giant Branch isfound between the disk and old disk galactic populations, confirming itsdependence on the mass in the main sequence. LPVs with a thin envelopeare distinguished using the estimated mean IRAS luminosities. The levelof attraction (in the classification sense) of each group for the usualclassifying parameters of LPVs (variability and spectral types) isexamined. Table only available in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/374/968 or via ASTRIDdatabase (http://astrid.graal.univ-montp2.fr). Catalogue of Apparent Diameters and Absolute Radii of Stars (CADARS) - Third edition - Comments and statisticsThe Catalogue, available at the Centre de Données Stellaires deStrasbourg, consists of 13 573 records concerning the results obtainedfrom different methods for 7778 stars, reported in the literature. Thefollowing data are listed for each star: identifications, apparentmagnitude, spectral type, apparent diameter in arcsec, absolute radiusin solar units, method of determination, reference, remarks. Commentsand statistics obtained from CADARS are given. The Catalogue isavailable in electronic form at the CDS via anonymous ftp tocdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcar?J/A+A/367/521 Sixth Catalogue of Fundamental Stars (FK6). Part III. Additional fundamental stars with direct solutionsThe FK6 is a suitable combination of the results of the HIPPARCOSastrometry satellite with ground-based data, measured over a longinterval of time and summarized mainly in the FK5. Part III of the FK6(abbreviated FK6(III)) contains additional fundamental stars with directsolutions. Such direct solutions are appropriate for single stars or forobjects which can be treated like single stars. Part III of the FK6contains in total 3272 stars. Their ground-based data stem from thebright extension of the FK5 (735 stars), from the catalogue of remainingSup stars (RSup, 732 stars), and from the faint extension of the FK5(1805 stars). From the 3272 stars in Part III, we have selected 1928objects as "astrometrically excellent stars", since their instantaneousproper motions and their mean (time-averaged) ones do not differsignificantly. Hence most of the astrometrically excellent stars arewell-behaving "single-star candidates" with good astrometric data. Thesestars are most suited for high-precision astrometry. On the other hand,354 of the stars in Part III are Δμ binaries in the sense ofWielen et al. (1999). Many of them are newly discovered probablebinaries with no other hitherto known indication of binarity. The FK6gives, besides the classical "single-star mode" solutions (SI mode),other solutions which take into account the fact that hidden astrometricbinaries among "apparently single-stars" introduce sizable "cosmicerrors" into the quasi-instantaneously measured HIPPARCOS proper motionsand positions. The FK6 gives, in addition to the SI mode, the "long-termprediction (LTP) mode" and the "short-term prediction (STP) mode". TheseLTP and STP modes are on average the most precise solutions forapparently single stars, depending on the epoch difference with respectto the HIPPARCOS epoch of about 1991. The typical mean error of anFK6(III) proper motion in the single-star mode is 0.59 mas/year. This isa factor of 1.34 better than the typical HIPPARCOS errors for thesestars of 0.79 mas/year. In the long-term prediction mode, in whichcosmic errors are taken into account, the FK6(III) proper motions have atypical mean error of 0.93 mas/year, which is by a factor of about 2better than the corresponding error for the HIPPARCOS values of 1.83mas/year (cosmic errors included). Speckle Interferometry of New and Problem HIPPARCOS BinariesThe ESA Hipparcos satellite made measurements of over 12,000 doublestars and discovered 3406 new systems. In addition to these, 4706entries in the Hipparcos Catalogue correspond to double star solutionsthat did not provide the classical parameters of separation and positionangle (rho,theta) but were the so-called problem stars, flagged ``G,''``O,'' ``V,'' or ``X'' (field H59 of the main catalog). An additionalsubset of 6981 entries were treated as single objects but classified byHipparcos as ``suspected nonsingle'' (flag ``S'' in field H61), thusyielding a total of 11,687 ``problem stars.'' Of the many ground-basedtechniques for the study of double stars, probably the one with thegreatest potential for exploration of these new and problem Hipparcosbinaries is speckle interferometry. Results are presented from aninspection of 848 new and problem Hipparcos binaries, using botharchival and new speckle observations obtained with the USNO and CHARAspeckle cameras. The Infrared Spectral Classification of Oxygen-rich Dust ShellsThis paper presents infrared spectral classifications for a flux-limitedsample of 635 optically identified oxygen-rich variables includingsupergiants and sources on the asymptotic giant branch (AGB). Severalclasses of spectra from oxygen-rich dust exist, and these can bearranged in a smoothly varying sequence of spectral shapes known as thesilicate dust sequence. Classification based on this sequence revealsseveral dependencies of the dust emission on the properties of thecentral star. Nearly all S stars show broad emission features fromalumina dust, while most of the supergiants exhibit classic featuresfrom amorphous silicate dust. Mira variables with symmetric light curvesgenerally show broad alumina emission, while those with more asymmetriclight curves show classic silicate emission. These differences may arisefrom differences in the photospheric C/O ratio. Classification and Identification of IRAS Sources with Low-Resolution SpectraIRAS low-resolution spectra were extracted for 11,224 IRAS sources.These spectra were classified into astrophysical classes, based on thepresence of emission and absorption features and on the shape of thecontinuum. Counterparts of these IRAS sources in existing optical andinfrared catalogs are identified, and their optical spectral types arelisted if they are known. The correlations between thephotospheric/optical and circumstellar/infrared classification arediscussed. Small Amplitude Red Variables in the AAVSO Photoelectric Program: Light Curves and PeriodsSmall-amplitude red variables (SARVs) are M giants or supergiants whichare pulsating with small amplitudes (up to 2.5 mag) and with time scalesof 20 to 200 days or more. This paper reports on a ten-year study ofabout two dozen SARVs, carried out through the American Association ofVariable Star Observers (AAVSO) photoelectric photometry program. It hasprovided detailed information on the regularity, period and amplitude ofthese stars. Most have well-defined periods in the 20 to 200 day range.Several also have a long secondary period. One (W Boo) appears to havetwo periods with a ratio of 2.3. (SECTION: Stars) The pulsation, temperatures and metallicities of Mira and semiregular variables in different stellar systemsData on angular diameters and infrared photometry for late-type starsare assembled. It is shown that a consistent T_eff scale can beestablished, combining results for Mira and non-Mira M-type stars. Thelog T_eff versus (J-K) relation is much steeper than previously adopted,but is consistent with predictions from model stellar atmospheres.Comparison of the linear diameters of Miras measured in the red spectralregion with those measured in the infrared shows that modelssuccessfully predict the extension observed in the red, and the combineddata provide strong evidence that Miras are pulsating in their firstovertone. Data on Miras and semiregular (SR) variables in globularclusters are compared with predictions from stellar evolution andpulsation theory. These data also support a steep log T_eff versus (J-K)relation at low temperatures. The Miras and SR variables in 47 Tucconform to theoretical expectation if they are undergoing an averagemass loss of ~3x10^-7 M_ yr^-1. SR variables in both metal-rich andmetal-poor globular clusters are probably pulsating, like the Miras intheir first overtone. The general agreement between observations andtheory now found suggests that infrared colour-period relations can beused to investigate overall metallicity differences between Miras indifferent stellar systems, at least at the shorter periods wherecircumstellar extinction is probably negligible. A comparison of Mirasin Galactic globular clusters of known metallicity with those in the LMCand in the SgrI window of the Galactic Bulge indicates that Miras ofperiods 100 to 300d in the LMC have a mean metallicity log z~-0.6,whilst those in SgrI have log z~-0.2, close to that of K giants in theNGC 6522 Bulge window. No evidence has yet been found for a dependenceof the Mira period-luminosity relation on metallicity, and it is pointedout that theory does not at present give a definitive prediction of suchan effect. Some stars of special interest are discussed in an appendix. The energy distribution in the visible spectrum for 27 class M giants and supergiantsNot Available Transformations from Theoretical Hertzsprung-Russell Diagrams to Color-Magnitude Diagrams: Effective Temperatures, B-V Colors, and Bolometric CorrectionsAbstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1996ApJ...469..355F&db_key=AST Ca II H and K Filter Photometry on the UVBY System. II. The Catalog of ObservationsAbstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1995AJ....109.2828T&db_key=AST Vitesses radiales. Catalogue WEB: Wilson Evans Batten. Subtittle: Radial velocities: The Wilson-Evans-Batten catalogue.We give a common version of the two catalogues of Mean Radial Velocitiesby Wilson (1963) and Evans (1978) to which we have added the catalogueof spectroscopic binary systems (Batten et al. 1989). For each star,when possible, we give: 1) an acronym to enter SIMBAD (Set ofIdentifications Measurements and Bibliography for Astronomical Data) ofthe CDS (Centre de Donnees Astronomiques de Strasbourg). 2) the numberHIC of the HIPPARCOS catalogue (Turon 1992). 3) the CCDM number(Catalogue des Composantes des etoiles Doubles et Multiples) byDommanget & Nys (1994). For the cluster stars, a precise study hasbeen done, on the identificator numbers. Numerous remarks point out theproblems we have had to deal with. On the spectra and photometry of M-giant starsFrom a sample of 97 very bright M-giant stars in the Solarneighbourhood, high-quality "intrinsic" spectra in the spectral range380 <~ λ[nm] <~ 900 for all M-spectral subtypes of the Caseand MK classification systems are obtained. The results are fitted tophotospheric synthetic spectra in the range 99 <~ λ [nm]<=12500 in order to infer the corresponding continua. The syntheticspectra are also compared to the intrinsic spectra. The effectivetemperatures are derived and mathematical spectral classificationcriteria are found. The (UB)_j_(VRI)_c_(JHKLM)_ESO_ photometric data ofthe sample are also given. The data are available on the StrasbourgAstronomical Data Centre (CDS). The second Quito astrolabe catalogueThe paper contains 515 individual corrections {DELTA}α and 235corrections {DELTA}δ to FK5 and FK5Supp. stars and 50 correctionsto their proper motions computed from observations made with theclassical Danjon astrolabe OPL-13 at Quito Astronomical Observatory ofEcuador National Polytechnical School during a period from 1964 to 1983.These corrections cover the declination zone from -30deg to +30deg. Meanprobable errors of catalogue positions are 0.047" in αcosδand 0.054" in δ. The systematic trends of the catalogue{DELTA}αalpha_cosδ,{DELTA}αdelta_cosδ,{DELTA}δalpha_, {DELTA}δdelta_ arepresented for the observed zone. The American Association of Variable Star Observers (AAVSO) Photoelectric Photometry ArchiveNot Available Asymptotic giant branch stars near the sunAvailable red and near-infrared photometry and apparent motions of M, S,and C asymptotic giant branch (AGB) stars in the Bright Star Catalogueare tabulated and discussed. It is shown that the red and near infraredindices normally used for late-type stars are interchangeable except forcarbon stars. The M-type giants are variable with visual amplitudegreater than 0.05 mag. The reddening-free parameter m2 from Genevaphotometry is essentially a temperature parameter for M giants, whilethe reddening-free parameter d is a sensitive detector of blue stellarcompanions. The space density of AGB stars near the sun decreases by afactor of 35 in a temperature range 3800 to 3400 K. Two of the S starsnear the sun were found to have nearly equal space motions and may becomembers of the Arcturus group. Fifth fundamental catalogue. Part 2: The FK5 extension - new fundamental starsThe mean positions and proper motions for 3117 new fundamental starsessentially in the magnitude range about 4.5 to 9.5 are given in thisFK5 extension. Mean apparent visual magnitude is 7.2 and is on average2.5 magnitudes fainter then the basic FK5 which has a mean magnitude of4.7. (The basic FK5 gives the mean positions and proper motions for theclassical 1535 fundamental stars). The following are discussed: theobservational material, reduction of observations, star selection, andthe system for the FK5 extension. An explanation and description of thecatalog are given. The catalog of 3117 fundamental stars for the equinoxand epoch J2000.0 and B1950.0 is presented. The parallaxes and radialvelocities for 22 extension stars with large forecasting effects aregiven. Catalogs used in the compilation of the FK5 fundamental catalogare listed. Carbon abundances and isotope ratios in 70 bright M giantsApproximate carbon abundances and C-12/C-13 isotope ratios are obtainedfor 70 M giant stars from intermediate-resolution spectrophotometry ofthe CO bands near 2.3 microns. A low mean carbon abundance (C/H = -0.64+ or - 0.29) is obtained, suggesting that standard mixing isinsufficient to explain atmospheric abundances in M giants. HR 8795appears to be exceptionally carbon deficient, and is worthy of furtherstudy as a possible weak G-band star descendant. Third list of corrections to the identifications of IRAS sources in Astron. & Astrophys Suppl. 65, 607 and Astron. J. 98, 931Not Available Mass-losing M supergiants in the solar neighborhoodA list of the 21 mass-losing red supergiants (20 M type, one G type; Lgreater than 100,000 solar luminosities) within 2.5 kpc of the sun iscompiled. These supergiants are highly evolved descendants ofmain-sequence stars with initial masses larger than 20 solar masses. Thesurface density is between about 1 and 2/sq kpc. As found previously,these stars are much less concentrated toward the Galactic center thanW-R stars, which are also highly evolved massive stars. Although withconsiderable uncertainty, it is estimated that the mass return by the Msupergiants is somewhere between 0.00001 and 0.00003 solar mass/sq kpcyr. In the hemisphere facing the Galactic center there is much less massloss from M supergiants than from W-R stars, but, in the anticenterdirection, the M supergiants return more mass than do the W-R stars. Theduration of the M supergiant phase appears to be between 200,000 and400,000 yr. During this phase, a star of initially at least 20 solarmasses returns perhaps 3-10 solar masses into the interstellar medium. Chromospheres of metal-deficient field giantsObservations of the 2800-A Mg II line have been obtained with IUE for asample of 10 metal-deficient field giant stars to search forchromospheric emission and signatures of mass loss, as well as toestablish the level of chromospheric radiative energy losses from thesestars. Mg II emission is probably present in all stars. High-resolutionspectra of three of the brightest giants show asymmetric Mg II profileswhich indicate a differentially expanding atmosphere, signaling thepresence of outward mass motions. Surprisingly, the stellar surfacefluxes in the Mg II lines are commensurate with the values found fordisk giant stars (population I) of similar color. In spite ofsubstantially depleted Mg abundances in the target stars (by factors of10-100 relative to the solar abundance), the radiative losses implied bythe Mg II fluxes, and possibly the chromospheric heating mechanism,appear to be reasonably independent of metallicity and age. Spectral classification of the cool component in the CH Cygni system (1975-1988)Results are presented from the spectral classification of the coolcomponent in the CH Cyg system in the quiescent and active phases.During the observed active phases, the spectral type is constant within+ or - 0.4 of a subclass and is classified as M(6.9 + or - 0.4) III. Thecontribution of a hotter source is visible in the region below 0.8micron, resulting in a quiescent-phase spectral type of about M5 and anactive phase type less than M4. An analysis of spectral and multicolorphotometric observations between 1975 and 1988 is used to examine thenature of dust particles in the dust envelope which formed in 1987. The Perkins catalog of revised MK types for the cooler starsA catalog is presented listing the spectral types of the G, K, M, and Sstars that have been classified at the Perkins Observatory in therevised MK system. Extensive comparisons have been made to ensureconsistency between the MK spectral types of stars in the Northern andSouthern Hemispheres. Different classification spectrograms have beengradually improved in spite of some inherent limitations. In thecatalog, the full subclasses used are the following: G0, G5, G8, K0, K1,K2, K3, K4, K5, M0, M1, M2, M3, M4, M5, M6, M7, and M8. Theirregularities are the price paid for keeping the general scheme of theoriginal Henry Draper classification. Lunar occultations of IRAS point sources, 1991-2000Abstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1989ApJS...69..651C&db_key=AST The cool components of symbiotic stars. II - Infrared photometryThis paper reports IR photometry for a sample of symbiotic binaries andK-M comparison stars. Measured CO absorption-band strengths of the coolcomponents in symbiotic stars generally are comparable to those ofsingle red giant and bright giant stars, but it is difficult todetermine the luminosity classes of these objects from their photometricCO indices. The 12-micron excesses observed in symbiotics require theircool components to lose mass more rapidly than do single red giantstars. Thus, mass-loss rates derived for red giants in close binarysystems may not be accurate estimates for mass loss in single redgiants.
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Constellation: Pisces Right ascension: 23h54m46.60s Declination: +00°06'33.0" Apparent magnitude: 5.61 Distance: 197.239 parsecs Proper motion RA: -40.5 Proper motion Dec: -14.9 B-T magnitude: 7.74 V-T magnitude: 6.002
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http://math.stackexchange.com/questions/356215/flow-by-curvature | # Flow by Curvature
In the case of plane curves the flow by curvature is, $$\frac{\partial F}{\partial u}=kN,$$ where $F:S^1\times [0, T)\rightarrow \mathbb R^2$ is a family of plane curves, $k$ is the curvature and $N$ is the inner unit normal..How to show the above curvature equation is equivalent to $$\frac{\partial x}{\partial t}=\frac{\partial^2 x}{\partial s^2}\ \textrm{e}\ \frac{\partial y}{\partial t}=\frac{\partial^2 y}{\partial s^2},$$ where $s$ is the arc length parameter and $F=(x, y)$?
-
The curvature vector of $F(\cdot, u)$ is $\vec{\kappa} = \frac{\partial^2 F}{\partial s^2}(\cdot,u)$, the unit normal is $N = \frac{\vec{\kappa}}{\|\vec{\kappa}\|}$ and the curvature is $k = \|\vec{\kappa}\|$. The right-hand side of the flow equation is just the curvature vector of the time $u$ curve, so by writing the equation out in Cartesian coordinates you get the result. | {"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": 0.9810655117034912, "perplexity": 102.53612397448882}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657137056.60/warc/CC-MAIN-20140914011217-00169-ip-10-234-18-248.ec2.internal.warc.gz"} |
http://tex.stackexchange.com/questions/55301/images-on-latex-not-appearing | # Images on latex not appearing
I cannot seem to get the images to appear on latex. I get no error messages and, it has no problems compiling. However, the produced (.pdf) which is what I am using, does not have the image. Essentially, everything I am using is in
\documentclass[12pt,a4paper,epsf,portrait,times,epsfig]{article}
\usepackage[dvips]{graphics}
\usepackage{amsmath}
\usepackage{xspace}
\usepackage{fancybox}
\usepackage{hyperref}
\usepackage{amsfonts}
\usepackage{graphicx}
\renewcommand{\baselinestretch}{1.5}
\setlength{\parskip}{0.2cm}
\setlength{\parindent}{0.0cm}
\setlength{\textheight}{8.5in}
\setlength{\textwidth}{16.0cm}
\setlength{\oddsidemargin}{0in}
\setlength{\evensidemargin}{0in}
\setlength{\topmargin}{0in}
\pagenumbering{arabic}
\numberwithin{equation}{subsection}
\begin{document}
\begin{figure}
\centering
\includegraphics{C:/Users/Reza/Desktop/Test/Untitled.jpg}
\label{fig:Untitled}
\end{figure}
\end{document}
I am using Texniccenter, and using LaTeX=>PDF. Help please!
-
Welcome to TeX.SE. I took the liberty to format your post a little. See this link for more details on available formatting. Please, try to make your example minimal, i.e. remove every line from your preamble that is not necessary. As a solution suggestion, try to move file Untitled.jpg to the folder where you .tex file is, and use \includegraphics{Untitled.jpg}. As well notice that LaTeX might be case-sensitive and Untitled.jpg is different from untitled.jpg. – tohecz May 10 '12 at 17:17
Also take a look at your .log file to see if there's a warning or error message. – Jake May 10 '12 at 17:18
The epsf and epsfig options in the \documentclass statement are obsolete. To auto-convert image files in .jpg format to .pdf -- the preferred format of the graphicx package -- be sure to load the epstopdf package. By the way, the \label instruction inside the figure environment won't have any desired effects unless you precede it with a \caption statement. (The "label" is associated by hyperref and other packages with the closest "label-able" item. In the case of your MWE, there is no such item so far. Hence, be sure to provide a \caption statement before the \label. – Mico May 10 '12 at 19:55
You use the packages graphics and graphix. Only one is needed. In addition, you specify the dvips driver for graphics. This is not the correct driver if you are using pdflatex (which is what I think you are using).
In addition, you are better off not using complete paths, but rather relative paths. This is what tohecz was suggesting with the \includegraphics{<filename>} and placing your picture in the same folder as your .tex file.
As an example, the following file (by the way, this is what tohecz meant by minimal example) works:
\documentclass[]{article}
\usepackage[]{graphics}
%\usepackage{graphicx}
\begin{document}
\begin{figure}
\includegraphics{Untitled.jpg}
\end{figure}
\end{document}
If you really want to use the dvips and the other options, then your images must be in .eps format. This means you must convert your .jpg image to .eps. In addition, you will have to compile with something of the form latex -> dvi -> pdf.
- | {"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": 0.8425220847129822, "perplexity": 2295.481983540831}, "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/1394678699721/warc/CC-MAIN-20140313024459-00085-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://tug.org/pipermail/texhax/2014-December/021477.html | # [texhax] LaTeX and non-ASCII file system
Victor Ivrii vivrii at gmail.com
Thu Dec 4 23:13:37 CET 2014
One of my colleagues uses TeX on Russian Windows and the following code
works
\documentclass[12pt]{article}
\usepackage{cmap}
%\usepackage[utf8x]{inputenc}
\usepackage[T2A]{fontenc}
\usepackage[russian]{babel}
\usepackage{graphicx}
\begin{document}
\includegraphics{RUSSNAME.png}
\end{document}
where RUSSNAME.png is a name of the file (in Russian) but uncommenting
\usepackage[utf8x]{inputenc}
Package pdftex.def Error: File \T2A\cyrzh \T2A\cyro \T2A\c
(Document is indeed in utf8). How to fix it? It looks like it was discussed
Actually on MacOSX one can name file in any language and the same problem
is observed
Thank you
Victor
Victor Ivrii
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://tug.org/pipermail/texhax/attachments/20141204/923487f9/attachment.html>
` | {"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": 0.977226734161377, "perplexity": 29511.025905731258}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039742963.17/warc/CC-MAIN-20181115223739-20181116005739-00471.warc.gz"} |
https://www.nag.com/numeric/nl/nagdoc_latest/clhtml/f08/f08jsc.html | # NAG CL Interfacef08jsc (zsteqr)
Settings help
CL Name Style:
## 1Purpose
f08jsc computes all the eigenvalues and, optionally, all the eigenvectors of a complex Hermitian matrix which has been reduced to tridiagonal form.
## 2Specification
#include
void f08jsc (Nag_OrderType order, Nag_ComputeZType compz, Integer n, double d[], double e[], Complex z[], Integer pdz, NagError *fail)
The function may be called by the names: f08jsc, nag_lapackeig_zsteqr or nag_zsteqr.
## 3Description
f08jsc computes all the eigenvalues and, optionally, all the eigenvectors of a real symmetric tridiagonal matrix $T$. In other words, it can compute the spectral factorization of $T$ as
$T=ZΛZT,$
where $\Lambda$ is a diagonal matrix whose diagonal elements are the eigenvalues ${\lambda }_{i}$, and $Z$ is the orthogonal matrix whose columns are the eigenvectors ${z}_{i}$. Thus
$Tzi=λizi, i=1,2,…,n.$
The function stores the real orthogonal matrix $Z$ in a complex array, so that it may also be used to compute all the eigenvalues and eigenvectors of a complex Hermitian matrix $A$ which has been reduced to tridiagonal form $T$:
$A =QTQH, where Q is unitary =(QZ)Λ(QZ)H.$
In this case, the matrix $Q$ must be formed explicitly and passed to f08jsc, which must be called with ${\mathbf{compz}}=\mathrm{Nag_UpdateZ}$. The functions which must be called to perform the reduction to tridiagonal form and form $Q$ are:
full matrix f08fsc and f08ftc full matrix, packed storage f08gsc and f08gtc band matrix f08hsc with ${\mathbf{vect}}=\mathrm{Nag_FormQ}$.
f08jsc uses the implicitly shifted $QR$ algorithm, switching between the $QR$ and $QL$ variants in order to handle graded matrices effectively (see Greenbaum and Dongarra (1980)). The eigenvectors are normalized so that ${‖{z}_{i}‖}_{2}=1$, but are determined only to within a complex factor of absolute value $1$.
If only the eigenvalues of $T$ are required, it is more efficient to call f08jfc instead. If $T$ is positive definite, small eigenvalues can be computed more accurately by f08juc.
## 4References
Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
Greenbaum A and Dongarra J J (1980) Experiments with QR/QL methods for the symmetric triangular eigenproblem LAPACK Working Note No. 17 (Technical Report CS-89-92) University of Tennessee, Knoxville https://www.netlib.org/lapack/lawnspdf/lawn17.pdf
Parlett B N (1998) The Symmetric Eigenvalue Problem SIAM, Philadelphia
## 5Arguments
1: $\mathbf{order}$Nag_OrderType Input
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by ${\mathbf{order}}=\mathrm{Nag_RowMajor}$. See Section 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.
Constraint: ${\mathbf{order}}=\mathrm{Nag_RowMajor}$ or $\mathrm{Nag_ColMajor}$.
2: $\mathbf{compz}$Nag_ComputeZType Input
On entry: indicates whether the eigenvectors are to be computed.
${\mathbf{compz}}=\mathrm{Nag_NotZ}$
Only the eigenvalues are computed (and the array z is not referenced).
${\mathbf{compz}}=\mathrm{Nag_UpdateZ}$
The eigenvalues and eigenvectors of $A$ are computed (and the array z must contain the matrix $Q$ on entry).
${\mathbf{compz}}=\mathrm{Nag_InitZ}$
The eigenvalues and eigenvectors of $T$ are computed (and the array z is initialized by the function).
Constraint: ${\mathbf{compz}}=\mathrm{Nag_NotZ}$, $\mathrm{Nag_UpdateZ}$ or $\mathrm{Nag_InitZ}$.
3: $\mathbf{n}$Integer Input
On entry: $n$, the order of the matrix $T$.
Constraint: ${\mathbf{n}}\ge 0$.
4: $\mathbf{d}\left[\mathit{dim}\right]$double Input/Output
Note: the dimension, dim, of the array d must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
On entry: the diagonal elements of the tridiagonal matrix $T$.
On exit: the $n$ eigenvalues in ascending order, unless ${\mathbf{fail}}\mathbf{.}\mathbf{code}=$ NE_CONVERGENCE (in which case see Section 6).
5: $\mathbf{e}\left[\mathit{dim}\right]$double Input/Output
Note: the dimension, dim, of the array e must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}-1\right)$.
On entry: the off-diagonal elements of the tridiagonal matrix $T$.
On exit: e is overwritten.
6: $\mathbf{z}\left[\mathit{dim}\right]$Complex Input/Output
Note: the dimension, dim, of the array z must be at least
• $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{pdz}}×{\mathbf{n}}\right)$ when ${\mathbf{compz}}=\mathrm{Nag_UpdateZ}$ or $\mathrm{Nag_InitZ}$;
• $1$ when ${\mathbf{compz}}=\mathrm{Nag_NotZ}$.
The $\left(i,j\right)$th element of the matrix $Z$ is stored in
• ${\mathbf{z}}\left[\left(j-1\right)×{\mathbf{pdz}}+i-1\right]$ when ${\mathbf{order}}=\mathrm{Nag_ColMajor}$;
• ${\mathbf{z}}\left[\left(i-1\right)×{\mathbf{pdz}}+j-1\right]$ when ${\mathbf{order}}=\mathrm{Nag_RowMajor}$.
On entry: if ${\mathbf{compz}}=\mathrm{Nag_UpdateZ}$, z must contain the unitary matrix $Q$ from the reduction to tridiagonal form.
If ${\mathbf{compz}}=\mathrm{Nag_InitZ}$, z need not be set.
On exit: if ${\mathbf{compz}}=\mathrm{Nag_UpdateZ}$ or $\mathrm{Nag_InitZ}$, the $n$ required orthonormal eigenvectors stored as columns of $Z$; the $i$th column corresponds to the $i$th eigenvalue, where $i=1,2,\dots ,n$, unless ${\mathbf{fail}}\mathbf{.}\mathbf{code}=$ NE_CONVERGENCE.
If ${\mathbf{compz}}=\mathrm{Nag_NotZ}$, z is not referenced.
7: $\mathbf{pdz}$Integer Input
On entry: the stride separating row or column elements (depending on the value of order) in the array z.
Constraints:
• if ${\mathbf{compz}}=\mathrm{Nag_UpdateZ}$ or $\mathrm{Nag_InitZ}$, ${\mathbf{pdz}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$;
• if ${\mathbf{compz}}=\mathrm{Nag_NotZ}$, ${\mathbf{pdz}}\ge 1$.
8: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
## 6Error Indicators and Warnings
NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM
On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.
NE_CONVERGENCE
The algorithm has failed to find all the eigenvalues after a total of $30×{\mathbf{n}}$ iterations. In this case, d and e contain on exit the diagonal and off-diagonal elements, respectively, of a tridiagonal matrix unitarily similar to $T$. $⟨\mathit{\text{value}}⟩$ off-diagonal elements have not converged to zero.
NE_ENUM_INT_2
On entry, ${\mathbf{compz}}=⟨\mathit{\text{value}}⟩$, ${\mathbf{pdz}}=⟨\mathit{\text{value}}⟩$ and ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: if ${\mathbf{compz}}=\mathrm{Nag_UpdateZ}$ or $\mathrm{Nag_InitZ}$, ${\mathbf{pdz}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$;
if ${\mathbf{compz}}=\mathrm{Nag_NotZ}$, ${\mathbf{pdz}}\ge 1$.
NE_INT
On entry, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{n}}\ge 0$.
On entry, ${\mathbf{pdz}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{pdz}}>0$.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
## 7Accuracy
The computed eigenvalues and eigenvectors are exact for a nearby matrix $\left(T+E\right)$, where
$‖E‖2 = O(ε) ‖T‖2 ,$
and $\epsilon$ is the machine precision.
If ${\lambda }_{i}$ is an exact eigenvalue and ${\stackrel{~}{\lambda }}_{i}$ is the corresponding computed value, then
$|λ~i-λi| ≤ c (n) ε ‖T‖2 ,$
where $c\left(n\right)$ is a modestly increasing function of $n$.
If ${z}_{i}$ is the corresponding exact eigenvector, and ${\stackrel{~}{z}}_{i}$ is the corresponding computed eigenvector, then the angle $\theta \left({\stackrel{~}{z}}_{i},{z}_{i}\right)$ between them is bounded as follows:
$θ (z~i,zi) ≤ c(n)ε‖T‖2 mini≠j|λi-λj| .$
Thus the accuracy of a computed eigenvector depends on the gap between its eigenvalue and all the other eigenvalues.
## 8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
f08jsc is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
f08jsc makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.
## 9Further Comments
The total number of real floating-point operations is typically about $24{n}^{2}$ if ${\mathbf{compz}}=\mathrm{Nag_NotZ}$ and about $14{n}^{3}$ if ${\mathbf{compz}}=\mathrm{Nag_UpdateZ}$ or $\mathrm{Nag_InitZ}$, but depends on how rapidly the algorithm converges. When ${\mathbf{compz}}=\mathrm{Nag_NotZ}$, the operations are all performed in scalar mode; the additional operations to compute the eigenvectors when ${\mathbf{compz}}=\mathrm{Nag_UpdateZ}$ or $\mathrm{Nag_InitZ}$ can be vectorized and on some machines may be performed much faster.
The real analogue of this function is f08jec.
## 10Example
See Section 10 in f08ftc, f08gtc or f08hsc, which illustrate the use of this function to compute the eigenvalues and eigenvectors of a full or band Hermitian matrix. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 116, "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": 0.9643978476524353, "perplexity": 1165.7562873427032}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030338280.51/warc/CC-MAIN-20221007210452-20221008000452-00222.warc.gz"} |
https://www.thieme-connect.de/products/ejournals/html/10.1055/s-2002-35795?lang=de | Semin Speech Lang 2002; 23(4): 219-220
DOI: 10.1055/s-2002-35795
FOREWORD
Copyright © 2002 by Thieme Medical Publishers, Inc., 333 Seventh Avenue, New York, NY 10001, USA. Tel.: +1(212) 584-4662
# Diagnostic and Treatment Issues of Apraxia
Nancy Helm
• Aphasia Research Center, Boston VA Healthcare System, Boston, Massachusetts
Weitere Informationen
### Publikationsverlauf
Publikationsdatum:
03. Dezember 2002 (online)
Inhaltsübersicht
The disorder apraxia of speech'' (AOS) has been a subject of some controversy during the 30 or so years since Frederick Darley and his colleagues at the Mayo Clinic first described it, particularly with regard to its distinction from aphasia syndromes such as Broca's aphasia and the pure articulatory impairment called aphemia.''
Interestingly, the schools of thought regarding AOS have had a rather regional bias in the United States. Those trained in the Boston'' tradition of aphasia classification (as delineated by Norman Geschwind and Harold Goodglass) tend to believe that the term apraxia'' should be reserved for disorders of purposeful movement that are not specific to language (e.g., limb apraxia, buccofacial apraxia). Furthermore, they argue that many of the speech behaviors described in association with AOS can be explained on a linguistic basis. Those trained by Darley and his colleagues and their students at the Mayo Clinic in Minnesota accept AOS as a disorder that can exist in a pure form, although it often accompanies aphasia.
The issue of accurate diagnosis is of great importance to rehabilitation in so far as any diagnosis implies a certain understanding of the underlying nature of the disorder. For example, it is known that naming'' problems are a core symptom of aphasia. The approach to treating word-retrieval problems may differ, however, according to the form of aphasia. For example, using a serial-stage, cognitive model of naming, a person with anomic aphasia may have greater deficits in the semantic system than the person with Wernicke's aphasia, whose deficits are mainly at the level of the phonological lexicon. It is also the case that many speech-language disorders are associated with distinct lesion sites. This knowledge is important to neurobehavioral treatment approaches based on spared and impaired brain regions and pathways such as Alexander Luria's intersystemic and intrasystemic reorganization methods.
Trained as I am in the Boston'' school of thought, my understanding of AOS was fuzzy'' because AOS was never used to describe the individuals seen in our clinical service. Yet, I think it is important for all of us to understand this disorder because it is frequently diagnosed by speech-language pathologists who choose treatment approaches in accordance with this diagnosis. Some individuals who have been referred to our clinic with diagnoses of apraxia'' (which we assume means apraxia of speech'') have been treated accordingly for sound production problems. These same individuals may then be diagnosed as having Broca's aphasia and treated for language problems.
With all these considerations in mind, it seemed time to dedicate an issue of Seminars in Speech and Language to the topic of apraxia of speech. I could think of no better person to serve as Guest Editor for this issue than Dr. Malcolm McNeil. Dr. McNeil has been a leading investigator of this disorder and has written extensively and in great depth about it. He is also part of an international community of scientific and clinical researchers pursuing this line of study. I am most grateful that he agreed to take on the task of putting this issue together and that he was able to recruit such a prestigious group of contributors.
Here, then, is an issue of Seminars directed at students and clinicians who have questions about AOS: what it is, what causes it, how to recognize it, and how to treat it. I have learned a great deal about AOS in the process of reading and editing the papers. It has helped enormously in overcoming the regional'' bias of my training. I think that other readers will find it highly educational and that it has good clinical applicability. | {"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": 0.19858334958553314, "perplexity": 2765.586015660321}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655901509.58/warc/CC-MAIN-20200709193741-20200709223741-00055.warc.gz"} |
https://cms.math.ca/cjm/msc/11S99?fromjnl=cjm&jnl=CJM | location: Publications → journals
Search results
Search: MSC category 11S99 ( None of the above, but in this section )
Expand all Collapse all Results 1 - 2 of 2
1. CJM 2003 (vol 55 pp. 432)
Zaharescu, Alexandru
Pair Correlation of Squares in $p$-Adic Fields Let $p$ be an odd prime number, $K$ a $p$-adic field of degree $r$ over $\mathbf{Q}_p$, $O$ the ring of integers in $K$, $B = \{\beta_1,\dots, \beta_r\}$ an integral basis of $K$ over $\mathbf{Q}_p$, $u$ a unit in $O$ and consider sets of the form $\mathcal{N}=\{n_1\beta_1+\cdots+n_r\beta_r: 1\leq n_j\leq N_j, 1\leq j\leq r\}$. We show under certain growth conditions that the pair correlation of $\{uz^2:z\in\mathcal{N}\}$ becomes Poissonian. Categories:11S99, 11K06, 1134
2. CJM 2000 (vol 52 pp. 47)
Chinburg, T.; Kolster, M.; Snaith, V. P.
Comparison of $K$-Theory Galois Module Structure Invariants We prove that two, apparently different, class-group valued Galois module structure invariants associated to the algebraic $K$-groups of rings of algebraic integers coincide. This comparison result is particularly important in making explicit calculations. Categories:11S99, 19F15, 19F27
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(1882) Electric and Gas Illumination By Charles Marshall Lungren
THE
POPULAR SCIENCE
MONTHLY.
SEPTEMBER, 1882.
ELECTRIC AND GAS ILLUMINATION.
By C. M. LUNGREN.
THE period of contest and denial over the question of the possibility of producing a light of low intensity by means of electricity, that would be suitable for the general purposes of interior lighting, has about drawn to a close. It is now pretty generally conceded—what there has never been any reason for denying—that the known laws of electric transmission interpose no bar to the successful solution of the problem, but that the difficulties in the way are solely of a practical kind. And it is, further, quite generally agreed that these practical difficulties have been for the most part resolved, and the question reduced down to one of cost simply; and, while a good deal of discussion has taken place upon this point, but little has been written that will enable the general public to form a judgment upon the subject, and arrive at a trustworthy opinion of the relative cost of it and gas under actual commercial conditions.
In estimating the relative cost of the two illuminants, it has been common to compare simply the cost of the materials consumed in their production, or, when the cost of the apparatus necessary to generate the electricity has been taken into account, this has usually been upon the basis of a limited production, and, to this extent, unfair to electricity. A comparison, to be of any value, should be between plants of a size sufficient to reduce the cost to the lowest point at which it can be commercially maintained, and should include all of the items entering into it. The attempt has been made, in the following pages, to institute such a comparison, and present the facts in the case as they are, so far as they can be obtained. The comparison is upon the basis of works capable of producing a million feet a day, as, in such works, gas can be made as cheaply as in any that are larger. The figures for the electric plant are based upon the work of Mr. Edison, as he is the only one who has so far made any attempt to put in an electric plant upon an industrial scale. And, for that reason further, only his system of distribution is considered, though it may be a question whether it is the one which will prove most satisfactory in practice. An objection to it of considerable force in the opinion of some, is, the difficulty of handling engines and boilers with sufficient rapidity to meet great and sudden variations of demand, such as not unfrequently occur during the seasons of the year in which the weather is changeable. The variation that experience has shown takes place at different periods of the day can be met readily enough. On this account, and on account of the greater freedom secured in the matter of working various pieces of apparatus without interference, it would seem that the system of distribution which includes a storage-battery would be preferable, and may, perhaps, become the final form, adopted in electric installations. It can not well enter into the present calculation, however, as there are no data with reference to the first cost and depreciation available, and because the present secondary batteries do not seem to have yet reached a satisfactory commercial form.
The cost of such a plant for coal-gas will vary in this country from $2,500 to$4,000 for each million feet of the yearly make, but $3,000 may be taken as a fair average. Owing to the great variability in the demand for light at different seasons of the year, a gas-works of this size will be called upon to furnish but 200,000,000 instead of 365,000,000. feet a year. The plant will therefore cost$600,000. Of this, $250,000 may be taken as the cost of the mains, which, in average conditions, will have, for a works of this size, a total length of fifty miles, covering a district of about three square miles. To compare an electric with a gas plant, it is necessary to know the number of five-foot burners that will be maintained at the time of greatest consumption, as on this depend both the amount of horse-power required and the size of the mains to transmit the current. The variation in the demand for light from hour to hour, as it would occur in average conditions on a bright December day, is exhibited in the following table, in percentages of the total make for the twenty-four hours: 7-8 a. m. 1½ per cent. 7-8 p. m. 12 per cent. 8-9 " ½ " 8-9 " 12 " 9-10 " ½ " 9-10 " 10 " 10-11 " ½ " 10-11 " 6 " 11-12 " ½ " 11-12 " 5 " 12-1 p. m. ½ " 12-1 a. m. 17/10 " 1-2 " ½ " 1-2 " 17/10 " 2-3 " ½ " 2-3 " 17/10 " 3-4 " ½ " 3-4 " 17/10 " 4-5 " 7½ " 4-5 " 17/10 " 5-6 " 16 to 20 " 5-6 " 16/10 " 6-7 " 14 " 6-7 " 17/10 " This shows the time of greatest consumption to be between the hours of five and six, and the demand as high as twenty per cent of the entire daily make. In the case of the plant under consideration, the maximum number of burners that will have to be maintained at any one time is therefore 40,000. Before proceeding to estimate the cost of the plant to generate and distribute electricity sufficient to maintain this number of burners, a few words descriptive of Mr. Edison's system will be desirable, especially as there appears to be considerable misapprehension on the subject. The distribution is what is known as in multiple arc—that is, the lamps are placed upon cross-wires between the conductors. Imagine a ladder erected upon an ordinary railway, so that it stands across the track, each foot resting upon one of the rails. Then these rails will represent the outgoing and returning street-conductors; the sidebars of the ladder, the house-conductors; and each rung, a lamp. The dynamo-machines generating the current are arranged in exactly the same way with regard to the circuit, all the positive poles being joined to one main conductor, and all the negative ones to the other. The arrangement is what is known, in the case of electric batteries, as coupling for quantity, as opposed to coupling for intensity, and is similar, to that of a number of pumps discharging water into a common main. This disposition of the electric-producing apparatus has the important advantage that the reserve plant, to meet contingencies, needs to be but a fraction of the total one; while, if each machine supplied an independent circuit, the plant would have to be in duplicate. As is well known, the steam-engines driving the dynamos are coupled directly to the machines, without the intervention of belts or gearing, the combination being termed the steam-dynamo. The street-mains consist of wrought-iron tubes about two inches in diameter, containing two half-round copper rods imbedded in an insulating resinous cement. A main of this kind is carried continuously around each city block. At the intersections of the streets the conductors are brought together and joined to a main somewhat larger, termed a feeder, which supplies the current to these four blocks. It will thus be seen that the system of mains and the mode of production of the electricity are as readily capable of expansion to meet increased business as in the case of gas. The mains can be tapped anywhere for new consumers, and to meet this increased demand it is only necessary to run a feeder to the place of enlarged consumption, and increase the producing plant sufficiently. What, then, will be the cost of such an electric plant to do the same amount of lighting as the above gas plant? If we take eight sixteen-candle lamps, maintained throughout the whole system for each actual horse-power applied to the dynamo-machine, engines with a normal capacity of five thousand horse-power will be required to sustain the maximum number of burners. This will include the reserve plant, as engines of a normal capacity of forty-two hundred can readily be forced to five thousand horse, or twenty per cent, to meet this extreme demand, and, with the generators arranged after Mr. Edison's plan, this per cent is an ample reserve. The maximum demand can, of course, be met either by forcing, or by running the entire plant at its normal rate, and forcing only in case of accident. To cover a district of three square miles, two distributing stations will be sufficient. The steam-dynamos may be taken as of two hundred horse each, working normally. The present steam-dynamos are of but one hundred and twenty-five horse, but they can be made two hundred horse with but slight increase of cost, which Mr. Edison contemplates doing in future installations. This will give thirteen steam-dynamos to one station and twelve to the other. These may each be placed at$8,000, making a total for the two stations of $200,000. That this is. a sufficient allowance will be evident upon considering the machines in detail. There are first the two hundred horse-power engines. No one will question that these can be obtained by a large buyer at$18 per horse-power, or $3,600 each.[1] This leaves$4,400 to cover the cost of the dynamo. The material in these, as now being constructed, is as follows:
Iron (wrought and cast) 40,700 pounds at 3 12 cents $=$ $1,425 00 Zinc (cast) 680 " 6 " $=$ 40 80 Copper 3,440 " 28 " $=$ 963 20 ——— ————— 44,820$2,429 00
This leaves $2,071 for the cost of construction, which will be recognized as more than enough, when it is remembered that the cost of the iron as above given includes its shaping, and that the copper on the armature is in the form of bars and disks, which, with suitable tools, can be expeditiously constructed. Adding twenty-five per cent to the cost of material for the 200 horse machine, there is still left$1,364 to be expended in construction. It seems to me, therefore, that $8,000 is a safe estimate of the cost of such steam-dynamos. Regarding the boilers, the sectional or water tube boiler, on account of its freedom from dangerous explosions, the smaller space occupied by it, its higher efficiency, and less cost for repairs, is in every way the best suited for a purpose of this kind. Such a boiler set ready for use, including stack and apparatus for handling coal and firing, will cost$20 per horse-power. The total boilers would therefore cost $100,000, making the entire producing portion of the plant, exclusive of real estate,$300,000.
As the Edison mains are now being laid, they will transmit a current sufficient to maintain from sixteen thousand to eighteen thousand sixteen-candle lamps. Taking the former figure, this is one and a quarter mile per 1,000 lamps. Basing the calculation for mains upon this mileage and the size of the present mains, the same number of miles of electric mains would be required as for gas. The present conductors are, as stated, in the form of half-round copper rods, of varying sizes, diminishing of course as they proceed from the station. They are, however, equivalent to round rods with a uniform diameter of one half inch. Such rods weigh 7551000 of a pound per foot, and 3986·4 pounds per mile, costing, at 28 cents per pound, 81,116 per mile. As there are two rods in each main, the cost per mile for copper would be $2,232. To this must be added$1,200 per mile for wrought-iron tube, boxes at the joints between the mains and house wires, and insulating material, and $1,000 per mile for laying, making the total cost of the main per mile, laid ready for use,$4,432. Four fifths of the mains would be of this size, the other fifth being feeders equivalent to round rods three fourths of an inch in diameter. These latter weigh 1·69 pound per foot, and would therefore cost $2,340 per mile, and, taking the cost of inclosing tube, insulation, and laying the same as above, their total cost per mile would be$7,196. The total cost of the mains, forty miles at $4,432 per mile, and ten miles at$7,196 per mile, would therefore amount to the same as the gas mains, viz., $250,000. If real estate be added at$50,000, which in most cities requiring this size of plant would be ample, the total cost of the electric plant would be the same as one for gas.[2]
The elements entering into the cost of the light to the company furnishing it are, in each case, the interest on the investment, depreciation, or the amount spent each year in keeping the property in good condition, the labor of all kinds—in the manufacture, distribution, and management—and lastly the cost of the materials used in its production. In the case of gas but a few of these items as they occur in American works are obtainable, so that recourse must be had to the published reports of foreign companies, and the like items estimated for this country. Of these, the reports of the London companies as analyzed by Mr. Field will best serve for the purpose of the present comparison.[3] Taking first the item of depreciation, we find that for the four metropolitan companies this was, for the year 1880, on the producing portion of the plant 9·86 cents per 1,000 feet of gas sold, or about five and a half per cent on the cost of this part of the plant as it has been taken in this paper. Calling this ten cents a thousand feet, we have $20,000 a year as the expenditure under this head, which is probably well within the actual figures of most American works. In the case of the electric plant four per cent is a sufficient allowance for the same item, which gives a yearly charge of$12,000, and a cost of six cents per 1,000 feet.
Depreciation of this part of the plant varies but little with different works, as the conditions upon which it depends are relatively constant, but that of the mains is, on the other hand, exceedingly variable. In a dry, open soil, gas-mains will last a great length of time, and even when they become entirely rusted through they will still continue efficient if undisturbed. They do not, however, remain undisturbed, so that in the most favorable conditions some expenditure is necessary to keep them in working condition. We shall probably not be far wrong if we take this at two per cent of the entire cost of the mains, which includes, of course, that of laying them. This item then becomes in the case of our gas plant $5,000 per year, and 212 cents per 1,000 feet. In the case of the electric mains, this percentage must be reckoned only upon their cost, exclusive of the copper, as this latter is practically indestructible, and can be used again and again. The amount upon which to reckon the two per cent depreciation is therefore$2,200 X 50$=$$110,000, and the yearly charge$2,200, which gives 1·1 cent per 1,000 feet. The interest on the investment is the same in each case, and amounts to $24,000 a year, at four per cent, and to 12 cents per 1,000 feet. These items include all that are properly chargeable to the expense account of the plant save taxes, which would be about the same in each case, and which maybe neglected for the present. The plant account, then, stands, in the two cases, for each thousand feet or its equivalent: Gas. Electricity. Interest 12 · 12 · Depreciation of producing works 10 · 6 · " of mains 2 ·5 1 ·1 ——— ——— Total 24 ·5 19 ·1 19 ·1 ——— Balance in favor of electricity 5 ·4 The items entering into the cost of coal-gas are, exclusive of management, rent and taxes, etc., the cost of coal, of manufacturing, and of distribution. Taking the last first, we find 4·4 cents per 1,000 feet as the cost of this item for the four metropolitan companies. Putting this at 5 cents for American works, and deducting from this 212 cents for the depreciation of mains, which is included in this charge, there is left 212 cents for the cost of the labor of inspection of meters, etc., which constitutes the charge of distribution, and which would be about the same in both systems. As the depreciation of the mains is not given separately, this item is liable to error, due to a wrong estimate of such depreciation, but, as it affects both systems similarly, it will not vitiate the results. Under manufacturing, the English report includes purifying, salaries, the wages for carbonizing, and wear and tear, which latter item has already been carried to the plant account. The first of these amounts to 1·82 cent; the second ·82 of a cent, and the third to 7·16 cents, making a total of 9·8 cents per 1,000 feet. This is probably much below the actual amount paid for these items in American works, but I am assured on excellent authority that, in works constructed after the best modern models, purification should cost the gas company nothing, and that all labor in the manufacturing department should be covered by an outlay equivalent to one man's wages ($2.50 per day) for each 40,000 feet of gas made per day. As the same amount of labor would have to be paid for each day in the year as on the days of greatest demand, this would amount, for a daily make of 1,000,000 feet, to 25 men whose wages at $65 per month (26 X 212) would be$19,500[4] a year, or 934 cents per 1,000 feet of the actual make. Including the cost of purification, and calling the amount 12 cents, we shall not be far wrong, or at least shall not exceed the actual outlay in the average works of this size. In the case of electricity the labor required at each station would be:
One chief-engineer $125 per month. Three assistants (at$75) 225 " Five firemen (at $60) 300 " —— Total$650
—— making $15,600 a year for the whole manufacturing plant, and 7·8 cents per 1,000 feet. To this may be added 115 cent to cover salary of electrician and incidental labor, bringing the item up to 9 cents. There remains to be considered the cost of the coal in the case of gas, and the expense of running the engines in the case of electricity. The cost of coal per 1,000 feet of gas made was, in the case of the London companies, 3686100 cents, corresponding to$3.51 per ton, the make of gas being for this amount of coal 9,529 feet. This was offset by the sale of residuals, as below:
Coke and breeze 11·16 cents. Tar and products 7·13 " Ammonia and products 5·72 " ——— Total 24·06 "
—— which leaves 12·8 cents as the net cost of the coal.
Compared with foreign companies, both in England and on the Continent, but very little is done with the residual products in this country, and the amounts received vary greatly between different works. Reliable data on this point can not be obtained, but under the most favorable conditions this item can not be taken as amounting to more than one half the cost of the coal, while with most works it is probably inconsiderable. The average price of the coal used may be placed at $4.50 a ton, and the amount of gas produced 10,000 feet, making the cost 45 cents per 1,000 feet. This make of gas can hardly be maintained with a production of residuals equal to one half the cost of the coal, but. assuming that it is, the cost of the coal becomes 22 cents per 1,000 feet. In the foregoing estimate of the electric plant, it has been assumed that eight lamps could be maintained throughout the entire distributive system for each actual horse-power expended upon the pulley of the dynamo-machine. That this is entirely feasible has been proved by careful tests made by experts in no way interested in any of the lamps, and their results can therefore be accepted without question. For such a use as electric lighting, the cost of a horse-power may safely be taken as not above the best results hitherto obtained in practice. In general manufacturing, the item of power, while important, is not sufficiently so to demand that constant and great care necessary to obtain the very best results, and hence few engines and boilers yield in practice the same results as in special tests. With electric-light companies, this item, on the contrary, is vital, and we may confidently expect to see them in time obtaining their power at a considerably less cost than is now common. Mr. Edison finds as a matter of fact confirmed by several months' test at Menlo Park, that he is able to maintain a horse-power an hour with five pounds of slack (one third pea and two thirds dust), costing$2.45 a ton. For the purpose of the present comparison, however, it is best to make a liberal allowance, and take for a 200-horse-power engine a consumption of four pounds of coal an hour, the coal costing $4.50 per ton of 2,240 pounds, delivered. A horsepower will then cost 810 of a cent an hour, and we may rightly abate our liberality sufficiently to include in this the cost of the oil for lubricating the engine and dynamo. The maintenance for an hour of 200 electric burners, the equivalent of the 1,000 feet of gas, will therefore cost 20 cents, as against 2212 cents for the gas. Summing up the results so far obtained, the two accounts stand as follows: Plant Account. Per 1,000 Feet. Gas. Electricity. Interest 12 · 12 · Depreciation of producing works 10 · 6 · Depreciation of mains 2 ·5 1 ·1 ——— 24 ·5 ——— 19 ·1 Manufacturing expenses: Labor 12 · 9 · Coal 22 ·5 20 · ——— 34 ·5 ——— 29 · Working expenses: Distribution 2 ·5 2 ·5 ——— ——— Total 61 ·5 50 ·6 Under this last heading there should be added rent and taxes, management, law charges, bad debts, and various incidentals. These can not be separately arrived at with any closeness, but they may be taken in the lump as about the same part of the total charges as in the case of the London companies, which is 16 per cent, exclusive of the interest on investment. This in the present case would be 9*4 cents per 1,000, bringing the total cost per 1,000 up to 71 cents with gas and 60 cents with electricity. The promoters of the electric light would probably demur to this statement, so far as rent and taxes are concerned, as they insist upon the much smaller real estate required with the electric than with a gas plant. This difference does not, however, seem to me sufficient to be of any practical moment, as the real estate in the case of electricity is in the district supplied, where the price of land is relatively high, while the gas companies can readily place their works in such locality as to compensate in lowered land value for the greater amount required. Gas companies can, moreover, build within much smaller limits than usual when for any reason it is desirable, and closely approach the space requisite for an electric installation. An item of considerable amount which has been omitted from the estimate for electricity is the cost of the renewal of the lamps. With the general introduction of incandescent electric lighting, this is a charge which would fall directly upon the consumer, but it is one which would steadily diminish with improvement in lamps. Assuming, however, that it is a legitimate charge upon the company supplying the light, the item amounts to 10 cents per 1,000, if the lamps have a life of 600[5] hours and cost 30 cents. This brings the electric account up to 70 cents per 1,000. So far as coal-gas is concerned, then, these figures show a slight advantage in favor of electricity, and while they are only approximative they are near enough to the truth, I think, to represent the actual relation of the two illuminants. While very much doubtless remains to be done in the improvement of coal-gas manufacture, it does not seem probable that this will affect its cost of production to the same extent as future improvements of electric apparatus may be expected to decrease that of the electric light. Looking closely at the two accounts, it does not seem probable that the item relative to plant will be materially lessened in the future. The cost of the plant has already been taken at a figure very near the lower limit, so near that the substitution of this in its place would make a difference in the yearly plant account of but 212 cents per 1,000. We may, on the other hand, expect improvements to largely reduce the cost of the electric plant. On Mr. Edison's system of distribution, the size of the conductors varies inversely as the resistance of the lamps, so that they may be materially reduced if the resistance of these latter can be increased; while any improvements affecting the number of lamps per horsepower diminishes both the interest account by reducing the plant and the actual cost of production. How far coal-gas can go in a reduction of the cost of production it is difficult to say, but I think the lower limit may safely be taken at the point at which the sale of residuals pays for the coal. Both of these items—cost of coal and prices of residuals—are practically beyond the control of a gas company. The coal is already purchased in the open market at the lowest figures at which it can be obtained, and the market for residuals depends chiefly upon the development of chemical industries, which can hardly be hastened by the action of a gas company. This market is a steadily growing one, and it is not impossible that the residuals will in time pay for the coal, though it is hardly probable. The items of labor and distribution can not probably undergo any considerable reduction. The limit, then, below which it does not appear that there is any probability of coal-gas falling in this country is 46 cents per 1,000, which is a figure that may be reached by electricity without assuming anything less, probable than the above supposition respecting gas. It is only necessary to get ten lamps per horse-power, and produce the latter with three pounds of coal an hour, to bring the cost down to 47 cents, exclusive of the lamps. As a present competitor, however, what is known as water-gas— gas produced by the decomposition of steam in the presence of coal or oil—appears to be the more formidable. This mode of gas-manufacture has the advantage of coal-gas in a lessened cost of the producing plant, a smaller labor account, and a decreased depreciation of the generating apparatus. Its successful competition with coal-gas ultimately depends upon what the latter can make of its residuals, as there is no offset of this kind in its case, but with present conditions it can go below it. The producing portion of the plant costs but little more than half that for coal-gas, while the labor is about a third, and depreciation but slightly more than this. A sixteen-candle gas will require three gallons of oil per 1,000 feet, and can be made with oil at 5 cents a gallon and coal at 84.50 a ton, at an expenditure of 28 cents per 1,000 feet for materials. The total cost will not exceed 60 cents. Such, then, appears to be the relation of these two agents on the basis of illumination solely, but it must not be forgotten that the amount of light which each plant can furnish does not represent the actual relative capacity of the two. The electric plant can be run not only four hours a day for light, but any further number of hours for power, without any increase of the machines. The gas-plant, on the other hand, would have to be increased, to furnish both power and light. That this advantage of electricity is liable to be a very important one will hardly be questioned, when the extent of the field open to electro-motors is borne in mind. On these figures the cost of electricity is near enough to that of gas to enable it to offer a very substantial competition, and one which may be expected to grow stronger with increased experience and future improvements. That under the stimulus of this competition considerable improvement will be made in lighting by gas seems very probable. Already it has been shown that in the matter of burners there is a wide field for invention, and that the results now usually obtained are much under what are possible. With the high-power burners of Siemens, the illumination obtained from sixteen-candle gas has been more than doubled, and in others it has been carried up to from five to five and a half candles per foot. How suitable burners yielding such a great increase of light will be for the general purposes of lighting, and whether they can with advantage displace the simple flat tip, remains to be seen, but the present indications are that it is chiefly through the use of improved burners that gas must endeavor to resist the assaults of the incandescent light. Competition on the basis of a gas of higher illuminating power simply, without a resort to improved burners, does not seem very promising. The recently published report of the sub-commission, appointed to test the incandescent lamps at the Paris Exhibition, of which Mr. Crookes was a member, shows that a thirty-two candle lamp can be maintained with an increase of from 28 to 37 per cent of the power required to sustain one of sixteen candles, while with gas such an increase of illumination will require an additional expense of fully 50 per cent of the cost of one of the lower candle-power. This is so with the Lowe gas, with which three gallons of oil are sufficient to give sixteen candles, but six are required for thirty-two, and it is not probable that coal-gas can be enriched any cheaper. Whether the limit to progress in gas-lighting—both in the matter of improvement of manufacture and burners—is sufficiently far off to give gas unquestioned possession of the field of lighting or not, the result can alone determine. But, if the figures presented in this paper can be at all relied upon, they show that gas manufacturers and those interested in gas property will do well not to underrate the strength in their own domain of this rising industrial power. 1. Mr. Edison informs me that engines of 200 indicated horse-power are being purchased by him for$1,750 each, delivered in New York. This estimate is, therefore, much too high, but, as the comparison of plant in the text is based upon it, I have thought it best to let it stand, and point out the needed correction here.
2. While this estimate seems to me not far from the expenditure that would be actually required for this size of plant, it should be stated that it is lower than any of those given by the electrical experts examined by the select committee of the House of Commons in its consideration of the Electric Lighting Bill.
3. Having been unable to obtain a copy of Mr. Field's "Annual," I have taken the figures as quoted from this for the year 1880 by Mr. Dowson, in a recent lecture before the Society of Arts.
4. The engineer furnishing the information on which this statement is based informs me that this should be $12,500, or$2.50 per 40,000 feet of the actual yearly, instead of the maximum daily, make. This would reduce the item 934 cents to 614 cents per 1,000 feet.
5. I am informed by Mr. Edison that the average life of the lamps is now 900 hours, including 3 per cent breakage in handling. | {"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": 4, "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": 0.5564534068107605, "perplexity": 1204.130752522855}, "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-2014-23/segments/1406510272329.26/warc/CC-MAIN-20140728011752-00040-ip-10-146-231-18.ec2.internal.warc.gz"} |
https://www.statisticssolutions.com/assumptions-of-linear-regression/ | # Assumptions of Linear Regression
Linear regression is an analysis that assesses whether one or more predictor variables explain the dependent (criterion) variable. The regression has five key assumptions:
• Linear relationship
• Multivariate normality
• No or little multicollinearity
• No auto-correlation
• Homoscedasticity
A note about sample size. In Linear regression the sample size rule of thumb is that the regression analysis requires at least 20 cases per independent variable in the analysis.
In the free software below, its really easy to conduct a regression and most of the assumptions are preloaded and interpreted for you.
First, linear regression needs the relationship between the independent and dependent variables to be linear. It is also important to check for outliers since linear regression is sensitive to outlier effects. The linearity assumption can best be tested with scatter plots, the following two examples depict two cases, where no and little linearity is present.
Secondly, the linear regression analysis requires all variables to be multivariate normal. This assumption can best be checked with a histogram or a Q-Q-Plot. Normality can be checked with a goodness of fit test, e.g., the Kolmogorov-Smirnov test. When the data is not normally distributed a non-linear transformation (e.g., log-transformation) might fix this issue.
Thirdly, linear regression assumes that there is little or no multicollinearity in the data. Multicollinearity occurs when the independent variables are too highly correlated with each other.
Multicollinearity may be tested with three central criteria:
1) Correlation matrix – when computing the matrix of Pearson’s Bivariate Correlation among all independent variables the correlation coefficients need to be smaller than 1.
2) Tolerance – the tolerance measures the influence of one independent variable on all other independent variables; the tolerance is calculated with an initial linear regression analysis. Tolerance is defined as T = 1 – R² for these first step regression analysis. With T < 0.1 there might be multicollinearity in the data and with T < 0.01 there certainly is.
3) Variance Inflation Factor (VIF) – the variance inflation factor of the linear regression is defined as VIF = 1/T. With VIF > 10 there is an indication that multicollinearity may be present; with VIF > 100 there is certainly multicollinearity among the variables.
If multicollinearity is found in the data, centering the data (that is deducting the mean of the variable from each score) might help to solve the problem. However, the simplest way to address the problem is to remove independent variables with high VIF values.
Fourth, linear regression analysis requires that there is little or no autocorrelation in the data. Autocorrelation occurs when the residuals are not independent from each other. For instance, this typically occurs in stock prices, where the price is not independent from the previous price.
4) Condition Index – the condition index is calculated using a factor analysis on the independent variables. Values of 10-30 indicate a mediocre multicollinearity in the linear regression variables, values > 30 indicate strong multicollinearity.
If multicollinearity is found in the data centering the data, that is deducting the mean score might help to solve the problem. Other alternatives to tackle the problems is conducting a factor analysis and rotating the factors to insure independence of the factors in the linear regression analysis.
Fourthly, linear regression analysis requires that there is little or no autocorrelation in the data. Autocorrelation occurs when the residuals are not independent from each other. In other words when the value of y(x+1) is not independent from the value of y(x).
While a scatterplot allows you to check for autocorrelations, you can test the linear regression model for autocorrelation with the Durbin-Watson test. Durbin-Watson’s d tests the null hypothesis that the residuals are not linearly auto-correlated. While d can assume values between 0 and 4, values around 2 indicate no autocorrelation. As a rule of thumb values of 1.5 < d < 2.5 show that there is no auto-correlation in the data. However, the Durbin-Watson test only analyses linear autocorrelation and only between direct neighbors, which are first order effects.
The last assumption of the linear regression analysis is homoscedasticity. The scatter plot is good way to check whether the data are homoscedastic (meaning the residuals are equal across the regression line). The following scatter plots show examples of data that are not homoscedastic (i.e., heteroscedastic):
The Goldfeld-Quandt Test can also be used to test for heteroscedasticity. The test splits the data into two groups and tests to see if the variances of the residuals are similar across the groups. If homoscedasticity is present, a non-linear correction might fix the problem.
Statistics Solutions can assist with your quantitative analysis by assisting you to develop your methodology and results chapters. Fill-out the form to the right to see how we can help.
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Related Pages:
Multicollinearity
Autocorrelation
Linear Regression-Video Tutorial
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https://www.iacr.org/cryptodb/data/paper.php?pubkey=29322 | ## CryptoDB
### Paper: Make Some Noise. Unleashing the Power of Convolutional Neural Networks for Profiled Side-channel Analysis
Authors: Jaehun Kim , Delft University of Technology, Delft Stjepan Picek , Delft University of Technology, Delft Annelie Heuser , Univ Rennes, Inria, CNRS, IRISA Shivam Bhasin , Physical Analysis and Cryptographic Engineering, Temasek Laboratories at Nanyang Technological University Alan Hanjalic , Delft University of Technology, Delft DOI: 10.13154/tches.v2019.i3.148-179 URL: https://tches.iacr.org/index.php/TCHES/article/view/8292 Search ePrint Search Google Profiled side-channel analysis based on deep learning, and more precisely Convolutional Neural Networks, is a paradigm showing significant potential. The results, although scarce for now, suggest that such techniques are even able to break cryptographic implementations protected with countermeasures. In this paper, we start by proposing a new Convolutional Neural Network instance able to reach high performance for a number of considered datasets. We compare our neural network with the one designed for a particular dataset with masking countermeasure and we show that both are good designs but also that neither can be considered as a superior to the other one.Next, we address how the addition of artificial noise to the input signal can be actually beneficial to the performance of the neural network. Such noise addition is equivalent to the regularization term in the objective function. By using this technique, we are able to reduce the number of measurements needed to reveal the secret key by orders of magnitude for both neural networks. Our new convolutional neural network instance with added noise is able to break the implementation protected with the random delay countermeasure by using only 3 traces in the attack phase. To further strengthen our experimental results, we investigate the performance with a varying number of training samples, noise levels, and epochs. Our findings show that adding noise is beneficial throughout all training set sizes and epochs.
##### BibTeX
@article{tches-2019-29322,
title={Make Some Noise. Unleashing the Power of Convolutional Neural Networks for Profiled Side-channel Analysis},
journal={IACR Transactions on Cryptographic Hardware and Embedded Systems},
publisher={Ruhr-Universität Bochum},
volume={2019, Issue 3},
pages={148-179},
url={https://tches.iacr.org/index.php/TCHES/article/view/8292},
doi={10.13154/tches.v2019.i3.148-179},
author={Jaehun Kim and Stjepan Picek and Annelie Heuser and Shivam Bhasin and Alan Hanjalic},
year=2019
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https://ftp.aimsciences.org/article/doi/10.3934/proc.2015.0562 | # American Institute of Mathematical Sciences
2015, 2015(special): 562-568. doi: 10.3934/proc.2015.0562
## The Nehari solutions and asymmetric minimizers
1 Daugavpils University, Parades str. 1, Daugavpils, LV 5400, Latvia 2 Insitute of Mathematics and Computer Science, University of Latvia, Rainis boul. 29, Riga, LV 1459, Latvia
Received September 2014 Revised November 2014 Published November 2015
We consider the boundary value problem $x'' = -q(t,h) x^3,$ $x(-1)=x(1)=0$ which exhibits bifurcation of the Nehari solutions. The Nehari solution of the problem is a solution which minimizes certain functional. We show that for $h$ small there is exactly one Nehari solution. Then under the increase of $h$ there appear two Nehari solutions which supply the functional smaller value than the remaining symmetrical solution does. So the bifurcation of the Nehari solutions is observed and the previously studied in the literature phenomenon of asymmetrical Nehari solutions is confirmed.
Citation: Armands Gritsans, Felix Sadyrbaev. The Nehari solutions and asymmetric minimizers. Conference Publications, 2015, 2015 (special) : 562-568. doi: 10.3934/proc.2015.0562
##### References:
[1] Z.Nehari, Characteristic values associated with a class of nonlinear second order differential equations, Acta Math., 105 (1961), 141-176. MR0123775 Google Scholar [2] A. Gritsans and F. Sadyrbaev, Characteristic numbers of non-autonomous Emden-Fowler type equations, Mathematical Modelling and Analysis., 11 (2006), 243-252. MR2268126 Google Scholar [3] A. Gritsans and F. Sadyrbaev, Lemniscatic functions in the theory of the Emden - Fowler diferential equation, Mathematics. Differential equations (Univ. of Latvia, Institute of Math. and Comp. Sci.), 3: 5 - 27, 2003. (electr. version http://www.lumii.lv/Pages/sbornik/s3f3v1.pdf ). Google Scholar [4] R. Kajikiya, Non-even least energy solutions of the Emden-Fowler equation, Proc. Amer. Math. Soc., 140 (2012), no. 4, 1353-1362. MR2869119 Google Scholar [5] F. Zh. Sadyrbaev, Solutions of an equation of Emden-Fowler type. (Russian), Differentsial'nye Uravneniya, 25 (1989), no. 5, 799-805; translation in Differential Equations 25 (1989), no. 5, 560-565. MR1003036 Google Scholar
show all references
##### References:
[1] Z.Nehari, Characteristic values associated with a class of nonlinear second order differential equations, Acta Math., 105 (1961), 141-176. MR0123775 Google Scholar [2] A. Gritsans and F. Sadyrbaev, Characteristic numbers of non-autonomous Emden-Fowler type equations, Mathematical Modelling and Analysis., 11 (2006), 243-252. MR2268126 Google Scholar [3] A. Gritsans and F. Sadyrbaev, Lemniscatic functions in the theory of the Emden - Fowler diferential equation, Mathematics. Differential equations (Univ. of Latvia, Institute of Math. and Comp. Sci.), 3: 5 - 27, 2003. (electr. version http://www.lumii.lv/Pages/sbornik/s3f3v1.pdf ). Google Scholar [4] R. Kajikiya, Non-even least energy solutions of the Emden-Fowler equation, Proc. Amer. Math. Soc., 140 (2012), no. 4, 1353-1362. MR2869119 Google Scholar [5] F. Zh. Sadyrbaev, Solutions of an equation of Emden-Fowler type. (Russian), Differentsial'nye Uravneniya, 25 (1989), no. 5, 799-805; translation in Differential Equations 25 (1989), no. 5, 560-565. MR1003036 Google Scholar
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https://www.vistrails.org/index.php/User:Tohline/2DStructure/AxisymmetricInstabilities | # Axisymmetric Instabilities to Avoid
When constructing rotating equilibrium configurations that obey a barotropic equation of state, keep in mind that certain physical variable profiles should be avoided because they will lead to structures that are unstable toward the dynamical development of shape-distorting or convective-type motions. Here are a few well-known examples.
## Rayleigh-Taylor Instability
Referencing both p. 101 of [ Shu92 ], and volume I, p. 410 of [ P00 ], a Rayleigh-Taylor instability is a bouyancy-driven instability that arises when a heavy fluid rests on top of a light fluid in an effective gravitational field, $~\vec{g}$. In the simplest case of spherically symmetric, self-gravitating configurations, the condition for stability against a Rayleigh-Taylor instability may be written as,
$~(- \vec{g} ) \cdot \nabla\rho$ $~<$ $~0$ [stable] ,
that is to say, the mass density must decrease outward. In an expanded discussion, [ P00 ] — see pp. 410 - 413 — derives a dispersion relation that describes the development of the Rayleigh-Taylor instability in a plane-parallel fluid layer that initially contains a discontinuous jump/drop in the density.
In addition, [ P00 ] — see pp. 413 - 416 — and [ Shu92 ] — see pp. 101 - 105 — both discuss circumstances that can give rise to the so-called Kelvin-Helmholtz instability. It is another common two-fluid instability, but one that depends on the existence of transverse velocity flows and that is independent of the gravitational field.
## Poincaré-Wavre Theorem
As [ T78 ] points out — see his pp. 78 - 81 — Poincaré and Wavre were the first to, effectively, prove the following theorem:
For rotating, self-gravitating configurations "any of the following statements implies the three others: (i) the angular velocity is a constant over cylinders centered about the axis of rotation, (ii) the effective gravity can be derived from a potential, (iii) the effective gravity is normal to the isopycnic surfaces, (iv) the isobaric- and isopycnic-surfaces coincide."
Among other things, this implies that for rotating barotropic configurations not only is the equation of state given by a function of the form, $~P = P(\rho)$, but it must also be true that,
$~\frac{\partial \dot\varphi}{\partial z}$ $~=$ $~0 \, .$ [ T78 ], §4.3, Eq. (30)
## Høiland Criterion
"For an incompressible liquid contained between concentric cylinders and rotating with angular velocity $~\Omega(\varpi)$, Rayleigh's criterion — that $~\varpi^4 \Omega^2$ increase outwards — is necessary and sufficient for stability to axisymmetric disturbances. In a star rotating with angular velocity $~\Omega(\varpi)$ if we continue to restrict attention to axisymmetric disturbances, this criterion must be modified by buoyancy effects; that is, some combination of the Rayleigh and Schwarzschild criteria should obtain. Such a combination has been found, for example, by Høiland (1941) (see also Ledoux's Chapter 10, pp. 499-574 of Stellar Structure (1965), and indicates, as one would expect, that a stable stratification of angular velocity exerts a stabilizing influence on an unstable distribution of temperature, and vice versa. The combined criterion has not been placed on the solid analytical foundation of its two component criteria, however." — Drawn from p. 475 of N. R. Lebovitz (1967), ARAA, 5, 465
As is stated on p. 166 of [ T78 ], in rotating barotropic configurations, axisymmetric stability requires the simultaneous satisfaction of the following pair of conditions:
$~\biggl(\frac{1}{\varpi^3} \biggr) \frac{\partial j^2}{\partial \varpi} + \frac{1}{c_P} \biggl( \frac{\gamma - 1}{\Gamma_3 - 1}\biggr) (- \vec{g} ) \cdot \nabla s$ $~>$ $~0$ [stable] ; [ T78 ], §7.3, Eq. (41) see also[ KW94 ], §43.2, Eq. (43.22) $~-g_z \biggl[ \frac{\partial j^2}{\partial \varpi} \biggl(\frac{\partial s}{\partial z} \biggr) - \frac{\partial j^2}{\partial z} \biggl(\frac{\partial s}{\partial \varpi} \biggr)\biggr]$ $~>$ $~0$ [stable] . [ T78 ], §7.3, Eq. (42) see also[ KW94 ], §43.2, Eq. (43.23)
where, $~s$, is the local specific entropy, and $~j \equiv \dot\varphi \varpi^2$, is the local specific angular momentum of the fluid. According to [ T78 ] — see p. 168 — this pair of mathematically expressed conditions has the following meaning:
"A baroclinic star in permanent rotation is dynamically stable with respect to axisymmetric motions if and only if the two following conditions are satisfied: (i) the entropy per unit mass, $~s$, never decreases outward, and (ii) on each surface $~s$ = constant, the angular momentum per unit mass, $~j$, increases as we move from the poles to the equator."
### Schwarzschild Criterion
In the case of nonrotating equilibrium configurations, the Høiland Criterion reduces to the Schwarzschild criterion. That is, thermal convection arises when the condition,
$~(- \vec{g} ) \cdot \nabla s$ $~>$ $~0$ [stable] , [ T78 ], §7.3, Eq. (43) see also[ KW94 ], §6.1, Eq. (6.13) … or … pp. 93 - 98 of [ Shu92 ]
is violated. This means that, in order for a spherical system to be stable against dynamical convective motions, the specific entropy must increase outward.
### Solberg/Rayleigh Criterion
In the case of an homentropic equilibrium configuration, the Høiland Criterion reduces to the Solberg criterion. That is, an axisymmetric exchange of fluid "rings" will occur on a dynamical time scale if the condition,
$~\frac{dj^2}{d\varpi}$ $~>$ $~0$ [stable] , [ T78 ], §7.3, Eq. (44) see also[ KW94 ], §43.2, Eq. (43.18) … or … pp. 98 - 101 of [ Shu92 ]
is violated. This means that, for stability, the specific angular momentum must necessarily increase outward. As [ T78 ] points out, this "Solberg criterion generalizes to homentropic bodies the well-known Rayleigh (1917) criterion for an inviscid, incompressible fluid."
Here are some recommendations to keep in mind as you attempt to construct equilibrium models of self-gravitating astrophysical fluids.
Rayleigh-Taylor instability: In order to avoid constructing configurations that are subject to the Rayleigh-Taylor instability, be sure that lower density material is never placed "beneath" higher density material. For example …
• When building a bipolytropic configuration, a value for the (imposed) discontinuous jump in the mean-molecular weight will need to be specified at the interface between the envelope and the core. If you choose a ratio, $~{\bar\mu}_e/{\bar\mu}_c$, that is greater than unity, the resulting equilibrium model will exhibit a discontinuous density jump that makes the density higher at the base of the envelope than it is at the surface of the core. The core/envelope interface of this configuration will be unstable to the Rayleigh-Taylor instability, but you won't know that until and unless you examine the hydrodynamic stability of the configuration.
Schwarzschild criterion: In order to avoid constructing configurations that violate the Schwarzschild criterion, be sure that the specific entropy of the fluid is uniform (marginally stable) or increases outward throughout the equilibrium structure, where the word "outward" is only meaningful when referenced against the direction that the effective gravity points. For example …
• Suppose that you build a spherically symmetric polytropic configuration whose structural index is, $~n$, but then you want to test the stability of the configuration assuming that compressions/expansions of individual fluid elements occur along adiabats for which the adiabatic index is, $~\gamma \ne (n+1)/n$. Although we generally think of polytropes as being homentropic configurations, if $~\gamma \ne (n+1)/n$, then different fluid elements will, in practice, evolve along adiabats that are characterized by different values of the specific entropy; that is, throughout the equilibrium model, $~\nabla s$ will not be zero. Whether the specific entropy increase (stable) or decreases (unstable) outward will depend on whether you select a value for the evolutionary $~\gamma$ that is greater than (stable) or less than (unstable) $~(n+1)/n$.
• According to Woosley's class lecture notes, $~\frac{d\ln \rho}{d\ln P}\biggr|_\mathrm{structure} = \frac{n}{n+1}$ $~>$ $~\frac{1}{\gamma_g}$ $~\Rightarrow$ stable $~<$ $~\frac{1}{\gamma_g}$ $~\Rightarrow$ unstable
This is another way of expressing the same stability criterion for polytopes.
• Examples: An n = 1 polytope is unstable toward convection if expansions (or contractions) occur along an adiabat with $~\gamma_g < 2$. Alternatively, an n = 5 polytope is unstable toward convection if expansions (or contractions) occur along an adiabat with $~\gamma_g < \tfrac{6}{5}$. | {"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": 44, "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": 0.9028725624084473, "perplexity": 1332.982117307573}, "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/1570986677964.40/warc/CC-MAIN-20191018055014-20191018082514-00008.warc.gz"} |
http://www.red-dingo.sk/dutch-darts-sow/projection-matrix-formula-426af1 | Projection matrix Last updated October 07, 2020. Sign in to vote. ⢠The vanishing point is the perspective projection of that point at infinity, resulting from multiplication by the camera matrix. Let the vectors $${\bf u}_1 , \ldots {\bf u}_n$$ form a basis for the range of the projection, and assemble these vectors in the m -by- n matrix A . This can be written as a linear mapping between homogeneous coordinates (the equation is only up to a scale factor): where a projection matrix represents a map from 3D to 2D. So I'll give you a few moments to consider the problem for yourselves. I'm trying to implement a way to generate this matrix in order to use it for a game engine I'm working on. We will explain how to derive these formulas in the chapter devoted to the OpenGL perspective projection matrix. Projection Matrix. If b is perpendicular to the column space, then itâs in the left nullspace N(AT) of A and Pb = 0. The second picture above suggests the answerâ orthogonal projection onto a line is a special case of the projection defined above; it is just projection along a subspace perpendicular to the line. General Formula for Perspective Projection Matrix. We have covered projection in Dot Product. Suppose CTCb = 0 for some b. bTCTCb = (Cb)TCb = (Cb) â¢(Cb) = Cb 2 = 0. 3.1.1 Introduction More than one explanatory variable In the foregoing chapter we considered the simple regression model where the dependent variable is related to one explanatory variable. After having gone through the stuff given above, we hope that the students would have understood," Projection of Vector a On b" Apart from the stuff given in "Projection of Vector a On b", if you need any other stuff in math, please use our google custom search here. Therefore, we have to keep in mind that both clipping (frustum culling) and NDC transformations are integrated into GL_PROJECTION matrix.The following sections describe how to build the projection matrix from 6 parameters; left, right, bottom, top, near and far boundary values. Our modified perspective projection matrix that projects P to P' and remaps the z'-coordinate of P' from 0 to 1 now looks like this: In this article we will try to understand in details one of the core mechanics of any 3D engine, the chain of matrix transformations that allows to represent a 3D object on a 2D monitor.We will try to enter into the details of how the matrices are constructed and why, so this article is not meant for absolute beginners. Leave a comment below, or ask me on Twitter: https://twitter.com/VinoBS Can anyone please tell me what is the general formula to implement the Perspective Projection Matrix? When TRUE, the function returns a matrix of single-degree-of-freedom projections of the response variable onto the columns of the predictor matrix. Vector projection formula, Vector projection explained, vector projection examples, Vector projection formula derivation with solved problems Cb = 0 b = 0 since C has L.I. Let C be a matrix with linearly independent columns. A formula for the matrix representing the projection with a given range and null space can be found as follows. Orthogonal Projection Matrix â¢Let C be an n x k matrix whose columns form a basis for a subspace W ðð= ð â1 ð n x n Proof: We want to prove that CTC has independent columns. The basic perspective projection function is simple. The formula for projection onto a line does not immediately apply because the line doesn't pass through the origin, and so isn't the span of any â. You can make do with just the formula; and if you're using a graphics API like Direct3D that will build a projection matrix for you, you don't even need that. Camera: perspective projection. Introduction. Can anyone please tell me what is the general formula to implement the Perspective Projection Matrix? Learning Objective: (1) Understanding the the camera projection matrix and (2) estimating it using fiducial objects for camera projection matrix estimation and pose estimation. Watch Queue Queue Construct an age or stage-structure projection model from a transition table listing stage in time t, fate in time t+1, and one or more individual fertility columns. If we knew what that vector y was, if we could always find it, then we would have a formula, so to speak, for figuring out the projection of x onto v. But we don't have that yet. Thus CTC is invertible. xScale 0 0 0 0 yScale 0 0 0 0 zf/(zf-zn) 1 0 0 -zn*zf/(zf-zn) 0. As long as you understand what projection does, you needn't concern yourself with how it works if you don't want to. eqs: x =X, y =Y (drop Z)-Using matrix notation: xh yh zh w = 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 Question? ! CSE486, Penn State Robert Collins Imaging Geometry V U W Object of Interest in World Coordinate System (U,V,W) CSE486, Penn State Robert Collins Imaging Geometry Z f ... Perspective Matrix Equation (in Camera Coordinates) 1 0 0 0 1 0 0 0 0 0 1. K Camera projection of world point: r 3 Remember that since the position vector is multiplied on the right hand side that matrix is actually the last. CS252A, Fall 2012 Computer Vision I Construct projection matrix models using transition frequency tables. There are three coordinate systems involved --- camera, image and world. Description. ... As the math works out, the following two formulas for w and h use the viewport's dimensions, and are equivalent to the preceding formulas. ... Whatever formula you decide to use, be sure to set Zâ to as large a value as possible, because z-values extremely close to the camera don't vary by much. Suppose they are: (x0,y0,z0), (x1,y1,z1) and (x2,y2,z2). Hi again. This video is unavailable. The formula itself is returned in the formula attribute. First we scale, then rotate, translate and finally project. I'm trying to implement a way to generate this matrix in order to use it for a game engine I'm working on. This makes depth comparisons using 16-bit z-buffers somewhat complicated. All I've said is, any member of v can be represented as a product of our matrix A, which has the basis for v ⦠A projection matrix takes any vector in three-space--well, just in this case, we are dealing with a three-space--and projects it down onto the plane, a two-dimensional subspace of R^3. Article - World, View and Projection Transformation Matrices Introduction. Camera Projection (Pure Rotation) X C 1 R W Coordinate transformation from world to camera: Camera World 3 C C W 3 == ªº «» «» «» ¬¼ X X R X r r r r 1: world x axis seen from the camera coord. In this first part you will perform pose estimation in an image taken by an uncalibrated camera. General Formula for Perspective Projection Matrix. Following is a typical implemenation of perspective projection matrix. Now, we will take deep dive into projections and projection matrix. Finding the formula for a projection matrix. ¥" Find (a) the projection of vector on the column space of matrix ! The Perspective Divide. I have 3 points in a 3D space of which I know the exact locations. Projection matrices and least squares Projections Last lecture, we learned that P = A(AT )A â1 AT is the matrix that projects a vector b onto the space spanned by the columns of A. Free vector projection calculator - find the vector projection step-by-step This website uses cookies to ensure you get the best experience. The default method does not use this argument. Projection Matrix A 3x4 projection matrix P transforms a world coordinate point v (given in homogeneous coordinates) into a image pixel coordinate p (also in homogeneous coordinates): Since the resulting pixel vector is normalized before usage, a scaling of P does not affect the resulting pixel. 3.1 Least squares in matrix form E Uses Appendix A.2âA.4, A.6, A.7. r1r2 r 3 r 2: world y axis seen from the camera coord. Saturday, June 30, 2012 11:38 AM. In statistics, the projection matrix (), [1] sometimes also called the influence matrix [2] or hat matrix (), maps the vector of response values (dependent variable values) to the vector of fitted values (or predicted values). # # # $% & & & A= 10 11 01! " As the new vector r shares the direction with vector a, it could be represented as a⦠Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share ⦠And then you'll see my take on it. Part 1: Camera Projection Matrix Estimation. Thus, perspective projection is simply the task of applying that simple formula to every vertex that the vertex shader receives. Corresponding points Augmented reality CS252A, Fall 2012 Computer Vision I Vanishing Point ⢠In the projective space, parallel lines meet at a point at infinity. math matrix graphics projection perspective . Also I have a camera that is looking at these 3 points and I know the 2D 6 b= 1 1 1! " H matrix? Camera Projection Reading: T&V Section 2.4. according to the formula of perspective projection matrix. and (b) the projection matrix P that projects any vector in R 3 to the C(A). And here is a good link to explain everything OpenGL Projection Matrix. So, if the details of this article seem a little overwhelming, fear not. If b is in the column space then b = Ax for some x, and Pb = b. Orthographic Projection-Itisthe projection of a 3D object onto a plane by a set of parallel rays orthogonal to the image plane.-Itisthe limit of perspective projection as f â> â(i.e., f /Z â>1) orthographic proj. To adjust for this, we start by shifting the entire map down two units. By using this website, you agree to our Cookie Policy. Answers text/html 7/3/2012 11:00:56 PM Chuck Walbourn - MSFT 1. We add the perspective projection matrix as the first element in the multiplication that generates the complete transformation. Note that the frustum culling (clipping) is performed in the clip coordinates, just before dividing by w c. columns. Create a perspective projection matrix to give our scene depth. 3x4 Projection Matrix. 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Uses cookies to ensure you get the best experience then rotate, translate finally. Some x, and Pb = b matrix in order to use it for a game engine I trying... At infinity, resulting from multiplication by the camera coord form E Uses Appendix,! That point at infinity, resulting from multiplication by the camera coord to use it a... Is typically a scale and perspective projection matrix PM Chuck Walbourn - MSFT 1 take on.. Taken by an uncalibrated camera vector a, it could be represented as a⦠general formula implement... Projection calculator - Find the vector projection calculator - Find the vector projection calculator - Find the projection. Is the general formula for perspective projection matrix % & & & A= 10 11 01! create perspective! We start by shifting the entire map down two units to ensure you get the experience! R 3 r 2: world y axis seen from the camera matrix watch Queue Queue the matrix. 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Predictor matrix - world, View and projection Transformation Matrices Introduction working.! - camera, image and world to adjust for this, we start by the! How to derive these formulas in the formula attribute for some x and... Our Cookie Policy projections and projection matrix is typically a scale and perspective projection matrix representing the projection.... Camera matrix explain everything OpenGL projection matrix resulting from multiplication by the camera matrix axis seen the... Does, you agree to our Cookie Policy from the camera coord r:. Down two units is typically a scale and perspective projection matrix null space can be found as.! Use it for a game engine I 'm working on -zn * zf/ zf-zn! Applying that simple formula to every vertex that the vertex shader receives:. | {"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": 0.6454225778579712, "perplexity": 677.5183796510844}, "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/1618038076819.36/warc/CC-MAIN-20210414034544-20210414064544-00529.warc.gz"} |
http://gradestack.com/Electromagnetic-Field/Magnetostatics/Biot-Savart-Law/19375-3931-38756-study-wtw | # Biot-Savart Law
The Biot–Savart law is used to find the magnetic field intensity produced by a steady current.
The Biot–Savart law states that the magnetic field intensity produced at a point P due to a differential current element Idl is
1. directly proportional to the product of current I and differential length dl,
2. directly proportional to the sine of the angle between the element and the line joining P to the element, and
3. inversely proportional to the square of the distance r. | {"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": 0.8736792802810669, "perplexity": 488.04704230964705}, "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-2017-22/segments/1495463605188.47/warc/CC-MAIN-20170522151715-20170522171715-00623.warc.gz"} |
http://math.stackexchange.com/questions/5904/must-basis-of-an-euclidean-space-be-ordered | # Must Basis of an Euclidean Space Be Ordered
Does the basis of an Euclidean space have to be ordered by definition? Or can be left unordered?
I was also wondering about what is the morphism (i.e. the mapping that can preserve all the structures) on Euclidean spaces? Is it Euclidean transformation (rigid transformation), consisting of rotation, translation and reflection? Or the reflection is not part of it, because the basis of a Euclidean space must be ordered.
Thanks and regards!
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From the answers below it appears the answer to your question is yes and no.:) A basis can be ordered or unordered, it depends on what you're using it for as to whether or not you want it ordered. For example, for representing linear maps I use the phrase "ordered basis" rather than the term "basis" to make it clear what conditions I need on the basis. – Ryan Budney Oct 3 '10 at 16:01
@Ryan: If what you're using it for intrinsically requires a basis order --- as opposed to it being merely convenient for presentation to label the basis vectors with an index set, which has a conventional ordering --- then I'm not sure that what you're studying is just "geometry" or "linear algebra" any more. Similarly, someone studying group theory, who finds that their problem simply requires that some notion of "distance" be continuously deformed, is not just working on "group theory", but algebraic topology. Do group actions have to preserve open sets? – Niel de Beaudrap Oct 8 '10 at 6:08
Bases must be ordered, otherwise you couldn't speak of coordinates as ordered tuples. And this could make things pretty messy. For instance, if the standard basis for $\mathbb{R}^2$ could be either $e_1, e_2$ or $e_2, e_1$ simultaneously, then it would be difficult to speak of "the point of coordinates $(2,1)$".
Reflexions send bases to bases, because they are isomorphisms. But this doesn't mean they necessarily send a particular basis to the same particular basis. So they can change the order of the vectors of the basis. They don't preserve orientation, but this is an extra piece of structure, not included in the definition of Euclidean space.
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Yes, a basis should be thought of as an ordered list of vectors. However, one should be aware that some textbooks define a basis (incorrectly, IMO) as a set of vectors; as far as I can see, there is no advantage to this. – Darsh Ranjan Oct 3 '10 at 4:31
@Darsh. It is in fact standard to define a basis as a set of vectors rather than as an ordered tuple. Most of the time we are interested in linear combination of basis vectors where order does not matter because vector addition is commutative. – Jyotirmoy Bhattacharya Oct 3 '10 at 5:41
### On bases
Bases do not have to be ordered. I respectfully present the following as a counterpoint to Agustí Roig's response.
First of all, a basis is simply a set of vectors, by definition; and sets are unordered. If you wish to enumerate the vectors in a basis, you will of course do so in some order, but this order is arbitrary.
This arbitrary order of enumeration is the reason why we describe vectors as tuples. The order of the coefficients in a tuple matters only in as much as it must be in agreement with the arbitrary order which was selected for the basis vectors. To wit: let x, y be two arbitrary linearly independent vectors. The tuple [ 7 5 ] with respect to the (enumeration of the) basis v1 = x, v2 = y represents the same vector as the tuple [ 5 7 ] with respect to the (different enumeration of the same) basis v2 = x, v1 = y. The tuple is just a representation of a vector, relative to an arbitrarily chosen order for the basis.
Even more foundationally: "tuples" can be regarded as functions from the integers (e.g. the indices '1', '2', etc.) to the reals, complex numbers, or whichever set you draw your coefficients from. So [ 7 5 ] can be thought of as 'really being' the function mapping
'1' $\mapsto$ 7,
'2' $\mapsto$ 5.
Our enumeration of the basis has a similar role: choosing the enumeration v1 = x, v2 = y is equivalent to defining a mapping
'1' $\mapsto$ x,
'2' $\mapsto$ y.
Why do I have '1' and '2' in quotes? Because they're just labels; any other labels would do just as well. For instance, I could replace '1' and '2' with the vectors x and y themselves. Then we could define vectors by coefficient functions such as
x $\mapsto$ 7,
y $\mapsto$ 5;
that is, the coefficient 7 is associated to the vector x, and the coefficient 5 is associated to y, to represent the vector 7x + 5y. This is what we really mean anyway; never mind any ordering of the vectors in your basis. With this, the arbitrary ordering of the basis disappears, leaving nothing but what it is we really mean by it all.
So: when we order our bases, its only to make it easier to present things — it is not part of the definition, or part of the structure of the objects we really care about.
### On morphisms
A morphism on a Euclidean space ought to preserve all of the structures of Euclidean geometry. In particular, it should map circles to other circles, to preserve the structures guaranteed by the third postulate; so it must be an isothety (a rigid transformation up to scaling). This includes, but is not restricted to, the rigid transformations.
Can you make any argument why the morphisms should consist only of rigid transformations (excluding isothetic maps such as v $\mapsto$ 2v)?
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This began as a reply to Jyotirmoy's comment on Agustí's answer, but it became way too long.
As I stated in my comment on Agustí's answer, some textbooks define a basis as a set, and I think this is wrong. Obviously, some people disagree (just read some of the other answers and comments). I'll try to explain why a basis should never be thought of as a set.
Do the columns of the following matrix form a basis for $\mathbb{R}^2$? $$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 1\end{bmatrix}$$ The answer is "yes" if a basis is a set, but obviously the right answer is "no." This makes it clear that whatever sort of collection to which we apply concepts like "linear [in]dependence" or "basis", it must allow repeated vectors; otherwise, a lot of basic theorems from linear algebra would require extra clauses to deal with matrices with repeated rows or columns. This rules out sets as our collections of choice.
To find out what our collection of choice should be, let's revisit the definition of a basic concept like linear dependence (in somewhat imprecise "collection-agnostic" language (whose meaning should nevertheless be clear)):
The vectors $v_1,\ldots,v_n$ are linearly dependent if there are scalars $c_1,\ldots,c_n$, not all zero, such that $c_1v_1+\cdots+c_nv_n=0$.
It's obvious here that the natural object to apply such a concept to is an indexed tuple of vectors (indexed by $\{1,\ldots,n\}$ above, but we could formulate the concept equally well for an arbitrary finite index set): we begin with an indexed tuple of vectors and then consider a tuple of scalars indexed by the same set, and then we apply a function to these two tuples that is now completely specified (taking the linear combination). We could have started with a completely unindexed, unordered collection of vectors with repetition allowed (i. e., a "multiset"), but then to consider a linear combination, we would have had to choose some indexing of the multiset first and then to consider some scalars indexed by our arbitrary index set in order to form a linear combination. The core point is that the natural input to the "linear combination" operation is a tuple of vectors and a tuple of scalars indexed by the same finite set. This is the fundamental operation on a vector space, so to me, it makes sense to formulate everything in terms of indexed tuples of vectors whenever possible.
I talked about indexing lists of vectors in the previous paragraph, but indexing isn't the same as ordering. When I say "order," though, I'm actually being a bit imprecise. It's usually not the order relation itself that matters, but the choice of index set does matter. For example, if you want to write down the coordinate matrix of a vector or the matrix of a linear transformation relative to a basis, then your index set pretty much has to be $\{1,...,n\}$ (or $\{0,...,n-1\}$ if you've ever programmed in a language other than Matlab or Fortran) because whatever you're using to index the elements of the basis, you're also using to index the rows or columns of your matrices. Since one of the main uses of bases is to reduce things to matrices, the sets $\{1,...,n\}$ are very convenient for indexing. In this very common context, all the basic concepts like "basis," "linear independence," "spanning," etc. would apply to finite sequences of vectors. In no context, however, do they naturally apply to finite sets of vectors.
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Your complaint is not so much that we should be using sequences instead of sets, as it is that we should be using bags (i.e. multi-sets, sets where membership has multiplicity) rather than sets. This obviously applies for the columns of the matrix you describe; and the case of the definition of linear independence hilights this, where even in the sum the particular order does not matter, nor does the choice of indexing scheme, so long as it is a bijection between some index-set and the vector-set (or vector-bag) under consideration. – Niel de Beaudrap Oct 3 '10 at 11:58
Anyway: I would readily concede that bags are a better choice than sets for describing collections of vectors for the purpose of describing linear independence, etc. However, I think that details such as a specific choice of indexing into the definitions only cloud details, and introduce distinctions which are on the whole totally uninteresting. – Niel de Beaudrap Oct 3 '10 at 12:02
@Niel, I think the definitions should be chosen to make the surrounding theory as natural and simple as possible, and as such, sequences are still better than multisets. Again, all of the definitions are about linear combinations, and "linear combination" is an operation on a tuple of vectors and a tuple of scalars. Moreover, while the property of "being a basis" is indeed independent of the indexing, it's still useful to talk about permuting a basis, e. g., when discussing orientation. – Darsh Ranjan Oct 3 '10 at 19:32
well, it's also useful to talk about permuting a basis when talking about permutation matrices, or anything where permutations play a role. (For instance, the sign of the cross product can be seen as taking the 'sign' of a permutation, rather than saying anything about the geometry per se.) — I respectfully disagree that 'sequences' make the theory more natural, or simple; and if it makes it pedagogically easier, this can just as easily be an accident of the fact that we teach sequences, but not multisets, in grade-school. – Niel de Beaudrap Oct 4 '10 at 6:32
Orientation does not play any role in Euclidean geometry. So it is most natural to define a Euclidean space as a finite-dimensional vector space with an inner product. Lengths, distances and angles are then defined in terms of this inner product. We are interested in transformations which preserve lengths and angles, which are precisely the orthogonal transformations including reflections. There is no need to explicitly choose a basis at any point.
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https://proxieslive.com/tag/before/ | ## How will the seats be allocated if I don’t reserve one before?
I booked two seats for one way flight. The ticket doesn’t have seat number yet so I am allowed to select any available seats for a fee usually 2 to 5 USD for a seat. What if I don’t select the seats? How will they be allocated? Is it random? I booked via an online travel agency.
Company is spicejet airline.
## With the Deflect Missiles monk feature, does the player know the damage of the attack before choosing to deflect?
The monk’s Deflect Missiles feature description says (PHB, pg. 78):
Starting at 3rd level, you can use your reaction to deflect or catch the missile when you are hit by a ranged weapon attack.
I take this to mean that the player controlling the monk gets to decide whether or not to use Deflect Missiles after they know whether or not the attack hits.
It continues:
When you do so, the damage you take from the attack is reduced by 1d10 + your Dexterity modifier + your monk level.
Does the monk’s player get to know the damage before they decide to use Deflect Missiles? Or is damage is rolled after they choose to use the feature?
## Prevent Word from automatically recognizing text before caption number as label
I’m using Word for Mac 16.24. I followed this excellent blog post to set up decent-looking equations in my Word docs, however I have an issue that it doesn’t address. If I surround the equation number in parentheses, Word automatically assumes the opening parenthesis is the label and so instead of e.g., ‘1’, I get ‘(1’ for my cross reference. It’s easy enough to delete this on a case-by-case basis, but when I update the references, all the cross-references are replaced with the versions with a leading parenthesis. For the time being, I’ve resorted to removing the parentheses from the captions, however I’d really like to have them there, as many (most?) publishers require them. The only alternative I can think of right now is to write a macro that updates references and then replaces all of the reference texts with the correct, parenthesis-less version.
## Flight departed from the gate 5 min before scheduled departure time. Refund options
This was Alaska Airlines flight from SJC to LAX. We ran later than we usually do on our way to flights and so we ended up reaching the gate 2 min before the scheduled departure time.
On our way from the security check to the gate we didn’t hear any call for our names asking us to make it to the gate asap. (Not that we were loitering around. We were running to the gate which was at the end of that terminal.)
So anyhow, we reached there 2 min prior but were advised that the flight already left and the gate was closed. We bought a ticket from SFO and continued with the rest of our trip because there was no point arguing as the flight had already left. We were very upset and I am looking into what can be done. A few things that I am not sure of here:
1. Flights can leave ahead of time (but that is if all passengers have already boarded or there is a clear indication of no-show in that the gate is advised that some passengers didn’t even checkin at the airport AND they have approval by the ATC of course). We did checkin and so we shouldn’t have been marked no-show.
2. Departure time is time to leave the gate and not take-off. Confirm this.
3. How could I prove the airline left minutes ago? Could I ask the airlines for the record of the flight on that particular day?
4. If I do prove this, can we ask for any sort of compensation?
Any other advice (other than “don’t go that late”). As I said, it doesn’t always happen but when it happens we should know our options.
## If a warlock loses their Book of Shadows, are others able to use it before the warlock restores it? [on hold]
If someone loses their Book of Shadows at any level, can someone who finds it (or maybe who had stolen it) make use of the spells before the warlock can restore it during a rest?
## Why does CTRL+U clear everything in terminal, not only the text before cursor, as expected
I always hear that in terminal (no matter which in MacOS or Linux), the hotkey `Ctrl + U` will erase the text JUST BEFORE THE CURSOR. However, I find it erases EVERYTHING in my MacOS terminals, no matter where the cursor is.
So I just wondering that, just my Macs do behave like this, or every mac does, and if they do, how to config it to behave like in linux.
## Can you shove before Attacking with Shield Master using a Readied action?
For instance, I have feat Shield Master, I ready the attack action with the condition that the enemy is prone, then I take the shove bonus action and knock him prone then I take my readied attack action.
Isn’t this legal exploit to reverse the action order?
## Directed graph that returns before all its child nodes are visited?
Give an example of a directed graph in which a depth-first search backs up from a vertex $$v$$ before all the vertices that can be reached from $$v$$ via one or more edges are discovered.
My professor recently asked this question as a warm up to lecture, but never answered it. I still have not figure how that is possible. Why would it return if it’s not complete?
I just can’t see a scenario where this would happen.
It would never return, since DFS is (essentially) recursive and it can’t return without having hit all base cases.
## Build automation tools before make?
I realized that make was “only” invented in 1976 and seems to be one of the first build automation tools (at least it’s probably the oldest still in use).
But we already had a history of large software projects in 1976. What did people use for e.g. OS/360 or the software for the F-14? Were there any real precursors for make or did make invent the concept of build automation?
## Efficient way to add a colon before and after every word in strings inside a Series
I was working with twitter data, and extracted every emoji from the data. But, when I passed that data through `CountVectorizer`, colons where substracted from the strings. So, the string emoji `:ok_hand: :thumbs_up:` turned into `ok_hand thumbs_up`. I wanted to re-add those colons so then I could emojize them back. I managed to do that, but I’m quite sure my method is very inefficient. The emojis are the indexes of a coefficients DataFrame, like this:
`` index coef ok_hand thumbs_up 0.4 airplane 0.2 ``
``to_emojize=pd.Series(coef_mat_emoji.index) to_emojize=to_emojize.apply(lambda x: x.split()) to_emojize=to_emojize.apply(lambda x:[':'+i+':' for i in x]) to_emojize=to_emojize.apply(lambda x: emoji.emojize(x, use_aliases=True)) coef_mat_emoji.index=to_emojize `` | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 2, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4878668785095215, "perplexity": 1688.4204723088465}, "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/1555578529962.12/warc/CC-MAIN-20190420180854-20190420202854-00455.warc.gz"} |
https://nl.mathworks.com/discovery/garch-models.html | # GARCH Models
## Estimating, simulating, and forecasting with GARCH models
GARCH models are conditionally heteroskedastic models with a constant unconditional variance. They have been widely used in financial and econometric modeling and analysis since the 1980s. These models are characterized by their ability to capture volatility clustering, and they are widely used to account for nonuniform variance in time-series data.
Effective approaches to modeling and analyzing univariate GARCH processes include:
• Estimating parameters of a univariate GARCH(p, q) model with Gaussian innovations
• Simulating univariate GARCH(p, q) processes
• Forecasting conditional variances
Additional time-series capabilities to consider for modeling stochastic processes include:
• Univariate ARMAX/GARCH composite models
• Multivariate VARMAX models
• Cointegration analysis
• estimate: Estimate ARMAX/GARCH Model Parameters - Function
• simulate: Simulate ARMAX/GARCH Model Responses - Function
• garch: Simulate Univariate GARCH Processes - Function | {"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": 0.7784663438796997, "perplexity": 7319.821657681776}, "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-2017-13/segments/1490218187744.59/warc/CC-MAIN-20170322212947-00184-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://blender.stackexchange.com/questions/210530/bl-options-register-undo-not-working-blender-2-9-trying-to-link-pr?noredirect=1 | # bl_options = {'REGISTER', 'UNDO'} not working… Blender 2.9 | trying to link props to my Operator in separate files
I have an add-on split into multiple files.
Here is my file structure:
blueprint
│ main_operator.py
│ main_panel.py
│ main_properties.py
│ __init__.py
│
├───buildings
│ Apartment.py
│ grid_build.py
│ Office.py
│ Skyscrappers.py
│ small_shops.py
│
└───tools
blender_tools.py
In my main_operator.py file I have this option in the class enabled: bl_options = {'REGISTER', 'UNDO'} Although when I run the add-on, all works but I get no 'Undo Panel' on the bottom left hand side once the add-on is run.
Typically in a simple file I would have the props variables defined inside the operator class.
bpy.props.BoolProperty()
bpy.props.FloatProperty()
bpy.props.IntProperty()
bpy.props.PointerProperty()
bpy.props.StringProperty()
All inside the Operator Class.
But in my complex file system I have successfully split them into a main_properties.py and main_operator.py
Here is my __init__.py:
bl_info = {
"name": "Blueprint",
"author": "Davi Silveira <vidasilveira85@gmail.com>",
"version": (1, 0, 8),
"blender": (2, 90, 1),
"location": "VIEW3D > BLueprint > UI",
"description": "We Built This City",
"warning": "Still under development",
"doc_url": "",
"tracker_url": "",
}
import bpy
from . main_operator import VIEW3D_OT_Blueprint
from . main_panel import OBJECT_PT_Blueprint
from . main_properties import Blueprint_Properties
classes = (
OBJECT_PT_Blueprint,
VIEW3D_OT_Blueprint,
Blueprint_Properties,
)
#### -----------------------------------------
#### Register Classes
def register():
for cls in classes:
bpy.utils.register_class(cls)
bpy.types.Scene.tools = bpy.props.PointerProperty(type=Blueprint_Properties)
def unregister():
for cls in classes:
bpy.utils.unregister_class(cls)
del bpy.types.Scene.tools
#### -----------------------------------------
I link in my main_panel.py to my Properties in my main_properties.py file by using: scene = context.scene.tools It all works as it should I guess. But in my main_operator.py file this scene = context.scene.tools does not work. All variables are frozen... They only change when I change the main add-on panel, the UNDO panel in the bottom will not change, only mirrors the main one.
Here is my '''main_operator:
import bpy
from .tools.blender_tools import move_it, re_size, hide, de_select, dimension
from .buildings.grid_build import grid
from . main_properties import Blueprint_Properties
class VIEW3D_OT_Blueprint(bpy.types.Operator):
"""Blueprint we built this city"""
bl_label = "Building Options".upper()
bl_idname = "mesh.blueprint"
bl_category = "View"
bl_context = "objectmode"
bl_options = {'REGISTER', 'UNDO'}
####--Execute
####------------------------------------------------------
def execute(self, context):
####--Pre Start
de_select(True, 'OBJECT') # Select All Objs
hide(True)
# deactivate others
for obj in bpy.data.objects:
if obj.select_get() is True:
obj.select_set(False)
current_coll = bpy.context.collection # list of all collections
new_coll = bpy.data.collections.new('Buildings') # new collection
####-----------------------------------------------------
####--Call Functions to Run Script
scene = bpy.context.scene
tool = scene.tools
# bpy.context.scene.tool_settings.use_snap = True
grid(tool.x_location, tool.y_location, current_coll, new_coll)
####-----------------------------------------------------
return {'FINISHED'}
#def draw(self, context):
#layout = self.layout
#scene = context.scene.tools
#row = layout.row()
#box = row.box()
#box.label(text='The Grid Blueprint', icon='LIGHTPROBE_GRID')
#layout.separator()
#col = layout.column(align=True)
#box = col.box()
#box.prop(scene, "density", icon='GROUP_VERTEX')
#box.label(text='Location Options')
#box.prop(scene, "random_placement", icon='SNAP_GRID')
#box.prop(scene, "rotation_variation", icon='DRIVER_ROTATIONAL_DIFFERENCE')
#col = layout.column(align=True)
#col.label(text='Grid Properties', icon='SNAP_GRID')
#col.prop(scene, "x_location", icon='AXIS_SIDE')
#col.prop(scene, "y_location", icon='AXIS_FRONT')
#col = layout.column()
#box = col.box()
#box.prop(scene, "random_memory", icon='MEMORY')
Here is my main_properties.py:
import bpy
from bpy.props import IntProperty, StringProperty, BoolProperty, FloatProperty
class Blueprint_Properties(bpy.types.PropertyGroup):
density: IntProperty(
name = "City Density",
description = "How far apart building are to each other",
default = 45,
min = 1,
max = 100
)
####---------------------------------------------------
####---Buildings
apartment_building: BoolProperty(
name = "Apartment Buildings",
description = "Variety of Apartment Complexes",
default = True
)
office_building: BoolProperty(
name = "Office Buildings",
description = "Variety of Office Buildings",
default = False
)
skyscraper_building: BoolProperty(
name = "Skyscraper Buildings",
description = "Variety of Skyscrapers",
default = False
)
####---------------------------------------------------
####---------------------------------------------------
####---Buildings Floors
apartment_floors: IntProperty(
name = "Maximum Floors",
description = "How many floors per Apartment",
default = 14,
min = 3,
max = 100
)
office_floors: IntProperty(
name = "Maximum Floors",
description = "How many floors per Office Building",
default = 25,
min = 5,
max = 100
)
skyscraper_floors: IntProperty(
name = "Maximum Floors",
description = "How many floors per Skyscraper",
default = 53,
min = 30,
max = 100
)
####---------------------------------------------------
random_placement: BoolProperty(
name = "Random Placement",
description = "Randomize whether a building will be placed",
default = False
)
rotation_variation: BoolProperty(
name = "Rotation Variation",
description = "Allow variation in the rotation of objects",
default = True
)
x_location: IntProperty(
name= "X Location",
description="Number of buildings to build in X axis",
default=4, min=1, soft_max=10, max=20
)
y_location: IntProperty(
name= "Y Location",
description="Number of buildings to build in X axis",
default=4, min=1, soft_max=10, max=20
)
random_memory: IntProperty(
name = "Random Memory",
description = "Random Versions",
default = 1,
min = 1,
max = 100
)
THINGS I'VE TRIED
1. Got rid of the def draw function in the operator which gives me nothing... Why is that? Typically with the bl_options = {'REGISTER', 'UNDO'} I should get the properties in a small side panel.
2. When I add def draw with tool = context.scene.tools I can see everything in the UNDO but nothing works. All variables are frozen... anytime I try changing anything in the console it runs the script but nothing changes. ** What I do to the main panel shows up in the 'UNDO' Panel in the bottom of the screen like a mirror.
• going to be far less confusing if you use tools = context.scene.tools Could you please add the code to define and register scene tools propertygroup. – batFINGER Feb 3 at 19:39
• Sure, thing. Thanks Adding it now – Davi Silveira Feb 3 at 20:58
• I just found out that when I add a draw function to my operator class. Referencing the props by tool = context.scene.tools the UNDO options shows everything correctly, but I just figured out it's not exactly frozen but a copy of the main_panel class I can change the variables in the main side panel and it changes the 'UNDO' panel on the bottom left... – Davi Silveira Feb 3 at 21:14
• You need to register your property group and then refer to it by the name(space) you've registered it under. This line looks wrong to me: box.prop(Blueprint_Properties, "density", icon='GROUP_VERTEX'). Blender should already give you a hint at the source of the issue. Check the console/terminal for error messages (Linux, macOS - start Blender from a terminal; Window - Use Window > Toggle System Console). – Robert Gützkow Feb 3 at 22:00
• Robert G. Thanks, that line was totally wrong... it should of been scene` but you know when I fix that I get a duplicate of the main_panel on the 'UNDO' panel in the bottom left. It's frozen and only changes when I change the main Panel add-on. Like it's linked to it... I've been using the terminal this whole time, the "toggle_system_console" from Blender. I'll try starting Blender from the Terminal but I really don't know what it will tell me. Thanks again – Davi Silveira Feb 4 at 0:58 | {"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": 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": 0.20551832020282745, "perplexity": 17086.710204978215}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989856.11/warc/CC-MAIN-20210511184216-20210511214216-00145.warc.gz"} |
http://math.stackexchange.com/questions/120947/the-set-of-linear-fractional-transformations-that-preserves-the-open-unit-disk | # The set of linear fractional transformations that preserves the open unit disk is equicontinuous on every compact subset in it
Let $\Delta(a, r)$ be the open disk of radius $r$ centered at the point $a$ in the complex plane, and $\operatorname{Aut}(\Delta(0, 1))$ be the set of linear fractional transformations that preserves the open unit disk, i.e. transformations of the form $z\mapsto e^{i\theta}(z-a)/(1-\bar az)$, where $a\in\Delta(0, 1)$ and $\theta\in\mathbb R$.
1. I want to show $\operatorname{Aut}(\Delta(0, 1))$ is equicontinuous on every compact subset of $\Delta(0, 1)$. Does it suffice to show it is equicontinuous on $\overline{\Delta(0,r)}$ for any $r<1$? I think it surely suffices to show that it is continuous on every closed disk contained in the unit disk, but I'm unsure about the former.
2. I want to show $\operatorname{Aut}(\Delta(0, 1))$ is equicontinuous on $\overline{\Delta(b,r)}$ which is contained in the unit disk. To do this, I evaluated $|f(z)-f(w)|$ for an arbitrary $f$ in $\operatorname{Aut}(\Delta(0, 1))$ and got $|f(z)-f(w)| \le |z-w|/(|1-\bar az||1-\bar aw|)$. But I can't go further. How do you get an upper bound for this?
-
1. A compact subset $K$ of $\Delta(0,1)$ is contained on a set of the form $\overline{\Delta(0,r)}$ for some $r\in (0,1)$. Indeed, for each $x\in K$ we can find $r_x$ such that $\Delta(x,2r_x)\subset \Delta(0,1)$, so $K\subset \bigcup_{j=1}^N\Delta(x_j,r_{x_j})$ for some $N$ and $x_1,\ldots,x_N\in K$. Then put $r:=\max_{1\leq j\leq N}(1+r_{x_j})|x_j|$.
So it's enough to show equi-continuity on the sets of the form $\overline{\Delta(0,r)}$. 2. We have for $z_1,z_2\in\overline{\Delta(0,r)}$ that $$|f(z_1)-f(z_2)|\leq\frac{|z_1-z_2|}{|1-\bar az_1|\cdot |1-\bar az_2|}$$ and using triangular inequality and the fact that $|a|<1$ $$|1-\bar az_1|\cdot |1-\bar az_2|\geq (1-|z_1|)(1-|z_2|)\geq (1-r)^2$$ so $$|f(z_1)-f(z_2)|\leq \frac{|z_1-z_2|}{(1-r)^2},$$ which proves equi-continuity.
For 1., why is $K$ contained for some $\overline{\Delta(0, r)}$? – Pteromys Mar 17 '12 at 11:55 | {"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": 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": 0.9885532855987549, "perplexity": 45.76725067647535}, "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-2014-35/segments/1408500808153.1/warc/CC-MAIN-20140820021328-00359-ip-10-180-136-8.ec2.internal.warc.gz"} |
http://openstudy.com/updates/50f5f1a2e4b096587a2c89e7 | ## Got Homework?
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## Spartan_Of_Ares Group Title can i get help with some algebra 1? one year ago one year ago Edit Question Delete Cancel Submit
• This Question is Open
1. Spartan_Of_Ares Group Title
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0
$\frac{ x-7 }{ x }+2=\frac{ x-3 }{ }$
• one year ago
2. phi Group Title
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is there something missing on the right side? Is anything below x-3 ?
• one year ago
3. Spartan_Of_Ares Group Title
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sorry x
• one year ago
4. Spartan_Of_Ares Group Title
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x−7 x−3 ---- +2= ---- x x
• one year ago
5. phi Group Title
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my first thought is to multiply both sides by x like this $x \cdot \left(\frac{(x-7)}{x} +2\right)= x \cdot \frac{(x-3)}{x}$
• one year ago
6. Spartan_Of_Ares Group Title
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ok $\frac{ x(x-7) }{ x^2 } = (\frac{ x(x-3) }{ x^2 })$
• one year ago
7. phi Group Title
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interesting... time to learn a few algebra rules. First, $c\cdot \frac{a}{b} \text{ is the same as } \frac{c}{1}\cdot \frac{a}{b}$ you multiply top times top and bottom times bottom so for the right hand side $x \cdot \frac{(x-3)}{x}$ you could write it as $\frac{x(x-3)}{x}$ but the x on top and the x on the bottom make $\frac{x}{x} = 1$ anything divided by itself is 1
• one year ago
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but how would i multiply the equation?
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start with $x \cdot \left(\frac{(x-7)}{x} +2\right)= x \cdot \frac{(x-3)}{x}$ what do you get for the right-hand side of the = ? We'll get to the left after we get the right side done
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x^2-3x over x?
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@phi
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yes, but you should always look for the same thing in the top and bottom, because they divide out. so rather than doing x(x-3)/x --> (x^2 -3x)/x (which is correct) you should say: $\frac{\cancel{x}(x-3)}{\cancel{x}} = (x-3)$
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$x \cdot \left(\frac{(x-7)}{x} +2\right)= x -3$ on the left side, "distribute the x". that means multiply all the terms inside the parens by x (don't forget the 2) and notice that you will get x/x so you can cancel them.
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https://www.intechopen.com/chapters/58777 | Open access peer-reviewed chapter
Remote Sensing with Shipborne High-Frequency Surface-Wave Radar
Written By
Junhao Xie, Minglei Sun, Zhenyuan Ji and Guowei Yao
Submitted: March 15th, 2017 Reviewed: November 30th, 2017 Published: July 25th, 2018
DOI: 10.5772/intechopen.72833
From the Edited Volume
Recent Advances and Applications in Remote Sensing
Edited by Ming-Chih Hung and Yi-Hwa Wu
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Abstract
High-frequency surface-wave radar (HFSWR) has been successfully applied for moving target detection and remote sensing of ocean surface dynamic parameters for decades. Compared with conventional instruments such as buoys, anemometers, and microwave radars, HFSWR can be employed to an all-weather and all-time surveillance far beyond the visible horizon. Moreover, based on agility and maneuverability, shipborne HFSWR can not only enhance the survivability in complex ocean environment but also enlarge the detection distance on open sea, which will gradually become a popular deployment situation. In this chapter, ocean surface cross sections for shipborne HFSWR with linear platform motion and sway motion are derived theoretically. Then, the methods for ocean surface wind direction, wind field, and current extraction are presented. The computer simulations and experimental results of the real data are given to verify the detection accuracy and the distance limit of the abovementioned methods.
Keywords
• shipborne HFSWR (high-frequency surface-wave radar)
• ocean surface cross section
• ocean surface wind field
• ocean surface current
1. Introduction
High-frequency surface-wave radar (HFSWR) has been widely applied to early warning for decades, including the detection of airborne targets and surface targets. Its vertically polarized electromagnetic wave (3–30 MHz) follows the curvature of the Earth along the air-water interface and has a very low propagation loss on the ocean surface. In addition to early warning uses, HFSWR provides a unique ocean surface dynamics parameters remote-sensing capability based on the Doppler spectrum characteristics of the sea echo backscattered from the ocean surface. Compared with conventional instruments such as buoys, anemometers, and line-of-sight radar, HFSWR can provide an all-time, all-weather, and cost-effective surveillance far beyond the visible horizon.
HFSWR can be classified into onshore and shipborne cases based on the platform where it is employed. Besides the advantages of onshore HFSWR, shipborne case has the agility and maneuverability, which can not only enhance the survivability in complex ocean environment but also enlarge the detection distance on open sea. Thus, ocean remote sensing with shipborne HFSWR is expected to receive increasing attentions.
The main objective of this chapter is to reveal the potential and experimental results of remote sensing of ocean surface wind field and current with shipborne HFSWR, which is organized into four sections. Section 1 describes the concept of operation for shipborne HFSWR, the general characteristics and nominal capabilities of such systems, as well as their potential roles in early warning uses and ocean remote-sensing applications. Section 2 represents the first- and second-order ocean surface cross sections derived for an omnidirectional receiving sensor in monostatic shipborne HFSWR, where the essential characteristics of the sea echo backscattered from the ocean surface are shown. Understanding the characteristics of sea echo is essential for further theoretical and experimental investigation in remote-sensing applications. Section 3 discusses the potential of remote sensing of ocean surface wind field with shipborne HFSWR. The wind field of the region covered by radar can be measured using a single receiving antenna, which is more beneficial for shipborne platform with limited deck space. Experimental results verify the detection accuracy and distance limit of the presented method. Section 4 discusses the feasibility of ocean surface current inversion in shipborne HFSWR.
2. Ocean surface cross sections for shipborne HFSWR
To investigate the potential of ocean remote sensing with shipborne HFSWR, ocean surface cross sections, which incorporates abundant ocean dynamic parameter information such as wind direction and speed, ocean surface current, and wave spectrum parameters, should be first studied. In this section, we discuss the first- and second-order ocean surface cross sections in shipborne HFSWR with a uniform linear motion [1, 2]. Moreover, we explore the effects of the radar platform motion and sea-state parameters on Doppler spectrum and present that the spreading characteristic of the first-order Doppler spectra can be utilized to resolve the wind direction ambiguity problem. Following this research, we develop the corresponding cross sections in shipborne HFSWR with both uniform linear motion and sway motion [3]. Furthermore, the effects of sway motion on Doppler spectra are discussed in detail.
2.1. First-order ocean surface cross section
For a shipborne source, a small displacement from the origin, ρv, is caused by the forward movement of the platform at a constant speed, as shown in Figure 1, ρ1and ρ2denote the planar distances. Then, by analogy to the derivations in [4], the first-order cross section for shipborne HFSWR with a uniform linear motion is derived [1]
σωd=26π2k04m=±1S2mk0δωd+m2gk02k0vcosϕE1
where ωdis the Doppler frequency, k0is the wavenumber of the transmitting signal, m=±1corresponds to the receding and approaching waves, respectively, Sis the directional wave height spectrum, δis the Dirac delta function, gis the gravitational acceleration, vis the speed of shipborne platform, Scan be represented as a product of a P-M spectrum [5] and a modified cardioid directional factor G[6]. The directional factor is shown in Figure 2, where θis the incident direction of echo and αis the wind direction. When the shipborne platform is stationary (i.e., v=0), it is readily checked that the results in Eq. (1) can be reduced onshore case.
2.1.2.1. Experimental result
The fundamental data-collecting experiment was conducted on the Yellow Sea of China [7], the radar carrier frequency f0=5.283MHz, α90, the range resolution Δρ=5km, v=10knots. The simulated result with Gaussian noise and experimental result are, respectively, displayed in Figure 3a and b.
The simulated result with Gaussian noise in Figure 3a indicates that the platform motion results in the spreading sea clutter spectrum, whose theoretical width is indicated by the long-dashed lines. Such a simulated spreading spectrum is confirmed by the experimental result in Figure 3b with the similar overall shape.
2.1.2.2. Simulated results
Effects of the wind direction on the first-order cross section are displayed. Simulation parameters include f0=5.283MHz, Δρ=5km, and α=45,315. Simulation results of shipborne HFSWR for v=10knotsand onshore HFSWR for v=0knotsare shown in Figure 4.
For onshore case, the results show that the wind direction ambiguity exists, where the first-order echo has the same characteristics for different wind directions. Moreover, the first-order Bragg peaks simultaneously contain the sea clutter returns from different directions. Studies on wind direction extraction have to be conducted based on the receiving array or the compact antenna system in Coastal Ocean Dynamics Applications Radar (CODAR) system, where the problem of wind direction ambiguity is still unavoidable.
For shipborne case, however, the simulated cross sections show that the ratios of the spreading first-order Bragg lines vary with the wind directions, which demonstrates that shipborne HFSWR has the potential of wind direction extraction. Meanwhile, the wind directions of the whole sea area covered by radar may be obtained based on the spreading mechanism of the first-order spectrum. Thus, compared with onshore method, it should be more easily realized in wind direction extraction by the use of a single receiving sensor instead of the receiving array.
2.2. Second-order ocean surface cross section
By analogy to the derivation in [8], the second-order cross section for shipborne HFSWR with a uniform linear motion is derived as the summation of the hydrodynamic and electromagnetic components.
2.2.1. Hydrodynamic component
The hydrodynamic component can be directly obtained by replacing the first-order ocean wave spectrum SKωin Eq. (1) with the second-order spectrum S2Kω, which can be finally given by [2]
σ12ωd=26π2k04m1=±1m2=±1K1θK1ΓH2Sm1K1Sm2K2δωd2k0vcosϕ+m1gK1+m2gK2K1dK1dθK1E2
where S2Kω=2K1+K2=Kω1+ω2=ωSK1ω1SK2ω2ΓH2dK1dω1, and ΓHdenotes the hydrodynamic coupling coefficient. K1and θK1are the magnitude and direction of the wave vector K1, respectively. K2is a wave vector with a magnitude of K2. The frequencies ω1and ω2are related to K1and K2, respectively.
2.2.2. Electromagnetic component
The second-order field equation in the time domain can be thus obtained by [2]
E2tjη0ΔlΔρI0k02F2ρ0ω02πρ03/2ejk0ΔρK1K2KΓEMPK1PK2e/4ejKρ0ejvtKcosϕSincΔρ2K2k0E3
where η0is the intrinsic impedance, I0is the peak current for a dipole with length Δl, k0=ω0/c, ω0is the radian frequency, ρ0=ctτ0/2/2, Δρ=cτ0/2, cis the speed of light, and τ0is the length of the pulse. Sincdenotes the sinc function. PK1and PK2are random variables corresponding to the wave vectors K1and K2, respectively. K=K1+K2, Fis the Sommerfeld attenuation function, and ΓEMis the electromagnetic coupling coefficient.
The autocorrelation function with respect to the time shift τis given by
Rτ=E2t+τE2tAr/2η0E4
where and are the complex conjugate and statistical average, Ar=λ02Gr/4π, Gris the antenna gain, and λ0is the wavelength.
Then, Eq. (4) can be finally simplified as
Rτ=λ024πGr2η0η02Δl2Δρ2I02k04F4ρ0ω02πρ03m1=±1m2=±1KθKK1θK1K2ΓEM212Sm1K1Sm2K2ejKvτcosϕejm1gK1τejm2gK1τSinc2Δρ2K2k0K1dK1dθK1dθKE5
A Fourier transform of Eq. (5) yields the power density spectrum. Then, the second-order ocean surface cross section can be calculated by normalizing the power density spectrum per unit area, which is simplified by [2]
σ22ωd=26π2k04m1=±1m2=±1K1θK1ΓEM2Sm1K1Sm2K2δωd2k0vcosϕ+m1gK1+m2gK2K1dK1dθK1E6
2.2.3. Total second-order ocean surface cross section
Apart from the coupling coefficients, the hydrodynamic and electromagnetic cross sections in Eqs. (2) and (6) are identical. Thus, the total second-order ocean surface cross section in shipborne HFSWR can be written as [2]
σ2ωd=26π2k04m1=±1m2=±1K1θK1Γ2Sm1K1Sm2K2δωd2k0vcosϕ+m1gK1+m2gK2K1dK1dθK1E7
where the total coupling coefficient Γ=ΓH+ΓEM.
2.2.4.1. Simulated cross sections for different platform speeds
Simulation parameters: f0=5.283MHz, α=90, and wind speed U=15knots. From Figure 5a, the Bragg peaks are located at fB,M=±0.2344Hz, and the 2fB,Mpeaks (the harmonic peaks) and 23/4fB,Mpeaks (the electromagnetic “corner reflector” peaks) are also visible. From Eqs. (1) and (7), sea echoes at different incident directions correspond to different Doppler frequencies because an angle ϕexists between echo incident direction and the direction of the platform-forward movement. That is, the radar Doppler spectra are spread, as shown in Figure 5b. The dashed lines denote the theoretical spreading domains of the first-order sea clutter Doppler spectrum.
2.2.4.2. Simulated cross sections for different radar frequencies
Simulation parameters: U=15knots, v=10knots, and α=90. From Figure 6, the spreading domain increases and the energies of the second-order spectra increase with the increasing radar frequency. This shows that a high radar frequency may be negative for moving target detection and remote sensing.
2.2.4.3. Simulated cross sections for different wind speeds
Simulations parameters: α=90, v=10knots, and f0=5.283MHz. Simulation results show that the energies of the first- and second-order spectra increase as the wind speed increases, as shown in Figure 7. The first- and second-order spectra may be overlapped when the wind speed is high, which may be unfavorable for remote sensing of ocean surface wind direction and speed. This is because the wind direction is extracted from the ratio of the positive and negative Bragg energies, and the wind speed relates to the energies of the second-order backscatter echo.
2.2.4.4. Simulated cross sections for different wind directions
Simulation parameters: U=15knots, v=10knots, and f0=5.283MHz. From Figure 8, it is apparent that the spreading first-order Bragg lines vary with wind direction. However, the Bragg line energies may be contaminated by the second-order contributions. Thus, the high sea state may influence wind direction extraction from the spreading Bragg lines in shipborne HFSWR.
2.3. Ocean surface cross sections for shipborne HFSWR with sway motion
In practice, the shipborne platform exists six-degree-of-freedom (DOF) motion due to the interaction between the platform and the complicated ocean environment. In this subsection, following the research in the previous subsection, we derive corresponding cross sections which incorporate both the uniform linear motion and the sway motion [3].
2.3.1. First-order cross section
For a shipborne source in Figure 9, the small displacement δρfrom the origin is induced by the uniform linear motion ρv=vtρ̂vand the sway motion δρ0=asinωptρ̂p. Following the above-mentioned research, the first-order cross section can be written as [3]
σ1ωd=26π2k04m=±1S2mk0J022ak0cosθkθ0δωd+m2gk02k0vcosϕ+n=1Jn22ak0cosθKθ0δωd+m2gk02k0vcosϕnωp+δωd+m2gk02k0vcosϕ+nωpE8
where ωpand aare the sway frequency and amplitude related to sea state, respectively. ρ̂pis the unit vector of δρ0, Jnrepresents the nth order Bessel function, and θKis the direction of the wave vector K.
2.3.2. Second-order cross section
Similar to the derivation in Section 2.2, the second-order cross section for this new shipborne platform motion model can be derived as [3]
σ2ωd=26π2k04m1=±1m2=±1K1θK1Γ2Sm1K1Sm2K2J022ak0cosθkθ0δωd+m1gK1+m2gK22k0vcosϕ+n=1Jn22ak0cosθKθ0δωd+m1gK1+m2gK22k0vcosϕnωp+δωd+m1gK1+m2gK22k0vcosϕ+nωpK1dK1dθK1E9
2.3.3. Simulation results
For convenience, the sea echo Doppler spectral cross section is decomposed as the sum of the first- and second-order scattering terms
σωd=σ1ωd+σ2ωdE10
It can be inferred from Eq. (10) that the derived cross sections could be reduced to the existing results. Specifically, in the case of no uniform linear motion (i.e., v=0), it is readily checked that the derived expressions are consistent with Walsh’s results for an antenna on a floating platform [4, 8]. For the platform without sway motion (i.e., a=0), Eq. (10) agrees well with Xie’s results [1, 2]. For a=0and v=0, it is possible to reduce the derived results to the well-known cross sections derived by Barrick [5, 9] or Walsh [10] for onshore monostatic HF radar. This means that the derived cross section can be reasonably regarded as Xie’s results in shipborne HFSWR are modulated by sway motion, or Walsh’s results in HF radar on a floating platform are spread due to a uniform linear motion.
2.3.3.1. Cross sections for different platform speeds
Simulation parameters: f0=5.283MHz, α=90, and U=15knots. In Figure 10, Aand Aindicate the Doppler frequencies of sea echo with ϕ=0, whereas Band Brepresent the Doppler frequencies of sea echo with ϕ=π. For a given radar-operating frequency in Eq. (10), it is evident that the broadening region of the first-order sea echo is proportional to v. Because such Doppler spreading can potentially mask the target echo of interest, a significant challenge in shipborne HFSWR is the detection of moving targets whose Doppler frequencies appear in the spreading region. When the platform moves at a high speed, the first-order sea echo spectrum will overlap. To avoid the effect of Doppler overlap on wind direction extraction with shipborne HFSWR, the platform speed should be limited by a theoretical maximum value vmax=gλ0/4π. Additionally, it can be inferred that additional spectra induced by sway motion will repeatedly emerge and be located with uniform spacing of sway frequency, as shown in Figure 10.
2.3.3.2. Cross sections for different wind directions
Simulation parameters: f0=5.283MHz, U=15knots, and v=10knots. From Figure 11, there exists obvious envelop distortion in the Doppler spectrum, which is indicated by the circles. Under this condition, the positive and negative Bragg line energies are contaminated by the second-order contributions [2], and the “corner reflector” peaks in the positive Doppler spectrum are also masked by these sway-induced contributions. In remote-sensing applications, the sea echoes scattered from the ocean surface could be interpreted to extract the wave height spectrum, as well as to estimate the surface current and wind field. Therefore, the envelop distortions in the Doppler spectra may degrade the performance of ocean remote sensing. Specifically, this would be detrimental to the wind direction extraction from the ratio of the positive and negative Bragg line energies in shipborne HFSWR.
3. Remote sensing of ocean surface wind field with shipborne HFSWR
In this section, the potential of remote sensing of ocean surface wind direction and speed with shipborne HFSWR are presented [11, 12], respectively. Based on the spreading mechanism of the first-order Bragg lines, the unambiguous wind direction is extracted by the use of a single receiving sensor. Due to this single-side system consisting of a transmitter and a receiving sensor, it can be realized more easily and with less system cost, and it is more suitable for a shipborne platform with limited deck space.
3.1. Space: time distributions of first-order sea echo
From Eq. (1), it can be inferred that the locations of positive and negative Bragg lines are determined by the angle ϕ, which is consistent with the space-time distribution of the first-order sea clutter [7]
fd=fdpcosϕ±fBE11
where fd=ωd/2π, fdp=2v/λ, fB=g/πλis the first-order Bragg frequency in monostatic onshore HFSWR. Different Doppler frequencies in Bragg region correspond to the sea echoes from different incident directions and vice versa; therefore, the first-order Doppler spectrum is spread due to the forward movement of the platform. Then, the spreading domains of the first-order Doppler spectrum should be
fB2v/λfB+2v/λ,fB2v/λfB+2v/λE12
Taking the differential of fdin Eq. (11), the Doppler frequency resolution Δfdcan be expressed as a function of the azimuth resolution Δϕ, which can be expressed as
Δfd=fdpsinϕΔϕE13
Analogously to Doppler beam sharpening (DBS), the azimuth resolution can be obtained by
Δϕ=Δfd/fdpsinϕforϕ0E14
Generally, HFSWR can provide a very high-frequency resolution with long coherent integration time (CIT). Therefore, the shipborne HFSWR may provide a higher transverse resolution than onshore HFSWR with a huge antenna array aperture.
3.2. Wind direction extraction in shipborne HFSWR
3.2.1. Mathematical model
For onshore HFSWR, wind directions are sensitive to the ratio of energies of positive and negative Bragg peaks, which can be used to measure the wind direction [13]. To extract the wind direction with shipborne HFSWR, analogously to onshore HFSWR case, the ratio Rof the positive and negative Bragg lines energies, B+and B, is defined by
R=10log10B+/BE15
where B+B=σωdσωd=Gθ+παGθα. The application prerequisite of Eq. (15) is that the two spreading domains of the first-order Doppler spectrum in Eq. (12) are not overlapped, which means the maximum permitted speed of shipborne platform vmax=/4π.
Together with the modified cardioid directional factor in Eq. (1), the abovementioned ratio can be finally simplified as
R=10log10ξ+1ξsin4θα2ξ+1ξcos4θα2E16
where ξ=0.004is the strength ratio of upwind returns to downwind returns. For the convenience of description of Eq. (16), we can define yas
y=sin2θα2E17
Therefore, once yis calculated from Eq. (16), possible wind directions can be deduced by
αp=θ±2arcsinyE18
3.2.2. Method for resolving wind direction ambiguity
For a fully developed sea area, wind directions are generally considered to be spatially uniform or slow-varying over adjacent ocean patch. That means the differences of wind directions in adjacent ocean patches should be zero or near zero. Figure 12a describes four adjacent ocean patches with corresponding incident directions. For ocean patch A with the incident direction ϕA, the energies of positive and negative Bragg lines can be derived, as shown in Figure 12b. Then, two possible wind directions αA1and αA2can be calculated by Eq. (18). Similarly, the possible wind directions αB1and αB2for ocean patch B can also be derived. We define
Δαij=αBiαAjij=12E19
The value of αBithat minimizes Δαijis considered as the real wind direction of ocean patch B. Therefore, the wind directions of the whole ocean area covered by radar can be measured by sequentially applying this method.
3.2.3.1. Simulation for wind direction extraction
Simulation parameters:f0=5.283MHz, v=10knots. Consider that the input wind direction αslowly increasing from 135to 180is given for simulation. Due to the directional ambiguity, it is difficult to determine the unique wind direction from the two possible solutions with a single incident direction ϕas shown in Figure 13a. However, the problem of wind direction ambiguity can be effectively removed by comparing the possible results of adjacent sea cells, as shown in Figure 13b, where the circles denote the slow-varying wind directions for simulation. Simulation results visually illustrate the process of removing the directional ambiguity, and the good agreement between the derived wind direction and the simulation parameter shows the potential of unambiguity wind direction extraction with shipborne HFSWR.
3.2.3.2. Discussions of basic applications in shipborne HFSWR
In experiment, the effects of the coverage region shift due to platform motion, the real sailing conditions (fluctuations of platform speed and course) during CIT, and the external Gaussian noise on the wind direction extraction should be studied.
3.2.3.2.1. Effect of covered region shift due to platform motion
In order to investigate the effect of covered region shift, the ratio Rshiftis defined as
Rshift=ΔrΔRE20
where Δr=vTis the covered region shift during CIT T, ΔR=Δϕρis the transverse resolution, Δϕis the azimuth resolution in Eq. (14), and ρis the radar detection range.
Then, Eq. (20) can be rewritten as
Rshift=2v2T2sinϕλρ2v2T2λρE21
Reviewing the typical radar parameters in [7]: f0=5.283MHz, v=10knots, ρ=100km, and T=150s, Rshift<0.21can be obtained. That means Δris nearly one-fifth of ΔRduring T. In addition, wind directions are considered to be uniform or slow-varying within adjacent ocean patches. As mentioned earlier, we consider that the covered region shift during Twould not significantly influence the presented method.
3.2.3.2.2. Effect of real sailing conditions
In order to explore the effect of real sailing conditions, the sailing data [7] are exploited to derive the synthetic Doppler spectra. For comparison, then, the ideal Doppler spectra also are derived. The simulation parameters are f0=5.283MHz, v=10knots, α=90, and U=25knots.
A comparison of the ideal and synthetic spectra shows that the spreading regions of the latter are slightly more obvious, as shown in Figure 14. Although slight fluctuation exists in the speed and course, no apparent differences are found between the ideal and synthetic spectra except for the margin. In experiment, accordingly, the middle regions of the spreading spectra (e.g., ϕ30150) should be exploited to measure the wind direction.
3.2.3.2.3. Effect of external Gaussian noise
To examine the performance of the proposed method in externally noise-limited environment, time series of the backscattered electric field is provided as follows:
En1ϕt=MK,ωPK,ωKejωtejρ+vtcosϕKΔρsincK2k0Δρ/2E22
where Mis a constant, PK,ωis Fourier coefficients of ocean surface components, Kand ωare the wavenumber and radian angular frequency, respectively, Δρis the range resolution, and Sincis the sinc function.
The spreading spectra with the Gaussian noise can be derived by a periodogram method [14, 15]. The simulated spectra from 150 s time series are shown in Figure 15, where f0=5.283MHz, ρ=100km, v=5.07m/s, Δρ=5km, and αslowly increasing from 0in the stern to 45at the prow of shipborne platform. It is obvious that the noise floors decrease with the increasing signal-to-noise ratio (SNR). That means a high SNR can improve the performance of the wind direction estimation.
3.2.3.2.4. Effect of comprehensive factors
Together with the real sailing speed and heading data, the influence of external noise is shown in Figure 16. The performance is estimated via 100 independent Monte Carlo simulations for each SNR, where the simulation parameters are the same as those in Figure 15. It is apparent that the error of the wind direction estimation gradually decreases with the increasing SNR. There is no obvious deviation between the two error curves. Therefore, external Gaussian noise is the major factor affecting the performance of the wind direction estimation.
3.2.4. Experimental results
Shipborne HFSWR data were collected for moving target detection on 26 September 2016, in Taiwan Strait, China, by the Harbin Institute of Technology with a carrier frequency of 6.45 MHz. Due to the directional ambiguity problem, partial data collected by shipborne HFSWR sailing along the coast with a suitable speed can be exploited to validate the proposed method.
In this experiment, the data collected by a single antenna during CIT from 08:47:37 to 08:49:46 were used for wind direction extraction. The average speed of the platform is 4.67 m/s. The CIT is 129 s and the number of pulse during CIT is 512. The signal bandwidth is 50 kHz. The detection limit and azimuth are 120 km and 53.4°–151.1° north, respectively. It should be noted that an integral shift method is used to alleviate the effect of ocean surface current.
The radar-measured wind direction results are shown in Figure 17. Forecast data supported by the FUJIAN MARINE FORECASTS (FJMF) are exploited to preliminarily validate the performance of the presented method because of the lacking of in situ data. A comparison of Figures 17 and 18 shows that the radar-measured results agree well with the local wind direction forecasts over the same period. Given the data-observed time, Figure 18a is considered as the reference of the real wind field. That is, “real” wind directions are slow-varying from 27.5° to 10.6° northeast, and “real” wind speeds are slow-varying from 13.8 to 8 m/s in the detection region form north to south. A histogram of radar-measured wind direction results is shown in Figure 19. Only samples whose sampling number is greater than 10 are exploited to verify the performance of the wind direction measurement; 55.42% of the radar-measured results are located in the range of the “real” wind direction. The percentage can achieve 90.07% if the “real” wind direction range is extended to 0.6°–37.5° northeast. Meanwhile, the average value and the root-mean-square error (RMSE) of the radar-measured results are 14.56° northeast and 9.85°, respectively.
3.3. Wind field extraction in shipborne HFSWR
In Section 3.2, we proposed a method for extracting the unambiguous wind direction with an empirical spreading parameter value of 2. In view of [16, 17], the spreading parameter depends on the wind speed, which may be variable in the experiment. The optimum value for the spreading parameter should be estimated from the shipborne HFSWR experiment data itself. In this section, a method for simultaneously deriving the unambiguous wind direction and the unique spreading parameter will be presented. Then, a relationship between the wind speed and the spreading parameter will be developed by the drag coefficient. Therefore, the wind field can be measured by sequentially using the presented method.
3.3.1. Method for deriving unambiguous wind direction
Assuming that the spreading parameter sis a variable argument, analogously to Section 3.2.2, Eq. (15) can be rewritten as
R=10log10ξ+1ξysξ+1ξ1ysE23
where
y=sin2θα2E24
Therefore, the possible wind directions can be deduced by
αp=θ±2arcsinyE25
where αpvaries with s, the ±sign indicates the ambiguity of wind direction.
For each incident direction of sea echoes, analogously to Section 3.2.3, the derived wind directions for different spreading parameters can be determined by Eq. (25), as shown in Figure 20a. Obviously, the intersection of these two curves should be the unique solution for the wind direction and the spreading parameter. Figure 20b shows a two-solution case, and then the sea echo at the third incident direction from the adjacent cell will be necessary to determine the unique solution.
3.3.2. Method for calculating wind speed
A relationship between sand the wind speed Uis developed by a momentum transfer factor μ, which can be written as [18]
s=0.2μ0.11μ>0.12μ<0.1E26
where μ=CD1/24π/1/2U/κ, κ=0.4is von Karman’s constant and CDis a drag coefficient proposed by Wu [19]
CD=0.8+0.065U×103E27
Substituting Eq. (27) into Eq. (26) and using the Cardano formula, we have
s=0.2Uκ4πCD0.11U>U2U<UE28
where Uis related to the radar frequency.
When U>U, using the Cardano formula, we can derive the one-to-one correspondence relationship between Uand s. Therefore, scan be considered as an indicator of U.
3.3.3. Simulation results
Simulation parameters: f0=5.283MHz, v=10knots, the true wind direction and speed are αT=90and UT=25knots, respectively. The true spreading parameter is sT2.1calculated by Eq. (28).
The relationship between the derived wind directions αand sis shown in Figure 21a. The solid curve indicates αversus sfor the incident direction of ϕ1=100, while the dashed curve represents the situation of the incident direction of ϕ2=110. The intersection of these two curves determines a solution for αand s. Therefore, the extracted wind direction and the spreading parameter are αE90.02and sE=2.10, respectively. The corresponding wind speed is UE24.98knotscalculated by Eq. (28), as shown in Figure 21b.
3.3.4. Experimental results
The experimental data and the “real” wind field have been described in Section 3.2.4. Figure 22 intuitively shows the radar-measured wind field distribution. From Figure 22, the majority of wind directions are north-northeast and north. Meanwhile, wind speeds gradually decrease and wind directions are slow-varying from north-northeast to north in the detection region from north to south. Therefore, the radar-measured results are in good agreement with the local wind field forecast.
Experimental results in Sections 3.2.4 and 3.3.4 show that the wind direction and field estimation in shipborne HFSWR have derived very encouraging results. However, there are some “bad points” that appear over the edge of the detection area, as shown in Figures 17 and 22, where a larger deviation exists. This may be because the effect of directional ambiguity is not totally eliminated due to the complex coastline structures. In addition, the ocean surface current, six oscillating motions of shipborne platform, and swell may be have negative effects on the wind direction and field estimations. Note that the method for wind field estimation is presented for a fully developed sea area and the wind speed inversion is conducted out only under the condition of U>U. Otherwise, the second-order spectra or other methods should be introduced. These are the subjects of ongoing investigations.
4. Remote sensing of ocean surface current with shipborne HFSWR
HFSWR system has been widely deployed for remote sensing of ocean surface current. With the development of signal-processing technology of HFSWR, shipborne HFSWR has gradually become a more potential deployment situation with its agility and maneuverability. Some experimental results and theoretical analyses have been conducted to explore the feasibility of remote sensing of ocean surface current in shipborne HFSWR [20, 21, 22, 23]. In the previous works, however, the hull itself is either stationary or moving at a low speed without considering a high-speed case and effects of six DOFs motion on radar Doppler spectra. In this section, the potential of remote sensing of ocean surface radial current with shipborne HFSWR is presented [24]. Moreover, a stream function method is introduced to obtain current vector field using an improved music signal classification (MUSIC) algorithm and unitary transformation technique [25].
4.1. Remote sensing of ocean surface radial current
The shipborne platform exists six-DOF motion besides the forward movement owing to the effect of the complex ocean environment, which will introduce the superposed amplitude and phase modulations to the backscatter echoes [23], as shown in Figure 23. Considering antenna pattern, external noise, forward movement, and six-DOF motion, the time domain model of the received echo signal of the sea surface can be expressed as [25]
xRt=r,sσRrθstatgθstpθst+etE29
where σRrθstis the first-order radar cross section of ocean surface, Rrand θsare the detection range and azimuth, respectively, atand pθstare the amplitude and phase of the array steering vector, respectively, gθstis the receiving antenna pattern, and etis the background noise.
4.1.2. Effect of six-DOF motion on ocean surface radial current estimation
In the previous section, a single antenna is used to estimate the directions of arrival (DOA) of sea echoes. In this case, however, the effects of ocean surface current are not considered. In order to estimate ocean surface radical current accurately, an antenna array with a high-resolution technique is necessary. Theoretical analyses [26] and experimental results [27] have demonstrated that MUSIC algorithm can achieve a good azimuthal resolution in ocean surface current estimation with short aperture. In this section, therefore, the MUSIC algorithm is employed to derive DOA.
From Section 2.1, the first-order Doppler spectra are spread due to the forward movement of shipborne HFSWR, and the spreading region increases with the increasing speed of the platform. That means the Bragg energies have been distributed into more peaks, and the spreading peaks exhibit many more Doppler sampling points which can be exploited to estimate DOA. From Figure 24a, the sampling points increase with the increasing platform speed. However, the performance of radial current estimation decreases. In particular, a higher RMSE appears when the ship is still, which may be because of lacking of sampling points. Meanwhile, the radial current RMSE is really high when the ship moves at a high speed, which may be caused by a low SNR. Therefore, the relationship between the RMSE and the platform speed would be a significant reference for the real sailing speed.
From Figure 24b, the radial current RMSEs increase with the increasing amplitude of rotation (pitch, roll, and yaw) and sway. In particular, the surge has no severe influence on the measurement performance, which may be because the surge is generally in the direction of the platform-forward movement. Additionally, yaw plays the most important effect on the radial current estimation. Simulation results show the feasibility of remote sensing of ocean surface radial current in shipborne HFSWR. In addition, the performance of the current estimation is sensitive to the variation of amplitude of six-DOF motion besides surge, rather than the forward movement of the platform.
4.2. Remote sensing of ocean surface current vector field
4.2.1. Method for current vector measurement using RVSR-MUSIC
From Section 4.1, the estimate accuracy of DOA algorithm has significant influence on the performance of ocean surface current measurement. In order to take advantage of the limited radar data to improve the estimate accuracy of DOA, a real-valued MUSIC algorithm based on sparse-representing technique (RVSR-MUSIC) has been presented [25]. Once RVSR-MUSIC has been exploited to estimate DOA, the sea clutter spectra of shipborne HFSWR can be extracted with high resolution, and the Doppler frequency shift and the corresponding azimuth can be derived. Then, the radial velocity V̂rof ocean surface current at azimuth ϕ̂can be expressed as
V̂r=λ2f̂dgπλ2vcosϕ̂λE30
where λis the radiation wavelength, f̂dis the Doppler frequency shift, gis the gravitational acceleration, and ϕ̂is the corresponding azimuth.
As shown in Figure 25, the radial velocity of ocean surface current Vrxyin azimuth ϕcan be written as [25]
Vrxy=xuxy+ywxyx2+y2E31
According to the introduction of stream function in [28], we have [25]
Vxy=u2xy+w2xyE32
γxy=tan1wxy/uxy,ifuxy0π+tan1wxy/uxy,elseE33
where Vxyand γxyare the amplitude and the direction of ocean surface current vector Vxy, respectively.
4.2.2. Simulation results
Simulations are conducted under these conditions: the number of the receiving antenna is M=7, the space between antennas is d=λ/2, the radar-operating frequency f0=7.5MHz, the radar modulation period Tr=0.5s, and the platform speed v=10m/s[25]. We assume a uniform ocean surface current field with a velocity of 0.5 m/s. Three different methods including spatial smoothing MUSIC (SS-MUSIC), complex-valued SR-MUSIC (CVSR-MUSIC), and RVSR-MUSIC are exploited to estimate ocean surface radial current by 50 independent Monte Carlo trials, as shown in Figure 26. It is obvious that RVSR-MUSIC is the most efficient algorithm for ocean surface radial current estimation.
Figure 27 shows the amplitude errors of the uniform current field using RVSR-MUSIC algorithm for radial current measurements and the second-order stream function for surface current vector measurements. It is apparent that a majority of amplitude errors are within 0.1 m/s. Simulation results demonstrate that the remote sensing of ocean surface current field using a single shipborne HFSWR is feasible. RVSR-MUSIC algorithm obtains the best estimation performance compared with other algorithms.
Analyses of the simulation results show that the presented method here has derived very encouraging results. However, the effects of practical conditions in shipborne HFSWR should be considered. First, when HFSWR is mounted on a ship, the iron body distorts the electromagnetic field severely, which will lower azimuth resolution. Second, the nonideal motions will introduce a superposed amplitude and phase modulation to the backscatter echoes. Third, although RVSR-MUSIC algorithm can increase estimation accuracy and reduce the computational cost, unitary transformation is based on a centro-symmetrical array (CSA), which will severely limit the applications. In addition, the prerequisite of this method is that two-dimensional (2D) ocean surface current field is horizontally nondivergent (or incompressible). These are the subjects of ongoing investigations.
References
1. 1. Xie J, Sun M, Ji Z. First-order ocean surface cross-section for shipborne HFSWR. Electronics Letters. 2013;49(16):1025-1026
2. 2. Sun M, Xie J, Ji Z, Cai W. Second-order ocean surface cross section for shipborne HFSWR. IEEE Antennas and Wireless Propagation Letters. 2015;14:823-826
3. 3. Sun M, Xie J, Ji Z, Yao G. Ocean surface cross sections for shipborne HFSWR with sway motion. Radio Science. 2016;51(11):1745-1757
4. 4. Walsh J, Huang W, Gill E. The first-order high frequency radar ocean surface cross section for an antenna on a floating platform. IEEE Transactions on Antennas and Propagation. 2010;58(9):2994-3003
5. 5. Lipa BJ, Barrick DE. Extraction of sea state from HF radar sea echo: Mathematical theory and modeling. Radio Science. 1986;21(1):81-100
6. 6. Shearman ED. HF ground-wave radar for sea-state and swell measurements: Theoretical studies, experiments and proposals. In: IEEE International Conference on Radar; London, United Kingdom. October 1982. pp. 101-106
7. 7. Xie J, Yuan Y, Liu Y. Experimental analysis of sea clutter in shipborne HFSWR. IEEE Proceedings-Radar, Sonar and Navigation. 2001;148(2):67-71
8. 8. Walsh J, Huang W, Gill E. The second-order high frequency radar ocean surface cross section for an antenna on a floating platform. IEEE Transactions on Antennas and Propagation. October 201260(10):4804-4813
9. 9. Barrick DE. First-order theory and analysis of MF/HF/VHF scatter from the sea. IEEE Transactions on Antennas and Propagation. 1972;AP-20(1):2-10
10. 10. Walsh J, Gill E. An analysis of the scattering of high-frequency electromagnetic radiation from rough surfaces with application to pulse radar operating in backscatter mode. Radio Science. 2000;35(6):1337-1359
11. 11. Sun M, Xie J, Ji Z, Cai W. Remote sensing of ocean surface wind direction with shipborne high frequency surface wave radar. In: IEEE Radar Conference on Radar; Arlington, VA, USA. May 2015. pp. 39-44
12. 12. Xie J, Yao G, Sun M, Ji Z, Li G, Geng J. Ocean surface wind direction inversion using shipborne high frequency surface wave radar. IEEE Geoscience and Remote Sensing Letters. 2017;14(8):1283-1287
13. 13. Huang W, Gill E, Wu S, Wen B, Yang Z, Hou J. Measuring surface wind direction by monostatic HF ground–wave radar at the eastern China Sea. IEEE Journal of Oceanic Engineering. October 2004;29(4):1032-1037
14. 14. Zhang J, Walsh J, Gill E. Inherent limitations in high-frequency radar remote sensing based on Bragg scattering from the ocean surface. IEEE Journal of Oceanic Engineering. July 2012;37(3):395-406
15. 15. Shen C, Gill E, Huang W. Extraction of swell parameters from simulated noisy HF radar signals. In: IEEE Radar Conference on Radar; Ottawa, Canada. April 2013. pp. 1-6
16. 16. Heron ML. Applying a unified directional wave spectrum to the remote sensing of wind wave directional spreading. Canadian Journal of Remote Sensing. 2002;28(3):246-353
17. 17. Heron ML, Prytz A. Wave height and wind direction from the HF coastal ocean surface radar. Canadian Journal of Remote Sensing. 2002;28(3):385-393
18. 18. Tayler GL, Teague CC, Stewart RH, Munk AM, Joy JW. Wave directional spectra from synthetic observations of radio scatter. Deep-Sea Research. 1974;21(12):989-1016
19. 19. Wu J. Wind-stress coefficients over sea surface from breeze to hurricane. Journal of Geophysical Research. 1982;87(C12):9704-9706
20. 20. Teague CC. Multifrequency HF radar observations of currents and current shears. IEEE Journal of Oceanic Engineering. April 1986;OE-11(2):258-269
21. 21. Lipa BJ, Barrick DE, Isaacson J, Lilleboe PM. CODAR wave measurements from a north sea semisubmersible. IEEE Journal of Oceanic Engineering. April 1990;15(2):119-125
22. 22. Gurgel KW. Experience with shipborne measurements of surface current fields by HF radar. Oceanography. 1997;10(2):82-84
23. 23. Gurgel KW, Essen H. On the performance of a shipborne current mapping HF radar. IEEE Journal of Oceanic Engineering. January 2000;25(1):183-191
24. 24. Chang G, Li M, Xie J, Zhang L, Yu C, Ji Y. Ocean surface current measurement using shipborne HF radar: Model and analysis. IEEE Journal of Oceanic Engineering. October 2016;41(4):970-981
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26. 26. Laws KE, Fernandez DM, Paduan JD. Simulation-based evaluations of HF radar ocean current algorithms. IEEE Journal of Oceanic Engineering. October 2000;25(4):481-491
27. 27. Yang S, Ke H, Wu X, Tian J, Hou J. HF radar ocean current algorithm based on MUSIC and the validation experiments. IEEE Journal of Oceanic Engineering. July 2005;30(3):601-618
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Written By
Junhao Xie, Minglei Sun, Zhenyuan Ji and Guowei Yao
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https://socratic.org/questions/54f8c482581e2a3a7d3b2b2b | Chemistry
Topics
# Question b2b2b
Mar 5, 2015
$\text{XY}$ will have a lattice energy of $\text{-2980 kJ/mol}$.
This is a very simple problem if you're familiar with the Born-Lande equation for calculating lattice energies. Here's how that looks like
I won't list what all the terms in this equation mean because all but three of them are not important. The three terms that you should focus on are
${z}^{+}$ $\to$ the charge on the positive ion;
${z}^{-}$ $\to$ the charge on the negative ion;
${r}_{0}$ $\to$ the distance between the two opposite ions;
Now, I believe that you are supposed to ignore the terms that are specific to individual ionic compounds, and assume that all the constants for your hypothetical salt are identical to those for CsF".
If that's the case, you can rewrite the above equation like this
$\text{E} = \frac{- {N}_{A} \cdot M \cdot {e}^{2}}{4 \cdot \pi \cdot {\epsilon}_{0}} \cdot \left(1 - \frac{1}{n}\right) \cdot \frac{| z {|}^{+} \cdot | z {|}^{-}}{r} _ 0$
$E = \text{CONSTANT} \cdot \frac{| z {|}^{+} \cdot | z {|}^{-}}{r} _ 0$
Now, because X"^(2+) has the same radius as Cs"^(+) and ${\text{Y}}^{2 -}$ has the sameradius as ${\text{F}}^{-}$, the term ${r}_{0}$ will be the same for both salts. Therefore,
$E = \text{CONSTANT} \cdot \left(| z {|}^{+} \cdot | z {|}^{-}\right)$
In the case of $C s F$, ${z}^{+}$ is +1 and ${z}^{-}$ is -1; you can use this to write the lattice energy of $\text{XY}$ using the lattice energy of $C s F$
${E}_{\text{XY") = E_("CsF}} \cdot \left(| z {|}^{+} \cdot | z {|}^{-}\right)$
Since $\text{XY}$ has ${z}^{+}$ equal to +2 and ${z}^{-}$ equal to -2, you'll get
${E}_{\text{XY") = E_("CsF") * (|+2| * |-2|) = 4 * E_("CsF}}$
E_("XY") = 4 * ("-744 kJ/mol") = "-2976 kJ/mol"
Rounded to three sig figs, the answer will be
E_("XY") = "-2980 kJ/mol"#
Mar 5, 2015
The lattice energy of $X Y$ is $- 2976 \text{kJ/mol}$
If we consider 2 charges ${q}_{1}$ and ${q}_{2}$ separated by a distance $r$ they are attracted by a force which is proportional to the product of the charges and inversely proportional to the square of the distance between them:
$F \propto \frac{{q}_{1} {q}_{2}}{{r}^{2}}$
So $F = k \frac{{q}_{1} {q}_{2}}{{r}^{2}}$
We can find the work done in separating these charges from a distance $r$ to infinity by integrating between these limits:
$W = k {\int}_{r}^{\infty} \frac{{q}_{1} {q}_{2}}{{r}^{2}} . \mathrm{dr}$
From which we get:
$W = - k \frac{{q}_{1} {q}_{2}}{r}$
This means that if we double the charges the work done required to separate them would go up by 2 x 2 = 4.
This means that in your example the lattice energy would increase to 4 x -744 = $2976 \text{kJ/mol}$, provided $r$ does not change.
In this answer I have only considered 2 charges separated by a distance $r$. In reality ionic crystals are made up of giant lattices with attractive and repulsive forces moving out in 3 dimensions and decreasing with distance.
A more accurate expression for lattice enthalpy $U$ which accounts for this is given by:
$U = - \frac{N M {z}^{2} {e}^{2}}{4 \pi {\epsilon}_{0} {r}_{0}} \left(1 - \frac{1}{n}\right)$
I won't go further into the details of this. If you want you can look up "Madelung Constant".
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## Über dieses Buch
This book includes 58 selected articles that highlight the major contributions of Professor Radha Charan Gupta—a doyen of history of mathematics—written on a variety of important topics pertaining to mathematics and astronomy in India. It is divided into ten parts. Part I presents three articles offering an overview of Professor Gupta’s oeuvre. The four articles in Part II convey the importance of studies in the history of mathematics. Parts III–VII constituting 33 articles, feature a number of articles on a variety of topics, such as geometry, trigonometry, algebra, combinatorics and spherical trigonometry, which not only reveal the breadth and depth of Professor Gupta’s work, but also highlight his deep commitment to the promotion of studies in the history of mathematics. The ten articles of part VIII, present interesting bibliographical sketches of a few veteran historians of mathematics and astronomy in India. Part IX examines the dissemination of mathematical knowledge across different civilisations. The last part presents an up-to-date bibliography of Gupta’s work. It also includes a tribute to him in Sanskrit composed in eight verses.
## Inhaltsverzeichnis
### A Portrait of the Life of R. C. Gupta
Though I have known Prof. R. C. Gupta (RCG) for more than two decades through his writings, till recently I did not have an occasion to interact with him closely.
K. Ramasubramanian
### A Birthday Tribute to R. C. Gupta
The internationally renowned historian of mathematics, Radha Charan Gupta, celebrated his 60th birthday on October 26, 1995.
Christoph J. Scriba
### Professor R. C. Gupta Receives the Kenneth O. May Prize
Professor Radha Charan Gupta, who founded and nurtured Gaṇita Bhāratī as editor for over a quarter century, was awarded the Kenneth 0. May prize of 2009, jointly with Prof. Ivor Grattan—Guinness of UK—by the International Commission for the History of Mathematics (ICHM).
Kim Plofker
### On the Date of Śrīdhara
H. T. Colebrooke seems to be the first modern scholar who studied the work of Śrīdhara. He had an incomplete copy of Pāṭīgaṇitasāra from which he often quoted parallel passages in his translation (1817) of the Līlāvatī.
K. Ramasubramanian
### In the Name of Vedic Mathematics
In this category comes the genuine Vedic Mathematics as found in the Vedas or Vedic literature in general. The four Vedas consisting of various Vedic Saṃhitās, the several Brāhmaṇas, Āraṇyakas and Upaniṣads are the basic literary sources for this type of Vedic Mathematics.
K. Ramasubramanian
### Foreign Reviews and Evaluation of Indian Works on History of Science
Although studies and research in the field of history of exact sciences in India have been going on for the last two centuries, no comprehensive and authentic chronological history of Indian mathematics has been written so far.
K. Ramasubramanian
### The Study of History of Mathematical Sciences in India
Part I (1935) and Part II (1938) of the famous History of Hindu Mathematics by B. B. Datta and A. N. Singh were published from Lahore (now in Pakistan), while the promised Part III was never published in its authors’ lifetime. In 1962 a single volume edition (actually a mere reprint of Parts I and II) was brought out by the Asia Publishing House, Mumbai. This was reviewed by G. J. Toomer of Oxford (Math. Reviews, Vol. 26, 1963, p. 1142). He charged the authors of being ignorant of “historical matters” and of having “prejudice against admitting that there was any influence on Indian civilization from outside”. Their theories have been said to be often based on the “grossest errors of fact”.
K. Ramasubramanian
### Historical Notes: Kali Chronograms of Nārāyaṇa Bhaṭṭatiri
Nārāyaṇa Bhaṭṭatiri (sixteenth–seventeenth century ad), son of Māṭrdatta, is one of the greatest scholar-poets of Kerala. He composed many works on diverse subjects both literary as well as technical in Sanskrit. He was a Nambutiri Brāhmin hailing from the family of Melpattur situated not far from the bank of the river Bharatappuzha. According to his grammatical work (see below), he learned Mīmāṃsā from his father, Vedas from Mādhava, logic from Dāmodara and grammar from Acyuta who was a great authority in the subject of Vyākaraṇa-śāstra.
K. Ramasubramanian
### On Some Mathematical Rules from the Āryabhaṭīya
The paper deals with the controversies which arise due to different interpretations of certain mathematical rules as found in the Āryabhaṭīya of Āryabhaṭa I (born 476 ad).
K. Ramasubramanian
### Decimal Denominational Terms in Ancient and Medieval India
Although the choice of ten as a base for numeration is not the best, God favoured it by giving us ten fingers. In India, ten has been the basis for counting since very early days. Later on it served the base for the place-value system of numerals which was invented in India about two thousand years ago.
K. Ramasubramanian
### New Indian Values of from the Mānava-śulba-sūtra
India’s oldest written works are the Vedas. To assist their proper study, there are six ancillary texts, called Vedāṅgas (“limbs of the veda”), namely Śikṣā (Phonetics), Kalpa (Ritualistics), Vyākaraṇa (Grammar), Nirukta (Etymology), Chandas (Prosody) and Jyotiṣa (Astronomy and Astrology).
K. Ramasubramanian
### The Lakṣa Scale of the Vālmīki Rāmāyaṇa and Rāmā’s Army
C. N. Srinivasiengar was perhaps the first historian of mathematics to give a modern exposition of the Lakṣa Scale as found in the Yuddhakāṇḍa (the Sixth Book) of the Vālmīki Rāmāyaṇa, the national epic of India.
K. Ramasubramanian
### The Chronic Problem of Ancient Indian Chronology
Chronology is the backbone of history, and its knowledge is essential for a historian dealing with any period, culture area or subject. There cannot be a coherent history without a chronological order. Proper historical writing is not possible unless there is a sound chronology.
K. Ramasubramanian
### A Problem on Interest in the Nārada-purāṇa
The Sanskrit text of the Nārada-purāṇa (abbreviated NP hereafter) was, perhaps first, published by the Venkateshwara Press, Bombay in Śaka 1845 (or ad 1923). Chapter 54 of the Pūrvabhāga of NP is devoted to mathematics and astronomy (gaṇita-jyotiṣa). The next two chapters are on astrology (phalita-jyotiṣa).
K. Ramasubramanian
### Who Invented the Zero?
Obviously the answer depends on the meaning of ‘zero’. That is whether we mean the word zero or some concept of zero, the number zero or some symbol for zero, the mathematical zero or some philosophical zeroism. As a word for literal description, zero means a person or thing with no importance or independent existence.
K. Ramasubramanian
### World’s Longest Lists of Decuple Terms
Perhaps the practice of using fingers for counting was responsible for the choice of ten as a base for numeration. In India, ten has been the basis for counting since the very early days.
K. Ramasubramanian
### Circumference of the Jambūdvīpa in Jaina Cosmography
In Jain cosmography, the periphery of the Jambu Island is taken to be a circle of diameter 100,000 yojanas. The circumference of a circle of this size, as stated in Jain canonical and geographical works like the Anuyogadvāra-sūtra and Triloka-sāra etc. is equal to 316227 yojanas, 3 krośas, 128 daṇḍas and $$13\frac{1}{2}$$ aṅgulas nearly.
K. Ramasubramanian
### Mādhavacandra’s and Other Octagonal Derivations of the Jaina Value
$$\sqrt{10}$$ was one of the approximate values of $$\pi$$ used in ancient and medieval times especially in Jaina works. K. Hunrath derived it from a dodecagon a century ago, and G. Chakravarti from an octagon about fifty years ago. An ancient derivation given by Mādhavacandra (c. 1000 ad) in his Sanskrit commentary on Tiloya-sāra of Nemicandra. (c. 975 ad) has been examined in detail especially in the light of expositions given by Chakravarti and Āryikā Viśuddhamatī recently.
K. Ramasubramanian
### Chords and Areas of Jambūdvīpa Regions in Jaina Cosmography
In Jaina works, the Jambūdvīpa (“Jambu Island”) is circular and of diameter $$D=100000$$ yojanas (Tiloyapaṇṇattī $$=$$ TP, IV. 11; Vol. II, p. 4; Kota, 1986). It is divided into 13 main regions by boundary lines which are all parallel to the east–west direction.
K. Ramasubramanian
### The First Unenumerable Number in Jaina Mathematics
The definition of asaṃkhyāta (“unenumerable”) numbers in the ancient Indian Jaina Schools is linked to their cosmography according to which the Jambūdvīpa (“Jambū Island”) is circular in shape and has a diameter $$D_0$$ equal to one lakh yojanas. It is surrounded by a series of concentric rings (or annuli) of sea and land alternately (see Fig. 1).
K. Ramasubramanian
### गोलपृष्ठ के लिये महावीर-फेरू सूत्र और विदेशों में उनकी झलक
इस लेख में जिस व्यावहारिक सूत्र की चर्चा की गई है वह है
K. Ramasubramanian
### Brahmagupta’s Formulas for the Area and Diagonals of a Cyclic Quadrilateral
Let ABCD be a plane (convex) quadrilateral with sides AB, BC, CD and DA equal to a, b, c and d, respectively. Let the figure be drawn in such a manner that we may consider, according to the traditional terminology, the side BC to be the base (bhū), the side AD to be the face (mukha), and the sides AB and DC to be the flank, sides (bhujas or arms) of the quadrilateral.
K. Ramasubramanian
### On the Volume of a Sphere in Ancient India
Seidenberg’s paper “On the Volume of a Sphere” appeared in the Archive for the History of Exact Sciences, Vol. 39 (1988), pp. 97–119. He had conveyed it in January 1988 but could not see
K. Ramasubramanian
### Kamalākara’s Mathematics and Construction of Kuṇḍas
Kamalākara was a great astronomer and mathematician of India and was a senior contemporary of the famous Newton in Europe. He belonged to a family of jyotiṣīs and was the second son of Nṛsimha who wrote a commentary called Saurabhāṣya on the Sūrya-siddhānta in ad 1611.
K. Ramasubramanian
### Area of a Bow-Figure in India
In Fig. 1, PNQP is segment of a circle (i.e. circular disc) whose centre is at O and whose radius is $$OP=OQ=r$$. Due to the figure’s resemblance to an archer’s bow, the arc PNQ (= s in length) was called cāpa (‘bow’), the chord $$PQ (=c)$$ was called jyā or jīvā (‘bow-string’) and the segment’s height $$MN (=h)$$ was called bāṅa or śara (‘arrow’) in ancient India. The cāpakṣetra (‘bow-figure’) or segment of a circle had great importance in Indian cosmography and geography, especially in the Jaina school. The Bharata-kṣetra (=Bhārata-varṣa or ‘land of India’) of those times was in the shape of a bow-figure which formed the southernmost part of the central continent or Jambūdvīpa (‘Jambū Island’) which is stated to be circular and of diameter one lac (100,000) yojanas. This cartographic description may be taken to represent the oldest map of India as part of Asia. The maximum north–south breadth of the country was 526 $$\frac{6}{19}$$ yojanas.
K. Ramasubramanian
### Yantras or Mystic Diagrams: A Wide Area for Study in Ancient and Medieval Indian Mathematics
As an appliance, yantra may be an astronomical or surgical instrument, or a machine or mechanical device.
K. Ramasubramanian
### Second-Order Interpolation in Indian Mathematics up to the Fifteenth Century
The computational abilities of ancient Indian mathematicians are well known. The paper deals with the second-order interpolation schemes found in a few astronomical works of India.
K. Ramasubramanian
### Munīśvara’s Modification of Brahmagupta’s Rule for Second-Order Interpolation
When the values of a function are tabulated for some discrete values of the argument, the functional values corresponding to intermediary argumental values are obtained ordinarily by linear interpolation. For greater accuracy, higher order technique is necessary. It is known that the famous Indian mathematician Brahmagupta (seventh century ad) gave a rule for second-order interpolation.
K. Ramasubramanian
### Varāhamihira’s Calculation of and the Discovery of Pascal’s Triangle
In ancient time, the Jaina School of Indian mathematics took great interest in the subject of permutations and combinations as is clear from their canonical and other literature. The Bhagavatī-sūtra (dated about 300 bc) is said to have mentioned combinations of n objects taken one at a time (eka-saṃyoga), two at a time (dvika-saṃyoga), three at a time (trika-saṃyoga), or more at a time.
K. Ramasubramanian
### The Last Combinatorial Problem in Bhāskara’s Līlāvatī
There is no doubt that the most prominent name in the history of ancient and medieval Indian mathematics is that of Bhāskarācārya (ad twelfth century).
K. Ramasubramanian
### Early Pandiagonal Magic Squares in India
In ancient India, arts and sciences were hand-maiden of religions. In fact religion has been the dominant feature of Indian culture through the ages. Almost all sciences have been attributed a divine origin. For instance, the exposition of the 54th chapter (on astronomy and mathematics) of the Nārada-purāṇa commences with the line.
K. Ramasubramanian
### Bhāskara I’s Approximation to Sine
Accuracy of the rule is discussed and comparison with the actual values of sine is made and also depicted in a diagram. In addition to the two proofs given earlier by M. G. Inamdar (The Mathematics Student, Vol. XVIII, 1950, p. 10) and K. S. Shukla, three more derivations are included by the present author.
K. Ramasubramanian
### Fractional Parts of Āryabhaṭa’s Sines and Certain Rules Found in Govindasvāmin’s Bhāṣya on the Mahābhāskarīya
The commentary of Govindasvāmin (circa $${\textsc{ad}}$$ 800-850) on the Mahābhāskarīya contains the sexagesimal fractional parts of the 24 tabular Sine-differences given by Āryabhaṭa I (born $${\textsc{ad}}$$ 476). These lead to a more accurate table of Sines for the interval of 225 min. Thus the last tabular Sine becomes.
K. Ramasubramanian
### Early Indians on Second-Order Sine-Differences
The well-known property that the second order differences of sines are proportional to the sines themselves was known even to Āryabhaṭa I (born ad 476) whose Āryabhaṭīya is the earliest extant historical work (of the dated type) containing a sine table.
K. Ramasubramanian
### An Indian Form of Third-Order Taylor Series Approximation of the Sine
The paper describes an approximation formula for sine $$(x + h)$$ that differs from the first four terms of the Taylor expansion only by having 4 in place of 6 in the denominator of the fourth term. It appears in Sanskrit stanzas quoted in a work of about the fifteenth century and given here with translation and explanation.
K. Ramasubramanian
### Solution of the Astronomical Triangle as Found in the Tantrasaṅgraha (AD 1500)
The spherical triangle formed on the celestial sphere by the positions of the Sun, north pole and the zenith on it is called an astronomical triangle.
K. Ramasubramanian
### Addition and Subtraction Theorems for the Sine and the Cosine in Medieval India
The paper deals with the rules of finding the sines and the cosines of the sum and difference of two angles when those of the two angles are known separately. The rules, as found in the important medieval Indian works, are equivalent to the correct modern mathematical results. Indians of the said period also knew several proofs of the formulas. These proofs are based on simple algebraic and geometrical reasoning, including proportionality of sides of similar triangles and the Ptolemy’s theorem.
K. Ramasubramanian
The expression for the circum-radius of a cyclic quadrilateral in terms of its sides, usually attributed to L’Huilier in 1782, was known in India to Parameśvara (circa 1430). The present paper contains the original Sanskrit text of the rule, its English translation, and a discussion of its derivation as given by Saṅkara Vāriar in his Kriyākramakarī (sixteenth century) along with relevant historical remarks.
K. Ramasubramanian
### Indian Values of the Sinus Totus
The predecessor of the modern trigonometric function known as the sine of an angle was born, apparently, in India. The Greek trigonometry had been based on the functional relationship between the chords of a circle and the central angles they subtend. The Indians, on the other hand, used half of a chord of a circle as their basic trigonometric function. The Indian (or Hindu) Sine (usually written with a capital letter to distinguish it from the modern Sine) of an arc in a circle is defined as half the length of the chord of double the arc. Thus the (Indian) Sine of an arc $$\alpha$$ is equal to R $$\sin \theta$$ where R is the radius of the circle of reference and $$\sin \theta$$ is the modern sine of the angle $$\theta$$ subtended at the centre by the arc $$\alpha$$.
K. Ramasubramanian
### South Indian Achievements in Medieval Mathematics
The development of Hindu mathematics did not come to a standstill after the famous Bhāskarācārya or Bhāskara II (circa 1150 ad) although many scholars believed and still believe that.
K. Ramasubramanian
Munīśvara’s another name was Viśvarūpa. He was born in 1603 ad and his father was Raṅganātha (a commentator of Sūryasiddhānta). He resided at Varanasi and wrote the following works (in Sanskrit) related to Indian astronomy and mathematics (Census of Exact Sciences in Sanskrit, Vol. 4 of Series A, pp. 436–441; Philadelphia, 1981).
K. Ramasubramanian
### Prabodh Chandra Sengupta (1876–1962): Historian of Indian Astronomy and Mathematics
Prabodh Chandra Sengupta, the younger son of Ram Chandra Sengupta, was born in a village near Tangail in Mymensingh district (now in Bangladesh) on 21 June 1876. He had his early education in the Santosh Jahnavi H. E. School and passed the Entrance (Matric) examination with sufficient merit to obtain a scholarship.
K. Ramasubramanian
### Bibhutibhusan Datta (1888–1958): Historian of Indian Mathematics
Born to a poor Bengali family, Bibhutibhusan Datta (1888–1958) was indifferent to worldly pleasures and gains. He never married. His doctoral thesis was on hydrodynamics, but he is best known for his work on the history of mathematics.
K. Ramasubramanian
### Review of Pingree’s Census of Exact Sciences in Sanskrit (1992)
Series A, Volume 4, by David Pingree; American Philosophical Society, Philadelphia, 1981 (Memoirs of the A.P.S., Vol. 146); Pages 447, List Price U.S. \$ 30.00.
K. Ramasubramanian
### Homage to Professor Abraham Seidenberg (1916–1988)
Professor Abraham Seidenberg died on May 3, 1988. He belonged to the Department of Mathematics, University of California, Berkeley, USA, and was a member of the Editorial Board of the Gaṇita Bhāratī. He was a great scholar and was actively involved in research work on history of ancient mathematics. A few months before his death, he had sent his manuscript “On the Volume of a Sphere” for publication in the Archive for History of Exact Sciences (= AHES). He could not correct the proofs of the article which was published posthumously in December 1988. Perhaps this may be his last paper.
K. Ramasubramanian
### Sudhākara Dvivedī (1855–1910): Historian of Indian Astronomy and Mathematics
Once a king wanted to know as to why the Moon (candā) is addressed (candāmāmā) or “Moon, the Maternal Uncle” in India.
K. Ramasubramanian
### Clas-Olof Selenius (1922–1991): An Expert in Indian Cyclic Method
A great scholar as he was, Clas-Olof Selenius could successfully illustrate the use of modern mathematics in highlighting the significance of the ancient Indian masterpiece called Cakravāla or cyclic method in solving certain indeterminate equations.
K. Ramasubramanian
### Kripa Shankar Shukla (1918–2007): Veteran Historian of Hindu Astronomy and Mathematics
Kripa Shankar Shukla’s birth took place at Lucknow on July 10, 1918. From the very early years, he was a brilliant student of Mathematics and Sanskrit. He passed the High School Examination of U.P. Board in 1934 in First Division with Distinction in Mathematics and Sanskrit and the Intermediate Examination of that Board again in First Division with Distinction in Mathematics.
K. Ramasubramanian
### Obituary—T. A. Sarasvati Amma
Dr. T. A. Sarasvati Amma was born as the second daughter of her mother Kuttimalu Amma and father Marath Achutha Menon. The year of her birth was apparently 1094 of the Kollam (Kolamba) era which is prevalent in Kerala and which corresponds to ad 1918–1919.
K. Ramasubramanian
### The India-Born First President of the London Mathematical Society and His Discovery of Ramachandra
Augustus De Morgan (1806–1871), the founder President of the London Mathematical Society was born in Madurai of Madras Presidency (South India) on Friday, the 27th June, 1806. His father was associated with the East India Company. His great-grand father James Dodson (died 1757) was the author of Anti-Logarithmic Canon (1742) and Mathematical Repository (1755).
K. Ramasubramanian
### M. Rangacharya and His Century Old Translation of the Gaṇita-sāra-saṅgraha
Lots of Achievements in ancient Indian Mathematics as reflected in the works of Āryabhaṭa I (born 476 ad), Brahmagupta (seventh century ad) and Bhāskara II (twelfth century) were freshly made known in modern form to the Western world during the nineteenth century. Leading role in this regard was displayed by Western scholars such as R. Barrow, H. T. Colebrooke, S. Davies, C. Hutton, H. Kern, L. Rodet, E. Strachey and John Taylor.
K. Ramasubramanian
### Indian Astronomy and Mathematics in the Eleventh-Century Spain
According to Ibn al-Ādamī (c. 950 ad) as quoted by Qāḍī Ṣā’id al Andalūsī (d. 1070), Caliph al-Manṣūr of Baghdad (755–775 ad) ordered a Sanskrit astronomical work to be translated into Arabic.
K. Ramasubramanian
### Indian Astronomy in West Asia
It is difficult to gather trustworthy knowledge of astronomy in Iran before the reign of Ardashīr I (ad 226–240) and Shāpūr I (241–272) who encouraged the spread of Indian Science in the region. The ninth century Pahlavi (Middle Persian) Dēnkart informs us authoritatively that the two kings had Indian and Greek works translated into Pahlavi and that they were revised under Khusro Anūshirwān (sixth century) (Pingree, 1964–66, p. 119).
K. Ramasubramanian
### Spread and Triumph of Indian Numerals
According to Menninger, it is quite probable that due to active commercial relations with India, the first Indian numerals became known in Alexandria sometime in the fifth century ad and from there they might have penetrated farther westward.
K. Ramasubramanian
### Indian Mathematical Sciences Abroad During Pre-modern Times
Views regarding the origin of mathematics have been changing fast during the last 50 years. The publication of old Babylonian texts in the thirties has not only upset the theory of the Greek origin of mathematics but rather gave rise to the view that the Greek mathematics itself was a derivative of the Babylonian mathematics. According to a tradition, Thales visited Egypt and Pythagoras is said to have even visited India.
K. Ramasubramanian
### Sino-Indian Interaction and the Great Chinese Buddhist Astronomer-Mathematician I-Hsing (ad 683–727)
The rock edicts of king Aśoka (third century bc) show that he had already paved the way for the expansion of Buddhism outside India. Subsequently Buddhist missionaries took Buddhism to Central Asia, China, Korea, Japan and Tibet in the North, and to Burma, Ceylon, Thailand, Cambodia and other countries in the South. This helped in spreading Indian culture to these countries.
K. Ramasubramanian
### Indian Mathematical Sciences in Ancient and Medieval China
The great Indian emperor Aśoka (usually called Devānāṃpriya, ‘Beloved of Gods’) ruled from about 272–232 bc His missionary activities are recorded in Rock Edict No. XIII as follows (Sircar, p. 54, and P. Thomas, p. 15).
K. Ramasubramanian
### Indian Influence on Early Arabic and Persian Writers of Mathematical Sciences
India has given to the world outstanding gifts in sacred spiritual as well as in secular scientific fields. In spiritualism, India gave the great Buddhism through which all the Asian countries during the first millennium of our era “formed one fountainhead”.
K. Ramasubramanian
### Backmatter
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http://compilers.iecc.com/comparch/article/95-02-172 | # phi nodes in linear time
## "V.C. SREEDHAR" <sreedhar@bluebeard.cs.mcgill.ca>Wed, 22 Feb 1995 12:26:59 GMT
From comp.compilers
Related articles
phi nodes in linear time sreedhar@bluebeard.cs.mcgill.ca (V.C. SREEDHAR) (1995-02-22)
| List of all articles for this month |
Newsgroups: comp.compilers From: "V.C. SREEDHAR" Keywords: dataflow, FTP, report, available, analysis Organization: Compilers Central Date: Wed, 22 Feb 1995 12:26:59 GMT
The following paper is available from our ftp site
wally.cs.mcgill.ca (132.206.3.30):pub/doc/papers/POPL95.ps.gz
"A Linear Time Algorithm for Placing Phi-Nodes"
by Vugranam Sreedhar and Guang Gao
This paper was presented at the ACM Symposium on Principles
of Programming Languanges, 1995.
Sreedhar
============
Abstract:
Dataflow analysis framework based on Static Single
Assignment (SSA) form and Sparse Evaluation Graphs (SEGs)
demand fast computation of program points where data flow
information must be merged, the so-called {\bf $\phi$-nodes}.
In this paper, we present a surprisingly simple algorithm for
computing $\phi$-nodes for arbitrary flowgraphs (reducible
or irreducible) that runs in {\em linear} time. We employ
a novel program representation --- the {\bf DJ graph} --- by augmenting the
dominator tree of a flowgraph with edges which may lead to a potential
merge'' of dataflow information. In searching for \mbox{$\phi$-nodes} we
never visit an edge in the DJ-graph more than once by guiding the
search of nodes by their levels in the dominator tree.
The algorithm has been implemented and the results are compared with
the well known algorithm due to Cytron
et al.~\cite{CytronEtAl91}. A consistent and significant speedup
has been observed over a range of
46 Fortran procedures taken from a number of benchmark programs.
We also ran experiments on increasingly taller
ladder graphs and confirmed the linear time complexity of our algorithm.
--
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https://physionet.org/content/challenge-2010/1.0.0/sources/Luiz-Silva/ | Challenge Open Access
# Mind the Gap - The PhysioNet Computing in Cardiology Challenge 2010
Published: Dec. 1, 2010. Version: 1.0.0
Goldberger, A., Amaral, L., Glass, L., Hausdorff, J., Ivanov, P. C., Mark, R., ... & Stanley, H. E. (2000). PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals. Circulation [Online]. 101 (23), pp. e215–e220.
### Introduction
In settings ranging from sleep studies to surgery to sports medicine to intensive care, real-time monitoring of a variety of physiologic signals has become an essential tool for clinicians and researchers. Transient corruption or loss of one or more signals, common in all of these settings, can be disruptive, especially when continuous observations are required in order to rule out rare events or as a basis for forecasting. Signal corruption can be particularly challenging when it mimics features that are associated with pathologic states.
Humans can be remarkably adept at dealing with transient noise and signal loss in these settings. Filling in gaps, and making use of context to recognize and ignore noise, are processes that our sensory and cognitive abilities leave us well-equipped to do. Can algorithmic solutions that take account of the same data, in broader contexts and without fatigue, do as well?
The aim of this year's challenge is to develop robust methods for filling in gaps in multiparameter physiologic data (including ECG signals, continuous blood pressure waveforms, and respiration). In a real-world monitoring application, these methods can be applied for many purposes, including:
• robust estimation of parameters such as heart rate, mean arterial pressure, and respiration when the primary signals used to derive these parameters become unavailable or unreliable;
• detection of changes in patient state, when the relationships between signals remain consistent even as individual signals change their behavior; and
• recognition of intervals of signal corruption, when a signal becomes inconsistent not only with respect to its previous history but also with respect to its relationships with other signals.
In this Challenge, participants are asked to reconstruct, using any combination of available prior and concurrent information, segments of signals that have been removed from multiparameter recordings of patients in intensive care units (ICUs).
### Data for the Challenge
Participants are provided with three data sets of 100 records each. Each ten-minute record contains 6, 7, or 8 signals acquired from bedside ICU patient monitors. The recorded signals vary across records, and they include ECG, continuous invasive blood pressure, respiration, fingertip plethysmograms, and occasional other signals. In one of these signals, the final 30-second segment (the target signal) has been replaced by a gap (a flat line signal), and the goal is to reconstruct this missing 30-second target signal in each record.
• Set A is a set of 100 records for participants' use as a training set. Participants can obtain scores for Set A reconstructions at any time, but Set A scores are not included in the final rankings of Challenge entries. The target signals are provided for the records in this set. Additional training data can easily be constructed from any of the multiparameter data available in PhysioBank, such as the MIMIC II Waveform Database.
• Set B is a set of 100 records for which the target signals are withheld until the conclusion of the challenge. Participants can obtain scores for Set B reconstructions at any time, but Set B scores are not included in the final rankings of Challenge entries.
• Set C is a set of 100 records, with the target signals withheld. Participants may submit reconstructions of the target signals at any time for the duration of the challenge, but they will not receive scores except for their final submissions, which will determine the final rankings and the winners of the challenge.
Records in all three Challenge data sets are provided in standard PhysioBank (compact binary) formats; read them using the WFDB software package. The Set A files named with the suffix .missing are the target signals; these files are in text format. The datasets, together with the target signals for Set A, are available here
### Scoring
A detailed reconstruction of a signal, reproducing all characteristics of the original signal accurately, is more than is necessary in order to be useful. For example, a reconstruction of an invasive blood pressure signal may be useful if it allows a good estimation of mean pressure, or pulse pressure, even if none of the other details of the signal can be reproduced accurately; as another example, a reconstruction of an ECG signal that allows accurate estimation of RR intervals may be useful, even in the absence of other details.
For this reason, this challenge makes use of two scoring algorithms, detailed below. The first, used in event 1, measures the overall accuracy of the reconstruction, and as such will tend to favor those reconstruction methods that succeed in recovering properties of the signal that are derivable from the signal amplitude, such as MAP and pulse pressure. The second, used in event 2, is based on the correlation between the original signal and its reconstruction, and tends to favor those methods that accurately recover the timing of the major fluctuations in the original signal, such as QRS complexes in the ECG needed to derive RR interval series. Each reconstruction is scored using both algorithms, so a single submission is entered in both events of the Challenge.
### Scoring for individual reconstructions
Each reconstruction, Vrec, is compared with the corresponding target (reference) signal, Vref. Target signals are known in all cases, but those for the Set B and Set C records are not provided to participants.
Each submitted reconstruction is scored using two different methods, one for each of the two events. Since the scoring methods for the two events have different biases, a change in your reconstruction of a given record may improve your event 1 score and decrease your event 2 score, or vice versa.
#### Event 1
The target signal is subtracted (sample by sample) from the reconstruction to obtain the residual signal, Vres. The sum of the squares of the residuals, ssvres, is normalized by the energy (sample variance) of the target signal, Eref.
In event 1, the quality, Q1, of a reconstruction is defined as 1 - ssvres/Eref, or 0, whichever is larger. If ssvres is 0, Q1 is 1, even if Eref is also 0.
Use of a figure of merit based on the residual signal reflects the importance in many cases of obtaining a good estimate of target signal levels (such as systolic, mean, and diastolic pressures in a continuous blood pressure signal).
[Note that Q1 was previously defined as 1 - Eres/Eref, or 0, whichever is larger (where Eres is the energy of the residual signal). This definition was changed because it was independent of the magnitude of any constant (DC) component of the residual signal, unlike the revised definition.]
#### Event 2
In event 2, the quality Q2 of a reconstruction is defined as the correlation coefficient of Vref and Vrec, or 0, whichever is larger. (Correlation coefficients can of course be negative; for the purposes of this challenge, an anticorrelated reconstruction is equivalent to an uncorrelated one, however.)
Use of the correlation coefficient as a figure of merit is motivated by the observation that reconstruction of a filtered signal may be useful in many cases. Such a reconstruction might, for example, provide a basis for reliable estimation of the timing of major fluctuations in a signal (such as QRS complexes in an ECG signal), even if absolute signal levels are not recovered. Unlike Q1, Q2 is relatively insensitive to misestimation of the amplitudes of fluctuations.
### Aggregate (summed) scores
The final ranking of participants is based on summing the Q scores obtained for records in Set C. Participants are encouraged, but not required, to provide reconstructions of all records in Set C.
Both Q1 and Q2 are defined so they can vary between 0 and 1, and higher values are better. If you have submitted more than one reconstruction of the same record, only the last one submitted determines your Q1 and Q2 for that record. If you have not submitted a reconstruction for a given record, your Q1 and Q2 scores for that record are zero.
For event 1, your Set C summed score, C1, is the sum of the your final Q1 scores for each record in Set C. Similarly, for event 2, your Set C summed score, C2, is the sum of the your final Q2 scores for each record in Set C. Since Set C contains 100 records, C1 and C2 can vary between 0 and (in theory!) 100.
The summed scores are not normalized by the number of target signals reconstructed, to provide a strong incentive to submit reconstructions of as many of the Set C records as possible.
### Entering the Challenge
To be eligible for an award (see below):
1. Submit reconstructions (see below) of at least 10 Set B target signals, no later than noon GMT on Friday, 30 April 2010.
2. Submit an abstract (about 300 words) describing your work on the Challenge to Computing in Cardiology (CinC) by Saturday, 1 May 2010. Please select "PhysioNet/CinC Challenge" as the topic of your abstract, so it can be identified easily by the abstract review committee.
3. Submit reconstructions of as many Set C target signals as you wish no later than noon GMT on Wednesday, 1 September 2010. Since your ranking is determined by the sum of the scores you receive for Set C targets, it is to your advantage to attempt as many of the 100 Set C records as possible.
4. Attend Computing in Cardiology in Belfast, Northern Ireland, 26-29 September.
If your abstract is accepted, you will be expected to prepare a four-page paper for publication in Computing in Cardiology, and to present a talk or poster about your work at CinC.
### Submitting reconstructions for scoring
Reconstructions should be in the same format as the .missing files containing the Set A target signals (text format, with one sample of the reconstructed signal per line). Each file should contain 3750 samples (125 samples/second, for 30 seconds). Although the target signals consist entirely of samples with integer values, reconstructions may contain integer or floating point values. Use a decimal point (.) rather than a comma (,) to separate the integral and fractional components of floating point values.
You may replace any previously submitted reconstruction simply by submitting a new one. The corresponding scores are updated immediately.
Scores are calculated using the code in c2010-score.c, a short C program that you may download and use to compare any two time series.
Participants may submit reconstructions of as many Set A, B, and C target signals as they wish. Each reconstruction is scored separately. For each event, the final ranking of participants is based on the sum of the scores obtained for reconstructions of Set C target signals.
Keep in mind that Sets A and B are intended for experimentation with your methods for reconstruction. You can obtain scores for your Set A and B reconstructions at any time during the Challenge. Set C is the "final examination", and although you have until September to study it, you will not be able to obtain intermediate scores. "Tuning" your methods to Set C will not be possible, so learn what you can from Sets A and B and then apply it to Set C.
### Final scores and Challenge awards
Aggregate and individual scores for Set C records will be calculated based on reconstructions submitted no later than noon GMT on 1 September 2010. These scores, which will appear on your page when they have been calculated, determine the final ranking of participants.
During a plenary session of Computing in Cardiology in September, four awards will be presented to the eligible participants in attendance with the best final scores as follows:
1. (Event 1, open source) Highest C1 score for an open source entry
2. (Event 1, overall) Highest C1 score
3. (Event 2, open source) Highest C2 score for an open-source entry
4. (Event 2, overall) Highest C2 score
Participants may enter one or both events, and open source entries are eligible for the overall awards as well as for the open source awards. If the best results in any category are achieved by two or more entries, the first of these entries to be submitted will receive the award in that category.
### Entering the Open Source Division
As in previous years, the Challenge includes an open source division. You may enter the open source division by sending the source code for your challenge entry by email, before noon GMT on Wednesday, 1 September 2010, to PhysioNet. Use the subject line "Challenge 2010 entry source", and be sure to include:
• All sources needed to produce a working version of your software (except for readily available standard libraries and header files)
• A note describing how to produce a working version of your software (a commented Makefile is ideal), and how to run your software
Each source file submitted should begin with a comment block containing the names of its authors and a reference to the open source license you have chosen for it, if any; for example:
/* fill.c - fill signal gaps using large wads of duct tape
Copyright (C) 2010 Herman Foobar <hbar@uncertain.org>
This software is released under the terms of the GNU General
*/
Source files in C, C++, Fortran, or Matlab m-code are preferred; other languages may be acceptable, but please ask first. Do not submit any code that cannot be freely redistributed. Following the conclusion of the Challenge, selected entries will be posted, with full credit to their authors, on PhysioNet.
Must there be an automatic process to choose the set of signals used in the reconstruction of the target signal or is it acceptable that the choice of signals is not done by a program but by the participant?
Either method is acceptable. Keep in mind that the final rankings will be determined by your scores on set C, and that you will receive only one score for each of the set C records (in other words, you will not be able to try several different signal subsets for each set C record and choose the subset that yields the best score in each case).
There are some files in the challenge dataset, where there are several signals with zeros in the last 30 seconds. The determination of the target signal is ambiguous at the following signals: c21, c54, c67. What should be the way of handling this problem?
In each of these cases, there is only one signal that becomes flat (all zero values) after 9 minutes and 30 seconds (i.e., beginning at sample 71250). Reconstruct that signal, not the one that has been flat for a longer period.
• In c21, ABP and UAP are flat, but UAP is flat throughout; reconstruct ABP.
• In c54, CVP and ICP are flat, but CVP is flat beginning at sample 49556; reconstruct ICP.
• In c67, ABP and CVP are flat, but ABP is flat throughout; reconstruct CVP.
### Papers
The papers below were presented at Computers in Cardiology 2010. Please cite this publication when referencing any of these papers. These papers have been made available by their authors under the terms of the Creative Commons Attribution License 3.0 (CCAL). We wish to thank all of the authors for their contributions.
The first of these papers is an introduction to the challenge topic, with a summary of the challenge results and a discussion of their implications.
The remaining papers were presented by participants in the Challenge, who describe their approaches to the challenge problem.
Estimation of Missing Data in Multi-channel Physiological Time-series by Average Substitution with Timing from a Reference Channel
P Langley, S King, K Wang, D Zheng, R Giovannini, M Bojarnejad, A Murray
Reconstruction of Missing Physiological Signals Using Artificial Neural Networks
AM Sullivan, H Xia, JC McBride, X Zhao
Medical Multivariate Signal Reconstruction Using Recurrent Neural Network
LEV Silva, JJ Duque, MG Guzo, I Soares, R Tinós, LO Murta Jr
Reconstructing Missing Signals in Multi-Parameter Physiologic Data by Mining the Aligned Contextual Information
Y Li, Y Sun, P Sondhi, L Sha, C Zhai
A Wavelet Scheme for Reconstruction of Missing Sections in Time Series Signals
TR Rocha, SP Paredes, JH Henriques
Reconstruction of Multivariate Signals Using Q-Gaussian Radial Basis Function Network
LEV Silva, JJ Duque, R Tinós, LO Murta Jr
##### Access
Access Policy:
Anyone can access the files, as long as they conform to the terms of the specified license.
##### Corresponding Author
You must be logged in to view the contact information.
## Files
Total uncompressed size: 0 B.
##### Access the files
gsutil -m -u YOUR_PROJECT_ID cp -r gs://challenge-2010-1.0.0.physionet.org DESTINATION
wget -r -N -c -np https://physionet.org/files/challenge-2010/1.0.0/ | {"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": 0.4056171178817749, "perplexity": 1654.8362595712542}, "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/1637964360803.0/warc/CC-MAIN-20211201113241-20211201143241-00034.warc.gz"} |
http://rpg.stackexchange.com/questions/4794/legends-of-anglerre-chargen-questions | # Legends of Anglerre chargen questions
I looked over Legends of Anglerre's explanation of quick character generation and it doesn't seem to exactly explain what power scope is covers. What characters does it allow?
Additionally, I am not sure about skill points - how much do I give per power level (Good, Great and Superb in order)? How was the suggested base 20 points decided upon?
Finally, given I plan on running a one shot to players who've never played FATE or LoA, would it be wiser to pregen the characters completely?
-
I understand that the 20 point pyramid allows 1 Great skill. What I'm wondering is whether this applies to all 3 grades of characters (Doing step 4 and step 5 in chargen) in terms of abilities. Would Great characters get more points to get a Superb skill? Would Superb characters get more points to have a Fantastic skill?
Given the points values on p.17 for the various grades:
Superb: 35 points 5 phases 10 aspects 5 stunts<br>
Great: 20 points 4 phases 8 aspects 4 stunts<br>
Good: 15 points 3 phases 6 aspects 3 stunts
Because of the pyramid nature, a Good (15pt) character can not get above a Good. He has to have a pyramid, so in order to have a Great, he has to have at least one great, which requires at least 2 Goods, and that requires 3 Fairs, and those require 4 averages...
Best Skill Good Best Skill Great Best Skill Superb
minimum points minimum points Minimum Points
3 Gd x1 = 3 4 Gr x1 = 4 5 Su x1 = 5
2 2 Fa x2 = 4 3 3 Gd x2 = 6 4 4 Gr x2 = 8
1 1 1 Av x3 = 3 2 2 2 Fa x3 = 6 3 3 3 Gd x3 = 9
Total = 10 1 1 1 1 Av x4 = 4 2 2 2 2 Fa x4 = 8
Total = 20 1 1 1 1 1 Av x5 = 5
Total = 35
So, since a Good character has 15 points, he can't reach Great because great requires 20 points minimum to reach. (with Aspects, tho', he might be able to act with an effective skill of Superb when he uses an aspect; more on that later.)
So, what are the options for a 15 point Good Character?
3 Gd x1 = 3 3 Gd x1 = 3
2 2 2 Fa x3 = 6 2 2 Fa x2 = 4
1 1 1 1 1 1 Av x6 = 6 1 1 1 1 1 1 1 1 Av x8 = 8
Total = 15 Total = 15
He can't have 2 Goods, tho:
3 3 Gd x2 = 6
2 2 2 Fa x3 = 6
1 1 1 1 Av x4 = 4
Total = 16 « over by 1!
But you can also have a "Good" character with no "Good" skills:
Fa x4 = 8 Fa x3 = 6 Fa x2 = 4 Fa x1 = 2 Fa x0 = 0
Av x7 = 7 Av x9 = 9 Av x11 = 11 Av x13 = 13 Av x15 = 15
Total = 15 Total = 15 Total = 15 Total = 15 Total = 15
Great Characters, with 20 points of skills, can only have 1 Great... because the minimum pyramid for a great is 20 points.
He can, however, have any of the following Good-top pyramids:
Gd x2 = 6 Gd x2 = 6 Gd x1 = 3 Gd x1 = 3
Fa x4 = 8 Fa x3 = 6 Fa x5 = 10 Fa x4 = 8
Av x6 = 6 Av x8 = 8 Av x7 = 7 Av x9 = 9
Total = 20 Total = 20 Total = 20 Total = 20
Gd x1 = 3 Gd x1 = 3
Fa x3 = 6 Fa x2 = 4 Fa x6 = 12 Fa x5 = 10
Av x11 = 11 Av x13 = 13 Av x8 = 8 Av x10 = 10
Total = 20 Total = 20 Total = 20 Total = 20
Fa x4 = 8 Fa x3 = 6 Fa x2 = 4 Fa x1 = 2
Av x12 = 12 Av x14 = 14 Av x16 = 16 Av x18 = 18
Total = 20 Total = 20 Total = 20 Total = 20
Likewise, theres no way to have a valid pyramid with better than Superb with the 35 points a Superb character starts with, but he can have a lot of options for starting with less than a superb. Too many to list.
The character category determines how many phases, and what the maximum possible skill level at start is. Only for Good characters does that provide options if you want to be as Good as you can.
-
That was infinitely useful. I can't believe I missed page 17 entirely. Thank you for the answer. Flagged as accepted. Good day. – Nadav Ben Dov Nov 29 '10 at 12:11
It's hidden in plain sight by not being on a table on p.17. Easily missed. – aramis Nov 29 '10 at 18:50
You should spend skill points based on 1 point per + given--Average is 1 point, Fair is 2 points, and so on. The default for this game is a pyramid, like the other FATE games--this one, however, is less high-powered than Spirit of the Century (another FATE game) is at the beginning. This is the default 20 point pyramid:
4 -- Total: 4 = 4
3 3 -- Total: 4 + 6 = 10
2 2 2 -- Total: 4 + 6 + 6 = 16
1 1 1 1 -- Total: 4 + 6 + 6 + 4 = 20
By comparison, SotC's starting pyramid would be 35 points, because of the extra 1, 2, 3, 4, and 5 available for skills:
5 -- Total: 5 = 5
4 4 -- Total: 5 + 8 = 13
3 3 3 -- Total: 5 + 8 + 9 = 22
2 2 2 2 -- Total: 5 + 8 + 9 + 8 = 30
1 1 1 1 1 -- Total: 5 + 8 + 9 + 8 + 5 = 35
Pregens are very useful for a one-shot for FATE based systems--this system may be quicker than the Dresden Files RPG's system, but it still can easily take a while for newer players. Stick with pregens to avoid problems.
-
Thank you for the info, although the answer about skill points didn't quite cover what I was looking for. I understand that the 20 point pyramid allows 1 Great skill. What I'm wondering is whether this applies to all 3 grades of characters (Doing step 4 and step 5 in chargen) in terms of abilities. Would Great characters get more points to get a Superb skill? Would Superb characters get more points to have a Fantastic skill? – Nadav Ben Dov Nov 28 '10 at 7:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.37414297461509705, "perplexity": 1283.405339451276}, "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/1469257825358.53/warc/CC-MAIN-20160723071025-00095-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://ricekot.com/2020/mechanics-slender-structures/ | My notes from Chapter 3 of “An Introduction to the Mechanics of Solids” by Crandall and Dahl.
• Summary of Chapter 2, “Introduction to Mechanics of Deformable Bodies” (according to 3.1)
Analysis of Deformable Bodies
1. Study of forces and equilibrium requirements
2. Study of deformation and conditions of geometric fit
3. Application of force-deformation relations
• What is Chapter 3, “Forces and Moments Transmitted by Slender Members” all about?
We are going to be concerned with the study of forces and the equilibrium requirements, as applied to slender members.
• What are Slender Members?
Those members of engineering structures whose lengths are much longer as compared to either of their cross-sectional dimensions are called slender members. In case of loops, the diameter must be much larger than the thickness of the long rod that is looped.
• What is the subscript notation we are using to denote forces and moments at a section in slender members?
We usually have two letters in the subscript.
For a force $F_{ab}$, $a$ denotes the direction of the vector perpendicular to the area of cross-section in consideration and, $b$ denotes the direction of the Force.
Thus, $F_{xx}$ is an axial force while $F_{xy}$ and $F_{xz}$ are shear forces.
Similarly, for a moment $M_{ab}$, $a$ has the same meaning as above and $b$ is the direction of the force that is responsible for this moment.
Hence, $M_{xx}$ is a twisting moment while $M_{xy}$ and $M_{xz}$ are bending moments.
• What about the sign convention?
A positive force or moment on a positive face is positive. So is a negative force or moment on a negative face (implied by Newton’s third law). Here, positive and negative mean in a positive or negative coordinate direction respectively.
• What problem solving approach do we usually follow, when we have multiple loads on a slender member?
The Method of Sections
1. First, draw a free body diagram of the entire slender member and mark all the forces acting on it.
2. Then, use the equations of equilibrium $\Sigma F = 0$ and $\Sigma M = 0$ to get relations between them.
3. Finally, cut the member at a section of your choice and repeat step 2 on either of the resulting segments.
• What is a shear force diagram?
A graph of shear force on a body versus the distance along a beam (from a given point) where it acts.
• What is a bending moment diagram?
A graph of bending moment on a body versus the distance along a beam (from a given point) where it acts.
• Why do we need these diagrams?
If we wanted to design a durable engineering structure, we would need to know the maximum forces that can act on the members of the structure. Further, knowing the force distribution may allow us to better arrange all the different members in the structure together. I’ve not personally designed any such structures but in my opinion, a well engineered structure is one which is easy to put together and take apart, kind of like Legos.
• What is the Point of Contraflexure?
It is the point on a bending moment diagram where the bending moment changes its sign (i.e. positive to negative or vice versa). At this point the value of the bending moment is zero.
• What is Intensity of Loading?
Intensity of loading, $q$ is defined as the limit,
$q = \lim_{\Delta x\to0}\frac{\Delta F}{\Delta x}$
It’s dimensions are force per unit Length.
• How do we approach problems that have distributed loading conditions?
• Calculating the Resultant Force
One method is to calculate the resultant force on the slender member.
$\text{For forces acting in a single dimension,}\\ \text{Resultant Force, }R = \int qdx \\ \text{Centroid, }\bar{x} = \frac{\int qxdx}{R}$
where $q(x)$ is the intensity of loading - a function of $x$, the distance from an end of the member.
These can be obtained by writing the force and moment balance equations twice - once with $R$ and $\bar{x}$ and then with the RHS of the above equations - and comparing them.
The line of action of the resultant force passes through the centroid.
The formulae for forces acting in two and three dimensions are also similar.
• Using Differential Equilibrium Relationships
Consider a very small element of the given slender member, analyse the shear forces and bending moments acting on it and then limit the small segment of length / area / volume to zero. This will give us differential equations that we can integrate to find relationships between forces. Use boundary conditions to find out the values of constants of integration.
$\Sigma F=0 \\\implies -V+q(x)\Delta x+V+\Delta V=0 \\\implies q(x)\Delta x+\Delta V=0 \\\implies q(x)=-\frac{\Delta V}{\Delta x}$
Also,
$\Sigma M_A = 0 \\\implies -M_b + \Delta x\cdot(V+\Delta V) + (M_b + \Delta M_b) = 0 \\\implies V\Delta x + \Delta V\Delta x + \Delta M_b = 0 \\\implies V = -\frac{\Delta M_b}{\Delta x}-\Delta V$
In both the above equations, limiting $\Delta x\to0$ we get,
$q(x)=-\frac{dV}{dx}\\ V(x) = -\frac{dM_b}{dx}$
• What is the relationship between the shear force, bending moment and loading diagrams?
• The slope of the bending moment curve is the negative ordinate of the shear force curve.
• The slope of the shear force curve is the negative ordinate of the intensity of loading curve.
• How do we approach problems that have distributed loading conditions but only in some segments, or with different magnitudes?
Use the method of sections along with either of the two methods above or, use Singularity Functions.
• What are Singularity Functions?
Singularity functions are defined as,
$f_n(x)=\langle x - a\rangle^n ={\left\lbrace\begin{matrix}{0}&{\quad\text{if}\quad}{x}\le{a}\\ (x-a)^n&{\quad\text{if}\quad}{x}\gt{a}\end{matrix}\right.}\;\;(n\ge0)$
They have the following property,
$\int_{-\infty}^{x}\langle x-a\rangle^n\;dx = \frac{\langle x-a\rangle^{n+1}}{n+1}\;\;(n\ge0)$
There are two exceptions:
$\int_{-\infty}^{x}\langle x-a\rangle_{-1}dx=\langle x-a\rangle^0$ $\int_{-\infty}^{x}\langle x-a\rangle_{-2}\;dx=\langle x-a\rangle_{-1}$
$\langle x-a\rangle_{-1}$ and $\langle x-a\rangle_{-2}$ are zero everywhere except at $x=a$ where they are infinite.
• What do singularity functions represent?
• $\langle x-a\rangle_{-2}$
represents a unit concentrated moment.
• $\langle x-a\rangle_{-1}$
represents a unit concentrated load. This is also known as the Dirac Delta function in physics.
• $\langle x-a\rangle^{0}$
represents a unit step.
• $\langle x-a\rangle^{1}$
represents a unit ramp.
• $\langle x-a\rangle^{2}$
represents a unit parabolic curve.
• If there are no distributed loads present, where does the maximum bending moment occur?
It always occurs at a loading point.
• Why?
When all forces lie in the same plane, the bending moment diagram consists only of straight line segments. And even when they don’t, the bending moment diagram consists only of concave outward curves. | {"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": 0.9368945360183716, "perplexity": 592.7373246599371}, "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-2022-21/segments/1652662531762.30/warc/CC-MAIN-20220520061824-20220520091824-00725.warc.gz"} |
https://scholarworks.iu.edu/dspace/browse?value=Waldron+Formation&type=subject | # Browsing by Subject "Waldron Formation"
Sort by: Order: Results:
• (Indiana Division of Geology, 1948)
Silurian and Devonian outcrops of Indiana are divided roughly into two areas, northern and southeastern Indiana. The bedrock of the northern area is largely covered by glacial drift, whereas the bedrock of the southeastern ... | {"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": 0.8901545405387878, "perplexity": 27690.73560882727}, "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-2016-50/segments/1480698542828.27/warc/CC-MAIN-20161202170902-00455-ip-10-31-129-80.ec2.internal.warc.gz"} |
http://mathhelpforum.com/calculus/97849-particle-movement.html | 1. ## particle movement
particle that moves along a straight line has velocity
v(t)=t^2e^–2t
meters per second after t seconds. How many meters will it travel during the first t seconds
can anyone help me with this one
2. Originally Posted by dat1611
particle that moves along a straight line has velocity
v(t)=t^2e^–2t
meters per second after t seconds. How many meters will it travel during the first t seconds
can anyone help me with this one
$\int_0^t x^2 \cdot e^{-2x} \, dx$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3068516254425049, "perplexity": 719.7698757624805}, "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-2013-48/segments/1386164943590/warc/CC-MAIN-20131204134903-00049-ip-10-33-133-15.ec2.internal.warc.gz"} |
http://worldwidescience.org/topicpages/a/accreting+millisecond+pulsar.html | #### Sample records for accreting millisecond pulsar
1. Gravitational Radiation from Accreting Millisecond Pulsars
Vigelius, Matthias; Melatos, Andrew
2008-01-01
It is widely assumed that the observed reduction of the magnetic field of millisecond pulsars can be connected to the accretion phase during which the pulsar is spun up by mass accretion from a companion. A wide variety of reduction mechanisms have been proposed, including the burial of the field by a magnetic mountain, formed when the accreted matter is confined to the poles by the tension of the stellar magnetic field. A magnetic mountain effectively screens the magnetic dipole moment. On the other hand, observational data suggests that accreting neutron stars are sources of gravitational waves, and magnetic mountains are a natural source of a time-dependent quadrupole moment. We show that the emission is sufficiently strong to be detectable by current and next generation long-baseline interferometers. Preliminary results from fully three-dimensional magnetohydrodynamic (MHD) simulations are presented. We find that the initial axisymmetric state relaxes into a nearly axisymmetric configuration via toroidal ...
2. Electromagnetic Spindown of a Transient Accreting Millisecond Pulsar During Quiescence
Melatos, A.; Mastrano, A.
2016-02-01
The measured spindown rates in quiescence of the transient accreting millisecond pulsars IGR J00291+5934, XTE J1751-305, SAX J1808.4-3658, and Swift J1756.9-2508 have been used to estimate the magnetic moments of these objects assuming standard magnetic dipole braking. It is shown that this approach leads to an overestimate if the amount of residual accretion is enough to distort the magnetosphere away from a force-free configuration through magnetospheric mass loading or crushing, so that the lever arm of the braking torque migrates inside the light cylinder. We derive an alternative spindown formula and calculate the residual accretion rates where the formula is applicable. As a demonstration we apply the alternative spindown formula to produce updated magnetic moment estimates for the four objects above. We note that based on current uncertain observations of quiescent accretion rates, magnetospheric mass loading and crushing are neither firmly indicated nor ruled out in these four objects. Because quiescent accretion rates are not measured directly (only upper limits are placed), without more data it is impossible to be confident about whether the thresholds for magnetospheric mass loading or crushing are reached or not.
3. Improved methods for modeling pulse shapes of accreting millisecond pulsars
2006-01-01
Raytracing computations for light emitted from the surface of a rapidly rotating neutron star are carried out in order to construct light curves for accreting millisecond pulsars. These calculations are for realistic models of rapidly rotating neutron stars which take into account both the correct exterior metric and the oblate shape of the star. We find that the most important effect, comparing the full raytracing computations with simpler approximations currently in use, arises from the oblate shape of the rotating star. Approximating a rotating neutron star as a sphere introduces serious errors in fitted values of the star's radius and mass if the rotation rate is very large. However, for lower rotation rates acceptable mass and radius values can be obtained using the spherical approximation.
4. Simulations of the magnetospheres of accreting millisecond pulsars
Parfrey, Kyle; Beloborodov, Andrei M
2016-01-01
Accreting pulsars power relativistic jets, and display a complex spin phenomenology. These behaviours may be closely related to the large-scale configuration of the star's magnetic field. The total torque experienced by the pulsar comprises spin-up and spin-down contributions from different bundles of magnetic field lines; the spin-down braking' torque is applied both by closed stellar field lines which enter the disc beyond the corotation radius, and those which are open and not loaded with disc material. The rates of energy and angular momentum extraction on these open field lines have lower bounds in the relativistic, magnetically dominated limit, due to the effective inertia of the electromagnetic field itself. Here we present the first relativistic simulations of the interaction of a pulsar magnetosphere with an accretion flow. Our axisymmetric simulations, with the pseudospectral PHAEDRA code, treat the magnetospheric, or coronal, regions using a resistive extension of force-free electrodynamics. The m...
5. Timing and spectral properties of the accreting millisecond pulsar SWIFT J1756.9-2508
M. Linares; R. Wijnands; M. van der Klis; H. Krimm; C.B. Markwardt; D. Chakrabarty
2008-01-01
SWIFT J1756.9-2508 is one of the few accreting millisecond pulsars (AMPs) discovered to date. We report here the results of our analysis of its aperiodic X-ray variability, as measured with the Rossi X-Ray Timing Explorer during the 2007 outburst of the source. We detect strong (~35%) flat-topped br
6. Accretion, Ablation and Propeller Evolution in Close Millisecond Pulsar Binary Systems
Kiel, P D
2013-01-01
A model for the formation and evolution of binary millisecond radio pulsars in systems with low mass companions (< 0.1 Msun) is investigated using a binary population synthesis technique. Taking into account the non conservative evolution of the system due to mass loss from an accretion disk as a result of propeller action and from the companion via ablation by the pulsar, the transition from the accretion powered to rotation powered phase is investigated. It is shown that the operation of the propeller and ablation mechanisms can be responsible for the formation and evolution of black widow millisecond pulsar systems from the low mass X-ray binary phase at an orbital period of ~0.1 day. For a range of population synthesis input parameters, the results reveal that a population of black widow millisecond pulsars characterized by orbital periods as long as ~0.4 days and companion masses as low as ~0.005 Msun can be produced. The orbital periods and minimum companion mass of this radio millisecond pulsar popu...
7. Swinging between rotation and accretion power in a binary millisecond pulsar
Papitto, A; Bozzo, E; Rea, N
2013-01-01
We present the discovery of IGR J18245-2452, the first millisecond pulsar observed to swing between a rotation-powered, radio pulsar state, and an accretion-powered X-ray pulsar state (Papitto et al. 2013, Nature, 501, 517). This transitional source represents the most convincing proof of the evolutionary link shared by accreting neutron stars in low mass X-ray binaries, and radio millisecond pulsars. It demonstrates that swings between these two states take place on the same time-scales of luminosity variations of X-ray transients, and are therefore most easily interpreted in terms of changes in the rate of mass in-flow. While accreting mass, the X-ray emission of IGR J18245-2452 varies dramatically on time-scales ranging from a second to a few hours. We interpret a state characterised by a lower flux and pulsed fraction, and by sudden increases of the hardness of the X-ray emission, in terms of the onset of a magnetospheric centrifugal inhibition of the accretion flow. Prospects of finding new members of th...
8. The accreting millisecond X-ray pulsar IGR J00291+5934: evidence for a long timescale spin evolution
A. Patruno
2010-01-01
Accreting millisecond X-ray pulsars like IGR J00291+5934 are important because they can be used to test theories of pulsar formation and evolution. They give also the possibility of constraining gravitational wave emission theories and the equation of state of ultra-dense matter. Particularly crucia
9. Possible Fermi Detection of the Accreting Millisecond Pulsar Binary SAX J1808.4-3658
Xing, Yi; Wang, Zhongxiang; Jithesh, V.
2015-01-01
We report the Fermi Large Area Telescope (LAT) detection of a $\\gamma$-ray source at the position of SAX J1808.4$-$3658. This transient low-mass X-ray binary contains an accreting millisecond puslar, which is only seen during its month-long outbursts and likely switches to be rotation powered during its quiescent state. Emission from the $\\gamma$-ray source can be described by a power law with an exponential cutoff, the characteristic form for pulsar emission. Folding the source's 2.0--300 Ge...
10. SAX J1808.4-3658, an accreting millisecond pulsar shining in gamma rays?
Wilhelmi, E de Ona; Li, J; Rea, N; Torres, D F; Burderi, L; Di Salvo, T; Iaria, R; Riggio, A; Sanna, A
2015-01-01
We report the detection of a possible gamma-ray counterpart of the accreting millisecond pulsar SAX J1808.4-3658. The analysis of ~6 years of data from the Large Area Telescope on board the Fermi Gamma-ray Space Telescope (Fermi-LAT) within a region of 15deg radius around the position of the pulsar reveals a point gamma-ray source detected at a significance of ~6 sigma (Test Statistic TS = 32), with position compatible with that of SAX J1808.4-3658 within 95% Confidence Level. The energy flux in the energy range between 0.6 GeV and 10 GeV amounts to (2.1 +- 0.5) x 10-12 erg cm-2 s-1 and the spectrum is well-represented by a power-law function with photon index 2.1 +- 0.1. We searched for significant variation of the flux at the spin frequency of the pulsar and for orbital modulation, taking into account the trials due to the uncertainties in the position, the orbital motion of the pulsar and the intrinsic evolution of the pulsar spin. No significant deviation from a constant flux at any time scale was found, ...
11. Electromagnetic spin down of a transient accreting millisecond pulsar during quiescence
Melatos, Andrew
2015-01-01
The measured spin-down rates in quiescence of the transient accreting millisecond pulsars IGR J00291+5934, XTE J1751-305, SAX J1808.4-3658, and Swift J1756.9-2508 have been used to estimate the magnetic moments of these objects assuming standard magnetic dipole braking. It is shown that this approach leads to an overestimate, if the amount of residual accretion is enough to distort the magnetosphere away from a force-free configuration, through magnetospheric mass loading or crushing, so that the lever arm of the braking torque migrates inside the light cylinder. We derive an alternative spin-down formula and calculate the residual accretion rates where the formula is applicable. As a demonstration, we apply the alternative spin-down formula to produce updated magnetic moment estimates for the four objects above. We note that, based on current uncertain observations of quiescent accretion rates, magnetospheric mass loading and crushing are neither firmly indicated nor ruled out in these four objects. Because ...
12. Evidence of Fast Magnetic Field Evolution in an Accreting Millisecond Pulsar
Patruno, A
2012-01-01
The large majority of neutron stars (NSs) in low mass X-ray binaries (LMXBs) have never shown detectable pulsations despite several decades of intense monitoring. The reason for this remains an unsolved problem that hampers our ability to measure the spin frequency of most accreting NSs. The accreting millisecond X-ray pulsar (AMXP) HETE J1900.1--2455 is an intermittent pulsar that exhibited pulsations at about 377 Hz for the first 2 months and then turned in a non-pulsating source. Understanding why this happened might help to understand why most LMXBs do not pulsate. We present a 7 year long coherent timing analysis of data taken with the Rossi X-ray Timing Explorer. We discover new sporadic pulsations that are detected on a baseline of about 2.5 years. We find that the pulse phases anti-correlate with the X-ray flux as previously discovered in other AMXPs. We place stringent upper limits of 0.05% rms on the pulsed fraction when pulsations are not detected and identify an enigmatic pulse phase drift of ~180...
13. Eccentric Binary Millisecond Pulsars
Freire, Paulo C C
2009-01-01
In this paper we review the recent discovery of several millisecond pulsars (MSPs) in eccentric binary systems. Timing these MSPs we were able to estimate (and in one case precisely measure) their masses. These results suggest that, as a class, MSPs have a much wider range of masses (1.3 to > 2 solar masses) than the normal and mildly recycled pulsars found in double neutron star (DNS) systems (1.25 < Mp < 1.44 solar masses). This is very likely to be due to the prolonged accretion episode that is thought to be required to form a MSP. The likely existence of massive MSPs makes them a powerful probe for understanding the behavior of matter at densities larger than that of the atomic nucleus; in particular, the precise measurement of the mass of PSR J1903+0327 ($1.67 +/- 0.01 solar masses) excludes several "soft" equations of state for dense matter. 14. Binary and Millisecond Pulsars Lorimer Duncan R. 2008-11-01 Full Text Available We review the main properties, demographics and applications of binary and millisecond radio pulsars. Our knowledge of these exciting objects has greatly increased in recent years, mainly due to successful surveys which have brought the known pulsar population to over 1800. There are now 83 binary and millisecond pulsars associated with the disk of our Galaxy, and a further 140 pulsars in 26 of the Galactic globular clusters. Recent highlights include the discovery of the young relativistic binary system PSR J1906+0746, a rejuvination in globular cluster pulsar research including growing numbers of pulsars with masses in excess of 1.5M_⊙, a precise measurement of relativistic spin precession in the double pulsar system and a Galactic millisecond pulsar in an eccentric (e = 0.44 orbit around an unevolved companion. 15. Binary and Millisecond Pulsars Lorimer, D R 2008-01-01 We review the main properties, demographics and applications of binary and millisecond radio pulsars. Our knowledge of these exciting objects has greatly increased in recent years, mainly due to successful surveys which have brought the known pulsar population to over 1800. There are now 83 binary and millisecond pulsars associated with the disk of our Galaxy, and a further 140 pulsars in 26 of the Galactic globular clusters. Recent highlights include the discovery of the young relativistic binary system PSR J1906+0746, a rejuvination in globular cluster pulsar research including growing numbers of pulsars with masses in excess of 1.5 solar masses, a precise measurement of relativistic spin precession in the double pulsar system and a Galactic millisecond pulsar in an eccentric (e=0.44) orbit around an unevolved companion. 16. The binary millisecond pulsar PSR J1023+0038 during its accretion state - I. Optical variability Shahbaz, T; Nevado, S P; Rodríguez-Gil, P; Casares, J; Dhillon, V S; Marsh, T R; Littlefair, S; Leckngam, A; Poshyachinda, S 2015-01-01 We present time-resolved optical photometry of the binary millisecond redback' pulsar PSR J1023+0038 (=AY Sex) during its low-mass X-ray binary phase. The light curves taken between 2014 January and April show an underlying sinusoidal modulation due to the irradiated secondary star and accretion disc. We also observe superimposed rapid flaring on time-scales as short as ~20 s with amplitudes of ~0.1-0.5 mag and additional large flare events on time-scales of ~5-60 min with amplitudes ~0.5-1.0 mag. The power density spectrum of the optical flare light curves is dominated by a red-noise component, typical of aperiodic activity in X-ray binaries. Simultaneous X-ray and UV observations by the Swift satellite reveal strong correlations that are consistent with X-ray reprocessing of the UV light, most likely in the outer regions of the accretion disc. On some nights we also observe sharp-edged, rectangular, flat-bottomed dips randomly distributed in orbital phase, with a median duration of ~250 s and a median ingr... 17. Timing of the accreting millisecond pulsar SAX J1748.9-2021 during its 2015 outburst Sanna, A; Riggio, A; Pintore, F; Di Salvo, T; Gambino, A F; Iaria, R; Matranga, M; Scarano, F 2016-01-01 We report on the timing analysis of the 2015 outburst of the intermittent accreting millisecond X-ray pulsar SAX J1748.9-2021 observed on March 4 by the X-ray satellite XMM-Newton. By phase-connecting the time of arrivals of the observed pulses, we derived the best-fit orbital solution for the 2015 outburst. We investigated the energy pulse profile dependence finding that the pulse fractional amplitude increases with energy while no significant time lags are detected. Moreover, we investigated the previous outbursts from this source, finding previously undetected pulsations in some intervals during the 2010 outburst of the source. Comparing the updated set of orbital parameters, in particular the value of the time of passage from the ascending node, with the orbital solutions reported from the previous outbursts, we estimated for the first time the orbital period derivative corresponding with$\\dot{P}_{orb}=(1.1\\pm0.3)\\times 10^{-10}$s/s. We note that this value is significant at 3.5 sigma confidence level, ... 18. Quasi-periodic X-ray brightness fluctuations in an accreting millisecond pulsar Wijnands, R; Homan, J; Chakraborty, D; Markwardt, C B; Morgan, E H; Wijnands, Rudy; Klis, Michiel van der; Homan, Jeroen; Chakrabarty, Deepto; Markwardt, Craig B.; Morgan, Ed H. 2003-01-01 The relativistic plasma flows onto neutron stars that are accreting material from stellar companions can be used to probe strong-field gravity as well as the physical conditions in the supranuclear-density interiors of neutron stars. Plasma inhomogeneities orbiting a few kilometres above the stars are observable as X-ray brightness fluctuations on the millisecond dynamical timescale of the flows. Two frequencies in the kilohertz range dominate these fluctuations: the twin kilohertz quasi-periodic oscillations (kHz QPOs). Competing models for the origins of these oscillations (based on orbital motions) all predict that they should be related to the stellar spin frequency, but tests have been difficult because the spins were not unambiguously known. Here we report the detection of kHz QPOs from a pulsar whose spin frequency is known. Our measurements establish a clear link between kHz QPOs and stellar spin, but one not predicted by any current model. A new approach to understanding kHz QPOs is now required. We ... 19. The Accreting Millisecond X-ray Pulsar IGR J00291+5934: Evidence for a Long Timescale Spin Evolution Patruno, Alessandro 2010-01-01 Accreting Millisecond X-ray Pulsars like IGR J00291+5934 are important because it is possible to test theories of pulsar formation and evolution. They give also the possibility to constrain gravitational wave emission theories and the equation of state of ultra dense matter. Particularly crucial to our understanding is the measurement of the long term spin evolution of the accreting neutron star. An open question is whether these accreting pulsars are spinning up during an outburst and spinning down in quiescence as predicted by the recycling scenario. Until now it has been very difficult to measure torques, due to the presence of fluctuations in the pulse phases that compromise their measurements with standard coherent timing techniques. By applying a new method, I am now able to measure a spin up during an outburst and a spin down during quiescence. I ascribe the spin up (Fdot=5.1(3)x10^{-13}\\Hz/s) to accretion torques and the spin down (Fdot=-3.0(8)x10^{-15} Hz/s) to magneto dipole torques, as those observ... 20. DISCOVERY OF BURST OSCILLATIONS IN THE INTERMITTENT ACCRETION-POWERED MILLISECOND PULSAR HETE J1900.1-2455 We report the discovery of burst oscillations from the intermittent accretion-powered millisecond pulsar (AMP) HETE J1900.1-2455, with a frequency ∼1 Hz below the known spin frequency. The burst oscillation properties are far more similar to those of the non-AMPs and Aql X-1 (an intermittent AMP with a far lower duty cycle), than those of the AMPs SAX J1808.4-3658 and XTE J1814-338. We discuss the implications for models of the burst oscillation and intermittency mechanisms. 1. Constraints on Compact Star Parameters from Burst Oscillation Light Curves of the Accreting Millisecond Pulsar XTE J1814-338 Bhattacharya, S; Miller, M C; Markwardt, C B; Bhattacharyya, Sudip; Strohmayer, Tod E.; Markwardt, Craig B. 2004-01-01 Detailed modeling of the millisecond brightness oscillations from low mass X-ray binaries during thermonuclear bursts can provide us with important information about compact star parameters. Until now the implementation of this idea has not been entirely successful, largely because of the negligible amount of harmonic content in burst oscillation lightcurves. However, the recent discovery of unique, non-sinusoidal burst oscillation lightcurves from the accreting millisecond pulsar XTE J1814-338 has changed this situation. We, therefore, for the first time, make use of this opportunity to constrain compact star structure parameters effectively. In our detailed study of the lightcurves of 22 bursts we fit the burst oscillation lightcurves with fully general relativistic models that include light-bending and frame-dragging for lightcurve calculation, and compute numerically the structure of compact stars using realistic equations of state. We find that the 90% confidence interval of the dimensionless radius to m... 2. Swinging between rotation and accretion power in a binary millisecond pulsar Papitto A. 2014-01-01 While accreting mass, the X-ray emission of IGR J18245–2452 varies dramatically on time-scales ranging from a second to a few hours. We interpret a state characterised by a lower flux and pulsed fraction, and by sudden increases of the hardness of the X-ray emission, in terms of the onset of a magnetospheric centrifugal inhibition of the accretion flow. Prospects of finding new members of the newly established class of transitional pulsars are also briefly discussed. 3. Spin frequency distributions of binary millisecond pulsars A. Papitto; D.F. Torres; N. Rea; T.M. Tauris 2014-01-01 Rotation-powered millisecond radio pulsars have been spun up to their present spin period by a 108−109 yr long X-ray-bright phase of accretion of matter and angular momentum in a low-to-intermediate mass binary system. Recently, the discovery of transitional pulsars that alternate cyclically between 4. Broad-band spectral analysis of the accreting millisecond X-ray pulsar SAX J1748.9-2021 Pintore, F.; Sanna, A.; Di Salvo, T.; Del Santo, M.; Riggio, A.; D'Aì, A.; Burderi, L.; Scarano, F.; Iaria, R. 2016-04-01 We analysed a 115-ks XMM-Newton observation and the stacking of 8 d of INTEGRAL observations, taken during the raise of the 2015 outburst of the accreting millisecond X-ray pulsar SAX J1748.9-2021. The source showed numerous type-I burst episodes during the XMM-Newton observation, and for this reason we studied separately the persistent and burst epochs. We described the persistent emission with a combination of two soft thermal components, a cold thermal Comptonization component (˜2 keV) and an additional hard X-ray emission described by a power law (Γ ˜ 2.3). The continuum components can be associated with an accretion disc, the neutron star (NS) surface and a thermal Comptonization emission coming out of an optically thick plasma region, while the origin of the high-energy tail is still under debate. In addition, a number of broad (σ = 0.1-0.4 keV) emission features likely associated with reflection processes have been observed in the XMM-Newton data. The estimated 1.0-50 keV unabsorbed luminosity of the source is ˜5 × 1037 erg s-1, about 25 per cent of the Eddington limit assuming a 1.4 M⊙ NS. We suggest that the spectral properties of SAX J1748.9-2021 are consistent with a soft state, differently from many other accreting X-ray millisecond pulsars which are usually found in the hard state. Moreover, none of the observed type-I burst reached the Eddington luminosity. Assuming that the burst ignition and emission are produced above the whole NS surface, we estimate an NS radius of ˜7-8 km, consistent with previous results. 5. Discovery of the Accretion-Powered Millisecond Pulsar SWIFT 51756.9-2508 with a Low-Mass Companion Krimm, H.A.; Markwardt, C.B.; Deloye, C.J.; Romano, P.; Chakrabarty, S.; Campana. S.; Cummings, J.C.; Galloway, D.K.; Gehrels, N.; Hartman, J.M.; Kaaret, P.; Morgan, E.H.; Tueller, J 2007-01-01 We report on the discovery by the Swift Gamma-Ray Burst Explorer of the eighth known transient accretion-powered millisecond pulsar: SWIFT J1756.9-2508, as part of routine observations with the Swift Burst Alert Telescope hard X-ray transient monitor. The pulsar was subsequently observed by both the X-Ray Telescope on Swift and the Rossi X-Ray Timing Explorer Proportional Counter Array. It has a spin frequency of 182 Hz (5.5 ms) and an orbital period of 54.7 minutes. The minimum companion mass is between 0.0067 and 0.0086 Solar Mass, depending on the mass of the neutron star, and the upper limit on the mass is 0.030 Solar Mass (95% confidence level). Such a low mass is inconsistent with brown dwarf models. and comparison with white dwarf models suggests that the companion is a He-dominated donor whose thermal cooling has been at least modestly slowed by irradiation from the accretion flux. No X-ray bursts. dips, eclipses or quasi-periodic oscillations were detected. The current outburst lasted approx. 13 days and no earlier outbursts were found in archival data. 6. Application of the relativistic precession model to the accreting millisecond X-ray pulsar IGR J17511-3057 Stefanov, I. Zh. 2016-03-01 The observation of a pair of simultaneous twin kHz QPOs in the power density spectrum of a neutron star or a black hole allows its mass-angular-momentum relation to be constrained. Situations in which the observed simultaneous pairs are more than one allow the different models of the kHz QPOs to be falsified. Discrepancy between the estimates coming from the different pairs would call the used model into question. In the current paper, the relativistic precession model is applied to the twin kHz QPOs that appear in the light curves of three groups of observations of the accreting millisecond X-ray pulsar IGR J17511-3057. It was found that the predictions of one of the groups are practically in conflict with the other two. Another interesting result is that the region in which the kHz QPOs have been born is rather broad and extends quite far from the ISCO. 7. Application of the relativistic precession model to the accreting millisecond X-ray pulsar IGR J17511-3057 Stefanov, Ivan Zh 2015-01-01 The observation of a pair of simultaneous twin kHz QPOs in the power density spectrum of a neutron star or a black hole allows its mass-angular-momentum relation to be constrained. Situations in which the observed simultaneous pairs are more than one allow the different models of the kHz QPOs to be falsified. Discrepancy between the estimates coming from the different pairs would call the used model into question. In the current paper the relativistic precession model is applied to the twin kHz QPOs that appear in the light curves of three groups of observations of the accreting millisecond X-ray pulsar IGR J17511-3057. It was found that the predictions of one of the groups are practically in conflict with the other two. Another interesting result is that the region in which the kHz QPOs have been born is rather broad and extends quite far from the ISCO. 8. The Luminosity and Energy Dependence of Pulse Phase Lags in the Accretion-powered Millisecond Pulsar SAX J1808.4-3658 Hartman, Jacob M; Chakrabarty, Deepto 2008-01-01 Soft phase lags, in which X-ray pulses in lower energy bands arrive later than pulses in higher energy bands, have been observed in nearly all accretion-powered millisecond pulsars, but their origin remains an open question. In a study of the 2.5 ms accretion-powered pulsar SAX J1808.4-3658, we report that the magnitude of these lags is strongly dependent on the accretion rate. During the brightest stage of the outbursts from this source, the lags increase in magnitude as the accretion rate drops; when the outbursts enter their dimmer flaring-tail stage, the relationship reverses. We evaluate this complex dependence in the context of two theoretical models for the lags, one relying on the scattering of photons by the accretion disk and the other invoking a two-component model for the photon emission. In both cases, the turnover suggests that we are observing the source transitioning into the "propeller" accretion regime. 9. X-ray coherent pulsations during a sub-luminous accretion disk state of the transitional millisecond pulsar XSS J12270-4859 Papitto, A; Belloni, T M; Burgay, M; Pellizzoni, A; Possenti, A; Torres, D F 2014-01-01 Radio millisecond pulsars in binary systems are spun up to their present period by a Gyr-long phase of accretion of the mass transferred from a low-mass companion star. Recently, three such systems have been observed to switch between an accretion disk state and a radio pulsar regime over time-scales ranging from weeks to years, and were dubbed transitional millisecond pulsars. These sources have been often found in a sub-luminous accretion disk state, characterized by a lower X-ray luminosity (~1E33-1E34 erg/s) than the level usually attained by similar sources during X-ray outbursts (~1E36 erg/s), and by a bright radio and gamma-ray emission. The physical mechanism acting in this enigmatic state is still unclear. Here, we present the first detection of X-ray pulsations from the transitional millisecond pulsar XSS J12270-4859. Pulsations were detected by XMM-Newton during an observation performed while the source was in a sub-luminous accretion disk state. They had an rms amplitude of (7.7+/-0.5)% with a sec... 10. Formation of Binary Millisecond Pulsars by Accretion-Induced Collapse of White Dwarfs under Wind-Driven Evolution Ablimit, Iminhaji 2014-01-01 Accretion-induced collapse of massive white dwarfs (WDs) has been proposed to be an important channel to form binary millisecond pulsars (MSPs). Recent investigations on thermal timescale mass transfer in WD binaries demonstrate that the resultant MSPs are likely to have relatively wide orbit periods ($\\gtrsim 10$days). Here we calculate the evolution of WD binaries taking into account the excited wind from the companion star induced by X-ray irradiation of the accreting WD, which may drive rapid mass transfer even when the companion star is less massive than the WD. This scenario can naturally explain the formation of the strong-field neutron star in the low-mass X-ray binary 4U 1822$-$37. After AIC the mass transfer resumes when the companion star refills its Roche lobe, and the neutron star is recycled due to mass accretion. A large fraction of the binaries will evolve to become binary MSPs with a He WD companion, with the orbital periods distributed between$\\gtrsim 0.1$day and$\\lesssim 30$days, while... 11. The X-ray spectrum of the newly discovered accreting millisecond pulsar IGR J17511-3057 Papitto, A; Di Salvo, T; Burderi, L; D'Aì, A; Iaria, R; Bozzo, E; Menna, M T 2010-01-01 We report on an XMM-Newton observation of the accreting millisecond pulsar, IGR J17511-3057. Pulsations at 244.8339512(1) Hz are observed with an RMS pulsed fraction of 14.4(3)%. A precise solution for the P_orb=12487.51(2)s binary system is derived. The measured mass function indicates a main sequence companion with a mass between 0.15 and 0.44 Msun. The XMM-Newton spectrum of the source can be modelled by at least three components, multicoloured disc emission, thermal emission from the NS surface and thermal Comptonization emission. Spectral fit of the XMM-Newton data and of the RXTE data, taken in a simultaneous temporal window, constrain the Comptonization parameters: the electron temperature, kT_e=51(+6,-4) keV, is rather high, while the optical depth (tau=1.34(+0.03,-0.06)) is moderate. The energy dependence of the pulsed fraction supports the interpretation of the cooler thermal component as coming from the accretion disc, and indicates that the Comptonizing plasma surrounds the hot spots on the NS sur... 12. Broad-band spectral analysis of the accreting millisecond X-ray pulsar SAX J1748.9-2021 Pintore, Fabio; Di Salvo, Tiziana; Del Santo, Melania; Riggio, Alessandro; D'Aì, Antonino; Burderi, Luciano; Scarano, Fabiana; Iaria, Rosario 2016-01-01 We analyzed a 115 ks XMM-Newton observation and the stacking of 8 days of INTEGRAL observations, taken during the raise of the 2015 outburst of the accreting millisecond X-ray pulsar SAX J1748.9-2021. The source showed numerous type-I burst episodes during the XMM-Newton observation, and for this reason we studied separately the persistent and burst epochs. We described the persistent emission with a combination of two soft thermal components, a cold thermal Comptonization component (~2 keV) and an additional hard X-ray emission described by a power-law (photon index ~2.3). The continuum components can be associated with an accretion disc, the neutron star (NS) surface and a thermal Comptonization emission coming out of an optically thick plasma region, while the origin of the high energy tail is still under debate. In addition, a number of broad (~0.1-0.4 keV) emission features likely associated to reflection processes have been observed in the XMM-Newton data. The estimated 1.0-50 keV unabsorbed luminosity ... 13. Millisecond Pulsars in Close Binaries Tauris, Thomas M 2015-01-01 In this Habilitationsschrift (Habilitation thesis) I present my research carried out over the last four years at the Argelander Institute for Astronomy (AIfA) and the Max Planck Institute for Radio Astronomy (MPIfR). The thesis summarizes my main findings and has been written to fulfill the requirements for the Habilitation qualification at the University of Bonn. Although my work is mainly focused on the topic of millisecond pulsars (MSPs), there is a fairly broad spread of research areas ranging from the formation of neutron stars (NSs) in various supernova (SN) events, to their evolution, for example, via accretion processes in binary and triple systems, and finally to their possible destruction in merger events. The thesis is organized in the following manner: A general introduction to neutron stars and millisecond pulsars is given in Chapter 1. A selection of key papers published in 2011-2014 are presented in Chapters 2-10, ordered within five main research areas (ultra-stripped SNe in close binaries, ma... 14. The origin of planets orbiting millisecond pulsars Tavani, Marco; Brookshaw, Leigh 1992-01-01 A model for the formation of planets around millisecond pulsar which no longer have stellar companions is suggested. Detailed hydrodynamical models are presented which suggest that planet formation can occur either in a low-mass X-ray binary progenitor to a progenitor of a star-vaporizing millisecond pulsar when the neutron star is accreting material driven off its companion by X-ray irradiation or after a pulsar has formed and is vaporizing its companion. In both cases a circumbinary disk is created in which planets can form on a timescale of 10 exp 5 to 10 exp 6 yrs and the planets can survive a second phase in which the companion star moves toward the pulsar and is completely vaporized. 15. Orbital Evolution Measurement of the Accreting Millisecond X-ray Pulsar SAX J1808.4–3658 Chetana Jain; Anjan Dutta; Biswajit Paul 2007-12-01 We present results from a pulse timing analysis of the accretion-powered millisecond X-ray pulsar SAX J1808.4–3658 using X-ray data obtained during four outbursts of this source. Extensive observations were made with the proportional counter array of the Rossi X-ray Timing Explorer (RXTE) during the four outbursts that occurred in 1998, 2000, 2002 and 2005. Instead of measuring the arrival times of individual pulses or the pulse arrival time delay measurement that is commonly used to determine the orbital parameters of binary pulsars, we have determined the orbital ephemeris during each observation by optimizing the pulse detection against a range of trial ephemeris values. The source exhibits a significant pulse shape variability during the outbursts. The technique used by us does not depend on the pulse profile evolution, and is therefore, different from the standard pulse timing analysis. Using 27 measurements of orbital ephemerides during the four outbursts spread over more than 7 years and more than 31,000 binary orbits, we have derived an accurate value of the orbital period of 7249.156862(5) s (MJD = 50915) and detected an orbital period derivative of (3.14 ± 0.21) × 10-12 s s-1. We have included a table of the 27 mid-eclipse time measurements of this source that will be valuable for further studies of the orbital evolution of the source, especially with ASTROSAT. We point out that the measured rate of orbital period evolution is considerably faster than the most commonly discussed mechanisms of orbital period evolution like mass transfer, mass loss from the companion star and gravitational wave radiation. The present time scale of orbital period change, 73 Myr is therefore likely to be a transient high value of period evolution and similar measurements during subsequent outbursts of SAX J1808.4–3658 will help us to resolve this. 16. Millisecond pulsars: Timekeepers of the cosmos Kaspi, Victoria M. 1995-01-01 A brief discussion on the characteristics of pulsars is given followed by a review of millisecond pulsar discoveries including the very first, PRS B1937+21, discovered in 1982. Methods of timing millisecond pulsars and the accuracy of millisecond pulsars as clocks are discussed. Possible reasons for the pulse residuals, or differences between the observed and predicted pulse arrival times for millisecond pulsars, are given. 17. Formation of Millisecond Pulsars in Globular Clusters Ivanova, Natalia; Rasio, Frederic A 2007-01-01 In this contribution we discuss how neutron stars are produced and retained in globular clusters, outlining the most important dynamical channels and evolutionary events that affect thepopulation of mass-transferring binaries with neutron stars and result in the formation of recycled pulsars. We confirm the importance of electron-capture supernovae in globular clusters as the major supplier of retained neutron stars.By comparing the observed millisecond pulsar population and the results obtained from simulations, we discuss several constraints on the evolution of mass-transferring systems.In particular, we find that in our cluster model the following mass-gaining events create populations of MSPs that do not match the observations (with respect to binary periods and companion masses or the number of produced systems) and therefore likely do not lead to NSs spun up to millisecond periods: (i) accretion during a common envelope event with a NS formed through accretion-induced collapse, and (ii) mass transfer fr... 18. Identification of the High-Energy Gamma-Ray Source 3FGL J1544.6-1125 as a Transitional Millisecond Pulsar Binary in an Accreting State Bogdanov, Slavko 2015-01-01 We present X-ray, ultraviolet, and optical observations of 1RXS J154439.4-112820, the most probable counterpart of the unassociated Fermi LAT source 3FGL J1544.6-1125. The optical data reveal rapid variability, which is a feature of accreting systems. The X-ray data exhibit large-amplitude flux variations in the form of fast switching (within ~10 s) between two distinct flux levels that differ by a factor of$\\approx$10. The detailed optical and X-ray behavior is virtually identical to that seen in the accretion-disk-dominated states of the transitional millisecond pulsar binaries PSR J1023+0038 and XSS J12270-4859, which are also associated with$\\gamma$-ray sources. Based on the available observational evidence, we conclude that 1RXS J154439.4-112820 and 3FGL J1544.6-1125 are the same object, with the X-rays arising from intermittent low-luminosity accretion onto a millisecond pulsar and the$\\gamma$-rays originating from an accretion-driven outflow. 1RXS J154439.4-112820 is only the fourth$\\gamma$-ray emi... 19. Formation of millisecond pulsars with CO white dwarf companions - II. Accretion, spin-up, true ages and comparison to MSPs with He white dwarf companions Tauris, Thomas M; Kramer, Michael 2012-01-01 Millisecond pulsars (MSPs) are mainly characterised by their spin periods, B-fields and masses - quantities which are largely affected by previous interactions with a companion star in a binary system. In this paper, we investigate the formation mechanism of MSPs by considering the pulsar recycling process in both intermediate-mass X-ray binaries (IMXBs) and low-mass X-ray binaries (LMXBs). The IMXBs mainly lead to the formation of binary MSPs with a massive carbon-oxygen (CO) or an oxygen-neon-magnesium white dwarf (ONeMg WD) companion, whereas the LMXBs form recycled pulsars with a helium white dwarf (He WD) companion. We discuss the accretion physics leading to the spin-up line in the PPdot-diagram and demonstrate that such a line cannot be uniquely defined. We derive a simple expression for the amount of accreted mass needed for any given pulsar to achieve its equilibrium spin and apply this to explain the observed differences of the spin distributions of recycled pulsars with different types of companion... 20. Birth and evolution of neutron stars: Issues raised by millisecond pulsars; Proceedings of the eighth workshop, Green Bank, WV, June 6-8, 1984 Observations of millisecond pulsars are discussed, taking into account a review of millisecond pulsars, arrival time observations of the 1.6 millisecond pulsar 1937 + 214, a 6.1 millisecond binary pulsar, polarimetry of the two fastest pulsars, an optical synchrotron nebula around the X-ray pulsar 0540-693, optical observations of the millisecond pulsars PSR 1937 + 214 and PSR 1935 + 29, and a single pulse study of the millisecond pulsar 1937 + 214. The life history of millisecond pulsars is examined, giving attention to the origin of neutron stars, models for the formation of binary and millisecond radio pulsars, isolated and binary millisecond pulsars and accretion spun-up neutron stars, the period distribution of fast pulsars, the origin of pulsar velocities, a model of radio emission of the millisecond pulsar 1937 + 214, and a study of pulsar luminosities. Other subjects investigated are related to the physics of rapidly rotating neutron stars, a summary of general theoretical issues, and searches 1. Cosmic-ray positrons from millisecond pulsars Venter, C; Harding, A K; Gonthier, P L; Büsching, I 2015-01-01 Observations by the Fermi Large Area Telescope of gamma-ray millisecond pulsar light curves imply copious pair production in their magnetospheres, and not exclusively in those of younger pulsars. Such pair cascades may be a primary source of Galactic electrons and positrons, contributing to the observed enhancement in positron flux above ~10 GeV. Fermi has also uncovered many new millisecond pulsars, impacting Galactic stellar population models. We investigate the contribution of Galactic millisecond pulsars to the flux of terrestrial cosmic-ray electrons and positrons. Our population synthesis code predicts the source properties of present-day millisecond pulsars. We simulate their pair spectra invoking an offset-dipole magnetic field. We also consider positrons and electrons that have been further accelerated to energies of several TeV by strong intrabinary shocks in black widow and redback systems. Since millisecond pulsars are not surrounded by pulsar wind nebulae or supernova shells, we assume that the p... 2. Wideband Timing of Millisecond Pulsars Pennucci, Timothy; Demorest, Paul; Ransom, Scott M.; North American Nanohertz ObservatoryGravitational Waves (Nanograv) 2015-01-01 The use of backend instrumentation capable of real-time coherent dedispersion of relatively large fractional bandwidths has become commonplace in pulsar astronomy. However, along with the desired increase in sensitivity to pulsars' broadband signals, a larger instantaneous bandwidth brings a number of potentially aggravating effects that can lead to degraded timing precision. In the case of high-precision timing experiments, such as the one being carried out by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), subtle effects such as unmodeled intrinsic profile evolution with frequency, interstellar scattering, and dispersion measure variation are potentially capable of reducing the experiment's sensitivity to a gravitational wave signal. In order to account for some of these complications associated with wideband observations, we augmented the traditional algorithm by which the fundamental timing quantities are measured. Our new measurement algorithm accommodates an arbitrary two-dimensional model portrait'' of a pulsar's total intensity as a function of observing frequency and rotational phase, and simultaneously determines the time-of-arrival (TOA), the dispersion measure (DM), and per-frequency-channel amplitudes that account for interstellar scintillation. Our publicly available python code incorporates a Gaussian-component modeling routine that allows for independent component evolution with frequency, a fiducial component'', and the inclusion of scattering. Here, we will present results from the application of our wideband measurement scheme to the suite of NANOGrav millisecond pulsars, which aimed to determine the level at which the experiment is being harmed by unmodeled profile evolution. We have found thus far, and expect to continue to find, that our new measurements are at least as good as those from traditional techniques. At a minimum, by largely reducing the volume of TOAs we will decrease the computational demand 3. Binary Millisecond Pulsar Discovery via Gamma-Ray Pulsations Pletsch, H J; Fehrmann, H; Allen, B; Kramer, M; Aulbert, C; Ackermann, M; Ajello, M; de Angelis, A; Atwood, W B; Baldini, L; Ballet, J; Barbiellini, G; Bastieri, D; Bechtol, K; Bellazzini, R; Borgland, A W; Bottacini, E; Brandt, T J; Bregeon, J; Brigida, M; Bruel, P; Buehler, R; Buson, S; Caliandro, G A; Cameron, R A; Caraveo, P A; Casandjian, J M; Cecchi, C; Celik, Ö; Charles, E; Chaves, R C G; Cheung, C C; Chiang, J; Ciprini, S; Claus, R; Cohen-Tanugi, J; Conrad, J; Cutini, S; D'Ammando, F; Dermer, C D; Digel, S W; Drell, P S; Drlica-Wagner, A; Dubois, R; Dumora, D; Favuzzi, C; Ferrara, E C; Franckowiak, A; Fukazawa, Y; Fusco, P; Gargano, F; Gehrels, N; Germani, S; Giglietto, N; Giordano, F; Giroletti, M; Godfrey, G; Grenier, I A; Grondin, M -H; Grove, J E; Guiriec, S; Hadasch, D; Hanabata, Y; Harding, A K; Hartog, P R den; Hayashida, M; Hays, E; Hill, A B; Hou, X; Hughes, R E; Johannesson, G; Jackson, M S; Jogler, T; Johnson, A S; Johnson, W N; Kataoka, J; Kerr, M; Knödlseder, J; Kuss, M; Lande, J; Larsson, S; Latronico, L; Lemoine-Goumard, M; Longo, F; Loparco, F; Lovellette, M N; Lubrano, P; Massaro, F; Mayer, M; Mazziotta, M N; McEnery, J E; Mehault, J; Michelson, P F; Mitthumsiri, W; Mizuno, T; Monzani, M E; Morselli, A; Moskalenko, I V; Murgia, S; Nakamori, T; Nemmen, R; Nuss, E; Ohno, M; Ohsugi, T; Omodei, N; Orienti, M; Orlando, E; de Palma, F; Paneque, D; Perkins, J S; Piron, F; Pivato, G; Porter, T A; Raino, S; Rando, R; Ray, P S; Razzano, M; Reimer, A; Reimer, O; Reposeur, T; Ritz, S; Romani, R W; Romoli, C; Sanchez, D A; Parkinson, P M Saz; Schulz, A; Sgro, C; Silva, E do Couto e; Siskind, E J; Smith, D A; Spandre, G; Spinelli, P; Suson, D J; Takahashi, H; Tanaka, T; Thayer, J B; Thayer, J G; Thompson, D J; Tibaldo, L; Tinivella, M; Troja, E; Usher, T L; Vandenbroucke, J; Vasileiou, V; Vianello, G; Vitale, V; Waite, A P; Winer, B L; Wood, K S; Wood, M; Yang, Z; Zimmer, S; 10.1126/science.1229054 2012-01-01 Millisecond pulsars (MSPs), old neutron stars spun-up by accreting matter from a companion star, can reach high rotation rates of hundreds of revolutions per second. Until now, all such "recycled" rotation-powered pulsars have been detected by their spin-modulated radio emission. In a computing-intensive blind search of gamma-ray data from the Fermi Large Area Telescope (with partial constraints from optical data), we detected a 2.5-millisecond pulsar, PSR J1311-3430. This unambiguously explains a formerly unidentified gamma-ray source that had been a decade-long enigma, confirming previous conjectures. The pulsar is in a circular orbit with an orbital period of only 93 minutes, the shortest of any spin-powered pulsar binary ever found. 4. On Low Mass X-ray Binaries and Millisecond Pulsar Burderi, Luciano 2013-01-01 The detection, in 1998, of the first Accreting Millisecond Pulsar, started an exciting season of continuing discoveries in the fashinating field of compact binary systems harbouring a neutron star. Indeed, in these last three lustres, thanks to the extraordinary performances of astronomical detectors, on ground as well as on board of satellites, mainly in the Radio, Optical, X-ray, and Gamma-ray bands, astrophysicists had the opportunity to thoroughly investigate the so-called Recycling Scenario: the evolutionary path leading to the formation of a Millisecond Radio Pulsar. The most intriguing phase is certainly the spin-up stage during which, because of the accretion of matter and angular momentum, the neutron star accumulates an extraordinary amount of mechanical rotational energy, up to one percent of its whole rest-mass energy. These millisecond spinning neutron stars are truly extreme physical objects: General and Special Relativity are fully in action, since their surfaces, attaining speeds close to one ... 5. Stokes tomography of radio pulsar magnetospheres. II. Millisecond pulsars Chung, C T Y 2011-01-01 The radio polarization characteristics of millisecond pulsars (MSPs) differ significantly from those of non-recycled pulsars. In particular, the position angle (PA) swings of many MSPs deviate from the S-shape predicted by the rotating vector model, even after relativistic aberration is accounted for, indicating that they have non-dipolar magnetic geometries, likely due to a history of accretion. Stokes tomography uses phase portraits of the Stokes parameters as a diagnostic tool to infer a pulsar's magnetic geometry and orientation. This paper applies Stokes tomography to MSPs, generalizing the technique to handle interpulse emission. We present an atlas of look-up tables for the Stokes phase portraits and PA swings of MSPs with current-modified dipole fields, filled core and hollow cone beams, and two empirical linear polarization models. We compare our look-up tables to data from 15 MSPs and find that the Stokes phase portraits for a current-modified dipole approximately match several MSPs whose PA swings ... 6. The disturbance of a millisecond pulsar magnetosphere Shannon, R M; Kerr, M; Bailes, M; Bhat, N D R; Coles, W A; Dai, S; Dempsey, J; Hobbs, G; Keith, M J; Lasky, P D; Levin, Y; Manchester, R N; Oslowski, S; Ravi, V; Reardon, D J; Rosado, P A; Spiewak, R; van Straten, W; Toomey, L; Wang, J -B; Wen, L; You, X -P; Zhu, X -J 2016-01-01 Pulsar timing has enabled some of the strongest tests of fundamental physics. Central to the technique is the assumption that the detected radio pulses can be used to accurately measure the rotation of the pulsar. Here we report on a broad-band variation in the pulse profile of the millisecond pulsar J1643-1224. A new component of emission suddenly appears in the pulse profile, decays over 4 months, and results in a permanently modified pulse shape. Profile variations such as these may be the origin of timing noise observed in other millisecond pulsars. The sensitivity of pulsar-timing observations to gravitational radiation can be increased by accounting for this variability. 7. A Search for Radio Millisecond Pulsars Sayer, Ronald Winston 1996-01-01 We have built a data acquisition backend for radio pulsar search observations carried out at the NRAO 140 -foot telescope in Green Bank, West Virginia. Our system sampled 512 spectral channels over 40 MHz every 256 mus, reduced samples to one-bit precision, and wrote the resulting data stream onto magnetic tape for later, off-line processing. We have completed three surveys with this backend. In the first survey, we searched most of the Northern Hemisphere for millisecond radio pulsars. Previous surveys directed towards most of the region covered had not been as sensitive to pulsars with millisecond periods. We obtained high quality data for 15,876 deg^2 of sky. Eight new pulsars were discovered and 76 previously known pulsars were detected. Two of the eight new pulsars (PSR J1022+1001 and PSR J1518+4904) are millisecond pulsars in binary systems. PSR J1518+4904 is a 41 ms radio pulsar in an eccentric (e = 0.25) 8.6 day orbit with another stellar object, probably another neutron star. It is only the fifth double neutron star system known. The system's relativistic advance of periastron has been measured to be ˙omega = 0.0112 +/- 0.0002 ^circ yr^{-1}, implying that the total mass of the pair of stars is 2.65 +/-0.07Modot. We have searched for radio pulsar companions to 40 nearby OB runaway stars. No pulsar companions to OB runaways were discovered. One previously unknown pulsar, PSR J2044+4614, was discovered while observing towards target O star BD+45,3260. However, follow-up timing observations reveal that the pulsar is not associated with the target O star. Assuming standard models for the pulsar beaming fraction and luminosity function, we conclude that most OB runaways do not have pulsar companions. We have completed a survey for pulsed radio signals towards 27 gamma-ray sources detected by the EGRET instrument of the Compton Gamma Ray Observatory. No new pulsars were discovered. 8. The neutron star transient and millisecond pulsar in M28: from sub-luminous accretion to rotation-powered quiescence Linares, Manuel; Heinke, Craig; Wijnands, Rudy; Patruno, Alessandro; Altamirano, Diego; Homan, Jeroen; Bogdanov, Slavko; Pooley, David 2013-01-01 The X-ray transient IGR J18245-2452 in the globular cluster M28 contains the first neutron star (NS) seen to switch between rotation-powered and accretion-powered pulsations. We analyse its 2013 March-April 25d-long outburst as observed by Swift, which had a peak bolometric luminosity of ~6% of the Eddington limit (L$_{E}$), and give detailed properties of the thermonuclear burst observed on 2013 April 7. We also present a detailed analysis of new and archival Chandra data, which we use to study quiescent emission from IGR J18245-2452 between 2002 and 2013. Together, these observations cover almost five orders of magnitude in X-ray luminosity (L$_X$, 0.5-10 keV). The Swift spectrum softens during the outburst decay (photon index$\\Gamma$from 1.3 above L$_X$/L$_{E}$=10$^{-2}$to ~2.5 at L$_X$/L$_{E}$=10$^{-4}$), similar to other NS and black hole (BH) transients. At even lower luminosities, deep Chandra observations reveal hard ($\\Gamma$=1-1.5), purely non-thermal and highly variable X-ray emission in quiesce... 9. Formation of black widows and redbacks -- two distinct populations of eclipsing binary millisecond pulsars Chen, Hai-Liang; Tauris, Thomas M; Han, Zhanwen 2013-01-01 Eclipsing binary millisecond pulsars (the so-called black widows and redbacks) can provide important information about accretion history, pulsar irradiation of their companion stars and the evolutionary link between accreting X-ray pulsars and isolated millisecond pulsars. However, the formation of such systems is not well understood, nor the difference in progenitor evolution between the two populations of black widows and redbacks. Whereas both populations have orbital periods between$0.1-1.0\\;{\\rm days}$their companion masses differ by an order of magnitude. In this paper, we investigate the formation of these systems via evolution of converging low-mass X-ray binaries by employing the MESA stellar evolution code. Our results confirm that one can explain the formation of most of these eclipsing binary millisecond pulsars using this scenario. More notably, we find that the determining factor for producing either black widows or redbacks is the efficiency of the irradiation process, such that the redbacks ... 10. A millisecond pulsar timing array Hobbs, George; Manchester, Dick; Sarkissian, John; Bailes, Matthew; Bhat, Ramesh; Keith, Michael; Burke-Spolaor, Sarah; Coles, William; van Straten, Willem; Ravi, Vikram; Oslowski, Stefan; Khoo, Jonathan; Shannon, Ryan; Wang, Jingbo; Levin, Yuri 2013-10-01 The Parkes Pulsar Timing Array (PPTA) project has three primary goals: (a) detection of gravitational waves from astronomical sources, (b) establishment of a pulsar timescale, and (c) improvement of our understanding of Solar-system dynamics. There are many secondary goals, some astrophysical and some instrumental/technique oriented. Achievement of these ambitious primary goals requires frequent observations of at least 20 MSPs at two or preferably three widely spaced frequencies over several years. We wish to continue observing the PPTA sample at intervals of 2-3 weeks using both the 10/50cm and Multibeam receivers. The digital filterbanks (PDFB3, PDFB4) and the baseband systems (CPSR2; APSR) are used for data recording. With the new instruments and development of an efficient pipeline processing system, we have achieved the world's best pulsar timing precision. We are collaborating with the European and North American pulsar timing array groups (EPTA and NANOGrav, respectively) to obtain more frequent observations and a larger pulsar sample. Because of the high sensitivity and wide bandwidths required, RFI mitigation is an important part of the project. We request continuing status for this project. 11. Gemini optical observations of binary millisecond-pulsars Testa, V; Pallanca, C; Corongiu, A; Ferraro, F R 2015-01-01 Milli-second pulsars (MSPs) are rapidly spinning neutron stars, with spin periods P_s <= 10 ms, which have been most likely spun up after a phase of matter accretion from a companion star. In this work we present the results of the search for the companion stars of four binary milli-second pulsars, carried out with archival data from the Gemini South telescope. Based upon a very good positional coincidence with the pulsar radio coordinates, we likely identified the companion stars to three MSPs, namely PSRJ0614-3329 (g=21.95 +- 0.05), J1231-1411 (g=25.40 +-0.23), and J2017+0603 (g=24.72 +- 0.28). For the last pulsar (PSRJ0613-0200) the identification was hampered by the presence of a bright star (g=16 +- 0.03) at \\sim 2" from the pulsar radio coordinates and we could only set 3-sigma upper limits of g=25.0, r= 24.3, and i= 24.2 on the magnitudes of its companion star. The candidate companion stars to PSRJ0614-3329, J1231-1411, and J2017+0603 can be tentatively identified as He white dwarfs (WDs) on the bas... 12. ASSESSING THE ROLE OF SPIN NOISE IN THE PRECISION TIMING OF MILLISECOND PULSARS We investigate rotational spin noise (referred to as timing noise) in non-accreting pulsars: millisecond pulsars, canonical pulsars, and magnetars. Particular attention is placed on quantifying the strength and non-stationarity of timing noise in millisecond pulsars because the long-term stability of these objects is required to detect nanohertz gravitational radiation. We show that a single scaling law is sufficient to characterize timing noise in millisecond and canonical pulsars while the same scaling law underestimates the levels of timing noise in magnetars. The scaling law, along with a detailed study of the millisecond pulsar B1937+21, leads us to conclude that timing noise is latent in most millisecond pulsars and will be measurable in many objects when better arrival time estimates are obtained over long data spans. The sensitivity of a pulsar timing array to gravitational radiation is strongly affected by any timing noise. We conclude that detection of proposed gravitational wave backgrounds will require the analysis of more objects than previously suggested over data spans that depend on the spectra of both the gravitational wave background and of the timing noise. It is imperative to find additional millisecond pulsars in current and future surveys in order to reduce the effects of timing noise. 13. Phase Coherent Observations and Millisecond Pulsar Searches Shrauner, Jay Arthur 1997-07-01 new pulsars and detected 14 that were previously known. One of these new pulsars, PSR J0621+1002, is a millisecond pulsar with a relatively large mass companion. This system is of special interest because the relativistic advance of periastron should be measurable within a few years. 14. Implications of the PSR 1257+12 Planetary System for Isolated Millisecond Pulsars Miller, M C; Hamilton, Douglas P. 2000-01-01 The first extrasolar planets were discovered in 1992 around the millisecond pulsar PSR 1257+12. We show that recent developments in the study of accretion onto magnetized stars, plus the existence of the innermost, moon-sized planet in the PSR 1257+12 system, suggest that the pulsar was born with approximately its current rotation frequency and magnetic moment. If so, this has important implications for the formation and evolution of neutron star magnetic fields as well as for the formation of planets around pulsars. In particular, it suggests that some and perhaps all isolated millisecond pulsars may have been born with high spin rates and low magnetic fields instead of having been recycled by accretion. 15. Neutron Star Population Dynamics; 1, Millisecond Pulsars Cordes, J M; Chernoff, David F. 1997-01-01 We study the field millisecond pulsar (MSP) population to infer its intrinsic distribution in spin period and luminosity and to determine its spatial distribution within the Galaxy. Our likelihood analysis on data from extant surveys (22 pulsars with periods 0.65 ms (99% confidence), a period distribution proportional to P^{-2.0 +- 0.33} and a pseudo-luminosity distribution proportional to L_p^{-2.0 +- 0.2} (where L_p = flux density times distance^2, for L_p >= 1.1 mJy kpc^2). We find a vertical scale height 0.65{+0.16,-0.12} kpc. We use our results to estimate the total number and birthrate of MSPs in the disk of the Galaxy. We limit the density contribution of a diffuse halo-like component to <1% of the midplane value. The MSP velocity dispersion is smaller that that of young, long-period pulsars by about a factor of 5. Our best estimate of the 1D velocity kick that is unique to MSP evolution is approximately 40 km s^-1. We discuss the evolutionary relationship of MSPs and low-mass X-ray binaries and pr... 16. The 2015 outburst of the accreting millisecond pulsar IGR J17511-3057 as seen by INTEGRAL, Swift and XMM-Newton Papitto, A; Sanchez-Fernandez, C; Romano, P; Torres, D F; Ferrigno, C; Kajava, J J E; Kuulkers, E 2016-01-01 We report on INTEGRAL, Swift and XMM-Newton observations of IGR J17511-3057 performed during the outburst that occurred between March 23 and April 25, 2015. The source reached a peak flux of 0.7(2)E-9 erg/cm$^2$/s and decayed to quiescence in approximately a month. The X-ray spectrum was dominated by a power-law with photon index between 1.6 and 1.8, which we interpreted as thermal Comptonization in an electron cloud with temperature > 20 keV . A broad ({\\sigma} ~ 1 keV) emission line was detected at an energy (E = 6.9$^{+0.2}_{-0.3}$keV) compatible with the K{\\alpha} transition of ionized Fe, suggesting an origin in the inner regions of the accretion disk. The outburst flux and spectral properties shown during this outburst were remarkably similar to those observed during the previous accretion event detected from the source in 2009. Coherent pulsations at the pulsar spin period were detected in the XMM-Newton and INTEGRAL data, at a frequency compatible with the value observed in 2009. Assuming that the so... 17. X-ray bounds on the r-mode amplitude in millisecond pulsars Schwenzer, Kai; Güver, Tolga; Vurgun, Eda 2016-01-01 r-mode astroseismology provides a unique way to study the internal composition of compact stars. Due to their precise timing, recycled millisecond radio pulsars present a particularly promising class of sources. Although their thermal properties are still poorly constrained, X-ray data is very useful for astroseismology since r-modes could strongly heat a star. Using known and new upper bounds on the temperatures and luminosities of several non-accreting millisecond radio pulsars we derive bounds on the r-mode amplitude as low as$\\alpha\\lesssim10^{-8}$and discuss the impact on scenarios for their internal composition. 18. Rotation and Accretion Powered Pulsars Pulsar astrophysics has come a long way in the 40 years since the discovery of the first pulsar by Bell and Hewish. From humble beginnings as bits of 'scruff' on the Cambridge University group's chart recorder paper, the field of pulsars has blossomed into a major area of mainstream astrophysics, with an unparalleled diversity of astrophysical applications. These range from Nobel-celebrated testing of general relativity in the strong-field regime to constraining the equation-of-state of ultradense matter; from probing the winds of massive stars to globular cluster evolution. Previous notable books on the subject of pulsars have tended to focus on some particular topic in the field. The classic text Pulsars by Manchester and Taylor (1977 San Francisco, CA: Freeman) targeted almost exclusively rotation-powered radio pulsars, while the Meszaros book High-Energy Radiation from Magnetized Neutron Stars (1992 Chicago, IL: University of Chicago Press) considered both rotation- and accretion-powered neutron stars, but focused on their radiation at x-ray energies and above. The recent book Neutron Stars 1 by Haensel et al (2007 Berlin: Springer) considers only the equation of state and neutron-star structure. Into this context appears Rotation and Accretion Powered Pulsars, by Pranab Ghosh. In contrast to other books, here the author takes an encyclopedic approach and attempts to synthesize practically all of the major aspects of the two main types of neutron star. This is ambitious. The only comparable undertaking is the useful but more elementary Lyne and Graham-Smith text Pulsar Astronomy (1998 Cambridge: Cambridge University Press), or Compact Stellar X-ray Sources (eds Lewin and van der Klis, 2006 Cambridge: Cambridge University Press), an anthology of technical review articles that also includes black hole topics. Rotation and Accretion Powered Pulsars thus fills a clear void in the field, providing a readable, graduate-level book that covers nearly everything you 19. A LOFAR Census of Millisecond Pulsars Kondratiev, V I; Hessels, J W T; Bilous, A V; Stappers, B W; Kramer, M; Keane, E F; Noutsos, A; Osłowski, S; Breton, R P; Hassall, T E; Alexov, A; Cooper, S; Falcke, H; Grießmeier, J -M; Karastergiou, A; Kuniyoshi, M; Pilia, M; Sobey, C; ter Veen, S; Weltevrede, P; Bell, M E; Broderick, J W; Corbel, S; Eislöffel, J; Markoff, S; Rowlinson, A; Swinbank, J D; Wijers, R A M J; Wijnands, R; Zarka, P 2016-01-01 We report the detection of 48 millisecond pulsars (MSPs) out of 75 observed thus far using the LOFAR in the frequency range 110-188 MHz. We have also detected three MSPs out of nine observed in the frequency range 38-77 MHz. This is the largest sample of MSPs ever observed at these low frequencies, and half of the detected MSPs were observed for the first time at frequencies below 200 MHz. We present the average pulse profiles of the detected MSPs, their effective pulse widths and flux densities, and compare these with higher observing frequencies. The LOFAR pulse profiles will be publicly available via the EPN Database of Pulsar Profiles. We also present average values of dispersion measures (DM) and discuss DM and profile variations. About 35% of the MSPs show strong narrow profiles, another 25% exhibit scattered profiles, and the rest are only weakly detected. A qualitative comparison of the LOFAR MSP profiles with those at higher radio frequencies shows constant separation between profile components. Simi... 20. Cosmic-ray Positrons from Millisecond Pulsars Venter, C.; Kopp, A.; Harding, A. K.; Gonthier, P. L.; Büsching, I. 2015-07-01 Observations by the Fermi Large Area Telescope of γ-ray millisecond pulsar (MSP) light curves imply copious pair production in their magnetospheres, and not exclusively in those of younger pulsars. Such pair cascades may be a primary source of Galactic electrons and positrons, contributing to the observed enhancement in positron flux above ∼10 GeV. Fermi has also uncovered many new MSPs, impacting Galactic stellar population models. We investigate the contribution of Galactic MSPs to the flux of terrestrial cosmic-ray electrons and positrons. Our population synthesis code predicts the source properties of present-day MSPs. We simulate their pair spectra invoking an offset-dipole magnetic field. We also consider positrons and electrons that have been further accelerated to energies of several TeV by strong intrabinary shocks in black widow (BW) and redback (RB) systems. Since MSPs are not surrounded by pulsar wind nebulae or supernova shells, we assume that the pairs freely escape and undergo losses only in the intergalactic medium. We compute the transported pair spectra at Earth, following their diffusion and energy loss through the Galaxy. The predicted particle flux increases for non-zero offsets of the magnetic polar caps. Pair cascades from the magnetospheres of MSPs are only modest contributors around a few tens of GeV to the lepton fluxes measured by the Alpha Magnetic Spectrometer, PAMELA, and Fermi, after which this component cuts off. The contribution by BWs and RBs may, however, reach levels of a few tens of percent at tens of TeV, depending on model parameters. 1. Search for Millisecond Pulsars for the Pulsar Timing Array project Milia, S. 2012-03-01 Pulsars are rapidly rotating highly magnetised neutron stars (i.e. ultra dense stars, where about one solar mass is concentrated in a sphere with a radius of ~ 10 km), which irradiate radio beams in a fashion similar to a lighthouse. As a consequence, whenever the beams cut our line of sight we perceive a radio pulses, one (or two) per pulsar rotation, with a frequency up to hundred of times a second. Owing to their compact nature, rapid spin and high inertia, pulsars are in general fairly stable rotators, hence the Times of Arrival (TOAs) of the pulses at a radio telescope can be used as the ticks of a clock. This holds true in particular for the subÂclass of the millisecond pulsars (MSPs), having a spin period smaller than the conventional limit of 30 ms, whose very rapid rotation and relatively older age provide better rotational stability than the ordinary pulsars. Indeed, some MSPs rotate so regularly that they can rival the best atomic clocks on Earth over timespan of few months or years.This feature allows us to use MSPs as tools in a cosmic laboratory, by exploiting a procedure called timing, which consists in the repeated and regular measurement of the TOAs from a pulsar and then in the search for trends in the series of the TOAs over various timespans, from fraction of seconds to decades.For example the study of pulsars in binary systems has already provided the most stringent tests to date of General Relativity in strong gravitational fields and has unambiguously showed the occurrence of the emission of gravitational waves from a binary system comprising two massive bodies in a close orbit. In last decades a new exciting perspective has been opened, i.e. to use pulsars also for a direct detection of the so far elusive gravitational waves and thereby applying the pulsar timing for cosmological studies. In fact, the gravitational waves (GWs) going across our Galaxy pass over all the Galactic pulsars and the Earth, perturbing the spaceÂtime at the 2. An eccentric binary millisecond pulsar in the Galactic plane D.J. Champion; S.M. Ransom; P. Lazarus; F. Camilo; C. Bassa; V.M. Kaspi; D.J. Nice; P.C.C. Freire; I.H. Stairs; J. van Leeuwen; B.W. Stappers; J.M. Cordes; J.W.T. Hessels; D.R. Lorimer; Z. Arzoumanian; D.C. Backer; N.D.R. Bhat; S. Chatterjee; I. Cognard; J.S. Deneva; C.A. Faucher-Giguère; B.M. Gaensler; J. Han; F.A. Jenet; L. Kasian; V.I. Kondratiev; M. Kramer; J. Lazio; M.A. McLaughlin; A. Venkataraman; W. Vlemmings 2008-01-01 Binary pulsar systems are superb probes of stellar and binary evolution and the physics of extreme environments. In a survey with the Arecibo telescope, we have found PSR J1903+ 0327, a radio pulsar with a rotational period of 2.15 milliseconds in a highly eccentric ( e = 0.44) 95- day orbit around 3. Observations of Binary and Millisecond Pulsars at Xinjiang Astronomical Observatory Jingbo Wang; Na Wang; Jianping Yuan; Zhiyong Liu 2014-09-01 We present the first results of radio timing observations of binary and millisecond pulsars in China. We have timed four binary pulsars for 9 years, using Nanshan 25-m radio telescope. The long time span has enabled us to determine their rotation and orbital parameters. 4. The Aid of Optical Studies in Understanding Millisecond Pulsar Binaries Wadiasingh, Zorawar; Venter, Christo; Boettcher, Markus 2016-01-01 A large number of new "black widow" and "redback" energetic millisecond pulsars with irradiated stellar companions have been discovered through radio and optical searches of unidentified \\textit{Fermi} sources. Synchrotron emission, from particles accelerated up to several TeV in the intrabinary shock, exhibits modulation at the binary orbital period. Our simulated double-peaked X-ray light curves modulated at the orbital period, produced by relativistic Doppler-boosting along the intrabinary shock, are found to qualitatively match those observed in many sources. In this model, redbacks and transitional pulsar systems where the double-peaked X-ray light curve is observed at inferior conjunction have intrinsically different shock geometry than other millisecond pulsar binaries where the light curve is centered at superior conjunction. We discuss, and advocate, how current and future optical observations may aid in constraining the emission geometry, intrabinary shock and the unknown physics of pulsar winds. 5. An Eccentric Binary Millisecond Pulsar in the Galactic Plane Champion, David J.; Ransom, Scott M.; Lazarus, Patrick; Camilo, Fernando; Bassa, Cess; Kaspi, Victoria M.; Nice, David J.; Freire, Paulo C. C.; Stairs, Ingrid H.; vanLeeuwen, Joeri; Stappers, Ben W.; Cordes, James M.; Hessels, Jason W. T.; Lorimer, Duncan R.; Arzoumanian, Zaven; Backer, Don C.; Bhat, N. D. Ramesh; Chatterjee, Shami; Cognard, Ismael; Deneva, Julia S.; Faucher-Giguere, Claude-Andre; Gaensler, Bryan M.; Han, JinLin; Jenet, Fredrick A.; Kasian, Laura 2008-01-01 Binary pulsar systems are superb probes of stellar and binary evolution and the physics of extreme environments. In a survey with the Arecibo telescope, we have found PSR J1903+0327, a radio pulsar with a rotational period of 2.15 milliseconds in a highly eccentric (e = 0.44) 95-day orbit around a solar mass (M.) companion. Infrared observations identify a possible main-sequence companion star. Conventional binary stellar evolution models predict neither large orbital eccentricities nor main-sequence companions around millisecond pulsars. Alternative formation scenarios involve recycling a neutron star in a globular cluster, then ejecting it into the Galactic disk, or membership in a hierarchical triple system. A relativistic analysis of timing observations of the pulsar finds its mass to be 1.74 +/- 0.04 Solar Mass, an unusually high value. 6. Was the millisecond pulsar in SN1987A spun up or born spinning fast? The discovery of an optical pulsar in SN1987A with a period of 1,968.629 Hz raises many interesting issues, chief among them being the question of how the pulsar came to acquire such a rapid rotation rate. Here we argue that this millisecond pulsar, like others observed previously, has been spun up by accretion. In this case the accreted angular momentum comes from the mixed mantle and helium core of the ejecta, of which roughly 0.1 Msolar fell back during the first day after the explosion. This sizeable mass, and hence angular momentum, of the re-imploded material is at least partly a consequence of the blue supergiant nature of the progenitor star. (author) 7. Statistical Analysis of I Stokes Parameter of Millisecond Pulsars Panahi, Hossein; Eghdami, Issa; Monadi, Reza 2016-01-01 Using Detrended Fluctuation Analysis (DFA) and box counting method, we test spacial correlation and fractality of Polarization Pulse Profiles (PPPs) of 24 millisecond pulsars (MSPs) which were observed in Parkes Pulsar Timing Array (PPTA) project. DFA analysis indicates that MSPs' PPPs are persistent and the results of box counting method confirm the fractality in the majority of PPPs. A Kolmogorov-Smirnov test indicates that isolated MSPs have more complex PPPs than binary ones. Then we appl... 8. Cosmic-Lab: Optical companions to binary Millisecond Pulsars Pallanca, Cristina 2014-01-01 Millisecond Pulsars (MSPs) are fast rotating, highly magnetized neutron stars. According to the "canonical recycling scenario", MSPs form in binary systems containing a neutron star which is spun up through mass accretion from the evolving companion. Therefore, the final stage consists of a binary made of a MSP and the core of the deeply peeled companion. In the last years, however an increasing number of systems deviating from these expectations has been discovered, thus strongly indicating that our understanding of MSPs is far to be complete. The identification of the optical companions to binary MSPs is crucial to constrain the formation and evolution of these objects. In dense environments such as Globular Clusters (GCs), it also allows us to get insights on the cluster internal dynamics. By using deep photometric data, acquired both from space and ground-based telescopes, we identified 5 new companions to MSPs. Three of them being located in GCs and two in the Galactic Field. The three new identification... 9. Statistical Analysis of I Stokes Parameter of Millisecond Pulsars Panahi, Hossein; Monadi, Reza 2016-01-01 Using Detrended Fluctuation Analysis (DFA) and box counting method, we test spacial correlation and fractality of Polarization Pulse Profiles (PPPs) of 24 millisecond pulsars (MSPs) which were observed in Parkes Pulsar Timing Array (PPTA) project. DFA analysis indicates that MSPs' PPPs are persistent and the results of box counting method confirm the fractality in the majority of PPPs. A Kolmogorov-Smirnov test indicates that isolated MSPs have more complex PPPs than binary ones. Then we apply our analysis on a random sample of normal pulsars. Comparing the results of our analysis on MSPs and normal pulsars shows that MSPs have more complex PPPs which is resulted from smaller angular half-width of the emission cone and more peaks in MSPs PPPs. On the other hand, high values of Hurst exponent in MSPs confirm compact emission regions in these pulsars. 10. A glitch in the millisecond pulsar J0613-0200 McKee, J W; Stappers, B W; Lyne, A G; Caballero, R N; Lentati, L; Desvignes, G; Jessner, A; Jordan, C A; Karuppusamy, R; Kramer, M; Cognard, I; Champion, D J; Graikou, E; Lazarus, P; Osłowski, S; Perrodin, D; Shaifullah, G; Tiburzi, C; Verbiest, J P W 2016-01-01 We present evidence for a small glitch in the spin evolution of the millisecond pulsar J0613$-$0200, using the EPTA Data Release 1.0, combined with Jodrell Bank analogue filterbank TOAs recorded with the Lovell telescope and Effelsberg Pulsar Observing System TOAs. A spin frequency step of 0.82(3) nHz and frequency derivative step of${-1.6(39) \\times 10^{-19}\\,\\text{Hz} \\ \\text{s}^{-1}}$are measured at the epoch of MJD 50888(30). After PSR B1821$-$24A, this is only the second glitch ever observed in a millisecond pulsar, with a fractional size in frequency of${\\Delta \
11. Modelling the light curves of Fermi LAT millisecond pulsars
Venter, C; Harding, AK; Grove, JE
2014-01-01
We modelled the radio and gamma-ray light curves of millisecond pulsars using outer gap, two-pole caustic, low-altitude slot gap, and pair-starved polar cap geometric models, combined with a semi-empirical conal radio model. We find that no model fits all cases, with the outer gap and two-pole caustic models providing best fits for comparable numbers of millisecond pulsar light curves. We find a broad distribution of best-fit inclination angles as well as a clustering at large observer angles. The outer gap model furthermore seems to require relatively larger inclination angles, while the two-pole caustic model hints at an inverse trend between inclination angle and pulsar spin-down luminosity.
12. Progenitor neutron stars of the lightest and heaviest millisecond pulsars
Fortin, M.; Bejger, M.; Haensel, P.; Zdunik, J. L.
2016-02-01
Context. The recent mass measurements of two binary millisecond pulsars, PSR J1614-2230 and PSR J0751+1807 with a mass M = 1.97 ± 0.04 M⊙ and M = 1.26 ± 0.14 M⊙, respectively, indicate a wide range of masses for such objects and possibly also a broad spectrum of masses of neutron stars born in core-collapse supernovae. Aims: Starting from the zero-age main sequence binary stage, we aim at inferring the birth masses of PSR J1614-2230 and PSR J0751+1807 by taking the differences in the evolutionary stages preceding their formation into account. Methods: Using simulations for the evolution of binary stars, we reconstruct the evolutionary tracks leading to the formation of PSR J1614-2230 and PSR J0751+1807. We analyse in detail the spin evolution due to the accretion of matter from a disk in the intermediate-mass/low-mass X-ray binary. We consider two equations of state of dense matter, one for purely nucleonic matter and the other one including a high-density softening due to the appearance of hyperons. Stationary and axisymmetric stellar configurations in general relativity are used, together with a recent magnetic torque model and observationally-motivated laws for the decay of magnetic field. Results: The estimated birth mass of the neutron stars PSR J0751+1807 and PSR J1614-2230 could be as low as 1.0 M⊙ and as high as 1.9 M⊙, respectively. These values depend weakly on the equation of state and the assumed model for the magnetic field and its accretion-induced decay. Conclusions: The masses of progenitor neutron stars of recycled pulsars span a broad interval from 1.0 M⊙ to 1.9 M⊙. Including the effect of a slow Roche-lobe detachment phase, which could be relevant for PSR J0751+1807, would make the lower mass limit even lower. A realistic theory for core-collapse supernovæ should account for this wide range of mass.
13. A propeller model for the sub-luminous disk state of the transitional millisecond pulsar PSR J1023+0038
Papitto, A
2015-01-01
The discovery of millisecond pulsars switching between states powered either by the rotation of their magnetic field or by the accretion of matter, has recently proved the tight link shared by millisecond radio pulsars and neutron stars in low-mass X-ray binaries. Transitional millisecond pulsars also show an enigmatic intermediate state in which the neutron star is surrounded by an accretion disk, it emits coherent X-ray pulsations, but is sub-luminous in X-rays with respect to accreting neutron stars, and is brighter in gamma-rays than millisecond pulsars in the rotation-powered state. Here, we model the X-ray and gamma-ray emission observed from PSR J1023+0038 in such a state based on the assumption that most of the disk in-flow is propelled away by the rapidly rotating neutron star magnetosphere, and that electrons can be accelerated to energies of a few GeV at the turbulent disk-magnetosphere boundary. We show that the synchrotron and self-synchrotron Compton emission coming from such a region, together ...
14. Discovery of a Redback Millisecond Pulsar Candidate: 3FGL J0212.1+5320
Li, Kwan-Lok; Hou, Xian; Mao, Jirong; Strader, Jay; Chomiuk, Laura; Tremou, Evangelia
2016-01-01
We present a multi-wavelength study of the unidentified Fermi object, 3FGL J0212.1+5320. Within the 95% error ellipse, Chandra detects a bright X-ray source, which has a low-mass optical counterpart (M 64% of the Roche-lobe. Spectroscopic data taken in 2015 from the Lijiang observatory show no evidence of strong emission lines, revealing the accretion is currently inactive (the pulsar state). While the X-ray luminosity and the X-ray-to-gamma-ray flux ratio are both high that are comparable to that of the two known gamma-ray transitional millisecond pulsars, 3FGL J0212.1+5320 could be a promising target to search for future transition to the accretion active state.
15. On Detecting Millisecond Pulsars at the Galactic Center
Macquart, Jean-Pierre; Kanekar, Nissim
2015-06-01
The lack of detected pulsars at the Galactic Center (GC) region is a long-standing mystery. We argue that the high stellar density in the central parsec around the GC is likely to result in a pulsar population dominated by millisecond pulsars (MSPs), similar to the situation in globular cluster environments. Earlier GC pulsar searches have been largely insensitive to such an MSP population, accounting for the lack of pulsar detections. We estimate the best search frequency for such an MSP population with present and upcoming broad-band radio telescopes for two possible scattering scenarios, the “weak-scattering” case suggested by the recent detection of a magnetar close to the GC, and the “strong-scattering” case, with the scattering screen located close to the GC. The optimal search frequencies are ≈8 GHz (weak-scattering) and ≈25 GHz (strong-scattering), for pulsars with periods 1-20 ms, assuming that GC pulsars have a luminosity distribution similar to that those in the rest of the Milky Way. We find that 10-30 hr integrations with the Very Large Array and the Green Bank Telescope would be sufficient to detect MSPs at the GC distance in the weak-scattering case. However, if the strong-scattering case is indeed applicable to the GC, observations with the full Square Kilometre Array would be needed to detect the putative MSP population.
16. On Detecting Millisecond Pulsars at the Galactic Center
Macquart, Jean-Pierre
2015-01-01
The lack of detected pulsars at the Galactic Center (GC) region is a long-standing mystery. We argue that the high stellar density in the central parsec around the GC is likely to result in a pulsar population dominated by millisecond pulsars (MSPs), similar to the situation in globular cluster environments. Earlier GC pulsar searches have been largely insensitive to such an MSP population, accounting for the lack of pulsar detections. We estimate the best search frequency for such an MSP population with present and upcoming broad-band radio telescopes for two possible scattering scenarios, the "weak-scattering" case suggested by the recent detection of a magnetar close to the GC, and the "strong-scattering" case, with the scattering screen located close to the GC. The optimal search frequencies are $\\approx 8$ GHz (weak-scattering) and $\\approx 25$ GHz (strong-scattering), for pulsars with periods 1-20 ms, assuming that GC pulsars have a luminosity distribution similar to that those in the rest of the Milky ...
17. An eclipsing millisecond pulsar in the globular cluster Terzan 5
We have discovered an eclipsing binary millisecond pulsar in the globular cluster Terzan 5. This, the second known eclipsing binary pulsar after PSR1957+20, has a pulse period of 11.56 ms and a very short orbital period of 1.8 hours. In contrast to PSR1957+20, where the eclipses occupy about 10 per cent of the orbital period, the eclipse duration in this pulsar is very variable and never less than one-third of the orbital period. The pulsar is in a circular orbit of radius 0.11 light seconds, which implies a minimum companion mass of 0.089 solar masses, about four times the companion mass of PSR1957+20. Timing observations suggest an identification of the pulsar with a variable continuum source located about 30 arcsec west of the cluster centre. These observations and the variable eclipse duration show that the eclipse is due to absorption or scattering in a tenuous wind which flows from the companion star. We have also detected a second pulsar in the direction of Terzan 5. This pulsar, which has a period of 442 ms, may also be a cluster member, but is more likely to be a foreground object. (author)
18. Millisecond newly born pulsars as efficient accelerators of electrons
Zaza Osmanov; Swadesh Mahajan; George Machabeli; Nino Chkheidze
2015-01-01
The newly born millisecond pulsars are investigated as possible energy sources for creating ultra-high energy electrons. The transfer of energy from the star rotation to high energy electrons takes place through the Landau damping of centrifugally driven (via a two stream instability) electrostatic Langmuir waves. Generated in the bulk magnetosphere plasma, such waves grow to high amplitudes, and then damp, very effectively, on relativistic electrons driving them to even higher energies. We s...
19. Microarcsecond VLBI pulsar astrometry with PSRPI I. Two binary millisecond pulsars with white dwarf companions
Deller, A T; Kaplan, D L; Goss, W M; Brisken, W F; Chatterjee, S; Cordes, J M; Janssen, G H; Lazio, T J W; Petrov, L; Stappers, B W; Lyne, A
2016-01-01
Model-independent distance constraints to binary millisecond pulsars (MSPs) are of great value to both the timing observations of the radio pulsars, and multiwavelength observations of their companion stars. Very Long Baseline Interferometry (VLBI) astrometry can be employed to provide these model-independent distances with very high precision via the detection of annual geometric parallax. Using the Very Long Baseline Array, we have observed two binary millisecond pulsars, PSR J1022+1001 and J2145-0750, over a two-year period and measured their distances to be 700 +14 -10 pc and 613 +16 -14 pc respectively. We use the well-calibrated distance in conjunction with revised analysis of optical photometry to tightly constrain the nature of their massive (M ~ 0.85 Msun) white dwarf companions. Finally, we show that several measurements of their parallax and proper motion obtained by pulsar timing array projects are incorrect, and investigate possible causes for the discrepancy.
20. A millisecond pulsar in a stellar triple system
Ransom, S M; Archibald, A M; Hessels, J W T; Kaplan, D L; van Kerkwijk, M H; Boyles, J; Deller, A T; Chatterjee, S; Schechtman-Rook, A; Berndsen, A; Lynch, R S; Lorimer, D R; Karako-Argaman, C; Kaspi, V M; Kondratiev, V I; McLaughlin, M A; van Leeuwen, J; Rosen, R; Roberts, M S E; Stovall, K
2014-01-01
Gravitationally bound three-body systems have been studied for hundreds of years and are common in our Galaxy. They show complex orbital interactions, which can constrain the compositions, masses, and interior structures of the bodies and test theories of gravity, if sufficiently precise measurements are available. A triple system containing a radio pulsar could provide such measurements, but the only previously known such system, B1620-26 (with a millisecond pulsar, a white dwarf, and a planetary-mass object in an orbit of several decades), shows only weak interactions. Here we report precision timing and multi-wavelength observations of PSR J0337+1715, a millisecond pulsar in a hierarchical triple system with two other stars. Strong gravitational interactions are apparent and provide the masses of the pulsar (1.4378(13) Msun, where Msun is the solar mass and the parentheses contain the uncertainty in the final decimal places) and the two white dwarf companions (0.19751(15) Msun and 0.4101(3) Msun), as well ...
1. A millisecond pulsar in an extremely wide binary system
Bassa, C G; Stappers, B W; Tauris, T M; Wevers, T; Jonker, P G; Lentati, L; Verbiest, J P W; Desvignes, G; Graikou, E; Guillemot, L; Freire, P C C; Lazarus, P; Caballero, R N; Champion, D J; Cognard, I; Jessner, A; Jordan, C; Karuppusamy, R; Kramer, M; Lazaridis, K; Lee, K J; Liu, K; Lyne, A G; McKee, J; Oslowski, S; Perrodin, D; Sanidas, S; Shaifullah, G; Smits, R; Theureau, G; Tiburzi, C; Zhu, W W
2016-01-01
We report on 22 yrs of radio timing observations of the millisecond pulsar J1024$-$0719 by the telescopes participating in the European Pulsar Timing Array (EPTA). These observations reveal a significant second derivative of the pulsar spin frequency and confirm the discrepancy between the parallax and Shklovskii distances that has been reported earlier. We also present optical astrometry, photometry and spectroscopy of 2MASS J10243869$-$0719190. We find that it is a low-metallicity main-sequence star (K7V spectral type, $\\mathrm{[M/H]}=-1.0$, $T_\\mathrm{eff}=4050\\pm50$ K) and that its position, proper motion and distance are consistent with those of PSR J1024$-$0719. We conclude that PSR J1024$-$0719 and 2MASS J10243869$-$0719190 form a common proper motion pair and are gravitationally bound. The gravitational interaction between the main-sequence star and the pulsar accounts for the spin frequency derivatives, which in turn resolves the distance discrepancy. Our observations suggest that the pulsar and main...
2. ON THE FORMATION OF ECCENTRIC MILLISECOND PULSARS WITH HELIUM WHITE-DWARF COMPANIONS
Millisecond pulsars (MSPs) orbiting helium white dwarfs (WDs) in eccentric orbits challenge the established binary-evolution paradigm that predicts efficient orbital circularization during the mass-transfer episode that spins up the pulsar. Freire and Tauris recently proposed that these binary MSPs may instead form from the rotationally delayed accretion-induced collapse of a massive WD. However, their hypothesis predicts that eccentric systems preferably host low-mass pulsars and travel with small systemic velocities—in tension with new observational constraints. Here, I show that a substantial growth in eccentricity may alternatively arise from the dynamical interaction of the binary with a circumbinary disk. Such a disk may form from ejected donor material during hydrogen flash episodes, when the neutron star is already an active radio pulsar and tidal forces can no longer circularize the binary. I demonstrate that a short-lived (104-105 yr) disk can result in eccentricities of e ≅ 0.01-0.15 for orbital periods between 15 and 50 days. Finally, I propose that, more generally, the disk hypothesis may explain the lack of circular binary pulsars for the aforementioned orbital-period range
3. On the Formation of Eccentric Millisecond Pulsars with Helium White-dwarf Companions
2014-12-01
Millisecond pulsars (MSPs) orbiting helium white dwarfs (WDs) in eccentric orbits challenge the established binary-evolution paradigm that predicts efficient orbital circularization during the mass-transfer episode that spins up the pulsar. Freire & Tauris recently proposed that these binary MSPs may instead form from the rotationally delayed accretion-induced collapse of a massive WD. However, their hypothesis predicts that eccentric systems preferably host low-mass pulsars and travel with small systemic velocities—in tension with new observational constraints. Here, I show that a substantial growth in eccentricity may alternatively arise from the dynamical interaction of the binary with a circumbinary disk. Such a disk may form from ejected donor material during hydrogen flash episodes, when the neutron star is already an active radio pulsar and tidal forces can no longer circularize the binary. I demonstrate that a short-lived (104-105 yr) disk can result in eccentricities of e ~= 0.01-0.15 for orbital periods between 15 and 50 days. Finally, I propose that, more generally, the disk hypothesis may explain the lack of circular binary pulsars for the aforementioned orbital-period range.
4. Long-term timing of four millisecond pulsars
Janssen, G H; Bassa, C G; Cognard, I; Kramer, M; Theureau, G
2010-01-01
We have timed four millisecond pulses, PSRs J1721-2457, J1745-0952, J1810-2005, and J1918-0642, for up to a total of 10.5 years each using multiple telescopes in the European Pulsar Timing Array network: the Westerbork Synthesis Radio Telescope in The Netherlands, the Nancay Radio Telescope in France and the Lovell telescope at Jodrell Bank in the UK. The long time span has enabled us to measure the proper motions of J1745-0952 and J1918-0642, indicating that they have transverse velocities of 200(50) and 54(7) km/s respectively. We have obtained upper limits on the proper motion of J1721-2457 and J1810-2005, which imply that they have transverse velocities less than 140 and 400 km/s respectively. In all cases, the velocities lie in the range typical of millisecond pulsars. We present pulse profiles for each pulsar taken from observations at multiple frequencies in the range of 350 to 2600 MHz, and show that J1810-2005 shows significant profile evolution in this range. Using our multi-frequency observations, ...
5. High-Energy Emission at Shocks in Millisecond Pulsar Binaries
Kust Harding, Alice; Wadiasingh, Zorawar; Venter, Christo; Boettcher, Markus
2016-04-01
A large number of new Black Widow (BW) and Redback (RB) energetic millisecond pulsars have been discovered through radio searches of unidentified Fermi sources, increasing the known number of these systems from 4 to 28. We model the high-energy emission components from particles accelerated to several TeV in intrabinary shocks in BW and RB systems, and their predicted modulation at the binary orbital period. Synchrotron emission is expected at X-ray energies and such modulated emission has already been detected by Chandra and XMM. Inverse Compton emission from accelerated particles scattering the UV emission from the radiated companion star is expected in the Fermi and TeV bands. Detections or constraints on this emission will probe the unknown physics of pulsar winds.
6. BOOK REVIEW: Rotation and Accretion Powered Pulsars
Kaspi, V. M.
2008-03-01
Pulsar astrophysics has come a long way in the 40 years since the discovery of the first pulsar by Bell and Hewish. From humble beginnings as bits of 'scruff' on the Cambridge University group's chart recorder paper, the field of pulsars has blossomed into a major area of mainstream astrophysics, with an unparalleled diversity of astrophysical applications. These range from Nobel-celebrated testing of general relativity in the strong-field regime to constraining the equation-of-state of ultradense matter; from probing the winds of massive stars to globular cluster evolution. Previous notable books on the subject of pulsars have tended to focus on some particular topic in the field. The classic text Pulsars by Manchester and Taylor (1977 San Francisco, CA: Freeman) targeted almost exclusively rotation-powered radio pulsars, while the Mészáros book High-Energy Radiation from Magnetized Neutron Stars (1992 Chicago, IL: University of Chicago Press) considered both rotation- and accretion-powered neutron stars, but focused on their radiation at x-ray energies and above. The recent book Neutron Stars 1 by Haensel et al (2007 Berlin: Springer) considers only the equation of state and neutron-star structure. Into this context appears Rotation and Accretion Powered Pulsars, by Pranab Ghosh. In contrast to other books, here the author takes an encyclopedic approach and attempts to synthesize practically all of the major aspects of the two main types of neutron star. This is ambitious. The only comparable undertaking is the useful but more elementary Lyne and Graham-Smith text Pulsar Astronomy (1998 Cambridge: Cambridge University Press), or Compact Stellar X-ray Sources (eds Lewin and van der Klis, 2006 Cambridge: Cambridge University Press), an anthology of technical review articles that also includes black hole topics. Rotation and Accretion Powered Pulsars thus fills a clear void in the field, providing a readable, graduate-level book that covers nearly everything you
7. Detections of millisecond pulsars with the FERMI Large Area Telescope
The Fermi observatory was launched on June 11, 2008. It hosts the Large Area Telescope (LAT), sensitive to gamma-ray photons from 20 MeV to over 300 GeV. When the LAT began its activity, nine young and energetic pulsars were known in gamma ray range. At least several tens of pulsar detections by the LAT were predicted before launch. The LAT also allowed the study of millisecond pulsars (MSPs), never firmly detected in gamma ray range before Fermi. This thesis first presents the pulsar timing campaign for the LAT, in collaboration with large radio telescopes and X-ray telescopes, allowing for high sensitivity pulsed searches. Furthermore, it lead to quasi-homogeneous coverage of the galactic MSPs, so that the search for pulsations in LAT data for this population of stars was not affected by an a-priori bias. We present a search for pulsations from these objects in LAT data. For the first time, eight galactic MSPs have been detected as sources of pulsed gamma-ray emission over 100 MeV. In addition, a couple of good candidates for future detection are seen. A similar search for globular cluster MSPs was not successful so far. Comparison of the phase-aligned gamma-ray and radio light curves, as well as the spectral shapes, leads to the conclusion that their gamma-ray emission is similar to that of normal pulsars, and is probably produced in the outer-magnetosphere. This discovery suggests that many unresolved gamma-ray sources are unknown MSPs. (author)
8. On the formation of eccentric millisecond pulsars with helium white-dwarf companions
2014-01-01
Millisecond pulsars (MSPs) orbiting helium white-dwarfs (WD) in eccentric orbits challenge the established binary-evolution paradigm that predicts efficient orbital circularization during the mass-transfer episode that spins up the pulsar. Freire and Tauris (2014) recently proposed that these binary MSPs may instead form from the rotationally-delayed accretion-induced collapse of a massive WD. This scenario predicts that eccentric systems preferably host low-mass pulsars and travel with small systemic velocities -- in tension with new observational constraints. Here, I show that a substantial growth in eccentricity may alternatively arise from the dynamical interaction of the binary with a circumbinary disk. Such a disk may form from ejected donor material during hydrogen flash episodes, when the neutron star is already an active radio pulsar and tidal forces can no longer circularize the binary. I demonstrate that a short-lived (10^4-10^5 yrs disk can result to eccentricities of e ~ 0.01-0.15 for orbital per...
9. Timing of five millisecond pulsars discovered in the PALFA survey
Scholz, P; Lyne, A G; Stappers, B W; Bogdanov, S; Cordes, J M; Crawford, F; Ferdman, R D; Freire, P C C; Hessels, J W T; Lorimer, D R; Stairs, I H; Allen, B; Brazier, A; Camilo, F; Cardoso, R F; Chatterjee, S; Deneva, J S; Jenet, F A; Karako-Argaman, C; Knispel, B; Lazarus, P; Lee, K J; van Leeuwen, J; Lynch, R; Madsen, E C; McLaughlin, M A; Ransom, S M; Siemens, X; Spitler, L G; Stovall, K; Swiggum, J K; Venkataraman, A; Zhu, W W
2015-01-01
We present the discovery of five millisecond pulsars (MSPs) from the PALFA Galactic plane survey using Arecibo. Four of these (PSRs J0557+1551, J1850+0244, J1902+0300, and J1943+2210) are binary pulsars whose companions are likely white dwarfs, and one (PSR J1905+0453) is isolated. Phase-coherent timing solutions, ranging from $\\sim$1 to $\\sim$3 years in length, and based on observations from the Jodrell Bank and Arecibo telescopes, provide precise determinations of spin, orbital, and astrometric parameters. All five pulsars have large dispersion measures ($>100$ pc cm$^{-3}$, within the top 20% of all known Galactic field MSPs) and are faint (1.4 GHz flux density < 0.1 mJy, within the faintest 5% of all known Galactic field MSPs), illustrating PALFA's ability to find increasingly faint, distant MSPs in the Galactic plane. In particular, PSR J1850+0244 has a dispersion measure of 540 pc cm$^{-3}$, the highest of all known MSPs. Such distant, faint MSPs are important input for accurately modeling the total ...
10. Ultraviolet Emission from the Millisecond Pulsar J0437-4715
Kargaltsev, O; Romani, R W
2004-01-01
We observed PSR J0437-4715 with the FUV-MAMA detector of the Hubble Space Telescope Imaging Spectrometer (STIS) to measure the pulsar's spectrum and pulsations. For the first time, UV emission from a millisecond pulsar is detected. The measured flux, $(2.0\\pm 0.2)\\times 10^{-15}$ erg s$^{-1}$ cm$^{-2}$ in the 1150-1700 \\AA range, corresponds to the luminosity $L_{\\rm FUV}=(4.7\\pm 0.5)\\times 10^{27}$ erg s$^{-1}$, for the distance of 140 pc and negligible interstellar extinction. The shape of the observed spectrum suggests thermal emission from the neutron star surface with a surprisingly high temperature of about $1\\times 10^5$ K, above the upper limit on the surface temperature of the younger ordinary'' pulsar J0108-1431. For the few-Gyr-old J0437-4715, such a temperature requires a heating mechanism to operate. The spectrum of J0437-4715 shows marginal evidence of an emission line at 1372 \\AA, which might be a gravitationally redshifted Zeeman component of the Hydrogen Ly$\\alpha$ line in a magnetic field ...
11. Cyclic spectroscopy of the millisecond pulsar, B1937+21
Walker, Mark A. [Manly Astrophysics, 3/22 Cliff Street, Manly 2095 (Australia); Demorest, Paul B. [National Radio Astronomy Observatory, Charlottesville, VA 22903 (United States); Van Straten, Willem, E-mail: Mark.Walker@manlyastrophysics.org, E-mail: pdemores@nrao.edu, E-mail: willem@swin.edu.au [Swinburne University of Technology, Astrophysics and Supercomputing, Hawthorn 3122 (Australia)
2013-12-20
Cyclic spectroscopy is a signal processing technique that was originally developed for engineering applications and has recently been introduced into the field of pulsar astronomy. It is a powerful technique with many attractive features, not least of which is the explicit rendering of information about the relative phases in any filtering imposed on the signal, thus making holography a more straightforward proposition. Here we present methods for determining optimum estimates of both the filter itself and the statistics of the unfiltered signal, starting from a measured cyclic spectrum. In the context of radio pulsars these quantities tell us the impulse response of the interstellar medium (ISM) and the intrinsic pulse profile. We demonstrate our techniques by application to 428 MHz Arecibo data on the millisecond pulsar B1937+21, obtaining the pulse profile free from the effects of interstellar scattering. As expected, the intrinsic profile exhibits main- and inter-pulse components that are narrower than they appear in the scattered profile; it also manifests some weak, but sharp, features that are revealed for the first time at low frequency. We determine the structure of the received electric field envelope as a function of delay and Doppler shift. Our delay Doppler image has a high dynamic range and displays some pronounced, low-level power concentrations at large delays. These concentrations imply strong clumpiness in the ionized ISM, on AU-size scales, which must adversely affect the timing of B1937+21.
12. Timing of Five PALFA-Discovered Millisecond Pulsars
Stovall, K; Bogdanov, S; Brazier, A; Camilo, F; Cardoso, F; Chatterjee, S; Cordes, J M; Crawford, F; Deneva, J S; Ferdman, R; Freire, P C C; Hessels, J W T; Jenet, F; Kaplan, D L; Karako-Argaman, C; Kaspi, V M; Knispel, B; Kotulla, R; Lazarus, P; Lee, K J; van Leeuwen, J; Lynch, R; Lyne, A G; Madsen, E; McLaughlin, M A; Patel, C; Ransom, S M; Scholz, P; Siemens, X; Stairs, I H; Stappers, B W; Swiggum, J; Zhu, W W; Venkataraman, A
2016-01-01
We report the discovery and timing results for five millisecond pulsars (MSPs) from the Arecibo PALFA survey: PSRs J1906+0055, J1914+0659, J1933+1726, J1938+2516, and J1957+2516. Timing observations of the 5 pulsars were conducted with the Arecibo and Lovell telescopes for time spans ranging from 1.5 to 3.3 yr. All of the MSPs except one (PSR J1914+0659) are in binary systems with low eccentricities. PSR J1957+2516 is likely a redback pulsar, with a ~0.1 $M_\\odot$ companion and possible eclipses that last ~10% of the orbit. The position of PSR J1957+2516 is also coincident with a NIR source. All 5 MSPs are distant (>3.1 kpc) as determined from their dispersion measures, and none of them show evidence of $\\gamma$-ray pulsations in a search of Fermi Gamma-Ray Space Telescope data. These 5 MSPs bring the total number of MSPs discovered by the PALFA survey to 26 and further demonstrate the power of this survey in finding distant, highly dispersed MSPs deep in the Galactic plane.
13. The Parkes multibeam pulsar survey: VII. Timing of four millisecond pulsars and the underlying spin period distribution of the Galactic millisecond pulsar population
Lorimer, D R; Manchester, R N; Possenti, A; Lyne, A G; McLaughlin, M A; Kramer, M; Hobbs, G; Stairs, I H; Burgay, M; Eatough, R P; Keith, M J; Faulkner, A J; D'Amico, N; Camilo, F; Corongiu, A; Crawford, F
2015-01-01
We present timing observations of four millisecond pulsars discovered in the Parkes 20-cm multibeam pulsar survey of the Galactic plane. PSRs J1552-4937 and J1843-1448 are isolated objects with spin periods of 6.28 and 5.47 ms respectively. PSR J1727-2946 is in a 40-day binary orbit and has a spin period of 27 ms. The 4.43-ms pulsar J1813-2621 is in a circular 8.16-day binary orbit around a low-mass companion star with a minimum companion mass of 0.2 solar masses. Combining these results with detections from five other Parkes multibeam surveys, gives a well-defined sample of 56 pulsars with spin periods below 20 ms. We develop a likelihood analysis to constrain the functional form which best describes the underlying distribution of spin periods for millisecond pulsars. The best results were obtained with a log-normal distribution. A gamma distribution is less favoured, but still compatible with the observations. Uniform, power-law and Gaussian distributions are found to be inconsistent with the data. Galactic...
14. Rotation-induced deep crustal heating of millisecond pulsars
Gusakov, M E; Reisenegger, A
2015-01-01
The spin-down of a neutron star, e.g. due to magneto-dipole losses, results in compression of the stellar matter and induces nuclear reactions at phase transitions between different nuclear species in the crust. We show that this mechanism is effective in heating recycled pulsars, in which the previous accretion process has already been compressing the crust, so it is not in nuclear equilibrium. We calculate the corresponding emissivity and confront it with available observations, showing that it might account for the likely thermal ultraviolet emission of PSR J0437-4715.
15. Millisecond newly born pulsars as efficient accelerators of electrons
Osmanov, Z; Machabeli, G; Chkheidze, N
2015-01-01
The newly born millisecond pulsars are investigated as possible energy sources for creating ultra-high energy electrons. The transfer of energy from the star rotation to high energy electrons takes place through the Landau damping of centrifugally driven (via a two stream instability) electrostatic Langmuir waves. Generated in the bulk magnetosphere plasma, such waves grow to high amplitudes, and then damp, very effectively, on relativistic electrons driving them to even higher energies. We show that the rate of transfer of energy is so efficient that no energy losses might affect the mechanism of particle acceleration; the electrons might achieve energies of the order of 10^{18}eV for parameters characteristic of a young star.
16. Searches for millisecond pulsar candidates among the unidentified Fermi objects
Hui, C Y; Hu, C P; Lin, L C C; Li, K L; Kong, A K H; Tam, P H T; Takata, J; Cheng, K S; Jin, Ruolan; Yen, T -C; Kim, Chunglee
2015-01-01
Here we report the results of searching millisecond pulsar (MSP) candidates from the Fermi LAT second source catalog (2FGL). Seven unassociated $\\gamma-$ray sources in this catalog are identified as promising MSP candidates based on their $\\gamma$-ray properties. Through the X-ray analysis, we have detected possible X-ray counterparts, localized to an arcsecond accuracy. We have systematically estimated their X-ray fluxes and compared with the corresponding $\\gamma$-ray fluxes. The X-ray to $\\gamma$-ray flux ratios for 2FGL J1653.6-0159 and 2FGL J1946.4-5402 are comparable with the typical value for pulsars. For 2FGL J1625.2-0020, 2FGL J1653.6-0159 and 2FGL J1946.4-5402, their candidate X-ray counterparts are bright enough for performing a detailed spectral and temporal analysis to discriminate their thermal/non thermal nature and search for the periodic signal. We have also searched for possible optical/IR counterparts at the X-ray positions. For the optical/IR source coincident with the brightest X-ray obje...
17. Cool white dwarf companions to four millisecond pulsars
Bassa, C G; Camilo, F; Cognard, I; Koester, D; Kramer, M; Ransom, S R; Stappers, B W
2015-01-01
We report on photometric and spectroscopic observations of white dwarf companions to four binary radio millisecond pulsars, leading to the discovery of companions to PSRs J0614-3329, J1231-1411 and J2017+0603. We place limits on the brightness of the companion to PSR J0613-0200. Optical spectroscopy of the companion to PSR J0614-3329 identifies it as a DA type white dwarf with a temperature of Teff=6460+-80 K, a surface gravity log g=7.0+-0.2 cgs and a mass of Mwd=0.24+-0.04 Msun. We find that the distance to PSR J0614-3329 is smaller than previously estimated, removing the need for the pulsar to have an unrealistically high gamma-ray efficiency. Comparing the photometry with predictions from white dwarf cooling models allows us to estimate temperatures and cooling ages of the companions to PSRs J0613-0200, J1231-1411 and J2017+0603. We find that the white dwarfs in these systems are cool Teff5 Gyr. Thin Hydrogen envelopes are required for these white dwarfs to cool to the observed temperatures, and we sugges...
18. The millisecond pulsar contribution to the rising positron fraction
Venter, Christo; Harding, Alice K; Gonthier, Peter L; Buesching, Ingo
2015-01-01
Pair cascades from millisecond pulsars (MSPs) may be a primary source of Galactic electrons and positrons that contribute to the increase in positron flux above 10 GeV as observed by PAMELA and AMS-02. The Fermi Large Area Telescope (LAT) has increased the number of detected gamma-ray MSPs tremendously. Light curve modelling furthermore favours abundant pair production in MSP magnetospheres, so that models of primary cosmic-ray positrons from pulsars should include the contribution from the larger numbers of MSPs and their potentially higher positron output per source. We model the contribution of Galactic MSPs to the terrestrial cosmic-ray electron / positron flux by using a population synthesis code to predict the source properties of present-day MSPs. We simulate pair spectra assuming an offset-dipole magnetic field which boosts pair creation rates. We also consider positrons and electrons that have additionally been accelerated to very high energies in the strong intrabinary shocks in black widow (BW) and...
19. Population synthesis of radio and gamma-ray millisecond pulsars using Markov Chain Monte Carlo techniques
Gonthier, Peter L.; Koh, Yew-Meng; Kust Harding, Alice
2016-04-01
We present preliminary results of a new population synthesis of millisecond pulsars (MSP) from the Galactic disk using Markov Chain Monte Carlo techniques to better understand the model parameter space. We include empirical radio and gamma-ray luminosity models that are dependent on the pulsar period and period derivative with freely varying exponents. The magnitudes of the model luminosities are adjusted to reproduce the number of MSPs detected by a group of thirteen radio surveys as well as the MSP birth rate in the Galaxy and the number of MSPs detected by Fermi. We explore various high-energy emission geometries like the slot gap, outer gap, two pole caustic and pair starved polar cap models. The parameters associated with the birth distributions for the mass accretion rate, magnetic field, and period distributions are well constrained. With the set of four free parameters, we employ Markov Chain Monte Carlo simulations to explore the model parameter space. We present preliminary comparisons of the simulated and detected distributions of radio and gamma-ray pulsar characteristics. We estimate the contribution of MSPs to the diffuse gamma-ray background with a special focus on the Galactic Center.We express our gratitude for the generous support of the National Science Foundation (RUI: AST-1009731), Fermi Guest Investigator Program and the NASA Astrophysics Theory and Fundamental Program (NNX09AQ71G).
20. How to get the reduced B fields of millisecond pulsars: Flux expulsion by spindown before the LMXB phase
Alpar, Mehmet Ali; Gügercinoǧlu, Erbil
2016-07-01
The physical interaction between quantized flux lines of the Type II proton superconductor and the quantized vortex lines of the neutron superfluid is re-visited. Srinivasan et al. (1990) had proposed that this interaction led to reduction of the magnetic field to the B ˜10^9 G range as the flux lines were expelled together with vortex lines during the spindown of the neutron star in an early epoch of binary evolution. The model is discussed with reference to spindown by the wind from the companion prior to the Roche lobe filling LMXB phase. An evolutionary model for the magnetic field and the rotation rate is presented, with application to the 11 Hz accreting pulsar in the LMXB IGR J17480-2446 in Terzan 5 (Patruno et al 2012) as well as 'standard' accreting and radio millisecond pulsar evolution.
1. The Contribution of Millisecond Pulsars to the Galactic Cosmic-Ray Lepton Spectrum
Venter, C; Gonthier, P L; Harding, A K; Büsching, I
2014-01-01
Pulsars are believed to be sources of relativistic electrons and positrons. The abundance of detections of gamma-ray millisecond pulsars by Fermi Large Area Telescope coupled with their light curve characteristics that imply copious pair production in their magnetospheres, motivated us to investigate this old pulsar population as a source of Galactic electrons and positrons and their contribution to the enhancement in cosmic-ray positron flux at GeV energies. We use a population synthesis code to predict the source properties (number, position, and power) of the present-day Galactic millisecond pulsars, taking into account the latest Fermi and radio observations to calibrate the model output. Next, we simulate pair cascade spectra from these pulsars using a model that invokes an offset-dipole magnetic field. We assume free escape of the pairs from the pulsar environment. We then compute the cumulative spectrum of transported electrons and positrons at Earth, following their diffusion and energy losses as they...
2. Identification of Candidate Millisecond Pulsars from Fermi LAT Observations
Dai, Xuejie; Jithesh, V; Xing, Yi
2016-01-01
We report our detailed data analysis for 39 $\\gamma$-ray sources selected from the 992 unassociated sources in the \\textit{Fermi} Large Area Telescope (LAT) third source catalog. The selection criteria, which were set for finding candidate millisecond pulsars (MSPs), are non-variables with curved spectra and $>$5$^{\\circ}$ Galactic latitudes. From our analysis, 24 sources were found to be point-like sources not contaminated by background or nearby unknown sources. Three of them, J1544.6$-$1125, J1625.1$-$0021, and J1653.6$-$0158, have been previously studied, indicating that they are likely MSPs. The spectra of J0318.1+0252 and J2053.9+2922 do not have properties similar to that of known $\\gamma$-ray MSPs, and we thus suggest that they are not MSPs. Analysis of archival X-ray data for most of the 24 sources were also conducted. Four sources were found with X-ray objects in their error circles, and 16 with no detection. The ratios between the $\\gamma$-ray fluxes and X-ray fluxes or flux upper limits are genera...
3. Identification of candidate millisecond pulsars from Fermi LAT observations
Dai, Xue-Jie; Wang, Zhong-Xiang; Vadakkumthani, Jithesh; Xing, Yi
2016-06-01
We report our detailed data analysis of 39 γ-ray sources selected from the 992 unassociated sources in the third Fermi Large Area Telescope Third Source Catalog. The selection criteria, which were set for finding candidate millisecond pulsars (MSPs), are non-variables with curved spectra and >5° Galactic latitudes. From our analysis, 24 sources were found to be point-like sources not contaminated by background or nearby unknown sources. Three of them, J1544.6–1125, J1625.1–0021 and J1653.6–0158, have been previously studied, indicating that they are likely MSPs. The spectra of J0318.1+0252 and J2053.9+2922 do not have properties similar to known γ-ray MSPs, and we thus suggest that they are not MSPs. Analysis of archival X-ray data for most of the 24 sources was also conducted. Four sources were found with X-ray objects in their error circles, and 16 with no detection. The ratios between the γ-ray fluxes and X-ray fluxes or flux upper limits are generally lower than those of known γ-ray MSPs, suggesting that if the γ-ray sources are MSPs, none of the X-ray objects are their counterparts. Deep X-ray or radio observations of these sources are needed in order to identify their MSP nature.
4. NuSTAR Observations of the State Transition of Millisecond Pulsar Binary PSR J1023+0038
Tendulkar, Shriharsh P.; Yang, Chengwei; An, Hongjun;
2014-01-01
We report NuSTAR observations of the millisecond pulsar-low-mass X-ray binary (LMXB) transition system PSR J1023+0038 from 2013 June and October, before and after the formation of an accretion disk around the neutron star. Between June 10 and 12, a few days to two weeks before the radio disappear...... state changes in the similar transition systems PSR J1824-2452I and XSS J1227.0-4859 and discuss possible interpretations based on the transitions in the inner disk....
5. High-precision timing of 42 millisecond pulsars with the European Pulsar Timing Array
Desvignes, G; Lentati, L; Verbiest, J P W; Champion, D J; Stappers, B W; Janssen, G H; Lazarus, P; Osłowski, S; Babak, S; Bassa, C G; Brem, P; Burgay, M; Cognard, I; Gair, J R; Graikou, E; Guillemot, L; Hessels, J W T; Jessner, A; Jordan, C; Karuppusamy, R; Kramer, M; Lassus, A; Lazaridis, K; Lee, K J; Liu, K; Lyne, A G; McKee, J; Mingarelli, C M F; Perrodin, D; Petiteau, A; Possenti, A; Purver, M B; Rosado, P A; Sanidas, S; Sesana, A; Shaifullah, G; Smits, R; Taylor, S R; Theureau, G; Tiburzi, C; van Haasteren, R; Vecchio, A
2016-01-01
We report on the high-precision timing of 42 radio millisecond pulsars (MSPs) observed by the European Pulsar Timing Array (EPTA). This EPTA Data Release 1.0 extends up to mid-2014 and baselines range from 7-18 years. It forms the basis for the stochastic gravitational-wave background, anisotropic background, and continuous-wave limits recently presented by the EPTA elsewhere. The Bayesian timing analysis performed with TempoNest yields the detection of several new parameters: seven parallaxes, nine proper motions and, in the case of six binary pulsars, an apparent change of the semi-major axis. We find the NE2001 Galactic electron density model to be a better match to our parallax distances (after correction from the Lutz-Kelker bias) than the M2 and M3 models by Schnitzeler (2012). However, we measure an average uncertainty of 80\\% (fractional) for NE2001, three times larger than what is typically assumed in the literature. We revisit the transverse velocity distribution for a set of 19 isolated and 57 bina...
6. An eclipsing millisecond pulsar with a possible main-sequence companion in NGC 6397
D'Amico, N; Manchester, R N; Sarkissian, J M; Lyne, A G; Camilo, F M
2001-01-01
We present the results of one year of pulse timing observations of PSR J1740-5340, an eclipsing millisecond pulsar located in the globular cluster NGC 6397. We have obtained detailed orbital parameters and a precise position for the pulsar. The radio pulsar signal shows frequent interactions with the atmosphere of the companion, and suffers significant and strongly variable delays and intensity variations over a wide range of orbital phases. These characteristics and the binary parameters indicate that the companion may be a bloated main-sequence star or the remnant (still filling its Roche lobe) of the star that spun up the pulsar. In both cases, this would be the first binary millisecond pulsar system with such a companion.
7. High-precision timing of 42 millisecond pulsars with the European Pulsar Timing Array
Desvignes, G.; Caballero, R. N.; Lentati, L.; Verbiest, J. P. W.; Champion, D. J.; Stappers, B. W.; Janssen, G. H.; Lazarus, P.; Osłowski, S.; Babak, S.; Bassa, C. G.; Brem, P.; Burgay, M.; Cognard, I.; Gair, J. R.; Graikou, E.; Guillemot, L.; Hessels, J. W. T.; Jessner, A.; Jordan, C.; Karuppusamy, R.; Kramer, M.; Lassus, A.; Lazaridis, K.; Lee, K. J.; Liu, K.; Lyne, A. G.; McKee, J.; Mingarelli, C. M. F.; Perrodin, D.; Petiteau, A.; Possenti, A.; Purver, M. B.; Rosado, P. A.; Sanidas, S.; Sesana, A.; Shaifullah, G.; Smits, R.; Taylor, S. R.; Theureau, G.; Tiburzi, C.; van Haasteren, R.; Vecchio, A.
2016-05-01
We report on the high-precision timing of 42 radio millisecond pulsars (MSPs) observed by the European Pulsar Timing Array (EPTA). This EPTA Data Release 1.0 extends up to mid-2014 and baselines range from 7-18 yr. It forms the basis for the stochastic gravitational-wave background, anisotropic background, and continuous-wave limits recently presented by the EPTA elsewhere. The Bayesian timing analysis performed with TEMPONEST yields the detection of several new parameters: seven parallaxes, nine proper motions and, in the case of six binary pulsars, an apparent change of the semimajor axis. We find the NE2001 Galactic electron density model to be a better match to our parallax distances (after correction from the Lutz-Kelker bias) than the M2 and M3 models by Schnitzeler. However, we measure an average uncertainty of 80 per cent (fractional) for NE2001, three times larger than what is typically assumed in the literature. We revisit the transverse velocity distribution for a set of 19 isolated and 57 binary MSPs and find no statistical difference between these two populations. We detect Shapiro delay in the timing residuals of PSRs J1600-3053 and J1918-0642, implying pulsar and companion masses m_p=1.22_{-0.35}^{+0.5} M_{⊙}, m_c = 0.21_{-0.04}^{+0.06} M_{⊙} and m_p=1.25_{-0.4}^{+0.6} M_{⊙}, m_c = 0.23_{-0.05}^{+0.07} M_{⊙}, respectively. Finally, we use the measurement of the orbital period derivative to set a stringent constraint on the distance to PSRs J1012+5307 and J1909-3744, and set limits on the longitude of ascending node through the search of the annual-orbital parallax for PSRs J1600-3053 and J1909-3744.
8. DISCOVERY OF TWO MILLISECOND PULSARS IN FERMI SOURCES WITH THE NANCAY RADIO TELESCOPE
We report the discovery of two millisecond pulsars in a search for radio pulsations at the positions of Fermi-Large Area Telescope sources with no previously known counterparts, using the Nancay Radio Telescope. The two millisecond pulsars, PSRs J2017+0603 and J2302+4442, have rotational periods of 2.896 and 5.192 ms and are both in binary systems with low-eccentricity orbits and orbital periods of 2.2 and 125.9 days, respectively, suggesting long recycling processes. Gamma-ray pulsations were subsequently detected for both objects, indicating that they power the associated Fermi sources in which they were found. The gamma-ray light curves and spectral properties are similar to those of previously detected gamma-ray millisecond pulsars. Detailed modeling of the observed radio and gamma-ray light curves shows that the gamma-ray emission seems to originate at high altitudes in their magnetospheres. Additionally, X-ray observations revealed the presence of an X-ray source at the position of PSR J2302+4442, consistent with thermal emission from a neutron star. These discoveries along with the numerous detections of radio-loud millisecond pulsars in gamma rays suggest that many Fermi sources with no known counterpart could be unknown millisecond pulsars.
9. The accretion flow to the intermittent accreting ms pulsar, HETE J1900.1-2455, as observed by XMM-Newton and RXTE
Papitto, A.; D'Aì, A.; T. Di Salvo; Egron, E.; Bozzo, E.; Burderi, L.; Iaria, R.; Riggio, A.; Menna, M. T.
2012-01-01
We present a study of the accretion flow to the intermittent accreting millisecond pulsar, HETE J1900.1-2455, based on observations performed simultaneously by XMM-Newton and RXTE. The 0.33-50 keV spectrum is described by the sum of a hard Comptonized component originated in an optically thin {\\tau}~1 corona, a soft kTin~0.2 keV component interpreted as accretion disc emission, and of disc reflection of the hard component. Two emission features are detected at energies of 0.98(1) and 6.58(7) ...
10. The noise properties of 42 millisecond pulsars from the European Pulsar Timing Array and their impact on gravitational wave searches
Caballero, R N; Lentati, L; Desvignes, G; Champion, D J; Verbiest, J P W; Janssen, G H; Stappers, B W; Kramer, M; Lazarus, P; Possenti, A; Tiburzi, C; Perrodin, D; Osłowski, S; Babak, S; Bassa, C G; Brem, P; Burgay, M; Cognard, I; Gair, J R; Graikou, E; Guillemot, L; Hessels, J W T; Karuppusamy, R; Lassus, A; Liu, K; McKee, J; Mingarelli, C M F; Petiteau, A; Purver, M B; Rosado, P A; Sanidas, S; Sesana, A; Shaifullah, G; Smits, R; Taylor, S R; Theureau, G; van Haasteren, R; Vecchio, A
2015-01-01
The sensitivity of Pulsar Timing Arrays to gravitational waves depends critically on the noise present in the individual pulsar timing data. Noise may be either intrinsic or extrinsic to the pulsar. Intrinsic sources of noise might come from rotational instabilities, for example. Extrinsic sources of noise include contributions from physical processes which are not sufficiently well modelled, for example, dispersion and scattering effects, analysis errors and instrumental instabilities. We present the results from a noise analysis for 42 millisecond pulsars (MSPs) observed with the European Pulsar Timing Array. For characterising the low-frequency, stochastic and achromatic noise component, or "timing noise", we employ two methods, based on Bayesian and frequentist statistics. For 25 MSPs, we achieve statistically significant measurements of their timing noise parameters and find that the two methods give consistent results. For the remaining 17 MSPs, we place upper limits on the timing noise amplitude at the...
11. Prospects for Neutron Star Equation of State Constraints using "Recycled" Millisecond Pulsars
Bogdanov, Slavko
2015-01-01
Rotation-powered "recycled" millisecond pulsars are a variety of rapidly-spinning neutron stars that typically show thermal X-ray radiation due to the heated surface of their magnetic polar caps. Detailed numerical modeling of the rotation-induced thermal X-ray pulsations observed from recycled millisecond pulsars, including all relevant relativistic and stellar atmospheric effects, has been identified as a promising approach towards an astrophysical determination of the true neutron star mass-radius relation, and by extension the state of cold matter at densities exceeding those of atomic nuclei. Herein, I review the basic model and methodology commonly used to extract information regarding neutron star structure from the pulsed X-ray radiation observed from millisecond pulsars. I also summarize the results of past X-ray observations of these objects and the prospects for precision neutron star mass-radius measurements with the upcoming Neutron Star Interior Composition Explorer (NICER) X-ray timing mission.
12. A population of gamma-ray millisecond pulsars seen with the Fermi Large Area Telescope.
Abdo, A A; Ackermann, M; Ajello, M; Atwood, W B; Axelsson, M; Baldini, L; Ballet, J; Barbiellini, G; Baring, M G; Bastieri, D; Baughman, B M; Bechtol, K; Bellazzini, R; Berenji, B; Bignami, G F; Blandford, R D; Bloom, E D; Bonamente, E; Borgland, A W; Bregeon, J; Brez, A; Brigida, M; Bruel, P; Burnett, T H; Caliandro, G A; Cameron, R A; Camilo, F; Caraveo, P A; Carlson, P; Casandjian, J M; Cecchi, C; Celik, O; Charles, E; Chekhtman, A; Cheung, C C; Chiang, J; Ciprini, S; Claus, R; Cognard, I; Cohen-Tanugi, J; Cominsky, L R; Conrad, J; Corbet, R; Cutini, S; Dermer, C D; Desvignes, G; de Angelis, A; de Luca, A; de Palma, F; Digel, S W; Dormody, M; do Couto e Silva, E; Drell, P S; Dubois, R; Dumora, D; Edmonds, Y; Farnier, C; Favuzzi, C; Fegan, S J; Focke, W B; Frailis, M; Freire, P C C; Fukazawa, Y; Funk, S; Fusco, P; Gargano, F; Gasparrini, D; Gehrels, N; Germani, S; Giebels, B; Giglietto, N; Giordano, F; Glanzman, T; Godfrey, G; Grenier, I A; Grondin, M H; Grove, J E; Guillemot, L; Guiriec, S; Hanabata, Y; Harding, A K; Hayashida, M; Hays, E; Hobbs, G; Hughes, R E; Jóhannesson, G; Johnson, A S; Johnson, R P; Johnson, T J; Johnson, W N; Johnston, S; Kamae, T; Katagiri, H; Kataoka, J; Kawai, N; Kerr, M; Knödlseder, J; Kocian, M L; Kramer, M; Kuss, M; Lande, J; Latronico, L; Lemoine-Goumard, M; Longo, F; Loparco, F; Lott, B; Lovellette, M N; Lubrano, P; Madejski, G M; Makeev, A; Manchester, R N; Marelli, M; Mazziotta, M N; McConville, W; McEnery, J E; McLaughlin, M A; Meurer, C; Michelson, P F; Mitthumsiri, W; Mizuno, T; Moiseev, A A; Monte, C; Monzani, M E; Morselli, A; Moskalenko, I V; Murgia, S; Nolan, P L; Norris, J P; Nuss, E; Ohsugi, T; Omodei, N; Orlando, E; Ormes, J F; Paneque, D; Panetta, J H; Parent, D; Pelassa, V; Pepe, M; Pesce-Rollins, M; Piron, F; Porter, T A; Rainò, S; Rando, R; Ransom, S M; Ray, P S; Razzano, M; Rea, N; Reimer, A; Reimer, O; Reposeur, T; Ritz, S; Rochester, L S; Rodriguez, A Y; Romani, R W; Roth, M; Ryde, F; Sadrozinski, H F W; Sanchez, D; Sander, A; Saz Parkinson, P M; Scargle, J D; Schalk, T L; Sgrò, C; Siskind, E J; Smith, D A; Smith, P D; Spandre, G; Spinelli, P; Stappers, B W; Starck, J L; Striani, E; Strickman, M S; Suson, D J; Tajima, H; Takahashi, H; Tanaka, T; Thayer, J B; Thayer, J G; Theureau, G; Thompson, D J; Thorsett, S E; Tibaldo, L; Torres, D F; Tosti, G; Tramacere, A; Uchiyama, Y; Usher, T L; Van Etten, A; Vasileiou, V; Venter, C; Vilchez, N; Vitale, V; Waite, A P; Wallace, E; Wang, P; Watters, K; Webb, N; Weltevrede, P; Winer, B L; Wood, K S; Ylinen, T; Ziegler, M
2009-08-14
Pulsars are born with subsecond spin periods and slow by electromagnetic braking for several tens of millions of years, when detectable radiation ceases. A second life can occur for neutron stars in binary systems. They can acquire mass and angular momentum from their companions, to be spun up to millisecond periods and begin radiating again. We searched Fermi Large Area Telescope data for pulsations from all known millisecond pulsars (MSPs) outside of globular clusters, using rotation parameters from radio telescopes. Strong gamma-ray pulsations were detected for eight MSPs. The gamma-ray pulse profiles and spectral properties resemble those of young gamma-ray pulsars. The basic emission mechanism seems to be the same for MSPs and young pulsars, with the emission originating in regions far from the neutron star surface. PMID:19574349
13. A Population of Gamma-Ray Millisecond Pulsars Seen with the Fermi Large Area Telescope
Pulsars are born with sub-second spin periods and slow by electromagnetic braking for several tens of millions of years, when detectable radiation ceases. A second life can occur for neutron stars in binary systems. They can acquire mass and angular momentum from their companions, to be spun up to millisecond periods and begin radiating again. We searched Fermi Large Area Telescope data for pulsations from all known millisecond pulsars (MSPs) outside of globular clusters, using rotation parameters from radio telescopes. Strong gamma-ray pulsations were detected for eight MSPs. The gamma-ray pulse profiles and spectral properties resemble those of young gamma-ray pulsars. The basic emission mechanism seems to be the same for MSPs and young pulsars, with the emission originating in regions far from the neutron star surface. (authors)
14. Detection and Flux Density Measurements of the Millisecond Pulsar J2145-0750 below 100 MHz
Dowell, J; Taylor, G B; Blythe, J N; Clarke, T; Craig, J; Ellingson, S W; Helmboldt, J F; Henning, P A; Lazio, T J W; Schinzel, F; Stovall, K; Wolfe, C N
2013-01-01
We present flux density measurements and pulse profiles for the millisecond pulsar PSR J2145-0750 spanning 37 to 81 MHz using data obtained from the first station of the Long Wavelength Array. These measurements represent the lowest frequency detection of pulsed emission from a millisecond pulsar to date. We find that the pulse profile is similar to that observed at 102 MHz. We also find that the flux density spectrum between ~40 MHz to 5 GHz is suggestive of a break and may be better fit by a model that includes spectral curvature with a rollover around 730 MHz rather than a single power law.
15. Discovery of the Optical Counterparts to Four Energetic Fermi Millisecond Pulsars
Breton, R P; Roberts, M S E; Hessels, J W T; Camilo, F; McLaughlin, M A; Ransom, S M; Ray, P S; Stairs, I H
2013-01-01
In the last few years, over 43 millisecond radio pulsars have been discovered by targeted searches of unidentified gamma-ray sources found by the Fermi Gamma-Ray Space Telescope. A large fraction of these millisecond pulsars are in compact binaries with low-mass companions. These systems often show eclipses of the pulsar signal and are commonly known as black widows and redbacks because the pulsar is gradually destroying its companion. In this paper, we report on the optical discovery of four strongly irradiated millisecond pulsar companions. All four sources show modulations of their color and luminosity at the known orbital periods from radio timing. Light curve modelling of our exploratory data shows that the equilibrium temperature reached on the companion's dayside with respect to their nightside is consistent with about 10-30% of the available spin-down energy from the pulsar being reprocessed to increase the companion's dayside temperature. This value compares well with the range observed in other irra...
16. Optical and Infrared Lightcurve Modeling of the Gamma-ray Millisecond Pulsar 2FGL J2339.6-0532
Yen, Tzu-Ching; Kong, Albert Kwok-Hing; Yatsu, Yoichi; Hanayama, Hidekazu; Nagayama, Takahiro; Oister
2013-09-01
We report the detection of a quasi-sinusoidally modulated optical flux with a period of 4.6343 hour in the optical and infrared band of the Fermi source 2FGL J2339.7-0531. Comparing the multi-wavelength observations, we suggest that 2FGL J2339.7- 0531 is a γ-ray emitting millisecond pulsar (MSP) in a binary system with an optically visible late-type companion accreted by the pulsar, where the MSP is responsible for the γ-ray emission while the optical and infrared emission originate from the heated side of the companion. Based on the optical properties, the companion star is believed to be heated by the pulsar and reaches peak magnitude when the heated side faces the observer. We conclude that 2FGL J2339.7-0531 is a member of a subclass of γ-ray emitting pulsars -the "black widows"- recently revealed to be evaporating their companions in the late-stage of recycling as a prominent group of these newly revealed Fermi sources.
17. Do we see accreting magnetars in X-ray pulsars?
Postnov K.A.
2014-01-01
Full Text Available Strong magnetic field of accreting neutron stars (1014 G is hard to probe by Xray spectroscopy but can be indirectly inferred from spin-up/spin-down measurement in X-ray pulsars. The existing observations of slowly rotating X-ray pulsars are discussed. It is shown that magnetic fields of neutron stars derived from these observations (or lower limits in some cases fall within the standard 1012-1013 G range. Claims about the evidence for accreting magnetars are critically discussed in the light of recent progress in understanding of accretion onto slowly rotating neutron stars in the subsonic regime.
18. Optical Identification of He White Dwarfs Orbiting Four Millisecond Pulsars in the Globular Cluster 47 Tucanae
Cadelano, M.; Pallanca, C.; Ferraro, F. R.; Salaris, M.; Dalessandro, E.; Lanzoni, B.; Freire, P. C. C.
2015-10-01
We used ultra-deep UV observations obtained with the Hubble Space Telescope to search for optical companions to binary millisecond pulsars (MSPs) in the globular cluster 47 Tucanae. We identified four new counterparts (to MSPs 47TucQ, 47TucS, 47TucT, and 47TucY) and confirmed those already known (to MSPs 47TucU and 47TucW). In the color-magnitude diagram, the detected companions are located in a region between the main sequence and the CO white dwarf (WD) cooling sequences, consistent with the cooling tracks of He WDs with masses between 0.15 M⊙ and 0.20 M⊙. For each identified companion, mass, cooling age, temperature, and pulsar mass (as a function of the inclination angle) have been derived and discussed. For 47TucU we also found that the past accretion history likely proceeded at a sub-Eddington rate. The companion to the redback 47TucW is confirmed to be a non-degenerate star, with properties particularly similar to those observed for black widow systems. Two stars have been identified within the 2σ astrometric uncertainty from the radio positions of 47TucH and 47TucI, but the available data prevent us from firmly assessing whether they are the true companions of these two MSPs. Based on observations collected with the NASA/ESA HST (Prop. 12950), obtained at the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS5-26555.
19. One blind and three targeted searches for (sub)millisecond pulsars
Davoust, E.; Petit, G.; Fayard, T.
2011-10-01
Context. Millisecond pulsars are very useful for determining the properties of neutron stars, for testing General Relativity and for detecting gravitational waves. However, the number of known millisecond pulsars is very small compared to that of ordinary pulsars. Aims: We conducted one blind and three targeted searches for millisecond and submillisecond pulsars at radio frequencies. Methods: The blind search was conducted within 3° of the Galactic plane and at longitudes between 20° and 110°. It takes 22 073 pointings to cover this region, and 5487 different positions in the sky (i.e. 25% of the total) were actually observed. The first targeted search was aimed at Galactic globular clusters, the second one at 24 bright polarized and pointlike radiosources with steep spectra, and the third at 65 faint polarized and pointlike radiosources. The observations were conducted at the large radiotelescope of Nançay Observatory, at a frequency near 1400 MHz, the exact value depending on the backend. Two successive backends were used, first a VLBI S2 system, second a digital acquisition board and a PC with large storage capacity sampling the signal at 50 Mb/s on one bit, over a 24-MHz band and in one polarization. The bandwidth of acquisition of the second backend was later increased to 48 MHz and the sampling rate to 100 Mb/s. The survey used the three successive setups, with respective sensitivities of 3.5, 2.2, and 1.7 mJy. The targeted-search data were obtained with the third setup and reduced with a method based on the Hough transform, yielding a sensitivity of 0.9 mJy. The processing of the data was done in slightly differed time by soft-correlation in all cases. Results: No new short-period millisecond pulsars were discovered in the different searches. To better understand the null result of the blind survey, we estimate the probability of detecting one or more short-period pulsars among a given Galactic population of synthetic pulsars with our setup: 25% for the
20. What the Timing of Millisecond Pulsars Can Teach us about Their Interior
Alford, Mark G.; Schwenzer, Kai
2014-12-01
The cores of compact stars reach the highest densities in nature and therefore could consist of novel phases of matter. We demonstrate via a detailed analysis of pulsar evolution that precise pulsar timing data can constrain the star's composition, through unstable global oscillations (r modes) whose damping is determined by microscopic properties of the interior. If not efficiently damped, these modes emit gravitational waves that quickly spin down a millisecond pulsar. As a first application of this general method, we find that ungapped interacting quark matter is consistent with both the observed radio and x-ray data, whereas for ordinary nuclear matter some additional enhanced damping mechanism is required.
1. Limitations in timing precision due to single-pulse shape variability in millisecond pulsars
Shannon, R M; Dai, S; Bailes, M; Hobbs, G; Manchester, R N; van Straten, W; Raithel, C A; Ravi, V; Toomey, L; Bhat, N D R; Burke-Spolaor, S; Coles, W A; Keith, M J; Kerr, M; Levin, Y; Sarkissian, J M; Wang, J -B; Wen, L; Zhu, X -J
2014-01-01
High-sensitivity radio-frequency observations of millisecond pulsars usually show stochastic, broadband, pulse-shape variations intrinsic to the pulsar emission process. These variations induce jitter noise in pulsar timing observations; understanding the properties of this noise is of particular importance for the effort to detect gravitational waves with pulsar timing arrays. We assess the short-term profile and timing stability of 22 millisecond pulsars that are part of the Parkes Pulsar Timing Array sample by examining intra-observation arrival time variability and single-pulse phenomenology. In 7 of the 22 pulsars, in the band centred at approximately 1400MHz, we find that the brightest observations are limited by intrinsic jitter. We find consistent results, either detections or upper limits, for jitter noise in other frequency bands. PSR J1909-3744 shows the lowest levels of jitter noise, which we estimate to contribute $\\sim$10 ns root mean square error to the arrival times for hour-duration observati...
2. The contribution of millisecond pulsars to the Galactic cosmic-ray lepton spectrum
Venter, Christo; Kopp, Andreas; Harding, Alice K.; Gonthier, Peter L.; Büsching, Ingo
2015-03-01
Pulsars are believed to be sources of relativistic electrons and positrons. The abundance of detections of γ -ray millisecond pulsars by Fermi Large Area Telescope coupled with their light curve characteristics that imply copious pair production in their magnetospheres, motivated us to investigate this old pulsar population as a source of Galactic electrons and positrons and their contribution to the enhancement in cosmic-ray positron flux at GeV energies. We use a population synthesis code to predict the source properties (number, position, and power) of the present-day Galactic millisecond pulsars, taking into account the latest Fermi and radio observations to calibrate the model output. Next, we simulate pair cascade spectra from these pulsars using a model that invokes an offset-dipole magnetic field. We assume free escape of the pairs from the pulsar environment. We then compute the cumulative spectrum of transported electrons and positrons at Earth, following their diffusion and energy losses as they propagate through the Galaxy. Our results indicate that the predicted particle flux increases for non-zero offsets of the magnetic polar caps. Comparing our predicted local interstellar spectrum and positron fraction to measurements by AMS-02, PAMELA, and Fermi, we find that millisecond pulsars are only modest contributors at a few tens of GeV, after which this leptonic spectral component cuts off. The positron fraction is therefore only slightly enhanced above 10 GeV relative to a background flux model. This implies that alternative sources such as young, nearby pulsars and supernova remnants should contribute additional primary positrons within the astrophysical scenario.
3. The NANOGrav Nine-year Data Set: Astrometric Measurements of 37 Millisecond Pulsars
Matthews, Allison M; Fonseca, Emmanuel; Arzoumanian, Zaven; Crowter, Kathryn; Demorest, Paul B; Dolch, Timothy; Ellis, Justin A; Ferdman, Robert D; Gonzalez, Marjorie E; Jones, Glenn; Jones, Megan L; Lam, Michael T; Levin, Lina; McLaughlin, Maura A; Pennucci, Timothy T; Ransom, Scott M; Stairs, Ingrid H; Stovall, Kevin; Swiggum, Joseph K; Zhu, Weiwei
2015-01-01
Using the nine-year radio-pulsar timing data set from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), collected at Arecibo Observatory and the Green Bank Telescope, we have measured the positions, proper motions, and parallaxes for 37 millisecond pulsars. We report eleven significant parallax measurements and distance measurements, and nineteen lower limits on distance. We compare these measurements to distances predicted by the NE2001 interstellar electron density model and find them to be in general agreement. We use measured orbital-decay rates and spin-down rates to confirm two of the parallax distances and to place distance upper limits on other sources; these distance limits agree with the parallax distances with one exception, PSR J1024-0719, which we discuss at length. Using our measurements in combination with other published measurements, we calculate the velocity dispersion of the millisecond pulsar population in Galactocentric coordinates. We find the radial, azimuthal...
4. A New High-Frequency Search for Galactic Center Millisecond Pulsars using DSS-43
Lemley, Cameron; Prince, Thomas Allen; Majid, Walid A.; Murchikova, Elena
2016-01-01
The primary 70-meter Deep Space Network antenna (DSS-43) in Canberra, Australia was equipped with a new high-frequency (18-28 GHz) receiver system in May 2015 for use in a search for Galactic Center (GC) millisecond pulsars. The primary motivation for this search is that a pulsar in the Galactic Center region (especially one that is gravitationally bound to the massive black hole at the GC) would provide unprecedented tests of gravity in the strong-field regime and would offer an entirely new tool for probing the characteristics of the Galactic Center region. Preparation for the GC pulsar search has involved the development of a single-pulse search pipeline that integrates tools from both Fortran and Python as well as the implementation of this pipeline on high performance CPUs. The original version of the search pipeline was developed using Vela Pulsar data from DSS-43, and a more refined version that relies upon chi-squared fitting techniques was ultimately developed using Crab Pulsar data. Future work will involve continued testing of the single-pulse search pipeline using data from the rotating radio transient (RRAT) J1819-1458, the characterization of RRAT pulses using high time resolution data from the new receiver system on DSS-43, and ultimately the analysis of high-frequency data using the existing pipeline to search for millisecond pulsars in the Galactic Center.
5. A NuSTAR Observation of the Gamma-ray-emitting X-ray Binary and Transitional Millisecond Pulsar Candidate 1RXS J154439.4–112820
Bogdanov, Slavko
2016-07-01
I present a 40 ks Nuclear Spectroscopic Telescope Array observation of the recently identified low-luminosity X-ray binary and transitional millisecond pulsar (tMSP) candidate 1RXS J154439.4‑112820, which is associated with the high-energy γ-ray source 3FGL J1544.6‑1125. The system is detected up to ∼30 keV with an extension of the same power-law spectrum and rapid large-amplitude variability between two flux levels observed in soft X-rays. These findings provide further evidence that 1RXS J154439.4‑112820 belongs to the same class of objects as the nearby bona fide tMSPs PSR J1023+0038 and XSS J12270‑4859 and therefore almost certainly hosts a millisecond pulsar accreting at low luminosity. I also examine the long-term accretion history of 1RXS J154439.4‑112820 based on archival optical, ultraviolet, X-ray, and γ-ray light curves covering approximately the past decade. Throughout this period, the source has maintained similar flux levels at all wavelengths, which is an indication that it has not experienced prolonged episodes of a non-accreting radio pulsar state but may spontaneously undergo such events in the future.
6. The NANOGrav Nine-year Data Set: Astrometric Measurements of 37 Millisecond Pulsars
Matthews, Allison M.; Nice, David J.; Fonseca, Emmanuel; Arzoumanian, Zaven; Crowter, Kathryn; Demorest, Paul B.; Dolch, Timothy; Ellis, Justin A.; Ferdman, Robert D.; Gonzalez, Marjorie E.; Jones, Glenn; Jones, Megan L.; Lam, Michael T.; Levin, Lina; McLaughlin, Maura A.; Pennucci, Timothy T.; Ransom, Scott M.; Stairs, Ingrid H.; Stovall, Kevin; Swiggum, Joseph K.; Zhu, Weiwei
2016-02-01
Using the nine-year radio-pulsar timing data set from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), collected at Arecibo Observatory and the Green Bank Telescope, we have measured the positions, proper motions, and parallaxes for 37 millisecond pulsars. We report twelve significant parallax measurements and distance measurements, and eighteen lower limits on distance. We compare these measurements to distances predicted by the NE2001 interstellar electron density model and find them to be in general agreement. We use measured orbital-decay rates and spin-down rates to confirm two of the parallax distances and to place distance upper limits on other sources; these distance limits agree with the parallax distances with one exception, PSR J1024-0719, which we discuss at length. Using the proper motions of the 37 NANOGrav pulsars in combination with other published measurements, we calculate the velocity dispersion of the millisecond pulsar population in Galactocentric coordinates. We find the radial, azimuthal, and perpendicular dispersions to be 46, 40, and 24 {km} {{{s}}}-1, respectively, in a model that allows for high-velocity outliers; or 81, 58, and 62 {km} {{{s}}}-1 for the full population. These velocity dispersions are far smaller than those of the canonical pulsar population, and are similar to older Galactic disk populations. This suggests that millisecond pulsar velocities are largely attributable to their being an old population rather than being artifacts of their birth and evolution as neutron star binary systems. The components of these velocity dispersions follow similar proportions to other Galactic populations, suggesting that our results are not biased by selection effects.
7. Quasispherical subsonic accretion in X-ray pulsars
Shakura, Nikolai I.; Postnov, Konstantin A.; Kochetkova, A. Yu; Hjalmarsdotter, L.
2013-04-01
A theoretical model is considered for quasispherical subsonic accretion onto slowly rotating magnetized neutron stars. In this regime, the accreting matter settles down subsonically onto the rotating magnetosphere, forming an extended quasistatic shell. Angular momentum transfer in the shell occurs via large-scale convective motions resulting, for observed pulsars, in an almost iso-angular-momentum \\omega \\sim 1/R^2 rotation law inside the shell. The accretion rate through the shell is determined by the ability of the plasma to enter the magnetosphere due to Rayleigh-Taylor instabilities, with allowance for cooling. A settling accretion regime is possible for moderate accretion rates \\dot M \\lesssim \\dot M_* \\simeq 4\\times 10^{16} g s ^{-1}. At higher accretion rates, a free-fall gap above the neutron star magnetosphere appears due to rapid Compton cooling, and the accretion becomes highly nonstationary. Observations of spin-up/spin-down rates of quasispherically wind accreting equilibrium X-ray pulsars with known orbital periods (e.g., GX 301-2 and Vela X-1) enable us to determine the main dimensionless parameters of the model, as well as to estimate surface magnetic field of the neutron star. For equilibrium pulsars, the independent measurements of the neutron star magnetic field allow for an estimate of the stellar wind velocity of the optical companion without using complicated spectroscopic measurements. For nonequilibrium pulsars, a maximum value is shown to exist for the spin-down rate of the accreting neutron star. From observations of the spin-down rate and the X-ray luminosity in such pulsars (e.g., GX 1+4, SXP 1062, and 4U 2206+54), a lower limit can be put on the neutron star magnetic field, which in all cases turns out to be close to the standard value and which agrees with cyclotron line measurements. Furthermore, both explains the spin-up/spin-down of the pulsar frequency on large time-scales and also accounts for the irregular short
8. Quasispherical subsonic accretion in X-ray pulsars
A theoretical model is considered for quasispherical subsonic accretion onto slowly rotating magnetized neutron stars. In this regime, the accreting matter settles down subsonically onto the rotating magnetosphere, forming an extended quasistatic shell. Angular momentum transfer in the shell occurs via large-scale convective motions resulting, for observed pulsars, in an almost iso-angular-momentum ω∼1/R2 rotation law inside the shell. The accretion rate through the shell is determined by the ability of the plasma to enter the magnetosphere due to Rayleigh-Taylor instabilities, with allowance for cooling. A settling accretion regime is possible for moderate accretion rates .M∼*≅4×1016 g s-1. At higher accretion rates, a free-fall gap above the neutron star magnetosphere appears due to rapid Compton cooling, and the accretion becomes highly nonstationary. Observations of spin-up/spin-down rates of quasispherically wind accreting equilibrium X-ray pulsars with known orbital periods (e.g., GX 301-2 and Vela X-1) enable us to determine the main dimensionless parameters of the model, as well as to estimate surface magnetic field of the neutron star. For equilibrium pulsars, the independent measurements of the neutron star magnetic field allow for an estimate of the stellar wind velocity of the optical companion without using complicated spectroscopic measurements. For nonequilibrium pulsars, a maximum value is shown to exist for the spin-down rate of the accreting neutron star. From observations of the spin-down rate and the X-ray luminosity in such pulsars (e.g., GX 1+4, SXP 1062, and 4U 2206+54), a lower limit can be put on the neutron star magnetic field, which in all cases turns out to be close to the standard value and which agrees with cyclotron line measurements. Furthermore, both explains the spin-up/spin-down of the pulsar frequency on large time-scales and also accounts for the irregular short-term frequency fluctuations, which may correlate or
9. Discovery of an Unidentified Fermi Object as a Black Widow-Like Millisecond Pulsar
Kong, A. K. H.; Huang, R. H. H.; Cheng, K. S.; Takata, J.; Yatsu, Y.; Cheung, C. C.; Donato, D.; Lin, L. C. C.; Kataoka, J.; Takahashi, Y.; Maeda, K.; Hui, C. Y.; Tam, P. H. T.
2012-01-01
The Fermi Gamma-ray Space Telescope has revolutionized our knowledge of the gamma-ray pulsar population, leading to the discovery of almost 100 gamma-ray pulsars and dozens of gamma-ray millisecond pulsars (MSPs). Although the outer-gap model predicts different sites of emission for the radio and gamma-ray pulsars, until now all of the known gamma-ray MSPs have been visible in the radio. Here we report the discovery of a radio-quiet" gamma-ray emitting MSP candidate by using Fermi, Chandra, Swift, and optical observations. The X-ray and gamma-ray properties of the source are consistent with known gamma-ray pulsars. We also found a 4.63-hr orbital period in optical and X-ray data. We suggest that the source is a black widow-like MSP with a approx. 0.1 Stellar Mass late-type companion star. Based on the profile of the optical and X-ray light-curves, the companion star is believed to be heated by the pulsar while the X-ray emissions originate from pulsar magnetosphere and/or from intra-binary shock. No radio detection of the source has been reported yet and although no gamma-ray/radio pulsation has been found, we estimated that the spin period of the MSP is approx. 3-5 ms based on the inferred gamma-ray luminosity.
10. Quasi-spherical accretion in X-ray pulsars
Postnov, K; Kochetkova, A; Hjalmarsdotter, L
2011-01-01
Quasi-spherical accretion in wind-fed X-ray pulsars is discussed. At X-ray luminosities <4 10^{36} erg/s, a hot convective shell is formed around the neutron star magnetosphere, and subsonic settling accretion regime sets in. In this regime, accretion rate onto neutron star is determined by the ability of plasma to enter magnetosphere via Rayleigh-Taylor instability. A gas-dynamic theory of settling accretion is constructed taking into account anisotropic turbulence. The angular momentum can be transferred through the quasi-static shell via large-scale convective motions initiating turbulence cascade. The angular velocity distribution in the shell is found depending on the turbulent viscosity prescription. Comparison with observations of long-period X-ray wind-fed pulsars shows that an almost iso-angular-momentum distribution is most likely realized in their shells. The theory explains long-term spin-down in wind- fed accreting pulsars (e.g. GX 1+4) and properties of short-term torque-luminosity correlatio...
11. The evolution of helium white dwarfs: III. On the ages of millisecond pulsar systems
Schoenberner, D.; Driebe, T.; Bloecker, T.
2000-01-01
We employed recently computed evolutionary white-dwarf models with helium cores, supplemented by heavier models with carbon-oxygen cores, in order to investigate the ages of millisecond pulsar systems based on the cooling properties of the compact companions. Contrary to the behaviour of more massive white dwarfs, the evolutionary speed of low-mass white-dwarf models is substantially slowed down by ongoing hydrogen burning. By comparing the cooling ages of these models with the spin-down ages...
12. Discovery of two millisecond pulsars in Fermi sources with the Nancay Radio Telescope
Cognard, I; Johnson, T J; Smith, D A; Venter, C; Harding, A K; Wolff, M T; Cheung, C C; Donato, D; Abdo, A A; Ballet, J; Camilo, F; Desvignes, G; Dumora, D; Ferrara, E C; Freire, P C C; Grove, J E; Keith, M; Kramer, M; Lyne, A G; Michelson, P F; Parent, D; Ransom, S M; Ray, P S; Romani, R W; Parkinson, P M Saz; Stappers, B W; Theureau, G; Thompson, D J; Weltevrede, P; Wood, K S
2011-01-01
We report the discovery of two millisecond pulsars in a search for radio pulsations at the positions of \\emph{Fermi Large Area Telescope} sources with no previously known counterparts, using the Nan\\c{c}ay radio telescope. The two millisecond pulsars, PSRs J2017+0603 and J2302+4442, have rotational periods of 2.896 and 5.192 ms and are both in binary systems with low-eccentricity orbits and orbital periods of 2.2 and 125.9 days respectively, suggesting long recycling processes. Gamma-ray pulsations were subsequently detected for both objects, indicating that they power the associated \\emph{Fermi} sources in which they were found. The gamma-ray light curves and spectral properties are similar to those of previously-detected gamma-ray millisecond pulsars. Detailed modeling of the observed radio and gamma-ray light curves shows that the gamma-ray emission seems to originate at high altitudes in their magnetospheres. Additionally, X-ray observations revealed the presence of an X-ray source at the position of PSR ...
13. PSR J1723-2837: An Eclipsing Binary Radio Millisecond Pulsar
Crawford, F; Stairs, I H; Kaplan, D L; McLaughlin, M A; Freire, P C C; Burgay, M; Camilo, F; D'Amico, N; Faulkner, A; Kramer, M; Lorimer, D R; Manchester, R N; Possenti, A; Steeghs, D
2013-01-01
We present a study of PSR J1723-2837, an eclipsing, 1.86 ms millisecond binary radio pulsar discovered in the Parkes Multibeam survey. Radio timing indicates that the pulsar has a circular orbit with a 15 hr orbital period, a low-mass companion, and a measurable orbital period derivative. The eclipse fraction of ~15% during the pulsar's orbit is twice the Roche lobe size inferred for the companion. The timing behavior is significantly affected by unmodeled systematics of astrophysical origin, and higher-order orbital period derivatives are needed in the timing solution to account for these variations. We have identified the pulsar's (non-degenerate) companion using archival ultraviolet, optical, and infrared survey data and new optical photometry. Doppler shifts from optical spectroscopy confirm the star's association with the pulsar and indicate a pulsar-to-companion mass ratio of 3.3 +/- 0.5, corresponding to a companion mass range of 0.4 to 0.7 Msun and an orbital inclination angle range of between 30 and ...
14. Young and Millisecond Pulsar GeV Gamma-ray Fluxes from the Galactic Center and Beyond
O'Leary, Ryan M; Kerr, Matthew; Dexter, Jason
2016-01-01
Gamma-ray observations have shown pulsars to be efficient converters of rotational energy into GeV photons and it is of wide-ranging interest to determine their contribution to the gamma-ray background. We arrive at flux predictions from both the young (<~ Myr) and millisecond (~Gyr) Galactic pulsar populations. We find that unresolved pulsars can yield both a significant fraction of the excess GeV gamma rays near the Galactic Center and an inverse Compton flux in the inner kpc similar to that inferred by Fermi. We compare models of the young pulsar population and millisecond pulsar population to constraints from gamma-ray and radio observations. Overall, we find that the young pulsars should outnumber millisecond pulsars as unassociated gamma-ray point sources in this region. The number of young radio pulsars discovered near the Galactic Center is in agreement with our model of the young pulsar population. Deeper radio observations at higher latitudes can constrain the total gamma-ray emission from both y...
15. NuSTAR Observations of the State Transition of Millisecond Pulsar Binary PSR J1023+0038
Tendulkar, Shriharsh P; An, Hongjun; Kaspi, Victoria M; Archibald, Anne M; Bassa, Cees; Bellm, Eric; Bogdanov, Slavko; Harrison, Fiona A; Hessels, Jason W T; Janssen, Gemma H; Lyne, Andrew G; Patruno, Alessandro; Stappers, Benjamin; Stern, Daniel; Tomsick, John A; Boggs, Steven E; Chakrabarty, Deepto; Christensen, Finn E; Craig, William W; Hailey, Charles A; Zhang, William
2014-01-01
We report NuSTAR observations of the millisecond pulsar - low mass X-ray binary (LMXB) transition system PSR J1023+0038 from June and October 2013, before and after the formation of an accretion disk around the neutron star. Between June 10-12, a few days to two weeks before the radio disappearance of the pulsar, the 3-79 keV X-ray spectrum was well fit by a simple power law with a photon index of Gamma=1.17 +/-0.08 (at 90% confidence) with a 3-79 keV luminosity of 7.4+/-0.4 x 10^32 erg/s. Significant orbital modulation was observed with a modulation fraction of 36+/-10%. During the October 19-21 observation, the spectrum is described by a softer power law (Gamma=1.66+/-0.06) with an average luminosity of 5.8+/-0.2 x 10^33 erg/s and a peak luminosity of ~1.2 x 10^34 erg/s observed during a flare. No significant orbital modulation was detected. The spectral observations are consistent with previous and current multi-wavelength observations and show the hard X-ray power law extending to 79 keV without a spectra...
16. The gamma-ray millisecond pulsar deathline, revisited - New velocity and distance measurements
Guillemot, L; Laffon, H; Janssen, G H; Cognard, I; Theureau, G; Desvignes, G; Ferrara, E C; Ray, P S
2016-01-01
Millisecond pulsars (MSPs) represent nearly half of the more than 160 currently known $\\gamma$-ray pulsars detected by the Large Area Telescope on the \\textit{Fermi} satellite, and a third of all known MSPs are seen in $\\gamma$ rays. The least energetic $\\gamma$-ray MSPs enable us to probe the so-called deathline for high-energy emission, i.e., the spin-down luminosity limit under which pulsars (PSRs) cease to produce detectable high-energy radiation. Characterizing the MSP luminosity distribution helps to determine their contribution to the Galactic diffuse $\\gamma$-ray emission. We made use of the high-quality pulsar timing data recorded at the Nan\\c{c}ay Radio Telescope over several years to characterize the properties of a selection of MSPs. For one of the pulsars, the dataset was complemented with Westerbork Synthesis Radio Telescope observations. The rotation ephemerides derived from this analysis were also used to search the LAT data for new $\\gamma$-ray MSPs. For the MSPs considered in this study, we ...
17. High-Precision Timing of 5 Millisecond Pulsars: Space Velocities, Binary Evolution and Equivalence Principles
Gonzalez, M E; Ferdman, R D; Freire, P C C; Nice, D J; Demorest, P B; Ransom, S M; Kramer, M; Camilo, F; Hobbs, G; Manchester, R N; Lyne, A G
2011-01-01
We present high-precision timing of five millisecond pulsars (MSPs) carried out for more than seven years; four pulsars are in binary systems and one is isolated. We are able to measure the pulsars' proper motions and derive an estimate for their space velocities. The measured two-dimensional velocities are in the range 70-210 km/s, consistent with those measured for other MSPs. We also use all the available proper motion information for isolated and binary MSPs to update the known velocity distribution for these populations. As found by earlier works, we find that the velocity distribution of binary and isolated MSPs are indistinguishable with the current data. Four of the pulsars in our observing program are highly recycled with low-mass white dwarf companions and we are able to derive accurate binary parameters for these systems. For three of these binary systems we are able to place initial constraints on the pulsar masses with best-fit values in the range 1.0-1.6 M_sun. The implications of the results pr...
18. Properties and Evolution of the Redback Millisecond Pulsar Binary PSR J2129-0429
Bellm, Eric C; Breton, Rene P; Phinney, E Sterl; Bhalerao, Varun B; Camilo, Fernando; Dahal, Sumit; Djorgovski, S G; Drake, Andrew J; Hessels, J W T; Laher, Russ R; Levitan, David B; Lewis, Fraser; Mahabal, Ashish A; Ofek, Eran O; Prince, Thomas A; Ransom, Scott M; Roberts, Mallory S E; Russell, David M; Sesar, Branimir; Surace, Jason A; Tang, Sumin
2015-01-01
PSR J2129-0429 is a "redback" eclipsing millisecond pulsar binary with an unusually long 15.2 hour orbit. It was discovered by the Green Bank Telescope in a targeted search of unidentified Fermi gamma-ray sources. The pulsar companion is optically bright (mean $m_R = 16.6$ mag), allowing us to construct the longest baseline photometric dataset available for such a system. We present ten years of archival and new photometry of the companion from LINEAR, CRTS, PTF, the Palomar 60-inch, and LCOGT. Radial velocity spectroscopy using the Double-Beam Spectrograph on the Palomar 200-inch indicates that the pulsar is massive: $1.74\\pm0.18 M_\\odot$. The G-type pulsar companion has mass $0.44\\pm0.04 M_\\odot$, one of the heaviest known redback companions. It is currently 95\\% Roche-lobe filling and only mildly irradiated by the pulsar. We identify a clear 13.1 mmag yr$^{-1}$ secular decline in the mean magnitude of the companion as well as smaller-scale variations in the optical lightcurve shape. This behavior may indic...
19. Four Highly Dispersed Millisecond Pulsars Discovered in the Arecibo PALFA Galactic Plane Survey
Crawford, F; Lyne, A G; Stappers, B W; Nice, D J; Stairs, I H; Lazarus, P; Hessels, J W T; Freire, P C C; Allen, B; Bhat, N D R; Bogdanov, S; Brazier, A; Camilo, F; Champion, D J; Chatterjee, S; Cognard, I; Cordes, J M; Deneva, J S; Desvignes, G; Jenet, F A; Kaspi, V M; Knispel, B; Kramer, M; van Leeuwen, J; Lorimer, D R; Lynch, R; McLaughlin, M A; Ransom, S M; Scholz, P; Siemens, X; Venkataraman, A
2012-01-01
We present the discovery and phase-coherent timing of four highly dispersed millisecond pulsars (MSPs) from the Arecibo PALFA Galactic plane survey: PSRs J1844+0115, J1850+0124, J1900+0308, and J1944+2236. Three of the four pulsars are in binary systems with low-mass companions, which are most likely white dwarfs, and which have orbital periods on the order of days. The fourth pulsar is isolated. All four pulsars have large dispersion measures (DM > 100 pc cm-3), are distant (> 3.4 kpc), faint at 1.4 GHz (< 0.2 mJy), and are fully recycled (with spin periods P between 3.5 and 4.9 ms). The three binaries also have very small orbital eccentricities, as expected for tidally circularized, fully recycled systems with low-mass companions. These four pulsars have DM/P ratios that are among the highest values for field MSPs in the Galaxy. These discoveries bring the total number of confirmed MSPs from the PALFA survey to fifteen. The discovery of these MSPs illustrates the power of PALFA for finding weak, distant ...
20. CHANDRA X-RAY OBSERVATIONS OF 12 MILLISECOND PULSARS IN THE GLOBULAR CLUSTER M28
We present a Chandra X-ray Observatory investigation of the millisecond pulsars in the globular cluster M28 (NGC 6626). In what is one of the deepest X-ray observations of a globular cluster, we firmly detect seven and possibly detect two of the 12 known M28 pulsars. With the exception of PSRs B1821-24 and J1824-2452H, the detected pulsars have relatively soft spectra, with X-ray luminosities 1030-1031 erg s-1 (0.3-8 keV), similar to most recycledpulsars in 47 Tucanae and the field of the Galaxy, implying thermal emission from the pulsar magnetic polar caps. We present the most detailed X-ray spectrum to date of the energetic PSR B1821-24. It is well described by a purely non-thermal spectrum with spectral photon index Γ = 1.23 and luminosity 1.4 x 1033Θ(D/5.5 kpc)2 erg s-1 (0.3-8 keV), where Θ is the fraction of the sky covered by the X-ray emission beam(s). We find no evidence for the previously reported line emission feature around 3.3 keV, most likely as a consequence of improvements in instrument calibration. The X-ray spectrum and pulse profile of PSR B1821-24 suggest that the bulk of unpulsed emission from this pulsar is not of thermal origin, and is likely due to low-level non-thermal magnetospheric radiation, an unresolved pulsar wind nebula, and/or small-angle scattering of the pulsed X-rays by interstellar dust grains. The peculiar binary PSR J1824-2452H shows a relatively hard X-ray spectrum and possible variability at the binary period, indicative of an intrabinary shock formed by interaction between the relativistic pulsar wind and matter from its non-degenerate companion star.
1. Strong Support for the Millisecond Pulsar Origin of the Galactic Center GeV Excess.
Bartels, Richard; Krishnamurthy, Suraj; Weniger, Christoph
2016-02-01
Using γ-ray data from the Fermi Large Area Telescope, various groups have identified a clear excess emission in the Inner Galaxy, at energies around a few GeV. This excess resembles remarkably well a signal from dark-matter annihilation. One of the most compelling astrophysical interpretations is that the excess is caused by the combined effect of a previously undetected population of dim γ-ray sources. Because of their spectral similarity, the best candidates are millisecond pulsars. Here, we search for this hypothetical source population, using a novel approach based on wavelet decomposition of the γ-ray sky and the statistics of Gaussian random fields. Using almost seven years of Fermi-LAT data, we detect a clustering of photons as predicted for the hypothetical population of millisecond pulsar, with a statistical significance of 10.0σ. For plausible values of the luminosity function, this population explains 100% of the observed excess emission. We argue that other extragalactic or Galactic sources, a mismodeling of Galactic diffuse emission, or the thick-disk population of pulsars are unlikely to account for this observation. PMID:26894696
2. A parallax distance and mass estimate for the transitional millisecond pulsar system J1023+0038
Deller, A T; Brisken, W F; Chatterjee, S; Janssen, G H; Kaspi, V M; Lorimer, D; Lyne, A G; McLaughlin, M A; Ransom, S; Stairs, I H; Stappers, B
2012-01-01
The recently discovered transitional millisecond pulsar system J1023+0038 exposes a crucial evolutionary phase of recycled neutron stars for multiwavelength study. The system, comprising the neutron star itself, its stellar companion, and the surrounding medium, is visible across the electromagnetic spectrum from the radio to X-ray/gamma-ray regimes and offers insight into the recycling phase of millisecond pulsar evolution. Here, we report on multiple-epoch astrometric observations with the Very Long Baseline Array (VLBA) which give a system parallax of 0.731 +/- 0.022 milliarcseconds (mas) and a proper motion of 17.98 +/- 0.05 mas/yr. By combining our results with previous optical observations, we are able to use the parallax distance of 1368+42-39 pc to estimate the mass of the pulsar as 1.71 +/- 0.16 solar masses, and we are also able to measure the 3D space velocity of the system as 126 +/- 5 km/s. Despite the precise nature of the VLBA measurements, the remaining ~3% distance uncertainty dominates the 0...
3. "Hiccup" accretion in the swinging pulsar IGR J18245-2452
Ferrigno, C; Papitto, A; Rea, N; Pavan, L; Campana, S; Wieringa, M; Filipovic, M; Falanga, M
2013-01-01
IGR J18245-2452 is the fifteenth discovered accreting millisecond X-ray pulsar and the first source of this class showing direct evidence for transition between accretion and rotational powered emission states. These "swings" provided the strongest confirmation of the pulsar recycling scenario available so far. During the two XMM-Newton observations that were carried out while the source was in outburst in April 2013, IGR J18245-2452 displayed a unique and peculiar variability of its X-ray emission. In this work, we report on a detailed analysis of the XMM- Newton data and focus in particular on the timing and spectral variability of the source. IGR J18245-2452 continuously switches between lower and higher intensity states, with typical variations in flux up to a factor of about 100 in time scales as short as few seconds. These variations in the source intensity are sometimes associated to a dramatic spectral hardening, during which the power-law photon index of the source changes from Gamma=1.7 to Gamma=0.7...
4. A NuSTAR Observation of the Gamma-Ray-Emitting X-ray Binary and Transitional Millisecond Pulsar Candidate 1RXS J154439.4-112820
Bogdanov, Slavko
2015-01-01
I present a 40 kilosecond Nuclear Spectroscopic Telescope Array (NuSTAR) observation of the recently identified low-luminosity X-ray binary and transitional millisecond pulsar (tMSP) candidate 1RXS J154439.4-112820, which is associated with the high-energy gamma-ray source 3FGL J1544.6--1125. The system is detected up to ~30 keV with an extension of the same power-law spectrum and rapid large-amplitude variability between two flux levels observed in soft X-rays. These findings provide further evidence that 1RXS J154439.4-112820 belongs to the same class of objects as the nearby bona fide tMSPs PSR J1023+0038 and XSS J12270-4859 and therefore almost certainly hosts a millisecond pulsar accreting at low luminosities. I also examine the long-term accretion history of 1RXS J154439.4-112820 based on archival optical, ultraviolet, X-ray, and $\\gamma$-ray light curves covering the past $\\sim$decade. Throughout this period, the source has maintained similar flux levels at all wavelengths, which is an indication that ...
5. Evacuation of gas from globular clusters by winds from millisecond pulsars
Why is so little gas observed within globular clusters? A typical globular cluster contains ∼ 103 post-turnoff stars, each of which will lose ∼0.2 solar masses before its asymptotic giant branch phase of evolution, and ∼0.1 solar masses during this phase, and so should accumulate 102-103 solar masses of gas in the 108-year interval between passages of the globular cluster through the galactic disk. (At each disk passage, gas ram pressure will remove the accumulated material.) But observational searches show that there is scant intracluster gas; in many clusters, there is less than 1 solar mass of gas, orders of magnitude less than theoretical predictions. The recent discovery of multiple millisecond pulsars in globular clusters may resolve this long-standing problem: the relativistic wind from these pulsars is enough to drive gas from stellar mass loss out of the globular cluster. (author)
6. Rotochemical heating of millisecond and classical pulsars with anisotropic and density-dependent superfluid gap models
González-Jiménez, Nicolás; Reisenegger, Andreas
2014-01-01
When a rotating neutron star loses angular momentum, the progressive reduction of the centrifugal force makes it contract. This perturbs each fluid element, raising the local pressure and originating deviations from beta equilibrium, inducing reactions that release heat (rotochemical heating). This effect has previously been studied by Fern\\'andez & Reisenegger (2005) for non-superfluid neutron stars and by Petrovich & Reisenegger (2010) for superfluid millisecond pulsars. Both studies found that pulsars reach a quasi-steady state in which the compression driving the matter out of beta equilibrium is balanced by the reactions trying to restore the equilibrium. We extend previous studies by considering the effect of density-dependence and anisotropy of the superfluid energy gaps, for the case in which the dominant reactions are the modified Urca processes, the protons are non-superconducting, and the neutron superfluidity is parametrized by models proposed in the literature. By comparing our prediction...
7. PSR J1024-0719: A Millisecond Pulsar in an Unusual Long-Period Orbit
Kaplan, D L; Nice, D J; Irrgang, A; Heber, U; Arzoumanian, Z; Beklen, E; Crowter, K; DeCesar, M E; Demorest, P B; Dolch, T; Lynch, R S; McLaughlin, M A; Miller, A A; Ng, C; Pennucci, T T; Ellis, J A; Ferdman, R D; Ferrara, E C; Fonseca, E; Gentile, P A; Jones, G; Jones, M L; Kreuzer, S; Lam, M T; Levin, L; Lorimer, D R; Prince, T A; Ransom, S M; Ray, P S; Spiewak, R; Stairs, I H; Stovall, K; Swiggum, J; Zhu, W
2016-01-01
PSR J1024$-$0719 is a millisecond pulsar that was long thought to be isolated. However, puzzling results concerning its velocity, distance, and low rotational period derivative have led to reexamination of its properties. We present updated radio timing observations along with new and archival optical data that show PSR J1024$-$0719 is most likely in a long period (2$-$20 kyr) binary system with a low-mass ($\\approx 0.4\\,M_\\odot$) low-metallicity ($Z \\approx -0.9\\,$ dex) main sequence star. Such a system can explain most of the anomalous properties of this pulsar. We suggest that this system formed through a dynamical exchange in a globular cluster that ejected it into a halo orbit, consistent with the low observed metallicity for the stellar companion. Further astrometric and radio timing observations such as measurement of the third period derivative could strongly constrain the range of orbital parameters.
8. Preparing GLAST LAT studies of the millisecond pulsar PSR J0218+4232 and the blazar 3C 66A
Millisecond pulsars have weaker magnetic fields than normal pulsars, but their rapid rotation implies open field line voltages similar to those of young pulsars and they are therefore candidates for accelerating particles to the high energies required to emit in the GeV energy domain. PSR J0218+4232 was the only millisecond pulsar detected by EGRET. Its detection was rendered difficult by the powerful BL Lacertae 3C 66A a degree away, in spite of the low background (b= -16.8 degrees). Pulsations were detected at the 4.9 σ level, reinforcing the expectation that millisecond pulsars are a promising class for detection by the forthcoming high-energy mission GLAST. To estimate the GLAST LAT performance for both PSR J0218+4232 and 3C 66A, we have simulated LAT data using predictions for the 'polar cap' and the 'outer gap' pulsar models along with spectral energy distribution estimates for the blazar, normalizing to the EGRET observed fluxes. We demonstrate that GLAST is able to separate unambiguously the two objects in a few weeks. The spectral parameters of the pulsar derived in this context could be used to discriminate between the polar cap and outer gap models
9. HIGH-PRECISION TIMING OF FIVE MILLISECOND PULSARS: SPACE VELOCITIES, BINARY EVOLUTION, AND EQUIVALENCE PRINCIPLES
We present high-precision timing of five millisecond pulsars (MSPs) carried out for more than seven years; four pulsars are in binary systems and one is isolated. We are able to measure the pulsars' proper motions and derive an estimate for their space velocities. The measured two-dimensional velocities are in the range 70-210 km s–1, consistent with those measured for other MSPs. We also use all the available proper motion information for isolated and binary MSPs to update the known velocity distribution for these populations. As found by earlier works, we find that the velocity distribution of binary and isolated MSPs are indistinguishable with the current data. Four of the pulsars in our observing program are highly recycled with low-mass white dwarf companions and we are able to derive accurate binary parameters for these systems. For three of these binary systems, we are able to place initial constraints on the pulsar masses with best-fit values in the range 1.0-1.6 M☉. The implications of the results presented here to our understanding of binary pulsar evolution are discussed. The updated parameters for the binary systems studied here, together with recently discovered similar systems, allowed us to update previous limits on the violation of the strong equivalence principle through the parameter |Δ| to 4.6 × 10–3 (95% confidence) and the violation of Lorentz invariance/momentum conservation through the parameter |α-hat3| to 5.5 × 10–20 (95% confidence).
10. Properties and Evolution of the Redback Millisecond Pulsar Binary PSR J2129-0429
Bellm, Eric C.; Kaplan, David L.; Breton, Rene P.; Phinney, E. Sterl; Bhalerao, Varun B.; Camilo, Fernando; Dahal, Sumit; Djorgovski, S. G.; Drake, Andrew J.; Hessels, J. W. T.; Laher, Russ R.; Levitan, David B.; Lewis, Fraser; Mahabal, Ashish A.; Ofek, Eran O.; Prince, Thomas A.; Ransom, Scott M.; Roberts, Mallory S. E.; Russell, David M.; Sesar, Branimir; Surace, Jason A.; Tang, Sumin
2016-01-01
PSR J2129-0429 is a “redback” eclipsing millisecond pulsar binary with an unusually long 15.2 hr orbit. It was discovered by the Green Bank Telescope in a targeted search of unidentified Fermi gamma-ray sources. The pulsar companion is optically bright (mean mR = 16.6 mag), allowing us to construct the longest baseline photometric data set available for such a system. We present 10 years of archival and new photometry of the companion from the Lincoln Near-Earth Asteroid Research Survey, the Catalina Real-time Transient Survey, the Palomar Transient Factory, the Palomar 60 inch, and the Las Cumbres Observatory Global Telescope. Radial velocity spectroscopy using the Double-Beam Spectrograph on the Palomar 200 inch indicates that the pulsar is massive: 1.74 ± 0.18 {M}⊙ . The G-type pulsar companion has mass 0.44 ± 0.04 {M}⊙ , one of the heaviest known redback companions. It is currently 95 ± 1% Roche-lobe filling and only mildly irradiated by the pulsar. We identify a clear 13.1 mmag yr-1 secular decline in the mean magnitude of the companion as well as smaller-scale variations in the optical light curve shape. This behavior may indicate that the companion is cooling. Binary evolution calculations indicate that PSR J2129-0429 has an orbital period almost exactly at the bifurcation period between systems that converge into tighter orbits as black widows and redbacks and those that diverge into wider pulsar-white dwarf binaries. Its eventual fate may depend on whether it undergoes future episodes of mass transfer and increased irradiation.
11. Probing millisecond pulsar emission geometry using light curves from the Fermi Large Area Telescope
Venter, C; Guillemot, L
2009-01-01
An interesting new high-energy pulsar sub-population is emerging following early discoveries of gamma-ray millisecond pulsars (MSPs) by the Fermi Large Area Telescope (LAT). We present results from 3D emission modeling, including the Special Relativistic effects of aberration and time-of-flight delays and also rotational sweepback of B-field lines, in the geometric context of polar cap (PC), outer gap (OG), and two-pole caustic (TPC) pulsar models. In contrast to the general belief that these very old, rapidly-rotating neutron stars (NSs) should have largely pair-starved magnetospheres due to the absence of significant pair production, we find that most of the light curves are best fit by TPC and OG models, which indicates the presence of narrow accelerating gaps limited by robust pair production -- even in these pulsars with very low spin-down luminosities. The gamma-ray pulse shapes and relative phase lags with respect to the radio pulses point to high-altitude emission being dominant for all geometries. We...
12. Parkes Radio Searches of Fermi Gamma-Ray Sources and Millisecond Pulsar Discoveries
Camilo, F.; Kerr, M.; Ray, P. S.; Ransom, S. M.; Sarkissian, J.; Cromartie, H. T.; Johnston, S.; Reynolds, J. E.; Wolff, M. T.; Freire, P. C. C.; Bhattacharyya, B.; Ferrara, E. C.; Keith, M.; Michelson, P. F.; Saz Parkinson, P. M.; Wood, K. S.
2015-09-01
In a search with the Parkes radio telescope of 56 unidentified Fermi-Large Area Telescope (LAT) gamma-ray sources, we have detected 11 millisecond pulsars (MSPs), 10 of them discoveries, of which five were reported by Kerr et al. We did not detect radio pulsations from six other pulsars now known in these sources. We describe the completed survey, which included multiple observations of many targets conducted to minimize the impact of interstellar scintillation, acceleration effects in binary systems, and eclipses. We consider that 23 of the 39 remaining sources may still be viable pulsar candidates. We present timing solutions and polarimetry for five of the MSPs and gamma-ray pulsations for PSR J1903-7051 (pulsations for five others were reported in the second Fermi-LAT catalog of gamma-ray pulsars). Two of the new MSPs are isolated and five are in \\gt 1 day circular orbits with 0.2-0.3 {M}⊙ presumed white dwarf companions. PSR J0955-6150, in a 24 day orbit with a ≈ 0.25 {M}⊙ companion but eccentricity of 0.11, belongs to a recently identified class of eccentric MSPs. PSR J1036-8317 is in an 8 hr binary with a \\gt 0.14 {M}⊙ companion that is probably a white dwarf. PSR J1946-5403 is in a 3 hr orbit with a \\gt 0.02 {M}⊙ companion with no evidence of radio eclipses.
13. Parkes radio searches of Fermi gamma-ray sources and millisecond pulsar discoveries
Camilo, F; Ray, P S; Ransom, S M; Sarkissian, J; Cromartie, H T; Johnston, S; Reynolds, J E; Wolff, M T; Freire, P C C; Bhattacharyya, B; Ferrara, E C; Keith, M; Michelson, P F; Parkinson, P M Saz; Wood, K S
2015-01-01
In a search with the Parkes radio telescope of 56 unidentified Fermi-LAT gamma-ray sources, we have detected 11 millisecond pulsars (MSPs), 10 of them discoveries, of which five were reported in Kerr et al. (2012). We did not detect radio pulsations from another six pulsars now known in these sources. We describe the completed survey, which included multiple observations of many targets done to minimize the impact of interstellar scintillation, acceleration effects in binary systems, and eclipses. We consider that 23 of the 39 remaining sources may still be viable pulsar candidates. We present timing solutions and polarimetry for five of the MSPs, and gamma-ray pulsations for PSR J1903-7051 (pulsations for five others were reported in the second Fermi-LAT catalog of gamma-ray pulsars). Two of the new MSPs are isolated and five are in >1 d circular orbits with 0.2-0.3 Msun presumed white dwarf companions. PSR J0955-6150, in a 24 d orbit with a ~0.25 Msun companion but eccentricity of 0.11, belongs to a recentl...
14. The Contribution of Millisecond Pulsars to the Local Electron / Positron Spectrum
Venter, Christo; Buesching, Ingo; Harding, Alice; Kopp, Andreas; Gonthier, Peter
The high energies of gamma-ray photons (as well as the presence of lower-energy photons) coupled with the intense magnetic fields characterizing younger pulsars enable formation of electron-positron pair cascades which fills the pulsar magnetosphere with plasma and also feeds an outflowing particle wind that may create a surrounding pulsar wind nebula (PWN). Although this scenario was originally thought to be unique to the younger pulsar population, Fermi LAT demonstrated that the light curves of millisecond pulsars (MSPs) are generally very similar to those of younger pulsars, requiring copious pair production even for this older class with much lower surface magnetic fields and spin-down power. These pair cascades may thus be a primary source of Galactic electrons and positrons, and may present an astrophysical explanation for the observed enhancement in positron flux in the high-energy band. We investigate Galactic MSPs contribution to the flux of local cosmic-ray electrons and positrons. We use a population synthesis code to predict the source properties (number, position, and power) of the present-day Galactic MSPs, taking into account the latest Fermi observations to calibrate the model output. Next, we simulate pair cascade spectra from these MSPs using a model that invokes an offset-dipole magnetic field, as this increases the pair production rate relative to a standard dipole field geometry. The model source pair spectra may extend to several TeV, depending on pulsar properties, neutron star equation of state, and magnetic polar cap offset. Since MSPs are not surrounded by PWNe or supernova shells, we can assume that the pairs escape from the pulsar environment without energy loss and undergo losses only in the intergalactic medium. We lastly compute the spectrum of the transported electrons and positrons at Earth, following their diffusion and energy loss through the Galaxy. We will compare our results with the observed local interstellar spectrum and
15. Prospects for neutron star equation of state constraints using ''recycled'' millisecond pulsars
''Recycled'' millisecond pulsars are a variety of rapidly spinning neutron stars that typically show thermal X-ray radiation due to the heated surface of their magnetic polar caps. Detailed numerical modeling of the rotation-induced thermal X-ray pulsations observed from recycled millisecond pulsars, including all relevant relativistic and stellar atmospheric effects, has been identified as a promising approach towards an astrophysical determination of the true neutron star mass-radius relation, and by extension the state of cold matter at densities exceeding those of atomic nuclei. Herein, I review the basic model and methodology commonly used to extract information regarding neutron star structure from the pulsed X-ray radiation observed from millisecond pulsars. I also summarize the results of past X-ray observations of these objects and the prospects for precision neutron star mass-radius measurements with the upcoming Neutron Star Interior Composition Explorer (NICER) X-ray timing mission. (orig.)
16. Prospects for neutron star equation of state constraints using ''recycled'' millisecond pulsars
Bogdanov, Slavko [Columbia University, Columbia Astrophysics Laboratory, New York, NY (United States)
2016-02-15
''Recycled'' millisecond pulsars are a variety of rapidly spinning neutron stars that typically show thermal X-ray radiation due to the heated surface of their magnetic polar caps. Detailed numerical modeling of the rotation-induced thermal X-ray pulsations observed from recycled millisecond pulsars, including all relevant relativistic and stellar atmospheric effects, has been identified as a promising approach towards an astrophysical determination of the true neutron star mass-radius relation, and by extension the state of cold matter at densities exceeding those of atomic nuclei. Herein, I review the basic model and methodology commonly used to extract information regarding neutron star structure from the pulsed X-ray radiation observed from millisecond pulsars. I also summarize the results of past X-ray observations of these objects and the prospects for precision neutron star mass-radius measurements with the upcoming Neutron Star Interior Composition Explorer (NICER) X-ray timing mission. (orig.)
17. Discovery of near-ultraviolet counterparts to millisecond pulsars in the globular cluster 47 Tucanae
Rivera-Sandoval, L E; Heinke, C O; Cohn, H N; Lugger, P M; Freire, P; Anderson, J; Serenelli, A M; Althaus, L G; Cool, A M; Grindlay, J E; Edmonds, P D; Wijnands, R; Ivanova, N
2015-01-01
We report the discovery of the likely white dwarf companions to radio millisecond pulsars 47 Tuc Q and 47 Tuc S in the globular cluster 47 Tucanae. These blue stars were found in near-ultraviolet images from the Hubble Space Telescope for which we derived accurate absolute astrometry, and are located at positions consistent with the radio coordinates to within 0.016 arcsec (0.2sigma). We present near-ultraviolet and optical colours for the previously identified companion to millisecond pulsar 47 Tuc U, and we unambiguously confirm the tentative prior identifications of the optical counterparts to 47 Tuc T and 47 Tuc Y. For the latter, we present its radio-timing solution for the first time. We find that all five near-ultraviolet counterparts have U300-B390 colours that are consistent with He white dwarf cooling models for masses ~0.16-0.3 Msun and cooling ages within ~0.1-6 Gyr. The Ha-R625 colours of 47 Tuc U and 47 Tuc T indicate the presence of a strong Ha absorption line, as expected for white dwarfs with...
18. Probing Millisecond Pulsar Emission Geometry Using Light Curves From the Fermi Large Area Telescope
Venter, Christo; Harding, Alice; Guillemot, L.
2009-01-01
An interesting new high-energy pulsar sub-population is emerging following early discoveries of gamma-ray millisecond pulsars (MSPs) by the Fermi Large Area Telescope (LAT). We present results from 3D emission modeling, including the Special Relativistic effects of aberration and time-of-flight delays and also rotational sweepback of 13-field lines, in the geometric context of polar cap (PC), slot gap (SG), outer gap (OG), and two-pole caustic (TPC) pulsar models. In contrast to the general belief that these very old, rapidly-rotating neutron stars (NSs) should have largely pair-starved magnetospheres due to the absence of significant pair production, we find that most of the light curves are best fit by SG and OG models, which indicates the presence of narrow accelerating gaps limited by robust pair production -- even in these pulsars with very low spin-down luminosities. The gamma-ray pulse shapes and relative phase lags with respect to the radio pulses point to high-altitude emission being dominant for all geometries. We also find exclusive differentiation of the current gamma-ray MSP population into two MSP sub-classes: light curve shapes and lags across wavebands impose either pair-starved PC (PSPC) or SG / OG-type geometries. In the first case, the radio pulse has a small lag with respect to the single gamma-ray pulse, while the (first) gamma-ray peak usually trails the radio by a large phase offset in the latter case. Finally, we find that the flux correction factor as a function of magnetic inclination and observer angles is typically of order unity for all models. Our calculation of light curves and flux correction factor f(_, _, P) for the case of MSPs is therefore complementary to the "ATLAS paper" of Watters et al. for younger pulsars.
19. The High Time Resolution Universe Pulsar Survey - VII: discovery of five millisecond pulsars and the different luminosity properties of binary and isolated recycled pulsars
Burgay, M; Bates, S D; Bhat, N D R; Burke-Spolaor, S; Champion, D J; Coster, P; D'Amico, N; Johnston, S; Keith, M J; Kramer, M; Levin, L; Lyne, A G; Milia, S; Ng, C; Possenti, A; Stappers, B W; Thornton, D; Tiburzi, C; van Straten, W; Bassa, C G
2013-01-01
This paper presents the discovery and timing parameters for five millisecond pulsars (MSPs), four in binary systems with probable white dwarf companions and one isolated, found in ongoing processing of the High Time Resolution Universe Pulsar Survey (HTRU). We also present high quality polarimetric data on four of them. These further discoveries confirm the high potential of our survey in finding pulsars with very short spin periods. At least two of these five MSPs are excellent candidates to be included in the Pulsar Timing Array projects. Thanks to the wealth of MSP discoveries in the HTRU survey, we revisit the question of whether the luminosity distributions of isolated and binary MSPs are different. Using the Cordes and Lazio distance model and our new and catalogue flux density measurements, we find that 41 of the 42 most luminous MSPs in the Galactic disk are in binaries and a statistical analysis suggests that the luminosity functions differ with 99.9% significance. We conclude that the formation proc...
20. Two Millisecond Pulsars Discovered by the PALFA Survey and a Shapiro Delay Measurement
Deneva, J S; Cordes, J M; Lyne, A G; Ransom, S M; Cognard, I; Camilo, F; Nice, D J; Stairs, I H; Allen, B; Bhat, N D R; Bogdanov, S; Brazier, A; Champion, D J; Chatterjee, S; Crawford, F; Desvignes, G; Hessels, J W T; Jenet, F A; Kaspi, V M; Knispel, B; Kramer, M; Lazarus, P; van Leeuwen, J; Lorimer, D R; Lynch, R S; McLaughlin, M A; Scholz, P; Siemens, X; Stappers, B W; Stovall, K; Venkataraman, A
2012-01-01
We present two millisecond pulsar discoveries from the PALFA survey of the Galactic plane with the Arecibo telescope. PSR J1955+2527 is an isolated pulsar with a period of 4.87 ms, and PSR J1949+3106 has a period of 13.14 ms and is in a 1.9-day binary system with a massive companion. Their timing solutions, based on 4 years of timing measurements with the Arecibo, Green Bank, Nan\\c{c}ay and Jodrell Bank telescopes, allow precise determination of spin and astrometric parameters, including precise determinations of their proper motions. For PSR J1949+3106, we can clearly detect the Shapiro delay. From this we measure the pulsar mass to be 1.47(+0.43/-0.31) solar masses, the companion mass to be 0.85(+0.14/-0.11) solar masses and the orbital inclination to be i = 79.9(+1.6/-1.9) degrees, where uncertainties correspond to +/- 1-\\sigma\\ confidence levels. With continued timing, we expect to also be able to detect the advance of periastron for the J1949+3106 system. This effect, combined with the Shapiro delay, wil...
1. SDSS J102347.6+003841: A Millisecond Radio Pulsar Binary That Had A Hot Disk
Wang, Zhongxiang; Thorstensen, John R; Kaspi, Victoria M; Lorimer, Duncan R; Stairs, Ingrid; Ransom, Scott M
2009-01-01
The Sloan Digital Sky Survey (SDSS) source J102347.6+003841 is a binary star with a 4.75 hr orbital period. A recent radio pulsar survey showed that its primary is a millisecond pulsar (MSP). Here we analyze the SDSS spectrum of the source in detail. The spectrum was taken on 2001 February 1, when the source was in a bright state and showed broad, double-peaked hydrogen and helium lines -- dramatically different from the G-type absorption spectrum seen from 2003 onward. The lines are consistent with emission from a disk around the compact primary. We derive properties of the disk by fitting the SDSS continuum with a simple disk model, and find a temperature range of 2000--34000 K from the outer to inner edge of the disk. The disk inner and outer radii were approximately 10^9 and 5.7x10^10 cm, respectively. These results further emphasize the unique feature of the source: it is evidently a system at the beginning of its life as a recycled radio pulsar. The disk mass is estimated to have been ~10^23 g, most of ...
2. Discovery of the Optical/Ultraviolet/Gamma-ray Counterpart to the Eclipsing Millisecond Pulsar J1816+4510
Kaplan, D L; Ransom, S M; Roberts, M S E; Kotulla, R; Archibald, A M; Biwer, C M; Boyles, J; Dartez, L; Day, D F; Ford, A J; Garcia, A; Hessels, J W T; Jenet, F A; Karako, C; Kaspi, V M; Kondratiev, V I; Lorimer, D R; Lynch, R S; McLaughlin, M A; Rohr, M D W; Siemens, X; Stairs, I H; van Leeuwen, J
2012-01-01
The energetic, eclipsing millisecond pulsar J1816+4510 was recently discovered in a low-frequency radio survey with the Green Bank Telescope. With an orbital period of 8.7 hr and minimum companion mass of 0.16 Msun it appears to belong to an increasingly important class of pulsars that are ablating their low-mass companions. We report the discovery of the gamma-ray counterpart to this pulsar, and present a likely optical/ultraviolet counterpart as well. Using the radio ephemeris we detect pulsations in the unclassified gamma-ray source 2FGL J1816.5+4511, implying an efficiency of ~25% in converting the pulsar's spin-down luminosity into gamma-rays and adding PSR J1816+4510 to the large number of millisecond pulsars detected by Fermi. The likely optical/UV counterpart was identified through position coincidence (15,000 K it would be among the brightest and hottest of low-mass pulsar companions, and appears qualitatively different from other eclipsing pulsar systems. In particular, current data suggest that it ...
3. The low-mass X-ray binary-millisecond radio pulsar birthrate problem revisited
Hailang, Dai
2009-01-01
We investigate the birthrate problem for low-mass X-ray binaries (LMXBs) and millisecond radio pulsars (MRPs) in this paper. We consider intermediate-mass and low-mss X-ray binaries (I/LMXBs) as the progenitors of MRPs, and calculate their evolutionary response to the cosmic star formation rate (SFR) both semi-analytically and numerically. With typical value (~1 Gyr) of the LMXB lifetime, one may expect comparable birthrates of LMXBs and MRPs, but the calculated number of LMXBs is an order of magnitude higher than observed in the Galaxy. Instead, we suggest that the birthrate problem could be solved if most MRPs have evolved from faint rather bright LMXBs. The former may have a population of ~ 104 in the Galaxy.
4. The low-mass X-ray binary-millisecond radio pulsar birthrate problem revisited
2010-01-01
We investigate the birthrate problem for low-mass X-ray binaries(LMXBs) and millisecond radio pulsars(MRPs) in this paper.We consider intermediate-mass and low-mass X-ray binaries(I/LMXBs) to be the progenitors of MRPs,and calculate their evolutionary response to the cosmic star formation rate(SFR) both semi-analytically and numerically.With a typical value(1 Gyr) of the LMXB lifetime,one may expect comparable birthrates of LMXBs and MRPs,but the calculated number of LMXBs is an order of magnitude higher than that observed in the Galaxy.Instead,we suggest that the birthrate problem could be solved if most MRPs have evolved from faint to rather than bright LMXBs.The former may have a population of-104 in the Galaxy.
5. Properties and observability of glitches and anti-glitches in accreting pulsars
Ducci, L; Doroshenko, V; Santangelo, A; Mereghetti, S; Ferrigno, C
2015-01-01
Several glitches have been observed in young, isolated radio pulsars, while a clear detection in accretion-powered X-ray pulsars is still lacking. We use the "snowplow" model for pulsar glitches of Pizzochero (2011) and starquake models to determine for the first time the expected properties of glitches in accreting pulsars and their observability. Since some accreting pulsars show accretion-induced long-term spin-up, we also investigate the possibility that anti-glitches occur in these stars. We find that glitches caused by quakes in a slow accreting neutron star are very rare and their detection extremely unlikely. On the contrary, glitches and anti-glitches caused by a transfer of angular momentum between the superfluid neutron vortices and the non-superfluid component may take place in accreting pulsars more often. We calculate the maximum jump in angular velocity of an anti-glitch and we find that it is expected to be about 1E-5 - 1E-4 rad/s. We also note that since accreting pulsars usually have rotatio...
6. Dynamic effects on cyclotron scattering in pulsar accretion columns
Brainerd, J. J.; Meszaros, P.
1991-01-01
A resonant scattering model for photon reprocessing in a pulsar accretion column is presented. The accretion column is optically thin to Thomson scattering and optically thick to resonant scattering at the cyclotron frequency. Radiation from the neutron star surface propagates freely through the column until the photon energy equals the local cyclotron frequency, at which point the radiation is scattered, much of it back toward the star. The radiation pressure in this regime is insufficient to stop the infall. Some of the scattered radiation heats the stellar surface around the base of the column, which adds a softer component to the spectrum. The partial blocking by the accretion column of X-rays from the surface produces a fan beam emission pattern. X-rays above the surface cyclotron frequency freely escape and are characterized by a pencil beam. Gravitational light bending produces a pencil beam pattern of column-scattered radiation in the antipodal direction, resulting in a strongly angle-dependent cyclotron feature.
7. New limits on the population of normal and millisecond pulsars in the Large and Small Magellanic Clouds
Ridley, J P
2010-01-01
We model the potentially observable populations of normal and millisecond radio pulsars in the Large and Small Magellanic Clouds (LMC and SMC) where the known population currently stands at 19 normal radio pulsars. Taking into account the detection thresholds of previous surveys, and assuming optimal period and luminosity distributions based on studies of Galactic pulsars, we estimate there are (1.79 +/- 0.20) x 10^4 and (1.09 +/- 0.16) x 10^4 normal pulsars in the LMC and SMC respectively. When we attempt to correct for beaming effects, and the fraction of high-velocity pulsars which escape the clouds, we estimate birth rates in both the LMC and SMC to be comparable and in the range 0.5--1 pulsar per century. Although higher than estimates for the rate of core-collapse supernovae in the clouds, these pulsar birth rates are consistent with historical supernova observations in the past 300 yr. A substantial population of active radio pulsars (of order a few hundred thousand) have escaped the LMC and SMC and po...
8. Six New Millisecond Pulsars from Arecibo Searches of Fermi Gamma-Ray Sources
Cromartie, H T; Kerr, M; Deneva, J S; Ransom, S M; Ray, P S; Ferrara, E C; Michelson, P F; Wood, K S
2016-01-01
We have discovered six radio millisecond pulsars (MSPs) in a search with the Arecibo telescope of 34 unidentified gamma-ray sources from the Fermi Large Area Telescope (LAT) 4-year point source catalog. Among the 34 sources, we also detected two MSPs previously discovered elsewhere. Each source was observed at a center frequency of 327 MHz, typically at three epochs with individual integration times of 15 minutes. The new MSP spin periods range from 1.99 to 4.66 ms. Five of the six pulsars are in interacting compact binaries (period < 8.1 hr), while the sixth is a more typical neutron star-white dwarf binary with an 83-day orbital period. This is a higher proportion of interacting binaries than for equivalent Fermi-LAT searches elsewhere. The reason is that Arecibo's large gain afforded us the opportunity to limit integration times to 15 minutes, which significantly increased our sensitivity to these highly accelerated systems. Seventeen of the remaining 26 gamma-ray sources are still categorized as strong...
9. Einstein@Home Discovery of a PALFA Millisecond Pulsar in an Eccentric Binary Orbit
Knispel, B; Stappers, B W; Freire, P C C; Lazarus, P; Allen, B; Aulbert, C; Bock, O; Bogdanov, S; Brazier, A; Camilo, F; Cardoso, F; Chatterjee, S; Cordes, J M; Crawford, F; Deneva, J S; Eggenstein, H -B; Fehrmann, H; Ferdman, R; Hessels, J W T; Jenet, F A; Karako-Argaman, C; Kaspi, V M; van Leeuwen, J; Lorimer, D R; Lynch, R; Machenschalk, B; Madsen, E; McLaughlin, M A; Patel, C; Ransom, S M; Scholz, P; Siemens, X; Spitler, L G; Stairs, I H; Stovall, K; Swiggum, J K; Venkataraman, A; Wharton, R S; Zhu, W W
2015-01-01
We report the discovery of the millisecond pulsar (MSP) PSR J1950+2414 ($P=4.3$ ms) in a binary system with an eccentric ($e=0.08$) orbit in Pulsar ALFA survey observations with the Arecibo telescope. Its companion star has a median mass of 0.3 $M_\\odot$ and is most likely a white dwarf. Fully recycled MSPs like this one are thought to be old neutron stars spun-up by mass transfer from a companion star. This process should circularize the orbit, as is observed for the vast majority of binary MSPs, which predominantly have orbital eccentricities $e < 0.001$. However, four recently discovered binary MSPs have orbits with larger eccentricities ($0.03 < e < 0.4$); PSR J1950+2414 is only the fifth such system to be discovered. The upper limits for the the intrinsic spin period derivative and inferred surface magnetic field strength are comparable to those of the general MSP population. The large eccentricities of these systems are not compatible with the predictions of the standard recycling scenario: som...
10. Formation of the planet around the millisecond pulsar J1719-1438
van Haaften, L M; Voss, R; Jonker, P G
2012-01-01
Context. Recently the discovery of PSR J1719-1438, a 5.8 ms pulsar with a companion in a 2.2 hr orbit, was reported. The combination of this orbital period and the very low mass function is unique. The discoverers, Bailes et al., proposed an ultracompact X-ray binary (UCXB) as the progenitor system. However, the standard UCXB scenario would not produce this system as the time required to reach this orbital period exceeds the current estimate of the age of the Universe. The detached state of the system aggravates the problem. Aims. We want to understand the evolutionary history of PSR J1719-1438, and determine under which circumstances it could have evolved from an UCXB. Methods. We model UCXB evolution varying the donor size and investigate the effect of a wind mass loss from the donor, and compare the results with the observed characteristics of PSR J1719-1438. Results. An UCXB can reach a 2.2 hr orbit within the age of the Universe, provided that 1) the millisecond pulsar can significantly heat and expand t...
11. Thermal X-rays from Millisecond Pulsars: Constraining the Fundamental Properties of Neutron Stars
Bogdanov, Slavko; Rybicki, George B
2008-01-01
(Abridged) We model the X-ray properties of millisecond pulsars (MSPs) by considering hot spot emission from a weakly magnetized rotating neutron star (NS) covered by an optically-thick hydrogen atmosphere. We investigate the limitations of using the thermal X-ray pulse profiles of MSPs to constrain the mass-to-radius ($M/R$) ratio of the underlying NS. The accuracy is strongly dependent on the viewing angle and magnetic inclination. For certain systems, the accuracy is ultimately limited only by photon statistics implying that future X-ray observatories could, in principle, achieve constraints on $M/R$ and hence the NS equation of state to better than $\\sim$5%. We demonstrate that valuable information regarding the basic properties of the NS can be extracted even from X-ray data of fairly limited photon statistics through modeling of archival spectroscopic and timing observations of the nearby isolated PSRs J0030+0451 and J2124--3358. The X-ray emission from these pulsars is consistent with the presence of a...
12. Formation of the planet orbiting the millisecond pulsar J1719-1438
van Haaften, L M; Voss, R; Jonker, P G
2012-01-01
In 2011, Bailes et al. reported on the discovery of a detached companion in a 131 minute orbit around PSR J1719-1438, a 173 Hz millisecond pulsar. The combination of the very low mass function and such a short orbital period is unique. The discoverers suggested that the progenitor system could be an ultracompact X-ray binary (UCXB), which is a binary with a sub-hour orbital period in which a (semi-)degenerate donor fills its Roche lobe and transfers mass to a neutron star. The standard gravitational-wave driven UCXB scenario, however, cannot produce a system like PSR J1719-1438 as it would take longer than the age of the Universe to reach an orbital period of 131 min. We investigate two modifications to the standard UCXB evolution that may resolve this discrepancy. The first involves significant heating and bloating of the donor by pulsar irradiation, and in the second modification the system loses orbital angular momentum via a fast stellar wind from the irradiated donor, additional to the losses via the usu...
13. A Highly Eccentric 3.9-Millisecond Binary Pulsar in the Globular Cluster NGC 6652
DeCesar, Megan E; Kaplan, David L; Ray, Paul S; Geller, Aaron M
2015-01-01
We present the Robert C. Byrd Green Bank Telescope discovery of the highly eccentric binary millisecond pulsar PSR J1835$-$3259A in the Fermi Large Area Telescope-detected globular cluster NGC 6652. Timing over one orbit yields the pulse period 3.89 ms, orbital period 9.25 d, eccentricity $\\sim 0.95$, and an unusually high companion mass of $0.74\\,M_{\\odot}$ assuming a $1.4\\,M_{\\odot}$ pulsar. We caution that the lack of data near periastron prevents a precise measurement of the eccentricity, and that further timing is necessary to constrain this and the other orbital parameters. From tidal considerations, we find that the companion must be a compact object. This system likely formed through an exchange encounter in the dense cluster environment. Our initial timing results predict the measurements of at least two post-Keplerian parameters with long-term phase-connected timing: the rate of periastron advance $\\dot{\\omega} \\sim 0.1^{\\circ}\\,$yr$^{-1}$, requiring 1 yr of phase connection; and the Einstein delay ...
14. Radio Detection of the Fermi-LAT Blind Search Millisecond Pulsar J1311-3430
Ray, P. S.; Ransom, S. M.; Cheung, C. C.; Giroletti, M.; Cognard, I.; Camilo, F.; Bhattacharyya, B.; Roy, J.; Romani, R. W.; Ferrara, E. C.; Guillemot, L.; Johnston, S.; Keith, M.; Kerr, M.; Kramer, M.; Pletsch, H. J.; Parkinson, P. M. Saz
2013-01-01
We report the detection of radio emission from PSR J1311.3430, the first millisecond pulsar (MSP) discovered in a blind search of Fermi Large Area Telescope (LAT) gamma-ray data. We detected radio pulsations at 2 GHz, visible for less than 10% of approximately 4.5 hr of observations using the Green Bank Telescope (GBT). Observations at 5 GHz with the GBT and at several lower frequencies with Parkes, Nan cay, and the Giant Metrewave Radio Telescope resulted in non-detections. We also report the faint detection of a steep spectrum continuum radio source (0.1 mJy at 5 GHz) in interferometric imaging observations with the Jansky Very Large Array. These detections demonstrate that PSR J1311.3430 is not radio quiet and provide additional evidence that radio-quiet MSPs are rare. The radio dispersion measure of 37.8 pc cm(exp -3) provides a distance estimate of 1.4 kpc for the system, yielding a gamma-ray efficiency of 30%, typical of LAT-detected MSPs. We see apparent excess delay in the radio pulses as the pulsar appears from eclipse and we speculate on possible mechanisms for the non-detections of the pulse at other orbital phases and observing frequencies.
15. Constraints on the Emission Geometries and Spin Evolution of Gamma-ray Millisecond Pulsars
Johnson, T J; Harding, A K; Guillemot, L; Smith, D A; Kramer, M; Celik, O; Hartog, P R den; Ferrara, E C; Hou, X; Lande, J; Ray, P S
2014-01-01
Millisecond pulsars (MSPs) are a growing class of gamma-ray emitters. Pulsed gamma-ray signals have been detected from more than 40 MSPs with the Fermi Large Area Telescope (LAT). The wider radio beams and more compact magnetospheres of MSPs enable studies of emission geometries over a broader range of phase space than non-recycled radio-loud gamma-ray pulsars. We have modeled the gamma-ray light curves of 40 LAT-detected MSPs using geometric emission models assuming a vacuum retarded-dipole magnetic field. We modeled the radio profiles using a single-altitude hollow-cone beam, with a core component when indicated by polarimetry; however, for MSPs with gamma-ray and radio light curve peaks occurring at nearly the same rotational phase we assume that the radio emission is co-located with the gamma rays and caustic in nature. The best-fit parameters and confidence intervals are determined using a maximum likelihood technique. We divide the light curves into three model classes, with gamma-ray peaks trailing (Cl...
16. The noise properties of 42 millisecond pulsars from the European Pulsar Timing Array and their impact on gravitational-wave searches
Caballero, R. N.; Lee, K. J.; Lentati, L.; Desvignes, G.; Champion, D. J.; Verbiest, J. P. W.; Janssen, G. H.; Stappers, B. W.; Kramer, M.; Lazarus, P.; Possenti, A.; Tiburzi, C.; Perrodin, D.; Osłowski, S.; Babak, S.; Bassa, C. G.; Brem, P.; Burgay, M.; Cognard, I.; Gair, J. R.; Graikou, E.; Guillemot, L.; Hessels, J. W. T.; Karuppusamy, R.; Lassus, A.; Liu, K.; McKee, J.; Mingarelli, C. M. F.; Petiteau, A.; Purver, M. B.; Rosado, P. A.; Sanidas, S.; Sesana, A.; Shaifullah, G.; Smits, R.; Taylor, S. R.; Theureau, G.; van Haasteren, R.; Vecchio, A.
2016-04-01
The sensitivity of Pulsar Timing Arrays to gravitational waves (GWs) depends on the noise present in the individual pulsar timing data. Noise may be either intrinsic or extrinsic to the pulsar. Intrinsic sources of noise will include rotational instabilities, for example. Extrinsic sources of noise include contributions from physical processes which are not sufficiently well modelled, for example, dispersion and scattering effects, analysis errors and instrumental instabilities. We present the results from a noise analysis for 42 millisecond pulsars (MSPs) observed with the European Pulsar Timing Array. For characterizing the low-frequency, stochastic and achromatic noise component, or `timing noise', we employ two methods, based on Bayesian and frequentist statistics. For 25 MSPs, we achieve statistically significant measurements of their timing noise parameters and find that the two methods give consistent results. For the remaining 17 MSPs, we place upper limits on the timing noise amplitude at the 95 per cent confidence level. We additionally place an upper limit on the contribution to the pulsar noise budget from errors in the reference terrestrial time standards (below 1 per cent), and we find evidence for a noise component which is present only in the data of one of the four used telescopes. Finally, we estimate that the timing noise of individual pulsars reduces the sensitivity of this data set to an isotropic, stochastic GW background by a factor of >9.1 and by a factor of >2.3 for continuous GWs from resolvable, inspiralling supermassive black hole binaries with circular orbits.
17. The accretion flow to the intermittent accreting ms pulsar, HETE J1900.1-2455, as observed by XMM-Newton and RXTE
Papitto, A; Di Salvo, T; Egron, E; Bozzo, E; Burderi, L; Iaria, R; Riggio, A; Menna, M T
2012-01-01
We present a study of the accretion flow to the intermittent accreting millisecond pulsar, HETE J1900.1-2455, based on observations performed simultaneously by XMM-Newton and RXTE. The 0.33-50 keV spectrum is described by the sum of a hard Comptonized component originated in an optically thin {\\tau}~1 corona, a soft kTin~0.2 keV component interpreted as accretion disc emission, and of disc reflection of the hard component. Two emission features are detected at energies of 0.98(1) and 6.58(7) keV, respectively. The latter is identified as K{\\alpha} transition of Fe XXIII-XXV. A simultaneous detection in EPIC-pn, EPIC-MOS2, and RGS spectra favours an astrophysical origin also for the former, which has an energy compatible with Fe-L{\\alpha} and helium-like Ne-K{\\alpha} transitions. Broadness of the two features suggests a common origin, resulting from reflection in an accretion disc with inclination of (30+4{\\deg}), and extending down to Rin=25(+16,-11) gravitational radii from the compact object. However, the s...
18. CONSTRAINTS ON THE EMISSION GEOMETRIES AND SPIN EVOLUTION OF GAMMA-RAY MILLISECOND PULSARS
Millisecond pulsars (MSPs) are a growing class of gamma-ray emitters. Pulsed gamma-ray signals have been detected from more than 40 MSPs with the Fermi Large Area Telescope (LAT). The wider radio beams and more compact magnetospheres of MSPs enable studies of emission geometries over a broader range of phase space than non-recycled radio-loud gamma-ray pulsars. We have modeled the gamma-ray light curves of 40 LAT-detected MSPs using geometric emission models assuming a vacuum retarded-dipole magnetic field. We modeled the radio profiles using a single-altitude hollow-cone beam, with a core component when indicated by polarimetry; however, for MSPs with gamma-ray and radio light curve peaks occurring at nearly the same rotational phase, we assume that the radio emission is co-located with the gamma rays and caustic in nature. The best-fit parameters and confidence intervals are determined using a maximum likelihood technique. We divide the light curves into three model classes, with gamma-ray peaks trailing (Class I), aligned (Class II), or leading (Class III) the radio peaks. Outer gap and slot gap (two-pole caustic) models best fit roughly equal numbers of Class I and II, while Class III are exclusively fit with pair-starved polar cap models. Distinguishing between the model classes based on typical derived parameters is difficult. We explore the evolution of the magnetic inclination angle with period and spin-down power, finding possible correlations. While the presence of significant off-peak emission can often be used as a discriminator between outer gap and slot gap models, a hybrid model may be needed
19. CONSTRAINTS ON THE EMISSION GEOMETRIES AND SPIN EVOLUTION OF GAMMA-RAY MILLISECOND PULSARS
Johnson, T. J. [National Research Council Research Associate, National Academy of Sciences, Washington, DC 20001 (United States); Venter, C. [Centre for Space Research, North-West University, Potchefstroom Campus, Private Bag X6001, 2520 Potchefstroom (South Africa); Harding, A. K.; Çelik, Ö.; Ferrara, E. C. [NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Guillemot, L. [Laboratoire de Physique et Chimie de l' Environnement, LPCE UMR 6115 CNRS, F-45071 Orléans Cedex 02 (France); Smith, D. A.; Hou, X. [Centre d' Études Nucléaires de Bordeaux Gradignan, IN2P3/CNRS, Université Bordeaux 1, BP120, F-33175 Gradignan Cedex (France); Kramer, M. [Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn (Germany); Den Hartog, P. R. [W. W. Hansen Experimental Physics Laboratory, Kavli Institute for Particle Astrophysics and Cosmology, Department of Physics and SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94305 (United States); Lande, J. [Twitter Inc., 1355 Market Street 900, San Francisco, CA 94103 (United States); Ray, P. S., E-mail: tyrel.j.johnson@gmail.com, E-mail: Christo.Venter@nwu.ac.za, E-mail: ahardingx@yahoo.com [Space Science Division, Naval Research Laboratory, Washington, DC 20375-5352 (United States)
2014-07-01
Millisecond pulsars (MSPs) are a growing class of gamma-ray emitters. Pulsed gamma-ray signals have been detected from more than 40 MSPs with the Fermi Large Area Telescope (LAT). The wider radio beams and more compact magnetospheres of MSPs enable studies of emission geometries over a broader range of phase space than non-recycled radio-loud gamma-ray pulsars. We have modeled the gamma-ray light curves of 40 LAT-detected MSPs using geometric emission models assuming a vacuum retarded-dipole magnetic field. We modeled the radio profiles using a single-altitude hollow-cone beam, with a core component when indicated by polarimetry; however, for MSPs with gamma-ray and radio light curve peaks occurring at nearly the same rotational phase, we assume that the radio emission is co-located with the gamma rays and caustic in nature. The best-fit parameters and confidence intervals are determined using a maximum likelihood technique. We divide the light curves into three model classes, with gamma-ray peaks trailing (Class I), aligned (Class II), or leading (Class III) the radio peaks. Outer gap and slot gap (two-pole caustic) models best fit roughly equal numbers of Class I and II, while Class III are exclusively fit with pair-starved polar cap models. Distinguishing between the model classes based on typical derived parameters is difficult. We explore the evolution of the magnetic inclination angle with period and spin-down power, finding possible correlations. While the presence of significant off-peak emission can often be used as a discriminator between outer gap and slot gap models, a hybrid model may be needed.
20. Constraints On the Emission Geometries and Spin Evolution Of Gamma-Ray Millisecond Pulsars
Johnson, T. J.; Venter, C.; Harding, A. K.; Guillemot, L.; Smith, D. A.; Kramer, M.; Celik, O.; den Hartog, P. R.; Ferrara, E. C.; Hou, X.; Lande, J.; Ray, P. S.
2014-01-01
Millisecond pulsars (MSPs) are a growing class of gamma-ray emitters. Pulsed gamma-ray signals have been detected from more than 40 MSPs with the Fermi Large Area Telescope (LAT). The wider radio beams and more compact magnetospheres of MSPs enable studies of emission geometries over a broader range of phase space than non-recycled radio-loud gamma-ray pulsars. We have modeled the gamma-ray light curves of 40 LAT-detected MSPs using geometric emission models assuming a vacuum retarded-dipole magnetic field. We modeled the radio profiles using a single-altitude hollow-cone beam, with a core component when indicated by polarimetry; however, for MSPs with gamma-ray and radio light curve peaks occurring at nearly the same rotational phase, we assume that the radio emission is co-located with the gamma rays and caustic in nature. The best-fit parameters and confidence intervals are determined using amaximum likelihood technique.We divide the light curves into three model classes, with gamma-ray peaks trailing (Class I), aligned (Class II), or leading (Class III) the radio peaks. Outer gap and slot gap (two-pole caustic) models best fit roughly equal numbers of Class I and II, while Class III are exclusively fit with pair-starved polar cap models. Distinguishing between the model classes based on typical derived parameters is difficult. We explore the evolution of the magnetic inclination angle with period and spin-down power, finding possible correlations. While the presence of significant off-peak emission can often be used as a discriminator between outer gap and slot gap models, a hybrid model may be needed.
1. Ultra-High-Energy Cosmic Ray Acceleration by Magnetic Reconnection in Newborn Accretion Induced Collapse Pulsars
De Gouveia dal Pino, E M
2000-01-01
We here investigate the possibility that the ultra-high energy cosmic ray(UHECR) events observed above the GZK limit are mostly protons accelerated inreconnection sites just above the magnetosphere of newborn millisecond pulsarswhich are originated by accretion induced collapse (AIC). We find thatAIC-pulsars with surface magnetic fields $10^{12} G < B_{\\star} \\lesssim10^{15}$ G and spin periods $1 ms \\lesssim P_{\\star} < 60 ms$, are able toaccelerate particles to energies $\\geq 10^{20}$ eV. Because the expected rateof AIC sources in our Galaxy is very small (\\sim 10^{-5} yr^{-1}), thecorresponding contribution to the flux of UHECRs is neglegible, and the totalflux is given by the integrated contribution from AIC sources produced by thedistribution of galaxies located within the distance which is unaffected by theGZK cutoff ($\\sim 50$ Mpc). We find that the reconnection efficiency factorneeds to be only $\\xi \\gtrsim 3.6 \\times 10^{-3}$ in order to reproduce theobserved flux of UHECRs.
2. Scintillation Arcs in Low-frequency Observations of the Timing-array Millisecond Pulsar PSR J0437-4715
Bhat, N. D. R.; Ord, S. M.; Tremblay, S. E.; McSweeney, S. J.; Tingay, S. J.
2016-02-01
Low-frequency observations of pulsars provide a powerful means for probing the microstructure in the turbulent interstellar medium (ISM). Here we report on high-resolution dynamic spectral analysis of our observations of the timing-array millisecond pulsar PSR J0437-4715 with the Murchison Widefield Array (MWA), enabled by our recently commissioned tied-array beam processing pipeline for voltage data recorded from the high time resolution mode of the MWA. A secondary spectral analysis reveals faint parabolic arcs akin to those seen in high-frequency observations of pulsars with the Green Bank and Arecibo telescopes. Data from Parkes observations at a higher frequency of 732 MHz reveal a similar parabolic feature with a curvature that scales approximately as the square of the observing wavelength (λ2) to the MWA's frequency of 192 MHz. Our analysis suggests that scattering toward PSR J0437-4715 predominantly arises from a compact region about 115 pc from the Earth, which matches well with the expected location of the edge of the Local Bubble that envelopes the local Solar neighborhood. As well as demonstrating new and improved pulsar science capabilities of the MWA, our analysis underscores the potential of low-frequency pulsar observations for gaining valuable insights into the local ISM and for characterizing the ISM toward timing-array pulsars.
3. Modeling Light Curves of the Phase-Aligned Gamma-ray Millisecond Pulsar Subclass
Venter, C; Harding, A K
2011-01-01
The gamma-ray population of millisecond pulsars (MSPs) detected by the Fermi Large Area Telescope (LAT) has been steadily increasing. A number of the more recent detections, including PSR J0034-0534, PSR J1939+2134 (B1937+21; the first MSP ever discovered), PSR J1959+2048 (B1957+20; the first black widow system), and PSR J2214+3000 exhibit an unusual phenomenon: nearly phase-aligned radio and gamma-ray light curves (LCs). To account for the phase alignment, we explore geometric models where both the radio and gamma-ray emission originate either in the outer magnetosphere near the light cylinder (R_LC) or near the polar caps (PCs). We obtain reasonable fits for the first three of these MSPs in the context of "altitude-limited" outer gap (alOG) and two-pole caustic (alTPC) geometries. The outer magnetosphere phase-aligned models differ from the standard outer gap (OG) / two-pole caustic (TPC) models in two respects: first, the radio emission originates in caustics at relatively high altitudes compared to the us...
4. Estimating the GeV Emission of Millisecond Pulsars in Dwarf Spheroidal Galaxies
Winter, Miles; Bechtol, Keith; Vandenbroucke, Justin
2016-01-01
We estimate the conventional astrophysical emission intrinsic to dwarf spheroidal satellite galaxies (dSphs) of the Milky Way, focusing on millisecond pulsars (MSPs), and evaluate the potential for confusion with dark matter (DM) annihilation signatures at GeV energies. In low-density stellar environments, such as dSphs, the abundance of MSPs is expected to be proportional to stellar mass. Accordingly, we construct the $\\gamma$-ray luminosity function of MSPs in the Milky Way disk, where $>90$ individual MSPs have been detected with the $\\textit{Fermi}$ Large Area Telescope (LAT), and scale this luminosity function to the stellar masses of 30 dSphs to estimate the cumulative emission from their MSP populations. We predict that MSPs in the highest stellar mass dSphs, Fornax and Sculptor, produce a $\\gamma$-ray flux $>500$ MeV of $\\sim10^{-11}$~ph~cm$^{-2}$~s$^{-1}$, which is a factor $\\sim10$ below the current LAT sensitivity at high Galactic latitudes. The MSP emission in ultra-faint dSphs, including targets ...
5. High-fidelity radio astronomical polarimetry using a millisecond pulsar as a polarized reference source
van Straten, W
2012-01-01
A new method of polarimetric calibration is presented in which the instrumental response is derived from regular observations of PSR J0437-4715 based on the assumption that the mean polarized emission from this millisecond pulsar remains constant over time. The technique is applicable to any experiment in which high-fidelity polarimetry is required over long time scales; it is demonstrated by calibrating 7.2 years of high-precision timing observations of PSR J1022+1001 made at the Parkes Observatory. Application of the new technique followed by arrival time estimation using matrix template matching yields post-fit residuals with an uncertainty-weighted standard deviation of 880 ns, two times smaller than that of arrival time residuals obtained via conventional methods of calibration and arrival time estimation. The precision achieved by this experiment yields the first significant measurements of the secular variation of the projected semi-major axis, the precession of periastron, and the Shapiro delay; it al...
6. One blind and three targeted searches for (sub)millisecond pulsars
Davoust, E; Fayard, T
2011-01-01
We conducted one blind and three targeted searches for millisecond and submillisecond pulsars. The blind search was conducted within 3deg of the Galactic plane and at longitudes between 20 and 110deg. It takes 22073 pointings to cover this region, and 5487 different positions in the sky. The first targeted search was aimed at Galactic globular clusters, the second one at 24 bright polarized and pointlike radiosources with steep spectra, and the third at 65 faint polarized and pointlike radiosources. The observations were conducted at the large radiotelescope of Nancay Observatory, at a frequency near 1400 MHz. Two successive backends were used, first a VLBI S2 system, second a digital acquisition board and a PC with large storage capacity sampling the signal at 50 Mb/s on one bit, over a 24-MHz band and in one polarization. The bandwidth of acquisition of the second backend was later increased to 48 MHz and the sampling rate to 100 Mb/s. The survey used the three successive setups, with respective sensitiviti...
7. The millisecond pulsar mass distribution: Evidence for bimodality and constraints on the maximum neutron star mass
Antoniadis, John; Ozel, Feryal; Barr, Ewan; Champion, David J; Freire, Paulo C C
2016-01-01
The mass function of neutron stars (NSs) contains information about the late evolution of massive stars, the supernova explosion mechanism, and the equation-of-state of cold, nuclear matter beyond the nuclear saturation density. A number of recent NS mass measurements in binary millisecond pulsar (MSP) systems increase the fraction of massive NSs (with $M > 1.8$ M$_{\\odot}$) to $\\sim 20\\%$ of the observed population. In light of these results, we employ a Bayesian framework to revisit the MSP mass distribution. We find that a single Gaussian model does not sufficiently describe the observed population. We test alternative empirical models and infer that the MSP mass distribution is strongly asymmetric. The diversity in spin and orbital properties of high-mass NSs suggests that this is most likely not a result of the recycling process, but rather reflects differences in the NS birth masses. The asymmetry is best accounted for by a bimodal distribution with a low mass component centred at $1.393_{-0.029}^{+0.0... 8. A millisecond pulsar candidate in a 21-hr orbit: 3FGL J0212.1+5320 Linares, Manuel; Rodríguez-Gil, Pablo; Shahbaz, Tariq; Casares, Jorge; Fariña, Cecilia; Karjalainen, Raine 2016-01-01 We present the discovery of a variable optical counterpart to the unidentified gamma-ray source 3FGL J0212.1+5320, and argue this is a new compact binary millisecond pulsar (MSP) candidate. We show 3FGL J0212.1+5320 hosts a semi-detached binary with a 0.86955$\\pm$0.00015 d orbital period and a F6-type companion star at an estimated distance of D=1.1$\\pm$0.2 kpc, with a radial velocity curve semi-amplitude K$_2$=214.1$\\pm$5.0 km s$^{-1}$and a projected rotational velocity of Vsin(i)=73.2$\\pm$1.6 km s$^{-1}$. We find a hard X-ray source at the same location with a 0.5$-$10 keV luminosity L$_\\mathrm{X}$=2.6$\\times$10$^{32}$(D/1.1 kpc)$^2$erg s$^{-1}$, which strengthens the MSP identification. Our results imply a mass ratio q=M$_2$/M$_1$=0.26$^{+0.02}_{-0.03}$if the companion star fills its Roche lobe, and q$\\gtrsim$0.23 in any case. This classifies 3FGL J0212.1+5320 as a "redback" binary MSP; if its MSP nature is confirmed, this will be the brightest compact binary MSP in the optical band (r'$\\simeq$14.3 mag... 9. An eccentric binary millisecond pulsar with a helium white dwarf companion in the Galactic Field Antoniadis, John; Stovall, Kevin; Freire, Paulo C; Deneva, Julia S; Koester, Detlev; Jenet, Frederick; Martinez, Jose 2016-01-01 Low-mass white dwarfs (LMWDs) are believed to be exclusive products of binary evolution, as the Universe is not yet old enough to produce them from single stars. Because of the strong tidal forces operating during the binary interaction phase, the remnant host systems observed today are expected to have negligible eccentricities. Here, we report on the first unambiguous identification of a LMWD in an eccentric (e=0.13) orbit with a millisecond pulsar, which directly contradicts this picture. We use our spectra and radio-timing solution (derived elsewhere) to infer the WD temperature T_eff = 8600 +/- 190 K) and 3D systemic velocity (179.5 km\\s). We also place model-independent constraints on the WD radius (R_WD = 0.024+/- 0.004/0.002 R_sun) and surface gravity (log g = 7.11 +/- 0.08/0.16 dex). The WD and kinematic properties are consistent with the expectations for low-mass X-ray binary evolution and disfavour a three-body formation channel. In the case of the high eccentricity being the result of a spontaneou... 10. Low-Mass X-Ray Binaries, Millisecond Radio Pulsars, and the Cosmic Star Formation Rate White, N E; White, Nicholas E.; Ghosh, Pranab 1998-01-01 We report on the implications of the peak in the cosmic star-formation rate (SFR) at redshift z ~ 1.5 for the resulting population of low-mass X-ray binaries(LMXB) and for that of their descendants, the millisecond radio pulsars (MRP). Since the evolutionary timescales of LMXBs, their progenitors, and their descendants are thought be significant fractions of the time-interval between the SFR peak and the present epoch, there is a lag in the turn-on of the LMXB population, with the peak activity occurring at z ~ 0.5 - 1.0. The peak in the MRP population is delayed further, occurring at z < 0.5. We show that the discrepancy between the birthrate of LMXBs and MRPs, found under the assumption of a stead-state SFR, can be resolved for the population as a whole when the effects of a time-variable SFR are included. A discrepancy may persist for LMXBs with short orbital periods, although a detailed population synthesis will be required to confirm this. Further, since the integrated X-ray luminosity distribution of... 11. Statistical and polarization properties of giant pulses of the millisecond pulsar B1937+21 Zhuravlev, V I; Soglasnov, V A; Kondrat'ev, V I; Kovalev, Y Y; Bartel, N; Ghigo, F 2013-01-01 We have studied the statistical and polarization properties of giant pulses (GPs) emitted by the millisecond pulsar B1937+21, with high sensitivity and time resolution. The observations were made in June 2005 with the 100-m Robert C. Byrd Green Bank Telescope at S-band (2052-2116 MHz) using the Mk5A VLBI recording system, with formal time resolution of 16 ns. The total observing time was about 4.5 hours; the rate of detection of GPs was about 130 per hour at the average longitudes of the main pulse (MPGPs) and 60 per hour at the interpulse (IPGPs). While the average profile shows well-defined polarization behavior, with regular evolution of the linear polarization position angle (PA), GPs exhibit random properties, occasionally having high linear or circular polarization. Neither MPGPs nor IPGPs show a preferred PA. The cumulative probability distribution (CPD) of GP pulse energy was constructed down to the level where GPs merge with regular pulses and noise. For both MPGPs and IPGPs, the CPD follows a power ... 12. A 24-Hour Global Campaign To Assess Precision Timing of the Millisecond Pulsar J1713+0747 Dolch, T; Cordes, J M; Chatterjee, S; Bassa, C; Bhattacharyya, B; Champion, D J; Cognard, I; Crowter, K; Demorest, P B; Hessels, J W T; Janssen, G H; Jenet, F A; Jones, G; Jordan, C; Karuppusamy, R; Keith, M; Kondratiev, V I; Kramer, M; Lazarus, P; Lazio, T J W; Lee, K J; McLaughlin, M A; Roy, J; Shannon, R M; Stairs, I H; Stovall, K; Verbiest, J P W; Madison, D R; Palliyaguru, N; Perrodin, D; Ransom, S M; Stappers, B W; Zhu, W W; Dai, S; Desvignes, G; Guillemot, L; Liu, K; Lyne, A G; Perera, B B P; Petroff, E; Rankin, J M; Smits, R 2014-01-01 The radio millisecond pulsar J1713+0747 is regarded as one of the highest-precision clocks in the sky, and is regularly timed for the purpose of detecting gravitational waves. The International Pulsar Timing Array collaboration undertook a 24-hour global observation of PSR J1713+0747 in an effort to better quantify sources of timing noise in this pulsar, particularly on intermediate (1 - 24 hr) timescales. We observed the pulsar continuously over 24 hr with the Arecibo, Effelsberg, GMRT, Green Bank, LOFAR, Lovell, Nancay, Parkes, and WSRT radio telescopes. The combined pulse times-of-arrival presented here provide an estimate of what sources of timing noise, excluding DM variations, would be present as compared to an idealized root-N improvement in timing precision, where N is the number of pulses analyzed. In the case of this particular pulsar, we find that intrinsic pulse phase jitter dominates arrival time precision when the S/N of single pulses exceeds unity, as measured using the eight telescopes that ob... 13. A 24 hr global campaign to assess precision timing of the millisecond pulsar J1713+0747 The radio millisecond pulsar J1713+0747 is regarded as one of the highest-precision clocks in the sky and is regularly timed for the purpose of detecting gravitational waves. The International Pulsar Timing Array Collaboration undertook a 24 hr global observation of PSR J1713+0747 in an effort to better quantify sources of timing noise in this pulsar, particularly on intermediate (1-24 hr) timescales. We observed the pulsar continuously over 24 hr with the Arecibo, Effelsberg, GMRT, Green Bank, LOFAR, Lovell, Nançay, Parkes, and WSRT radio telescopes. The combined pulse times-of-arrival presented here provide an estimate of what sources of timing noise, excluding DM variations, would be present as compared to an idealized √N improvement in timing precision, where N is the number of pulses analyzed. In the case of this particular pulsar, we find that intrinsic pulse phase jitter dominates arrival time precision when the signal-to-noise ratio of single pulses exceeds unity, as measured using the eight telescopes that observed at L band/1.4 GHz. We present first results of specific phenomena probed on the unusually long timescale (for a single continuous observing session) of tens of hours, in particular interstellar scintillation, and discuss the degree to which scintillation and profile evolution affect precision timing. This paper presents the data set as a basis for future, deeper studies. 14. Statistical and polarization properties of giant pulses of the millisecond pulsar B1937+21 Zhuravlev, V. I.; Popov, M. V.; Soglasnov, V. A.; Kondrat'ev, V. I.; Kovalev, Y. Y.; Bartel, N.; Ghigo, F. 2013-04-01 We have studied the statistical and polarization properties of giant pulses (GPs) emitted by the millisecond pulsar B1937+21, with high sensitivity and time resolution. The observations were made in 2005 June with the 100-m Robert C. Byrd Green Bank Telescope at S-band (2052-2116 MHz) using the Mk5A Very Long Baseline Interferometry recording system, with formal time resolution of 16 ns. The total observing time was about 4.5 h; the rate of detection of GPs was about 130 per hour at the average longitudes of the main pulse (MPGPs) and 60 per hour at the interpulse (IPGPs). While the average profile shows well-defined polarization behaviour, with regular evolution of the linear polarization position angle (PA), GPs exhibit random properties, occasionally having high linear or circular polarization. Neither MPGPs nor IPGPs show a preferred PA. The cumulative probability distribution (CPD) of GP pulse energy was constructed down to the level where GPs merge with regular pulses and noise. For both MPGPs and IPGPs, the CPD follows a power law with a break, the power index changing from -2.4 at high energy to -1.6 for low energy. Pulse smearing due to scattering masks the intrinsic shape and duration of the detected GPs. The smearing time varied during the observing session within a range of a few hundred nanoseconds. The measured polarization and statistical properties of GPs impose strong constraints on physical models of GPs. Some of these properties support a model in which GPs are generated by the electric discharge caused by magnetic reconnection of field lines connecting the opposite magnetic poles of a neutron star. 15. Study of frame tie between planetary ephemerids and ICRF with millisecond and young pulsars Wang, Jingbo; Hobbs, George; Coles, William 2016-07-01 The positions of pulsar can be measured by pulsar timing technology and VLBI astrometry with high precision. They can be used to tie between referece frame based on solar system ephemerids and distant quasars with high accuracy. In this paper, we have collect the pulsar positions with VLBI measurement and obtain the pulsar timing position form Nanshan and Parkes data archive. We derive the rotation matrix between JPL DE and ICRF reference frame. 16. Evidence for Magneto-Levitation Accretion in Long-Period X-ray Pulsars Ikhsanov, Nazar; Likh, Yury 2014-01-01 Study of observed spin evolution of long-period X-ray pulsars challenges quasi-spherical and Keplerian disk accretion scenarios. It suggests that the magnetospheric radius of the neutron stars is substantially smaller than Alfven radius and the spin-down torque applied to the star from accreting material significantly exceeds the value predicted by the theory. We show that these problems can be avoided if the fossil magnetic field of the accretion flow itself is incorporated into the accretion model. The initially spherical flow in this case decelerates by its own magnetic field and converts into a non-Keplerian disk (magnetic slab) in which the material is confined by its intrinsic magnetic field ("levitates") and slowly moves towards the star on a diffusion timescale. Parameters of pulsars expected within this magneto-levitation accretion scenario are evaluated. 17. The NANOGrav Nine-year Data Set: Observations, Arrival Time Measurements, and Analysis of 37 Millisecond Pulsars Arzoumanian, Z; Burke-Spolaor, S; Chamberlin, S; Chatterjee, S; Christy, B; Cordes, J M; Cornish, N; Crowter, K; Demorest, P B; Dolch, T; Ellis, J A; Ferdman, R D; Fonseca, E; Garver-Daniels, N; Gonzalez, M E; Jenet, F A; Jones, G; Jones, M; Kaspi, V M; Koop, M; Lazio, T J W; Lam, M T; Levin, L; Lommen, A N; Lorimer, D R; Luo, J; Lynch, R S; Madison, D; McLaughlin, M A; McWilliams, S T; Nice, D J; Palliyaguru, N; Pennucci, T T; Ransom, S M; Siemens, X; Stairs, I H; Stinebring, D R; Stovall, K; Swiggum, J K; Vallisneri, M; van Haasteren, R; Wang, Y; Zhu, W 2015-01-01 We present high-precision timing observations spanning up to nine years for 37 millisecond pulsars monitored with the Green Bank and Arecibo radio telescopes as part of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) project. We describe the observational and instrumental setups used to collect the data, and methodology applied for calculating pulse times of arrival; these include novel methods for measuring instrumental offsets and characterizing low signal-to-noise ratio timing results. The time of arrival data are fit to a physical timing model for each source, including terms that characterize time-variable dispersion measure and frequency-dependent pulse shape evolution. In conjunction with the timing model fit, we have performed a Bayesian analysis of a parameterized timing noise model for each source, and detect evidence for time-correlated "red" signals in 10 of the pulsars. Subsequent papers in this series will present further analysis of this data set aimed at detecting o... 18. A Shapiro delay detection in the binary system hosting the millisecond pulsar PSR J1910-5959A Corongiu, A; Possenti, A; Camilo, F; D'Amico, N; Lyne, A G; Manchester, R N; Sarkissian, J M; Bailes, M; Johnston, S; Kramer, M; van Straten, W 2012-01-01 PSR J1910-5959A is a binary pulsar with a helium white dwarf companion located about 6 arcmin from the center of the globular cluster NGC6752. Based on 12 years of observations at the Parkes radio telescope, the relativistic Shapiro delay has been detected in this system. We obtain a companion mass Mc = 0.180+/-0.018Msun (1sigma) implying that the pulsar mass lies in the range 1.1Msun <= Mp <= 1.5Msun. We compare our results with previous optical determinations of the companion mass, and examine prospects for using this new measurement for calibrating the mass-radius relation for helium white dwarfs and for investigating their evolution in a pulsar binary system. Finally we examine the set of binary systems hosting a millisecond pulsar and a low mass helium white dwarf for which the mass of both stars has been measured. We confirm that the correlation between the companion mass and the orbital period predicted by Tauris & Savonije reproduces the observed values but find that the predicted Mp - Pb co... 19. Pulsed Gamma-Rays From the Millisecond Pulsar J0030+0451 with the Fermi Large Area Telescope We report the discovery of gamma-ray pulsations from the nearby isolated millisecond pulsar PSR J0030+0451 with the Large Area Telescope (LAT) on the Fermi Gamma-ray Space Telescope (formerly GLAST). This discovery makes PSR J0030+0451 the second millisecond pulsar to be detected in gamma-rays after PSR J0218+4232, observed by the EGRET instrument on the Compton Gamma Ray Observatory. The spin-down power (dot E) = 3.5 x 1033 ergs s-1 is an order of magnitude lower than the empirical lower bound of previously known gamma-ray pulsars. The emission profile is characterized by two narrow peaks, respectively 0.07 ± 0.01 and 0.08 ± 0.02 wide, separated by 0.44 ± 0.02 in phase. The first gamma-ray peak falls 0.15 ± 0.01 after the main radio peak. The pulse shape is similar to that of the 'normal' gamma-ray pulsars. An exponentially cut-off power-law fit of the emission spectrum leads to an integral photon flux above 100 MeV of (6.76 ± 1.05 ± 1.35) x 10-8 cm-2 s-1 with cut-off energy (1.7 ± 0.4 ± 0.5) GeV. Based on its parallax distance of (300 ± 90) pc, we obtain a gamma-ray efficiency Lγ/(dot E) ≅ 15% for the conversion of spin-down energy rate into gamma-ray radiation, assuming isotropic emission. 20. The Helium White Dwarf orbiting the Millisecond Pulsar in the halo of the Globular Cluster NGC 6752 Ferraro, F R; Sabbi, E; D'Amico, N; Ferraro, Francesco R.; Possenti, Andrea; Sabbi, Elena; Amico, Nichi D' 2003-01-01 We have used deep high-resolution multiband images taken at the ESO Very Large Telescope to identify the optical binary companion to the millisecond pulsar (PSR J1911-5958A) located in the halo of the Galactic Globular Cluster NGC6752. The object turns out to be a blue star whose position in the Color Magnitude Diagram is consistent with the cooling sequence of a low mass (M~0.17-0.20Mo), low metallicity Helium white dwarf (He-WD) at the cluster distance. This is the second He-WD which has been found to orbit a millisecond pulsar in GGCs. Curiously both objects have been found to lie on the same mass He-WD cooling sequence. The anomalous position of PSR J1911-5958A with respect to the globular cluster center (~6') suggested that this system has recently (<1 Gyr) been ejected from the cluster core as the result of a strong dynamical interaction. The data presented here allows to constrain the cooling age of the companion within a fairly narrow range (~1.2-2.8 Gyr), therefore suggesting that such dynamical e... 1. THE NEAREST MILLISECOND PULSAR REVISITED WITH XMM-NEWTON: IMPROVED MASS-RADIUS CONSTRAINTS FOR PSR J0437-4715 I present an analysis of the deepest X-ray exposure of a radio millisecond pulsar (MSP) to date, an X-ray Multi Mirror-Newton European Photon Imaging Camera spectroscopic and timing observation of the nearest known MSP, PSR J0437-4715. The timing data clearly reveal a secondary broad X-ray pulse offset from the main pulse by ∼0.55 in rotational phase. In the context of a model of surface thermal emission from the hot polar caps of the neutron star, this can be plausibly explained by a magnetic dipole field that is significantly displaced from the stellar center. Such an offset, if commonplace in MSPs, has important implications for studies of the pulsar population, high energy pulsed emission, and the pulsar contribution to cosmic-ray positrons. The continuum emission shows evidence for at least three thermal components, with the hottest radiation most likely originating from the hot magnetic polar caps and the cooler emission from the bulk of the surface. I present pulse phase-resolved X-ray spectroscopy of PSR J0437-4715, which for the first time properly accounts for the system geometry of a radio pulsar. Such an approach is essential for unbiased measurements of the temperatures and emission areas of polar cap radiation from pulsars. Detailed modeling of the thermal pulses, including relativistic and atmospheric effects, provides a constraint on the redshift-corrected neutron star radius of R > 11.1 km (at 3σ conf.) for the current radio timing mass measurement of 1.76 M ☉. This limit favors 'stiff' equations of state. 2. DISCOVERY OF PSR J1227−4853: A TRANSITION FROM A LOW-MASS X-RAY BINARY TO A REDBACK MILLISECOND PULSAR XSS J12270−4859 is an X-ray binary associated with the Fermi Large Area Telescope gamma-ray source 1FGL J1227.9−4852. In 2012 December, this source underwent a transition where the X-ray and optical luminosity dropped and the spectral signatures of an accretion disk disappeared. We report the discovery of a 1.69 millisecond pulsar (MSP), PSR J1227−4853, at a dispersion measure of 43.4 pc cm−3 associated with this source, using the Giant Metrewave Radio Telescope (GMRT) at 607 MHz. This demonstrates that, post-transition, the system hosts an active radio MSP. This is the third system after PSR J1023+0038 and PSR J1824−2452I showing evidence of state switching between radio MSP and low-mass X-ray binary states. We report timing observations of PSR J1227−4853 with the GMRT and Parkes, which give a precise determination of the rotational and orbital parameters of the system. The companion mass measurement of 0.17–0.46 M⊙ suggests that this is a redback system. PSR J1227−4853 is eclipsed for about 40% of its orbit at 607 MHz with additional short-duration eclipses at all orbital phases. We also find that the pulsar is very energetic, with a spin-down luminosity of ∼1035 erg s−1. We report simultaneous imaging and timing observations with the GMRT, which suggests that eclipses are caused by absorption rather than dispersion smearing or scattering 3. DISCOVERY OF PSR J1227−4853: A TRANSITION FROM A LOW-MASS X-RAY BINARY TO A REDBACK MILLISECOND PULSAR Roy, Jayanta; Bhattacharyya, Bhaswati; Stappers, Ben [Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, M13 9PL (United Kingdom); Ray, Paul S.; Wolff, Michael; Wood, Kent S. [Space Science Division, Naval Research Laboratory, Washington, DC 20375-5352 (United States); Chengalur, Jayaram N. [National Centre for Radio Astrophysics, Tata Institute of Fundamental Research, Pune 411 007 (India); Deneva, Julia [NRC Research Associate, resident at Naval Research Laboratory, Washington, DC 20375-5352 (United States); Camilo, Fernando [Columbia Astrophysics Laboratory, Columbia University, New York, NY 10027 (United States); Johnson, Tyrel J. [College of Science, George Mason University, Fairfax, VA 22030, USA, resident at Naval Research Laboratory, Washington, DC 20375 (United States); Hessels, Jason W. T.; Bassa, Cees G. [ASTRON, the Netherlands Institute for Radio Astronomy, Postbus 2, 7990 AA, Dwingeloo (Netherlands); Keane, Evan F. [Centre for Astrophysics and Supercomputing, Swinburne University of Technology, Mail H30, P.O. Box 218, VIC 3122 (Australia); Ferrara, Elizabeth C.; Harding, Alice K. [NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States) 2015-02-10 XSS J12270−4859 is an X-ray binary associated with the Fermi Large Area Telescope gamma-ray source 1FGL J1227.9−4852. In 2012 December, this source underwent a transition where the X-ray and optical luminosity dropped and the spectral signatures of an accretion disk disappeared. We report the discovery of a 1.69 millisecond pulsar (MSP), PSR J1227−4853, at a dispersion measure of 43.4 pc cm{sup −3} associated with this source, using the Giant Metrewave Radio Telescope (GMRT) at 607 MHz. This demonstrates that, post-transition, the system hosts an active radio MSP. This is the third system after PSR J1023+0038 and PSR J1824−2452I showing evidence of state switching between radio MSP and low-mass X-ray binary states. We report timing observations of PSR J1227−4853 with the GMRT and Parkes, which give a precise determination of the rotational and orbital parameters of the system. The companion mass measurement of 0.17–0.46 M{sub ⊙} suggests that this is a redback system. PSR J1227−4853 is eclipsed for about 40% of its orbit at 607 MHz with additional short-duration eclipses at all orbital phases. We also find that the pulsar is very energetic, with a spin-down luminosity of ∼10{sup 35} erg s{sup −1}. We report simultaneous imaging and timing observations with the GMRT, which suggests that eclipses are caused by absorption rather than dispersion smearing or scattering. 4. Theory of quasi-spherical accretion in X-ray pulsars Shakura, N.; Postnov, K.; Kochetkova, A.; Hjalmarsdotter, L. 2012-02-01 A theoretical model for quasi-spherical subsonic accretion on to slowly rotating magnetized neutron stars is constructed. In this model, the accreting matter subsonically settles down on to the rotating magnetosphere forming an extended quasi-static shell. This shell mediates the angular momentum removal from the rotating neutron star magnetosphere during spin-down episodes by large-scale convective motions. The accretion rate through the shell is determined by the ability of the plasma to enter the magnetosphere. The settling regime of accretion can be realized for moderate accretion rates ? g s-1. At higher accretion rates, a free-fall gap above the neutron star magnetosphere appears due to rapid Compton cooling, and accretion becomes highly non-stationary. From observations of the spin-up/spin-down rates (the angular rotation frequency derivative ?, and ? near the torque reversal) of X-ray pulsars with known orbital periods, it is possible to determine the main dimensionless parameters of the model, as well as to estimate the magnetic field of the neutron star. We illustrate the model by determining these parameters for three wind-fed X-ray pulsars GX 301-2, Vela X-1 and GX 1+4. The model explains both the spin-up/spin-down of the pulsar frequency on large time-scales and the irregular short-term frequency fluctuations, which can correlate or anticorrelate with the X-ray flux fluctuations in different systems. It is shown that in real pulsars an almost iso-angular-momentum rotation law with ω˜ 1/R2, due to strongly anisotropic radial turbulent motions sustained by large-scale convection, is preferred. 5. Timing, polarimetry and physics of the bright, nearby millisecond pulsar PSR J0437-4715 - a single-pulse perspective Osłowski, S; Bailes, M; Jameson, A; Hobbs, G 2014-01-01 Single pulses from radio pulsars contain a wealth of information about emission and propagation in the magnetosphere and insight into their timing properties. It was recently demonstrated that single-pulse emission is responsible for limiting the timing stability of the brightest of millisecond pulsars. We report on an analysis of more than a million single-pulses from PSR J0437-4715 and present various statistical properties such as the signal-to-noise ratio (S/N) distribution, timing and polarimetry of average profiles integrated from subpulses with chosen S/N cut-offs, modulation properties of the emission, phase-resolved statistics of the S/N, and two dimensional spherical histograms of the polarization vector orientation. The last of these indicates the presence of orthogonally polarised modes (OPMs). Combined with the dependence of the polarisation fraction on the S/N and polarimetry of the brightest pulses, the existence of OPMs constrains pulsar emission mechanisms and models for the plasma physics in... 6. Scintillation arcs in low-frequency observations of the timing-array millisecond pulsar J0437-4715 Bhat, N D R; Tremblay, S E; McSweeney, S J; Tingay, S J 2015-01-01 Low-frequency observations of pulsars provide a powerful means for probing the microstructure in the turbulent interstellar medium (ISM). Here we report on high-resolution dynamic spectral analysis of our observations of the timing-array millisecond pulsar J0437-4715 with the Murchison Widefield Array (MWA), enabled by our recently commissioned tied-array beam processing pipeline for voltage data recorded from the high time resolution mode of the MWA. A secondary spectral analysis reveals faint parabolic arcs, akin to those seen in high-frequency observations of pulsars with the Green Bank and Arecibo telescopes. Data from Parkes observations at a higher frequency of 732 MHz reveal a similar parabolic feature, with a curvature that scales approximately as the square of the observing wavelength ($\\lambda^2$) to the MWA's frequency of 192 MHz. Our analysis suggests that scattering toward PSR J0437-4715 predominantly arises from a compact region about 115 pc from the Earth, which matches well with the expected l... 7. The Nearest Millisecond Pulsar Revisited with XMM-Newton: Improved Mass-Radius Constraints for PSR J0437-4715 Bogdanov, Slavko 2012-01-01 I present an analysis of the deepest X-ray exposure of a radio millisecond pulsar (MSP) to date, an X-ray Multi Mirror-Newton European Photon Imaging Camera spectroscopic and timing observation of the nearest known MSP, PSR J0437--4715. The timing data clearly reveal a secondary broad X-ray pulse offset from the main pulse by$\\sim$0.55 in rotational phase. In the context of a model of surface thermal emission from the hot polar caps of the neutron star, this can be plausibly explained by a magnetic dipole field that is significantly displaced from the stellar center. Such an offset, if commonplace in MSPs, has important implications for studies of the pulsar population, high energy pulsed emission, and the pulsar contribution to cosmic ray positrons. The continuum emission shows evidence for at least three thermal components, with the hottest radiation most likely originating from the hot magnetic polar caps and the cooler emission from the bulk of the surface. I present pulse phase-resolved X-ray spectrosco... 8. Settling accretion onto slowly rotating X-ray pulsars Shakura, N. I.; Postnov, K. A.; Kochetkova, A. Yu.; Hjalmarsdotter, L. 2013-01-01 Quasi-spherical subsonic accretion onto slowly rotating magnetized NS is considered, when the accreting matter settles down subsonically onto the rotating magnetosphere, forming an extended quasi-static shell. The shell mediates the angular momentum transfer to/from the rotating NS magnetosphere by large-scale convective motions, which lead to an almost iso-angular-momentum rotation law inside the shell. The accretion rate through the shell is determined by the ability of the plasma to enter ... 9. Application of a physical continuum model to recent X-ray observations of accreting pulsars Marcu-Cheatham, Diana Monica; Pottschmidt, Katja; Wolff, Michael Thomas; Becker, Peter A.; Wood, Kent S.; Wilms, Joern; Britton Hemphill, Paul; Gottlieb, Amy; Fuerst, Felix; Schwarm, Fritz-Walter; Ballhausen, Ralf 2016-04-01 We present a uniform spectral analysis in the 0.5-50 keV energy range of a sample of accreting pulsars by applying an empirical broad-band continuum cut-off power-law model. We also apply the newly implemented physical continuum model developed by Becker and Wolff (2007, ApJ 654, 435) to a number of high-luminosity sources. The X-ray spectral formation process in this model consists of the Comptonization of bremsstrahlung, cyclotron, and black body photons emitted by the hot, magnetically channeled, accreting plasma near the neutron star surface. This model describes the spectral formation in high-luminosity accreting pulsars, where the dominant deceleration mechanism is via a radiation-dominated radiative shock. The resulting spectra depend on five physical parameters: the mass accretion rate, the radius of the accretion column, the electron temperature and electron scattering cross-sections inside the column, and the magnetic field strength. The empirical model is fitted to Suzaku data of a sample of high-mass X-ray binaries covering a broad luminosity range (0.3-5 x 10 37 erg/s). The physical model is fitted to Suzaku data from luminous sources: LMC X-4, Cen X-3, GX 304-1. We compare the results of the two types of modeling and summarize how they can provide new insight into the process of accretion onto magnetized neutron stars. 10. Discovery of a millisecond pulsar in the 5.4 day binary 3FGL J1417.5-4402: observing the late phase of pulsar recycling Camilo, F; Ransom, S M; Halpern, J P; Bogdanov, S; Kerr, M; Ray, P S; Cordes, J M; Sarkissian, J; Barr, E D; Ferrara, E C 2016-01-01 In a search of the unidentified Fermi gamma-ray source 3FGL J1417.5-4402 with the Parkes radio telescope, we discovered PSR J1417-4402, a 2.66 ms pulsar having the same 5.4 day orbital period as the optical and X-ray binary identified by Strader et al. The existence of radio pulsations implies that the neutron star is currently not accreting. Substantial outflows from the companion render the radio pulsar undetectable for more than half of the orbit, and may contribute to the observed Halpha emission. Our initial pulsar observations, together with the optically inferred orbit and inclination, imply a mass ratio of 0.171+/-0.002, a companion mass of M_2=0.33+/-0.03 Msun, and a neutron star mass in the range 1.77 11. A new model for the X-ray continuum of the magnetized accreting pulsars Farinelli, R; Bozzo, E; Becker, P A 2016-01-01 Accreting highly magnetized pulsars in binary systems are among the brightest X-ray emitters in our Galaxy. Although a number of high statistical quality broad-band (0.1-100 keV) X-ray observations are available, the spectral energy distribution of these sources is usually investigated by adopting pure phenomenological models, rather than models linked to the physics of accretion. In this paper, a detailed spectral study of the X-ray emission recorded from the high-mass X-ray binary pulsars Cen X-3, 4U 0115+63, and Her X-1 is carried out by using BeppoSAX and joined Suzaku+NuStar data, together with an advanced version of the compmag model. The latter provides a physical description of the high energy emission from accreting pulsars, including the thermal and bulk Comptonization of cyclotron and bremsstrahlung seed photons along the neutron star accretion column. The compmag model is based on an iterative method for solving second-order partial differential equations, whose convergence algorithm has been impr... 12. Settling accretion onto slowly rotating X-ray pulsars Shakura, N I; Kochetkova, A Yu; Hjalmarsdotter, L 2013-01-01 Quasi-spherical subsonic accretion onto slowly rotating magnetized NS is considered, when the accreting matter settles down subsonically onto the rotating magnetosphere, forming an extended quasi-static shell. The shell mediates the angular momentum transfer to/from the rotating NS magnetosphere by large-scale convective motions, which lead to an almost iso-angular-momentum rotation law inside the shell. The accretion rate through the shell is determined by the ability of the plasma to enter the magnetosphere due to Rayleigh-Taylor instability while taking cooling into account. The settling regime of accretion is possible for moderate X-ray luminosities L <4 10^36 erg/s. At higher luminosities a free-fall gap above the NS magnetosphere appears due to rapid Compton cooling, and accretion becomes highly non-stationary. From observations of spin-up/spin-down rates of wind accreting equilibrium XPSRs with known orbital periods (GX 301-2, Vela X-1), the main dimensionless parameters of the model and be determin... 13. Polynomial regression calculation of the Earth's position based on millisecond pulsar timing Prior to achieving high precision navigation of a spacecraft using X-ray observations, a pulsar rotation model must be built and analysis of the precise position of the Earth should be performed using ground pulsar timing observations. We can simulate time-of-arrival ground observation data close to actual observed values before using pulsar timing observation data. Considering the correlation between the Earth's position and its short arc section of an orbit, we use polynomial regression to build the correlation. Regression coefficients can be calculated using the least square method, and a coordinate component series can also be obtained; that is, we can calculate Earth's position in the Barycentric Celestial Reference System according to pulse arrival time data and a precise pulsar rotation model. In order to set appropriate parameters before the actual timing observations for Earth positioning, we can calculate the influence of the spatial distribution of pulsars on errors in the positioning result and the influence of error source variation on positioning by simulation. It is significant that the threshold values of the observation and systematic errors can be established before an actual observation occurs; namely, we can determine the observation mode with small errors and reject the observed data with big errors, thus improving the positioning result. 14. Nustar Detection of Hard X-Ray Phase Lags from the Accreting Pulsar GS 0834-430 Miyasaka, Hiromasa; Bachetti, Matteo; Harrison, Fiona A.; Fu¨rst, Felix; Barret, Didier; Bellm, Eric C.; Boggs, Steven E.; Chakrabarty, Deepto; Chenevez, Jérôme; Christensen, Finn Erland; Craig, William W.; Grefenstette, Brian W.; Hailey, Charles J.; Madsen, Kristin K.; Natalucci, Lorenzo; Pottschmidt, Katja; Stern, Daniel; Tomsick, John A.; Walton, Dominic J.; Wilms, Jo¨rn; Zhang, William 2013-01-01 V with high statistical significance. We find the phase-averaged spectrum to be consistent with that observed in many other magnetized, accreting pulsars. We fail to detect cyclotron resonance scattering features that would allow us to constrain the pulsar's magnetic field in either phase-averaged or... 15. Constraints on the Emission Geometries of Gamma-ray Millisecond Pulsars Observed with the Fermi Large Area Telescope Johnson, T J 2012-01-01 Millisecond pulsars (MSPs) have been established as a class of high-energy ($\\geq$0.1 GeV) emitters with the Large Area Telescope (LAT) aboard the \\emph{Fermi Gamma-ray Space Telescope}. Most MSP gamma-ray light curves display sharp peaks indicative of thin accelerating gaps, suggesting copious pair-creation in the open volume. MSP gamma-ray and radio light curves have been simulated using geometric outer-gap (OG), slot-gap/two-pole caustic (TPC), and pair-starved polar cap gamma-ray models and either a hollow-cone beam or altitude-limited, outer-magnetospheric gap radio model, all assuming a vacuum retarded dipolar magnetic field geometry. A Markov chain Monte Carlo maximum likelihood technique has been developed to find the best-fit model parameters for nineteen MSPs using data from the LAT and various radio observatories. The best-fit viewing angles follow a uniform, angular distribution. The distribution of magnetic inclination angles favors all angles equally, contrary to analyses of non-recycled pulsars... 16. Timing and Fermi LAT Analysis of Four Millisecond Pulsars Discovered in Parkes Radio Searches of Gamma-ray Sources Ray, Paul S.; Ransom, Scott M.; Camilo, Fernando M.; Kerr, Matthew; Reynolds, John; Sarkissian, John; Freire, Paulo; Thankful Cromartie, H.; Barr, Ewan D. 2016-01-01 We present phase-connected timing solutions for four binary millisecond pulsars discovered in searches of Fermi LAT gamma-ray sources using the Parkes radio telescope. Follow-up timing observations of PSRs J0955-6150, J1012-4235, J1036-8317, and J1946-5403 have yielded timing models with precise orbital and astrometric parameters. For each pulsar, we also did a gamma-ray spectral analysis using LAT Pass 8 data and generated photon probabilities for use in a weighted H-test pulsation test. In all 4 cases, we detect significant gamma-ray pulsations, confirming the identification with the gamma-ray source originally targeted in the discovery observations. We describe the results of the pulse timing and gamma-ray spectral and timing analysis and the characteristics of each of the systems. The Fermi-LAT Collaboration acknowledges support for LAT development, operation and data analysis from NASA and DOE (United States), CEA/Irfu and IN2P3/CNRS (France), ASI and INFN (Italy), MEXT, KEK, and JAXA (Japan), and the K.A. Wallenberg Foundation, the Swedish Research Council and the National Space Board (Sweden). Science analysis support in the operations phase from INAF (Italy) and CNES (France) is also gratefully acknowledged. NRL participation was funded by NASA. 17. Multi-wavelength Observations of 3FGL J2039.6-5618: A Candidate Redback Millisecond Pulsar Salvetti, D.; Mignani, R. P.; De Luca, A.; Delvaux, C.; Pallanca, C.; Belfiore, A.; Marelli, M.; Breeveld, A. A.; Greiner, J.; Becker, W.; Pizzocaro, D. 2015-12-01 We present multi-wavelength observations of the unassociated γ-ray source 3FGL J2039.6-5618 detected by the Fermi Large Area Telescope. The source γ-ray properties suggest that it is a pulsar, most likely a millisecond pulsar, for which neither radio nor γ-ray pulsations have been detected. We observed 3FGL J2039.6-5618 with XMM-Newton and discovered several candidate X-ray counterparts within/close to the γ-ray error box. The brightest of these X-ray sources is variable with a period of 0.2245 ± 0.0081 days. Its X-ray spectrum can be described by a power law with photon index ΓX = 1.36 ± 0.09, and hydrogen column density NH star. The light curve profile of the companion star, which has two asymmetric peaks, suggests that the optical emission comes from two regions with different temperatures on its tidally distorted surface. Based upon its X-ray and optical properties, we consider this source as the most likely X-ray counterpart to 3FGL J2039.6-5618, which we propose to be a new redback system. 18. Multi-wavelength observations of 3FGL J2039.6-5618: a candidate redback millisecond pulsar Salvetti, D; De Luca, A; Delvaux, C; Pallanca, C; Belfiore, A; Marelli, M; Breeveld, A A; Greiner, J; Becker, W; Pizzoccaro, D 2015-01-01 We present multi-wavelength observations of the unassociated gamma-ray source 3FGL J2039.6-5618 detected by the Fermi Large Area Telescope. The source gamma-ray properties suggest that it is a pulsar, most likely a millisecond pulsar, for which neither radio nor$\\gamma$-ray pulsations have been detected yet. We observed 3FGL J2039.6-5618 with XMM-Newton and discovered several candidate X-ray counterparts within/close to the gamma-ray error box. The brightest of these X-ray sources is variable with a period of 0.2245$\\pm$0.0081 d. Its X-ray spectrum can be described by a power law with photon index$\\Gamma_X =1.36\\pm0.09$, and hydrogen column density$N_{\\rm H} < 4 \\times 10^{20}$cm$^{-2}$, which gives an unabsorbed 0.3--10 keV X-ray flux of$1.02 \\times 10^{-13}$erg cm$^{-2}$s$^{-1}$. Observations with the Gamma-Ray Burst Optical/Near-Infrared Detector (GROND) discovered an optical counterpart to this X-ray source, with a time-average magnitude$g'\\sim 19.5$. The counterpart features a flux modulation ... 19. PULSED GAMMA RAYS FROM THE MILLISECOND PULSAR J0030+0451 WITH THE FERMI LARGE AREA TELESCOPE We report the discovery of gamma-ray pulsations from the nearby isolated millisecond pulsar (MSP) PSR J0030+0451 with the Large Area Telescope on the Fermi Gamma-ray Space Telescope (formerly GLAST). This discovery makes PSR J0030+0451 the second MSP to be detected in gamma rays after PSR J0218+4232, observed by the EGRET instrument on the Compton Gamma-Ray Observatory. The spin-down power E-dot=3.5x1033 erg s-1 is an order of magnitude lower than the empirical lower bound of previously known gamma-ray pulsars. The emission profile is characterized by two narrow peaks, 0.07 ± 0.01 and 0.08 ± 0.02 wide, respectively, separated by 0.44 ± 0.02 in phase. The first gamma-ray peak falls 0.15 ± 0.01 after the main radio peak. The pulse shape is similar to that of the 'normal' gamma-ray pulsars. An exponentially cutoff power-law fit of the emission spectrum leads to an integral photon flux above 100 MeV of (6.76 ± 1.05 ± 1.35) x 10-8 cm-2 s-1 with cutoff energy (1.7 ± 0.4 ± 0.5) GeV. Based on its parallax distance of (300 ± 90) pc, we obtain a gamma-ray efficiency Lγ/E-dot≅15 percent for the conversion of spin-down energy rate into gamma-ray radiation, assuming isotropic emission. 20. TeV gamma-ray emission initiated by the population or individual millisecond pulsars within globular clusters Bednarek, W.; Sitarek, J.; Sobczak, T. 2016-05-01 Two energetic millisecond pulsars (MSPs) within globular clusters (GCs), J1823-3021A in NGC 6624 and PSR B1821-24 in M28, have been recently discovered to emit pulsed GeV γ-rays. These MSPs are expected to eject energetic leptons. Therefore, GCs have been proposed to produce GeV-TeV γ-rays as a result of the Comptonization process of the background radiation within a GC. We develop this general scenario by taking into account not only the diffusion process of leptons within a GC but also their advection with the wind from the GC. Moreover, we consider distribution of MSP within a GC and the effects related to the non-central location of the dominating, energetic MSP. Such more complete scenario is considered for the modelling of the GeV-TeV γ-ray emission from the core-collapsed GC M15 and also for GCs which contain recently discovered energetic MSPs within NGC 6624 and M28. The confrontation of the modelling of the γ-ray emission with the observations with the present Cherenkov telescopes and the future Cherenkov Telescope Array (CTA) allows us to constrain more reliably the efficiency of lepton production within the inner magnetosphere of the MSPs and re-accelerated in their vicinity. We discuss the expected limits on this parameter in the context of expectations from the pulsar models. We conclude that deep observations of GCs, even with the present sensitivity of Cherenkov telescopes (the High Energy Stereoscopic System, the Major Atmospheric Gamma-Ray Imaging Cherenkov, the Very Energetic Radiation Imaging Telescope Array System), should start to constrain the models for the acceleration and radiation processes of leptons within the inner pulsar magnetosphere and its surrounding. 1. The NANOGrav Nine-year Data Set: Mass and Geometric Measurements of Binary Millisecond Pulsars Fonseca, Emmanuel; Ellis, Justin A; Stairs, Ingrid H; Nice, David J; Ransom, Scott M; Demorest, Paul B; Arzoumanian, Zaven; Crowter, Kathryn; Dolch, Timothy; Ferdman, Robert D; Gonzalez, Marjorie E; Jones, Glenn; Jones, Megan L; Lam, Michael T; Levin, Lina; McLaughlin, Maura A; Stovall, Kevin; Swiggum, Joseph K; Zhu, Weiwei 2016-01-01 We analyse 24 binary radio pulsars in the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) nine-year data set. We made fourteen significant measurements of Shapiro delay, including new detections in four pulsar-binary systems (PSRs J0613$-$0200, J2017+0603, J2302+4442, and J2317+1439), and derive estimates of the binary-component masses and orbital inclination for these MSP-binary systems. We find a wide range of binary pulsar masses, with values as low as$m_{\\rm p} = 1.18^{+0.10}_{-0.09}\\text{ M}_{\\odot}$for PSR J1918$-$0642 and as high as$m_{\\rm p} = 1.928^{+0.017}_{-0.017}\\text{ M}_{\\odot}$for PSR J1614$-$2230 (both 68.3\\% confidence). We make an improved measurement of the Shapiro timing delay in the PSR J1918$-$0642 and J2043+1711 systems, measuring the pulsar mass in the latter system to be$m_{\\rm p} = 1.41^{+0.21}_{-0.18}\\text{ M}_{\\odot}$(68.3\\% confidence) for the first time. We measure secular variations of one or more orbital elements in many systems, and use these meas... 2. Multiwavelength Observations of the Redback Millisecond Pulsar J1048+2339 Deneva, J. S.; Ray, P. S.; Camilo, F.; Halpern, J. P.; Wood, K.; Cromartie, H. T.; Ferrara, E.; Kerr, M.; Ransom, S. M.; Wolff, M. T.; Chambers, K. C.; Magnier, E. A. 2016-06-01 We report on radio timing and multiwavelength observations of the 4.66 ms redback pulsar J1048+2339, which was discovered in an Arecibo search targeting the Fermi-Large Area Telescope source 3FGL J1048.6+2338. Two years of timing allowed us to derive precise astrometric and orbital parameters for the pulsar. PSR J1048+2339 is in a 6 hr binary and exhibits radio eclipses over half the orbital period and rapid orbital period variations. The companion has a minimum mass of 0.3 M ⊙, and we have identified a V ∼ 20 variable optical counterpart in data from several surveys. The phasing of its ∼1 mag modulation at the orbital period suggests highly efficient and asymmetric heating by the pulsar wind, which may be due to an intrabinary shock that is distorted near the companion, or to the companion’s magnetic field channeling the pulsar wind to specific locations on its surface. We also present gamma-ray spectral analysis of the source and preliminary results from searches for gamma-ray pulsations using the radio ephemeris. 3. Multiwavelength Observations of the Redback Millisecond Pulsar J1048+2339 Deneva, J S; Camilo, F; Halpern, J P; Wood, K; Cromartie, H T; Ferrara, E; Kerr, M; Ransom, S M; Wolff, M T; Chambers, K C; Magnier, E A 2016-01-01 We report on radio timing and multiwavelength observations of the 4.66 ms redback pulsar J1048+2339, which was discovered in an Arecibo search targeting the Fermi-LAT source 3FGLJ1048.6+2338. Two years of timing allowed us to derive precise astrometric and orbital parameters for the pulsar. PSR J1048+2339 is in a 6-hour binary, and exhibits radio eclipses over half the orbital period and rapid orbital period variations. The companion has a minimum mass of 0.3 solar masses, and we have identified a$V \\sim 20$variable optical counterpart in data from several surveys. The phasing of its$\\sim 1$~mag modulation at the orbital period suggests highly efficient and asymmetric heating by the pulsar wind, which may be due to an intrabinary shock that is distorted near the companion, or to the companion's magnetic field channeling the pulsar wind to specific locations on its surface. We also present gamma-ray spectral analysis of the source and preliminary results from searches for gamma-ray pulsations using the radi... 4. Pulsar spins from an instability in the accretion shock of supernovae. Blondin, John M; Mezzacappa, Anthony 2007-01-01 Rotation-powered radio pulsars are born with inferred initial rotation periods of order 300 ms (some as short as 20 ms) in core-collapse supernovae. In the traditional picture, this fast rotation is the result of conservation of angular momentum during the collapse of a rotating stellar core. This leads to the inevitable conclusion that pulsar spin is directly correlated with the rotation of the progenitor star. So far, however, stellar theory has not been able to explain the distribution of pulsar spins, suggesting that the birth rotation is either too slow or too fast. Here we report a robust instability of the stalled accretion shock in core-collapse supernovae that is able to generate a strong rotational flow in the vicinity of the accreting proto-neutron star. Sufficient angular momentum is deposited on the proto-neutron star to generate a final spin period consistent with observations, even beginning with spherically symmetrical initial conditions. This provides a new mechanism for the generation of neutron star spin and weakens, if not breaks, the assumed correlation between the rotational periods of supernova progenitor cores and pulsar spin. PMID:17203055 5. Thermonuclear Burning on the Accreting X-Ray Pulsar GRO J1744-28 Bildsten, L; Bildsten, Lars; Brown, Edward F. 1996-01-01 We investigate the thermal stability of nuclear burning on the accreting X-ray pulsar GRO J1744-28. The neutron star's dipolar magnetic field is 50 years. We also discuss the nature of the binary and point out that a velocity measurement of the stellar companion (most likely a Roche-lobe filling giant with m_K>17) will constrain the neutron star mass. 6. Soft X-Ray Properties of the Binary Millisecond Pulsar J0437-4715 Halpern, Jules P.; Martin, Christopher; Marshall, Herman, L.; Oliversen, Ronald (Technical Monitor) 2001-01-01 We obtained a light curve for the 5.75 ms pulsar J0437-4715 in the 65-120 A range with 0.5 ms time resolution using the Deep Survey instrument on the EUVE satellite. The single-peaked profile has a pulsed fraction of 0.27 +/- 0.05, similar to the ROSAT data in the overlapping energy band. A combined analysis of the EUVE and ROSAT data is consistent with a power-law spectrum of energy index alpha = 1.2 - 1.5, intervening column density N(sub H) = (5 - 8) x 10(exp 19)/sq cm, and luminosity 5.0 x 10(exp 30) ergs/s in the 0.1 - 2.4 keV band. We also use a bright EUVE/ROSAT source only 4.2 min. from the pulsar, the Seyfert galaxy RX J0437.4-4711 (= EUVE J0437-471 = IES 0435-472), to obtain an independent upper limit on the intervening absorption to the pulsar, N(sub H) less than 1.2 x 10(exp 20)/sq cm. Although a blackbody spectrum fails to fit the ROSAT data, two-component spectral fits to the combined EUVE/ROSAT data are used to limit the temperatures and surface areas of thermal emission that might make partial contributions to the flux. A hot polar cap of radius 50 - 600 m and temperature (1.0 - 3.3) x 10(exp 6) K could be present. Alternatively, a larger region with T = (4 - 12) x 10(exp 5) K and area less than 200 sq km, might contribute most of the EUVE and soft X-ray flux, but only if a hotter component were present as well. Any of these temperatures would require some mechanism(s) of surface reheating to be operating in this old pulsar, the most plausible being the impact of accelerated electrons and positrons onto the polar caps. The kinematically corrected spin-down power of PSR J0437-4715 is only 4 x 10(exp 33) ergs/s, which is an order of magnitude less than that of the lowest-luminosity gamma-ray pulsars Geminga and PSR B1055-52. The absence of high-energy gamma-rays from PSR J0437-4715 might signify an inefficient or dead outer gap accelerator, which in turn accounts for the lack of a more luminous reheated surface such as those intermediate-age gamma 7. Theory of quasi-spherical accretion in X-ray pulsars Shakura, N; Kochetkova, A; Hjalmarsdotter, L 2011-01-01 A theoretical model for quasi-spherical subsonic accretion onto slowly rotating magnetized neutron stars is constructed. In this model the accreting matter subsonically settles down onto the rotating magnetosphere forming an extended quasi-static shell. This shell mediates the angular momentum removal from the rotating neutron star magnetosphere during spin-down episodes by large-scale convective motions. The accretion rate through the shell is determined by the ability of the plasma to enter the magnetosphere. The settling regime of accretion can be realized for moderate accretion rates$\\dot M< \\dot M_*\\simeq 4\\times 10^{16}$g/s. At higher accretion rates a free-fall gap above the neutron star magnetosphere appears due to rapid Compton cooling, and accretion becomes highly non-stationary. From observations of the spin-up/spin-down rates (the angular rotation frequency derivative$\\dot \\omega^*$, and$\\partial\\dot\\omega^*/\\partial\\dot M$near the torque reversal) of X-ray pulsars with known orbital perio... 8. Quasi-spherical accretion in low-luminosity X-ray pulsars: Theory vs. observations Postnov, K; Kochetkova, A; Hjalmarsdotter, L 2012-01-01 Quasi-spherical subsonic accretion can be realized in slowly rotating wind-fed X-ray pulsars (XPSRs) at X-ray luminosities <4 10^{36} erg/s. In this regime the accreting matter settles down subsonically onto the rotating magnetosphere, forming an extended quasi-static shell. The shell mediates the angular momentum removal from the rotating NS magnetosphere by shear turbulent viscosity in the boundary layer or via large-scale convective motions. In the last case the differential rotation law in the shell is close to iso-angular-momentum rotation. The accretion rate through the shell is determined by the ability of the plasma to enter the magnetosphere due to Rayleigh-Taylor instabilities while taking cooling into account. Measurements of spin-up/spin-down rates of quasi-spherically wind accreting XPSRs in equilibrium with known orbital periods (like e.g. GX 301-2 and Vela X-1) enable determination of the main dimensionless parameters of the model and the NS magnetic field. For equilibrium pulsars with indep... 9. A new model for the X-ray continuum of the magnetized accreting pulsars Farinelli, Ruben; Ferrigno, Carlo; Bozzo, Enrico; Becker, Peter A. 2016-06-01 Context. Accreting highly magnetized pulsars in binary systems are among the brightest X-ray emitters in our Galaxy. Although a number of high-quality broad-band (0.1-100 keV) X-ray observations are available, the spectral energy distribution of these sources is usually investigated by adopting pure phenomenological models rather than models linked to the physics of accretion. Aims: In this paper, a detailed spectral study of the X-ray emission recorded from the high-mass X-ray binary pulsars Cen X-3, 4U 0115+63, and Her X-1 is carried out by using BeppoSAX and joined Suzaku +NuStar data, together with an advanced version of the compmag model, which provides a physical description of the high-energy emission from accreting pulsars, including the thermal and bulk Comptonization of cyclotron and bremsstrahlung seed photons along the neutron star accretion column. Methods: The compmag model is based on an iterative method for solving second-order partial differential equations, whose convergence algorithm has been improved and consolidated during the preparation of this paper. Results: Our analysis shows that the broad-band X-ray continuum of all considered sources can be self-consistently described by the compmag model. The cyclotron absorption features (not included in the model) can be accounted for by using Gaussian components. From the fits of the compmag model to the data we inferred the physical properties of the accretion columns in all sources, finding values reasonably close to those theoretically expected according to our current understanding of accretion in highly magnetized neutron stars. Conclusions: The updated version of the compmag model has been tailored to the physical processes that are known to occur in the columns of highly magnetized accreting neutron stars and it can thus provide a better understanding of the high-energy radiation from these sources. The availability of broad-band high-quality X-ray data, such as those provided by BeppoSAX in 10. Spectral formation in accreting X-ray pulsars: bimodal variation of the cyclotron energy with luminosity Becker, P. A.; Klochkov, D.; Schönherr, G.; Nishimura, O.; Ferrigno, C.; Caballero, I.; Kretschmar, P.; Wolff, M. T.; Wilms, J.; Staubert, R. 2012-08-01 Context. Accretion-powered X-ray pulsars exhibit significant variability of the cyclotron resonance scattering feature (CRSF) centroid energy on pulse-to-pulse timescales, and also on much longer timescales. Two types of spectral variability are observed. For sources in group 1, the CRSF energy is negatively correlated with the variable source luminosity, and for sources in group 2, the opposite behavior is observed. The physical basis for this bimodal behavior is currently not well understood. Aims: We explore the hypothesis that the accretion dynamics in the group 1 sources is dominated by radiation pressure near the stellar surface, and that Coulomb interactions decelerate the gas to rest in the group 2 sources. Methods: We derive a new expression for the critical luminosity, Lcrit, such that radiation pressure decelerates the matter to rest in sources with X-ray luminosity LX > Lcrit. The formula for Lcrit is based on a simple physical model for the structure of the accretion column in luminous X-ray pulsars that takes into account radiative deceleration, the energy dependence of the cyclotron cross section, the thermodynamics of the accreting gas, the dipole structure of the pulsar magnetosphere, and the diffusive escape of radiation through the column walls. We show that for typical neutron star parameters, Lcrit = 1.5 × 1037 B1216/15 erg s-1, where B12 is the surface magnetic field strength in units of 1012 G. Results: The formula for the critical luminosity is evaluated for five sources, using the maximum value of the CRSF centroid energy to estimate the surface magnetic field strength B12. The results confirm that the group 1 sources are supercritical (LX > Lcrit) and the group 2 sources are subcritical (LX function of LX for both the group 1 (supercritical) and the group 2 (subcritical) sources as a result of the variation of the emission height in the column. 11. Signs of Magnetic Accretion in the X-ray Pulsar Binary GX 301-2 Ikhsanov, N R 2012-01-01 Observations of the cyclotron resonance scattering feature in the X-ray spectrum of GX 301-2 suggest that the surface field of the neutron star is B_CRSF ~ 4 x 10^{12}G. The same value has been derived in modelling the rapid spin-up episodes in terms of the Keplerian disk accretion scenario. However, the spin-down rate observed during the spin-down trends significantly exceeds the value expected in currently used spin-evolution scenarios. This indicates that either the surface field of the star exceeds 50 x B_CRSF, or a currently used accretion scenario is incomplete. We show that the above discrepancy can be avoided if the accreting material is magnetized. The magnetic pressure in the accretion flow increases more rapidly than its ram pressure and, under certain conditions, significantly affects the accretion picture. The spin-down torque applied to the neutron star in this case is larger than that evaluated within a non-magnetized accretion scenario. We find that the observed spin evolution of the pulsar ca... 12. Pulsar spins from an instability in the accretion shock of supernovae Blondin, J M; Blondin, John M.; Mezzacappa, Anthony 2006-01-01 Rotation-powered radio pulsars are born with inferred initial rotation periods of order 300 ms (some as short as 20 ms) in core-collapse supernovae. In the traditional picture, this fast rotation is the result of conservation of angular momentum during the collapse of a rotating stellar core. This leads to the inevitable conclusion that pulsar spin is directly correlated with the rotation of the progenitor star. So far, however, stellar theory has not been able to explain the distribution of pulsar spins, suggesting that the birth rotation is either too slow or too fast. Here we report a robust instability of the stalled accretion shock in core-collapse supernovae that is able to generate a strong rotational flow in the vicinity of the accreting proto-neutron star. Sufficient angular momentum is deposited on the proto-neutron star to generate a final spin period consistent with observations, even beginning with spherically symmetrical initial conditions. This provides a new mechanism for the generation of neu... 13. New X-ray pulsar with a 67 millisecond period in the constellation Equuleus On 1977 November 18 and 19, the large area detector on the HEAO satellite pointed for 96 minutes toward one direction (centered at R. A. 21/sup h/3/sup m/ and decl.+9030'). At that time the 5 ms mode was employed, and 5 ms data accumulations were transmitted. Some 753,000 data points were epoch-folded to search for periods between 10 ms and 100 ms, and one period showed a very low expectation for random occurrences. This period was persistent for a long enough time to permit us to epoch-fold a large body of data and determine it precisely (to 0.1 μs), and see its light curve. All the tests which we performed indicate the existence of a pulsar in this place. The period of this pulsar is 67.5492 ms corrected for heliocentric coordinates (its local period is 67.55328 ms). Its expectation for random occurrence is lower than 5 x 10-9 14. VizieR Online Data Catalog: ATNF Pulsar Catalogue (Manchester+, 2005) Manchester, R. N.; Hobbs, G. B.; Teoh, A.; Hobbs, M. 2016-05-01 The catalogue is a compilation of the principal observed parameters of pulsars, including positions, timing parameters, pulse widths, flux densities, proper motions, distances, and dispersion, rotation, and scattering measures. It also lists the orbital elements of binary pulsars, and some commonly used parameters derived from the basic measurements. The catalogue includes all published rotation-powered pulsars, including those detected only at high energies. It also includes Anomalous X-ray Pulsars (AXPs) and Soft Gamma-ray Repeaters (SGRs) for which coherent pulsations have been detected. However, it excludes accretion-powered pulsars such as Her X-1 and the recently discovered X-ray millisecond pulsars. (2 data files). 15. Neutron star crustal plate tectonics. I. Magnetic dipole evolution in millisecond pulsars and low-mass X-ray binaries Crust lattices in spinning-up or spinning-down neutron stars have growing shear stresses caused by neutron superfluid vortex lines pinned to lattice nuclei. For the most rapidly spinning stars, this stress will break and move the crust before vortex unpinning occurs. In spinning-down neutron stars, crustal plates will move an equatorial subduction zone in which the plates are forced into the stellar core below the crust. The opposite plate motion occurs in spinning-up stars. Magnetic fields which pass through the crust or have sources in it move with the crust. Spun-up neutron stars in accreting low-mass X-ray binaries LMXBs should then have almost axially symmetric magnetic fields. Spun-down ones with very weak magnetic fields should have external magnetic fields which enter and leave the neutron star surface only near its equator. The lowest field millisecond radiopulsars seem to be orthogonal rotators implying that they have not previously been spun-up in LMXBs but are neutron stars initially formed with periods near 0.001 s that subsequently spin down to their present periods. Accretion-induced white dwarf collapse is then the most plausible genesis for them. 29 refs 16. Testing the millisecond pulsar scenario of the Galactic center gamma-ray excess with very high energy gamma-rays Yuan, Qiang 2014-01-01 The recent analyses of the Fermi Large Area Telescope data show an extended GeV$\\gamma$-ray excess on top of the expected diffuse background in the Galactic center region, which can be explained with annihilating dark matter or a population of millisecond pulsars (MSPs). We propose to observe the very high energy$\\gamma$-rays for distinguishing the MSP scenario from the dark matter scenario. The GeV$\\gamma$-ray MSPs should release most energy to the relativistic$e^{\\pm}$wind, which will diffuse in the Galaxy and radiate TeV$\\gamma$-rays through inverse Compton scattering and bremsstrahlung processes. By calculating the spectrum and spatial distribution, we show that such emission is detectable with the next generation very high energy$\\gamma$-ray observatory, the Cherenkov Telescope Array (CTA), under reasonable model parameters. It is essential to search for the multi-wavelength counterparts to the GeV$\\gamma$-ray excess for solving this mystery in the high energy universe. 17. Exploring the X-ray and gamma-ray properties of the redback millisecond pulsar PSR J1723-2837 Hui, C Y; Takata, J; Kong, A K H; Cheng, K S; Wu, J H K; Lin, L C C; Wu, E M H 2013-01-01 We have investigated the X-ray and$\\gamma$-ray properties of the redback millisecond pulsar PSR J1723-2837 with XMM-Newton, Chandra and Fermi. We have discovered the X-ray orbital modulation of this binary system with the minimum that coincides with the phases of radio eclipse. The X-ray emission is clearly non-thermal in nature which can be well described by a simple power-law with a photon index of$\\sim1.2$. The phase-averaged luminosity is$\\sim9\\times10^{31}$erg/s in 0.3-10 keV which consumes$\\sim0.2\\%$of the spin-down power. We have detected the$\\gamma-$ray emission in$0.1-300$GeV from this system at a significance of$\\sim6\\sigma$for the first time. The$\\gamma-$rays in this energy range consumes$\\sim2\\%$of the spin-down power and can be modeled by a power-law with a photon index of$\\sim2.6$. We discuss the high energy properties of the new redback in the context of a intrabinary shock model. 18. Radio detection prospects for a bulge population of millisecond pulsars as suggested by Fermi LAT observations of the inner Galaxy Calore, Francesca; Donato, Fiorenza; Hessels, Jason W T; Weniger, Christoph 2015-01-01 Analogously to globular clusters, the dense stellar environment of the Galactic center has been proposed to host a large population of as-yet undetected millisecond pulsars (MSPs). Recently, this hypothesis found support in the analysis of gamma rays from the inner Galaxy seen by the Large Area Telescope (LAT) aboard the Fermi satellite, which revealed a possible excess of diffuse GeV photons in the inner 15 deg about the Galactic center (Fermi GeV excess). The excess can be interpreted as the collective emission of thousands of MSPs in the Galactic bulge, with a spherical distribution that strongly peaks towards the Galactic center. In order to fully establish the MSP interpretation, it is essential to find corroborating evidence in multi-wavelength searches, most notably through the detection of radio pulsation from individual bulge MSPs. Based on globular cluster observations and the gamma-ray emission from the inner Galaxy, we investigate the prospects for detecting MSPs in the Galactic bulge. While previ... 19. TeV gamma-ray emission initiated by the population or individual millisecond pulsars within globular clusters Bednarek, W; Sobczak, T 2016-01-01 Two energetic millisecond pulsars (MSPs) within globular clusters (GC), J1823-3021A in NGC 6624 and PSR B1821-24 in M28, have been recently discovered to emit pulsed GeV gamma-rays. These MSPs are expected to eject energetic leptons. Therefore, GCs have been proposed to produce GeV-TeV gamma-rays as a result of the comptonization process of the background radiation within a GC. We develop this general scenario by taking into account not only the diffusion process of leptons within a GC but also their advection with the wind from the GC. Moreover, we consider distribution of MSP within a GC and the effects related to the non-central location of the dominating, energetic MSP. Such more complete scenario is considered for the modelling of the GeV-TeV gamma-ray emission from the core collapsed GC M15 and also for GCs which contain recently discovered energetic MSPs within NGC 6624 and M28. The confrontation of the modelling of the gamma-ray emission with the observations with the present Cherenkov telescopes and ... 20. A radiation-hydrodynamic model of accretion columns for ultra-luminous X-ray pulsars Kawashima, Tomohisa; Ohsuga, Ken; Ogawa, Takumi 2016-01-01 Prompted by the recent discovery of pulsed emission from an ultra-luminous X-ray source, M82 X-2 ("ULX-pulsar"), we perform a two-dimensional radiation-hydrodynamic simulation of a super-critical accretion flow onto a neutron star through a narrow accretion column. We set an accretion column with a cone shape filled with tenuous gas with density of$10^{-4} {\\rm g}~ {\\rm cm}^{-3}$above a neutron star and solve the two dimensional gas motion and radiative transfer within the column. The side boundaries are set such that radiation can freely escape, while gas cannot. Since the initial gas layer is not in a hydrostatic balance, the column gas falls onto the neutron-star surface, thereby a shock being generated. As a result, the accretion column is composed of two regions: an upper, nearly free-fall region and a lower settling region, as was noted by Basko \\& Sunyaev (1976). The average accretion rate is very high;${\\dot M}\\sim 10^{2-3} L_{\\rm E}/c^2$(with$L_{\\rm E}$being the Eddington luminosity), and s... 1. Hard X-ray Detection and Timing of Accretion-Powered Pulsars with BATSE Chakrabarty, Deepto; Prince, Thomas A. 1996-01-01 The BATSE all-sky monitor on the Compton Gamma Ray Observatory is a superb tool for the study of accretion-powered pulsars. In the first part of this thesis, I describe its capabilities for hard X-ray observations above 20 keV, present techniques for timing analysis of the BATSE data, and discuss general statistical issues for the detection of pulsed periodic signals in both the time and frequency domains. BATSE’s 1-day pulsed sensitivity in the 20–60 keV ... 2. Discovery and study of the accreting pulsar 2RXP J130159.6-635806 Chernyakova, M.; Lutovinov, A.; Rodriguez, J.; Revnivtsev, M. 2005-01-01 We report on analysis of the poorly studied source 2RXP J130159.6-635806 at different epochs with ASCA, Beppo-SAX, XMM-Newton, and INTEGRAL. The source shows coherent X-ray pulsations at a period ~700s with an average spin up rate of about dnu/dt ~ 2x10^{-13} Hz/s. A broad band (1-60 keV) spectral analysis of 2RXP J130159.6-635806 based on almost simultaneous XMM-Newton and INTEGRAL data demonstrates that the source has a spectrum typical of an accretion powered X-ray pulsar, i.e. an absorbed... 3. Fermi Study of gamma-ray Millisecond Pulsars: the Spectral Shape and Pulsed 25--200 GeV Emission from J0614-3329 Xing, Yi 2016-01-01 We report our analysis of the Fermi Large Area Telescope data for 39 millisecond pulsars (MSPs) listed in the second$\\gamma$-ray pulsar catalog. Spectra of the pulsars are obtained. We fit the spectra with a function of a power law with exponential cutoff, and find the best-fit parameters of photon index$\\Gamma = 1.54^{+0.10}_{-0.11}$and cutoff energy$E_{c} = 3.70^{+0.95}_{-0.70}$GeV. This spectral shape, which includes the intrinsic differences in the spectra of the MSPs, can be used for finding candidate MSPs and unidentified types of sources detected by Fermi at high Galactic latitudes. In one of the MSPs PSR J0614-3329, we find significant pulsed emission upto 200 GeV. The result has thus added this MSP to the group of the Crab and Vela pulsars that have been detected with >50 GeV pulsed emission. Comparing the$\\gamma$-ray spectrum of PSR J0614-3329 with those of the Crab and Vela pulsars, we discuss possible emission mechanisms for the very high-energy component. 4. Pulse-to-pulse variations in accreting X-ray pulsars Kretschmar Peter 2014-01-01 Full Text Available In most accreting X-ray pulsars, the periodic signal is very clear and easily shows up as soon as data covering sufficient pulse periods (a few ten are available. The mean pulse profile is often quite typical for a given source and with minor variations repeated and recognisable across observations done years or even decades apart. At the time scale of individual pulses, significant pulse-to-pulse variations are commonly observed. While at low energies some of these variations might be explained by absorption, in the hard X-rays they will reflect changes in the accretion and subsequent emission. The amount of these variations appears to be quite different between sources and contains information about the surrounding material as well ass possibly interactions at the magnetosphere. We investigate such variations for a sample of well-known sources. 5. Formation of millisecond pulsars with CO white dwarf companions - I. PSR J1614-2230: Evidence for a neutron star born massive Tauris, Thomas M.; Langer, Norbert; Kramer, Michael 2011-01-01 The recent discovery of a 2 M_sun binary millisecond pulsar (Demorest et al. 2010) has not only important consequences for the equation-of-state of nuclear matter at high densities but also raises the interesting question if the neutron star PSR J1614-2230 was born massive. The answer is vital for understanding neutron star formation in core collapse supernovae. Furthermore, this system raises interesting issues about the nature of the progenitor binary and how it evolved during its mass exch... 6. NuSTAR detection of 4s Hard X-ray Lags from the Accreting Pulsar GS 0834-430 Bachetti, Matteo; Miyasaka, Hiromasa; Harrison, Fiona; Fürst, Felix; Barret, Didier; Bellm, Eric C.; Boggs, Steven E.; Chakrabarty, Deepto; Chenevez, Jérôme; Christensen, Finn Erland; Craig, William W.; Grefenstette, Brian W.; Hailey, Charles J.; Madsen, Kristin K.; Natalucci, Lorenzo; Pottschmidt, Katja; Stern, Daniel; Tomsick, John A.; Walton, Dominic J.; Wilms, Jörn; Zhang, William 2014-01-01 consistent with that observed in many other magnetized accreting pulsars. We fail to detect cyclotron resonance scattering features in either phase-averaged nor phase-resolved spectra that would allow us to constrain the pulsar’s magnetic field. We detect a pulse period of ∼ 12.29 s in all energy bands. The... 7. Ordinary X-rays from Three Extraordinary Millisecond Pulsars: XMM-Newton Observations of PSRs J0337+1715, J0636+5129, and J0645+5158 Spiewak, Renée; Archibald, Anne; Gentile, Peter; Hessels, Jason; Lorimer, Duncan; Lynch, Ryan; McLaughlin, Maura; Ransom, Scott; Stairs, Ingrid; Stovall, Kevin 2016-01-01 We present the first X-ray observations of three recently discovered millisecond pulsars (MSPs) with interesting characteristics: PSR J0337+1715, PSR J0636+5129, and PSR J0645+5158. PSR J0337+1715 is a fast-spinning, bright, and so-far unique MSP in a hierarchical triple system with two white dwarf (WD) companions. PSR J0636+5129 is a MSP in a very tight 96-min orbit with a low-mass, 8$M_J\$ companion. PSR J0645+5158 is a nearby, isolated MSP with a very small duty cycle (1-2%), which has led to its inclusion in high-precision pulsar timing programs. Using data from XMM-Newton, we have analyzed X-ray spectroscopy for these three objects, as well as optical/ultraviolet photometry for PSR J0337+1715. The X-ray data for each are largely consistent with expectations for most MSPs with regards to the ratios of thermal and non-thermal emission. We discuss the implications of these data on the pulsar population, and prospects for future observations of these pulsars.
8. Ordinary X-Rays from Three Extraordinary Millisecond Pulsars: XMM-Newton Observations of PSRs J0337+1715, J0636+5129, and J0645+5158
Spiewak, Renée; Kaplan, David L.; Archibald, Anne; Gentile, Peter; Hessels, Jason; Lorimer, Duncan; Lynch, Ryan; McLaughlin, Maura; Ransom, Scott; Stairs, Ingrid; Stovall, Kevin
2016-05-01
We present the first X-ray observations of three recently discovered millisecond pulsars (MSPs) with interesting characteristics: PSR J0337+1715, PSR J0636+5129, and PSR J0645+5158. PSR J0337+1715 is a fast-spinning, bright, and so-far unique MSP in a hierarchical triple system with two white dwarf companions. PSR J0636+5129 is an MSP in a very tight 96-minute orbit with a low-mass, 8 M J companion. PSR J0645+5158 is a nearby, isolated MSP with a very small duty cycle (1%-2%), which has led to its inclusion in high-precision pulsar timing programs. Using data from XMM-Newton, we have analyzed X-ray spectroscopy for these three objects, as well as optical/ultraviolet photometry for PSR J0337+1715. The X-ray data for each are largely consistent with expectations for most MSPs with regards to the ratios of thermal and non-thermal emission. We discuss the implications of these data on the pulsar population, and prospects for future observations of these pulsars.
9. A Search for Rapidly Spinning Pulsars and Fast Transients in Unidentified Radio Sources with the NRAO 43-Meter Telescope
Schmidt, Deborah; Langston, Glen; Gilpin, Claire
2013-01-01
We have searched 75 unidentified radio sources selected from the NRAO VLA Sky Survey (NVSS) catalog for the presence of rapidly spinning pulsars and short, dispersed radio bursts. The sources are radio bright, have no identifications or optical source coincidences, are more than 5% linearly polarized, and are spatially unresolved in the catalog. If these sources are fast-spinning pulsars (e.g. sub-millisecond pulsars), previous large-scale pulsar surveys may have missed detection due to instrumental and computational limitations, eclipsing effects, or diffractive scintillation. The discovery of a sub-millisecond pulsar would significantly constrain the neutron star equation of state and would have implications for models predicting a rapid slowdown of highly recycled X-ray pulsars to millisecond periods from, e.g., accretion disk decoupling. These same sources were previously searched unsuccessfully for pulsations at 610 MHz with the Lovell Telescope at Jodrell Bank. This new search was conducted at a differe...
10. SPIN-DOWN OF THE LONG-PERIOD ACCRETING PULSAR 4U 2206+54
4U 2206+54 is a high-mass X-ray binary which has been suspected to contain a neutron star accreting from the wind of its companion, BD +530 2790. Reig et al. have recently detected 5560 s period pulsations in both Rossi X-ray Timing Explorer (RXTE) and International Gamma-ray Astrophysics Laboratory observations which they conclude are due to the spin of the neutron star. We present observations made with Suzaku which are contemporaneous with their RXTE observation of this source. We find strong pulsations at a period of 5554 ± 9 s in agreement with their results. We also present a reanalysis of BeppoSAX observations of 4U 2206+54 made in 1998, in which we find strong pulsations at a period of 5420 ± 28 s, revealing a spin-down trend in this long-period accreting pulsar. Analysis of these data suggests that the neutron star in this system is an accretion-powered magnetar. | {"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": 0.9201335310935974, "perplexity": 6077.9046060198825}, "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-2016-40/segments/1474738661778.22/warc/CC-MAIN-20160924173741-00110-ip-10-143-35-109.ec2.internal.warc.gz"} |
https://tex.stackexchange.com/questions/482107/reference-subpoints-of-lemma/482124 | # Reference Subpoints of Lemma
I have Lemmata consisting of several subpoints (basically a collection of similar formulas) and I want to reference these subpoints in text by "Lemma 1 (1)".
So far my code looks like this:
\documentclass[10pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{hyperref}
\newtheorem{lemma}{Lemma}
\usepackage[shortlabels]{enumitem}
\begin{document}
\begin{lemma}\label{lemma}
This is a collection of formulas
\begin{enumerate}
\item Equation 1 \label{sublemmaOne}
\item Equation 2
\end{enumerate}
\end{lemma}
A reference to the first item of the lemma \autoref{lemma}(\ref{sublemmaOne}).
\end{document}
This works somehow and I can even make a macro :
\newcommand{\refSublemmaOne}{\autoref{lemma}(\ref{sublemmaOne})}
However, I see two goals for improvement
• I would prefer it if there were a single hyperref link instead of two close to each other
• I would prefer to somehow use the usual \autoref{mylabel} syntax so on referencing I do not have to care whether I reference a normal lemma or a subpoint.
I am both open to suggestions that directly address the referencing and to ones to structure the lemma differently than by using enumerate if it is still a lemma with subpoints and that helps to solve the referencing.
When using the enumitem package you can set the format of the references with the option ref=format, see the enumitem manual page 3. In the example below the format is set to
\thelemma (\arabic*)
which prints \the value of the lemma counter followed by ( and the \arabic representation of the * (=current enumerate) counter followed by ).
Code:
\documentclass[10pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{hyperref}
\newtheorem{lemma}{Lemma}
\usepackage[shortlabels]{enumitem}
\begin{document}
\begin{lemma}
\label{mylemma}
This is a collection of formulas
\begin{enumerate}[ref=\thelemma (\arabic*)]
\item Equation 1 \label{sublemmaOne}
\item Equation 2 \label{sublemmaTwo}
\end{enumerate}
\end{lemma}
A reference to the first item of the lemma \ref{sublemmaOne} or the second item \ref{sublemmaTwo}.
\end{document}
Result: | {"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": 0.8418824672698975, "perplexity": 2069.5077772766454}, "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-2019-43/segments/1570987828425.99/warc/CC-MAIN-20191023015841-20191023043341-00267.warc.gz"} |
https://profet.at/blog/pe_part3/ | # PROFET
### Puncturable Encryption – A Fine-Grained Approach to Forward-Secure Encryption and More: Part III
April 23, 2021 | 22 Minute Read
In Part I and Part II, we have so far seen why forward security is an important property and discussed the state-of-the-art of puncturable encryption. In the last part of our blog series, we will focus on the applications of puncturable encryption. Finally we will then dive into the details of a concrete implementation which helps to explore the properties of puncturable-encryption schemes.
### Applications of Puncturable Encryption
Puncturable encryption (PE) schemes have a number of applications that range from Transport Layer Security (TLS) to encrypted backups. First, we take a look at zero round trip time (0-RTT) key exchange protocols. Second, we explore Cloudflare's Geo Key Manager and how PE could enable both fine-grained access control and forward security. Third, we review the use of PE in SafetyPin, a system for encrypted mobile-device backups.
#### 0-RTT Forward-Secure Key Exchange for TLS
Transport Layer Security (TLS), with TLS 1.3 representing its most recent version, is one of the most widespread protocols for secure communication over untrusted networks. One of the core goals of TLS is to establish shared keys with Ephemeral Diffie-Hellman (EDH) to establish a forward-secure channel.
In TLS, keys are established during the so-called handshake which describes the initial phase of the protocol (cf. Figure 1). First, a client sends a ClientHello message announcing its supported TLS versions, algorithms, etc. This message already includes the client’s EDH key share. When the server receives the client's message, it replies with ServerHello message containing its key share. The server can already compute the shared secret from the EDH key exchange. The client, however, must wait until it received the server’s answer. Once both parties completed the EDH key exchange, the remaining handshake is already performed in an encrypted fashion. Thereby, TLS achieves a forward-secure key exchange but requires at least two messages.
TLS 1.3 added a new feature that allows clients and servers to perform a reduced handshake whenever they have already performed one full handshake before. Then, the client is already allowed to send encrypted data in its first message (cf. Figure 2). This is achieved by storing a shared secret at the end of the handshake on both clients and servers. If a client then decides to use this shared secret on the next connection as pre-shared secret key (PSK), the stored PSK is used to derive the secret keys required for encryption. Note though, that if this key leaks, confidentiality is no longer guaranteed for the data sent as part of the early data.
As discussed above, EDH requires one round-trip. Only after the two shares have been exchanged, the shared key can be derived and thus a secure channel be established. Recent work has explored alternatives to the PSK-based approach to reduce the number of round trips. In particular, the possibility to reduce the complexity to zero round trips using PE or, more specifically, puncturable key encapsulation mechanisms (PKEM) has been investigated (cf [GHJL17, DKLRSS18]). In such a protocol, the client essentially encrypts a session key with respect to the public key of the server, and then sends it to the server. Thereby, the client can immediately start sending encrypted application data using the session key. The server decrypts the session key and can use the key as well. To achieve forward security, the secret key is punctured on the ciphertext. Consequently, the secret key is no longer able to decrypt ciphertexts from past sessions. Besides providing forward security, puncturing the key also provides replay protection. Besides TLS, these techniques can also be applied to QUIC [DDGHJKNRW20].
This approach requires the public key of the server to be known beforehand by the client. While this is not an issue after the first connection, with the trend to store public keys in DNS entries to support new features such as Encrypted Client Hello, this requirement does not hinder deployment of 0-RTT forward-secure key exchange.
Forward-secure transport of early data can also be achieved by employing puncturable pseudo random functions (PPRF) [AGJ19]. For this approach, the idea is that client and server store a PPRF secret key on the first full handshake. When performing a session-resumption handshake with early data, this stored state is then used to derive forward-secure keys. Compared to the PKEM-based approach, both, client and server, need to puncture their PPRF keys.
#### Forward Security for the Geo Key Manager
As the use of TLS for securing communication on the Internet grows, content distribution networks (CDNs) such as Cloudflare face new key management issues: all of their endpoints terminating TLS connections deployed in colocations all over the world need access to the secret keys associated to the certificate (i.e., public key) to guarantee low latency. As those secret keys might belong to the customers, they need to provide the keys to the CDNs or deploy solutions such as Keyless SSL, where customers are required to run their own keyserver answering signing requests from the CDN. The latter comes at the cost of higher latency if endpoints or users are not close to the location of the key server. The former faces a different issue since due to various differences in local laws or other regulations surrounding the use of secret keys, customers might not be interested in having their keys exposed to certain locations and areas.
Cloudflare's Geo Key Manager tackles this issue by giving customers the control on the locations their secret keys are stored when shared with Cloudflare (cf. Figure 3). Effectively, customers are able to put whole regions on allow-lists, e.g., Europe or the US. At the same time, they are able to put multiple colocations within those regions, e.g., London in Europe, on deny-lists. Finally, they are also able to directly put colocations on the allow-list that are not inside the regions already on allow-lists, e.g., Singapore. The currently used system combines identity-based broadcast encryption (IBBE) as well as identity-based revocation (IBR), but does not offer forward-security guarantees. Hence, if the keys of any colocation leak, the customer's secret keys are in danger of being leaked as well.
One can now obtain the same functionality also from PE schemes that support both negative and positive puncturing (cf. [DRSS21]). The idea is to manage region-based access using positive tags and denial of individual colocations by puncturing on unique negative tags assigned to each colocation. Next, one would derive keys for each region by using the name of the region as positive tag. Each colocation is assigned a unique negative tag and hence they receive the secret key positively punctured on the region and negatively punctured on that colocation specific tag. If customers now want to store their secret key, they encrypt the key for each allowed region using the region as positive tag and the denied colocations of the corresponding region as negative tags. If a colocation needs to access the key, it can only decrypt if one of the ciphertexts was encrypted for the region and that particular ciphertext was not tagged with the negative tag of the colocation. They are unable to decrypt ciphertexts for other regions, since they do not have access to the positively tagged keys.
If the PE scheme supports puncturing with respect to multiple negative tags, one can achieve even more. In that case, one can additionally obtain forward security as an additional feature. The tag space can be partitioned into one part containing the colocation (i.e., negative) tags, and another part identifying time periods by viewing this part as ordered sequence. Thereby, customers can specify a time epoch as additional negative tag, say 2021-04 for ciphertexts decryptable in April 2021. Once the month passed, all colocations puncture the secret keys on the month's tag and are then no longer able to decrypt those ciphertexts.
#### Bloom-Filter Encryption in SafetyPin
SafetyPin [DCM20] is a system for encrypted backups of mobile devices which uses only (short-digit) PINs at the user's side and several hardware security modules (HSMs) protecting user data at the server's side. No single HSM is capable of retrieving all the user data. Essentially, the motivation is that if one backups mobile-device data to the Cloud, one does not want the Cloud provider to gain access to it. The current state of the art (as used by Google for example) is to use a HSM which has public and secret keys ($$pk_{HSM},sk_{HSM}$$) with $$sk_{HSM}$$ baked into the HSM and thus even the Cloud provider cannot access it. Now, for a backup, one encrypts a PIN and a symmetric key $$k_{SYM}$$ under the public key $$pk_{HSM}$$ of the HSM as $$C_{B}=Enc(pk_{HSM},PIN|k_{SYM})$$ and also sends the backup data encrypted under $$k_{SYM}$$ as $$E(k_{SYM},data)$$ to the Cloud provider.
When one has lost the mobile device and wants to recover the backup to a new device, one send the PIN under the HSM public key $$pk_{HSM}$$ to the Cloud provider as $$C_{R}=Enc(pk_{SYM},PIN)$$. The Cloud provider sends both, $$C_{B}$$ and $$C_{R}$$ to the HSM which decrypts and compares the PINs. If the PINs match and only a limited number of trials was performed, then $$k_{SYM}$$ is returned to the user, which then allows to decrypt the backup data. In any case, the HSM can be seen as a single point of failure (and attacks on HSMs are reasonable and happening).
SafetyPin now mainly does two things. First, retain the scalability offered by today's (PIN-based) mobile backup systems and, second, protect against HSM compromises. This can be solved by applying threshold cryptography and in particular secret sharing in a way that some pre-defined number of HSMs out of all the HSMs are needed to recover the backup. Below a certain threshold of HSMs, no data is leaked. However, during recovery, the adversary can observe which HSMs were used and particularly target those subset of HSMs.
To mitigate such attack, the authors make use of puncturable encryption and in particular Bloom-Filter Encryption (BFE) to protect against future compromises. Interestingly, as we have seen, secret keys are large in BFE and usually will not fit into a small HSM. The authors cleverly outsource the puncturing of the secret key in a tree-like structure to the Cloud such that only logarithmically many read-and-write accesses are necessary to update the key, which yields very efficient puncturing. Moreover, this results in a very short key the HSM has to hold while achieving forward-security guarantees at the same time.
We recommend to watch the excellent talk by Henry Corrigan-Gibbs given at the ViSP Distinguished Lecture Series [C21] on SafetyPin.
### Implementation of Bloom-Filter Encryption
Finally, let us look at an implementation of a concrete PE scheme. In particular, we will demonstrate the use of Bloom-Filter Encryption (BFE) [DJSS18,DGJSS21] for forward-secure 0-RTT key exchange protocols. The example demonstrates how BFE can be used to establish a shared secret between a client and a server that is based on the BFE implementation available as part of pyrelic. We note that strictly speaking, we realize a Bloom-filter key encapsulation mechanisms (BFKEMs), but will call it BFE for the sake of simplicity.
First, we have to select parameters for the Bloom filter. Let us assume that we have a server that has to handle one new connection per second. If we want the server's public key to last for three months, a possible choice for the size of the Bloom filter is $$n = 524288 = 2^{19}$$ with a false-positive probability of $$p \approx 2^{-10}$$ (corresponding to the decryption error in BFE). Now, we can use the keygen function to generate a new key-pair for this choice of parameters:
import bfe
# Generate a key-pair
sk, pk = bfe.keygen(
32, # size of shared secret key
2 ** 19, # Bloom-filter size
0.0009765625, # false-positive probability
)
The key generation is the most expansive part of this scheme and will require some minutes to finish. Once it has completed, the public key pk can be shared with the clients. If a client now wants to establish a new connection with the server, it needs to encapsulate a new secret key:
# Encapsulate a new key
k, ctxt = bfe.encaps(pk)
The freshly sampled secret key k can now be used to derive keys for an authenticated encryption scheme such as AES-GCM:
import os
# Encrypt a message using AES-GCM
data = b"a secret message"
aad = b"authenticated but unencrypted data"
nonce = os.urandom(12)
ct = AESGCM(k).encrypt(nonce, data, aad)
The BFE ciphertext ctxt together with the encrypted message ct and the nonce can now be sent to the server. Note that the client does not need to wait for a reply of the server before encrypting its first message.
The server at some point receives the data from the client and decapsulates the BFE ciphertext to obtain the shared secret:
# Decapsulate the key
received_k = bfe.decaps(sk, ctxt)
The most important step is however still missing: the secret key needs to be punctured on the received ciphertext. Only after puncturing sk, forward security is ensured:
# Puncture the secret key on ciphertext
bfe.puncture(sk, ctxt)
Decapsulation of the same ciphertext fails after this step. Furthermore, it should be noted that after puncturing, all copies of the key have to be updated. If the old version of the key is kept in a backup or somewhere else in memory, an attacker could potentially obtain an old unpunctured key which voids the security guarantees.
Finally, the received shared secret can now be used to decrypt the messages sent by the client:
# Decrypt the message
received_data = AESGCM(received_k).decrypt(nonce, ct, aad)
Now that we know how to use the scheme, let us take a deeper look into its implementation. For the functions that we do not cover in full detail, please take a look at the example available in pyrelic. Without further ado, let's dive into the details. We require three ingredients to implement the BFE:
• Boneh-Franklin IBE [BF01]: The choice of the identity-based encryption (IBE) scheme is central to the instantiation of the BFE scheme.
• Bloom filter: The Bloom filter is required to manage the secret key. We associate an identity of the IBE to each bit index in the Bloom filter.
• Fujisaki-Okamoto transform [F099]: We use the FO-transform to achieve CCA security.
As the scheme uses bilinear groups, we note that the description in [DJSS18] uses multiplicative notation for the group operations. Hence, we present the implementation using the multiplicative interface from pyrelic.
Let us start with the key generation. Recall that a Bloom filter defines a set of hash functions that map elements to an index. Whenever an element is inserted into the Bloom filter, all the bits returned by the hash function will be set. Checking if an element is contained in the set consists of checking whether all bits returned by the hash function are set. In the BFE scheme, we associate an identity of the IBE to each bit in the Bloom filter. Hence, during key generation, the BFE keys are produced by outputting the IBE's public key and derived keys for each bit of the Bloom filter as secret key and the main secret key of the IBE is discarded (cf. Figure 4).
Consequently, we require an implementation of the hash function $$G$$ which is provided in map_identity and $$\mathsf{KGen}$$ itself:
def map_identity(identity: int) -> G2:
return hash_to_G2(struct.pack("<Q", identity))
def keygen(
key_size: int,
filter_size: int,
false_positive_probability: float
) -> Tuple[PrivateKey, PublicKey]:
exponent = rand_BN_order() # BF secret key
pk = generator_G1(exponent) # BF public key
bloom_filter = BloomFilter(
filter_size,
false_positive_probability
)
return (
PrivateKey(
bloom_filter,
# extract derived keys for all identities
[
map_identity(identity) ** exponent
for identity in range(bloom_filter.bitset_size)
],
key_size,
pk,
),
PublicKey(bloom_filter, key_size, pk),
)
The BloomFilter class computer the optimal number of hash functions based on the size of the Bloom filter $$n$$ and the false-positive probability $$p$$. It also provides the mapping of elements to its bit indices. When a bit is set in the Bloom filter, we will remove the corresponding key from the array stored in the PrivateKey instance. Conversely, checking if a key is available for an index can be done by checking if the array contains a key or is unset.
Before we come to encapsulation and decapsulation, we need a method to select the identities. Note that an BFE ciphertext consists of $$(g_1^r, E(e(pk, G(id))^r) \oplus K)$$ for a freshly sampled $$r$$ where $$E: G_T \to \{ 0, 1 \}^\ell$$ is a hash function. The idea is now to use the first component, i.e. $$u = g_1^r$$, as elements that are used to derived the identities, or in other words, which are collected in the Bloom filter. By hashing $$g_1^r$$ with the hash functions associated to the Bloom filter we obtain all the identities.
Now let's look at encapsulation and decapuslation. Figure 5 depicts both algorithms as well as the FO transform applied to BFE. The idea here is to first compute $$u$$, then use $$u$$ to derive the identities. By reusing the same randomness $$r$$ for all derived identities, we then produce all $$E(e(pk, G(id))^r) \oplus K$$.
$$R$$ used in the FO transform is implemented as hash_r. The function hash_and_xor implements $$E(y) \oplus K$$. Implementation-wise, there is an opportunity to optimize some of the operations. The scheme computes the input to $$E$$ as $$e(pk, G(id))^r)$$. Instead of performing the exponentiation with $$r$$ in the target group, the computation can be rewritten as $$e(pk^r, G(id))$$ which exchanges one exponentiation in the source group with multiple exponentiations in the target group. Let's take a look at the code:
def encaps(pk: PublicKey) -> Tuple[bytes, Ciphertext]:
# sample a random value for FO
key = os.urandom(pk.key_size)
# derive r and k
r, k = hash_r(key, pk.key_size)
u = generator_G1(r)
# instead of applying r to each pairing, precompute pk ** r
pkr = pk.pk ** r
return k, Ciphertext(
u,
tuple(
hash_and_xor(pair(pkr, map_identity(identity)), key)
for identity in get_bit_positions(
bytes(u),
pk.hash_count,
pk.filter_size
)
),
)
For decapsulation, we start of by deriving all the identities from the received $$u$$. We then check if the secret key contains the derived key associated to any of these identities. If there is one, this key is used to decrypt the corresponding ciphertext component:
def decaps(sk: PrivateKey, ctxt: Ciphertext) -> Optional[bytes]:
# obtain key from one of the ciphertexts
key: Optional[bytes] = None
bit_positions = sk.bloom_filter.get_bit_positions(
bytes(ctxt.u)
)
for v, identity in zip(ctxt.v, bit_positions):
# check if key is available for the identity
if identity in sk:
key = hash_and_xor(pair(ctxt.u, sk[identity]), v)
break
else:
return None
# if we were able to decrypt a key, recompute r, k and the
# ciphertext as in encaps and check that it matches
...
The last function that we have to implement is the puncturing itself. In the BFE scheme, this means that if we want punctures the secret key on a ciphertext, $$u$$ is inserted into the Bloom filter and all derived keys associated to the identities are deleted (see Figure 6).
For our implementation, this means that we just have to delete the corresponding entry in the array kept in the secret key:
class PrivateKey:
def __delitem__(self, identity: int) -> None:
key = self.secret_keys[identity]
if key is not None:
# remove key from the array
self.secret_keys[identity] = None
key.set_neutral() # clear key
del key
...
def puncture(sk: PrivateKey, ctxt: Ciphertext) -> None:
for identity in sk.bloom_filter.get_bit_positions(
bytes(ctxt.u)
):
del sk[identity] # remove the associated secret key
Note, however, that if there are copies of the secret key, all copies have to updated in the same way. Otherwise, the security guarantees obtained from puncturing a single copy are voided. The same care has to be taken if the secret key is stored in a file, for example. During the puncturing process, this copy would need to be updated as well.
This concludes our blog series on puncturable encryption. If you have any comments, suggestions or questions, please feel free to contact us (@sebastinas_, @drl3c7er, @CStriecks). | {"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": 0.3395674526691437, "perplexity": 1735.7803605620618}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991659.54/warc/CC-MAIN-20210516013713-20210516043713-00242.warc.gz"} |
http://mxnet.incubator.apache.org/versions/1.2.1/api/perl/symbol.html | # MXNet Perl Symbolic API¶
Topics:
## How to Compose Symbols¶
The symbolic API provides a way to configure computation graphs. You can configure the graphs either at the level of neural network layer operations or as fine-grained operations.
The following example configures a two-layer neural network.
pdl> use AI::MXNet qw(mx)
pdl> $data = mx->symbol->Variable("data") pdl>$fc1 = mx->symbol->FullyConnected(data => $data, name => "fc1", num_hidden => 128) pdl>$act1 = mx->symbol->Activation(data => $fc1, name => "relu1", act_type => "relu") pdl>$fc2 = mx->symbol->FullyConnected(data => $act1, name => "fc2", num_hidden => 64) pdl>$net = mx->symbol->SoftmaxOutput(data => $fc2, name => "out") The basic arithmetic operators (plus, minus, div, multiplication) are overloaded for element-wise operations of symbols. The following example creates a computation graph that adds two inputs together. pdl> use AI::MXNet qw(mx) pdl>$a = mx->symbol->Variable("a")
pdl> $b = mx->symbol->Variable("b") pdl>$c = $a +$b
## Symbol Attributes¶
You can add an attribute to a symbol by providing an attribute hash when you create a symbol.
$data = mx->symbol->Variable("data", attr => { mood => "angry" })$op = mx->symbol->Convolution(data => $data, kernel => [1, 1], num_filter => 1, attr => { mood => "so so" }) For proper communication with the C++ backend, both the key and values of the attribute dictionary should be strings. To retrieve the attributes, use ->attr($key):
$data->attr("mood") To attach attributes, you can use AI::MXNet::AttrScope. AI::MXNet::AttrScopeAttrScope automatically adds the specified attributes to all of the symbols created within that scope. The user can also inherit this object to change naming behavior. For example: use AI::MXNet qw(mx); use Test::More tests => 3; my ($data, $gdata); { local($mx::AttrScope) = mx->AttrScope(group=>4, data=>'great');
$data = mx->sym->Variable("data", attr => { dtype => "data", group => "1" });$gdata = mx->sym->Variable("data2");
}
ok($gdata->attr("group") == 4); ok($data->attr("group") == 1);
my $exceedScopeData = mx->sym->Variable("data3"); ok((not defined$exceedScopeData->attr("group")), "No group attr in global attr scope");
## Serialization¶
There are two ways to save and load the symbols. You can use the mx->symbol->save and mxnet->symbol->load functions to serialize the AI::MXNet::Symbol objects. The advantage of using save and load functions is that it is language agnostic and cloud friendly. The symbol is saved in JSON format. You can also get a JSON string directly using $symbol->tojson. The following example shows how to save a symbol to an S3 bucket, load it back, and compare two symbols using a JSON string. pdl> use AI::MXNet qw(mx) pdl>$a = mx->sym->Variable("a")
pdl> $b = mx->sym->Variable("b") pdl>$c = $a +$b
pdl> $c->save("s3://my-bucket/symbol-c.json") pdl>$c2 = $c->load("s3://my-bucket/symbol-c.json") pdl> ok($c->tojson eq $c2->tojson) ok 1 ## Executing Symbols¶ After you have assembled a set of symbols into a computation graph, the MXNet engine can evaluate them. If you are training a neural network, this is typically handled by the high-level AI::MXNet::Module package and the [fit()] function. For neural networks used in “feed-forward”, “prediction”, or “inference” mode (all terms for the same thing: running a trained network), the input arguments are the input data, and the weights of the neural network that were learned during training. To manually execute a set of symbols, you need to create an [AI::MXNet::Executor] object, which is typically constructed by calling the [simple_bind()] method on a AI::MXNet::Symbol. ## Multiple Outputs¶ To group the symbols together, use the AI::MXNet::Symbol->Group function. pdl> use AI::MXNet qw(mx) pdl> use Data::Dumper pdl>$data = mx->sym->Variable("data")
pdl> $fc1 = mx->sym->FullyConnected($data, name => "fc1", num_hidden => 128)
pdl> $act1 = mx->sym->Activation($fc1, name => "relu1", act_type => "relu")
pdl> $fc2 = mx->sym->FullyConnected($act1, name => "fc2", num_hidden => 64)
pdl> $net = mx->sym->SoftmaxOutput($fc2, name => "softmax")
pdl> $group = mx->sym->Group([$fc1, $net]) pdl> print Dumper($group->list_outputs())
\$VAR1 = [
'fc1_output',
'softmax_output'
];
After you get the Group, you can bind on group instead. The resulting executor will have two outputs, one for fc1_output and one for softmax_output. | {"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": 0.18395763635635376, "perplexity": 19825.854882074145}, "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-2019-22/segments/1558232256147.15/warc/CC-MAIN-20190520202108-20190520224108-00480.warc.gz"} |
https://www.shaalaa.com/question-bank-solutions/simplify-a2b2-a-2b-3a-b-multiplication-of-algebraic-expressions_60474 | # Simplify: A2b2(A + 2b)(3a + B) - Mathematics
Simplify:
a2b2(a + 2b)(3a + b)
#### SolutionShow Solution
To simplify, we will proceed as follows:
$a^2 b^2 \left( a + 2b \right)\left( 3a + b \right)$
$= \left[ a^2 b^2 \left( a + 2b \right) \right]\left( 3a + b \right)$
$= \left( a^3 b^2 + 2 a^2 b^3 \right)\left( 3a + b \right)$
$= 3a\left( a^3 b^2 + 2 a^2 b^3 \right) + b\left( a^3 b^2 + 2 a^2 b^3 \right)$
$= 3 a^4 b^2 + 6 a^3 b^3 + a^3 b^3 + 2 a^2 b^4$
$= 3 a^4 b^2 + 7 a^3 b^3 + 2 a^2 b^4$
Thus, the answer is $3 a^4 b^2 + 7 a^3 b^3 + 2 a^2 b^4$ .
Concept: Multiplication of Algebraic Expressions
Is there an error in this question or solution?
#### APPEARS IN
RD Sharma Class 8 Maths
Chapter 6 Algebraic Expressions and Identities
Exercise 6.5 | Q 22 | Page 31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5947722792625427, "perplexity": 6166.233821658167}, "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/1618038082988.39/warc/CC-MAIN-20210415005811-20210415035811-00461.warc.gz"} |
http://www.mzan.com/article/47706123-how-to-assign-values-after-the-program-finished-drawing-google-charts.shtml | Home How to assign values after the program finished drawing Google Charts?
# How to assign values after the program finished drawing Google Charts?
Travis Su
1#
Travis Su Published in 2017-12-08 00:48:28Z
I know that sounds a bit weird but I got a piece of code in here: let globalResult = []; let defaultData = ["None", 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200]; $(document).ready(() => { // set a listener on the textbox$('#input').on("change", (evt) => { let text = $('#input').val(); // the {text: text} sends a parameter named text with the // value of what was typed in the textbox$.get("/display", {text: text}) .done((data) => { globalResult = data['result']; $('#input').val(''); // reset the textbox //Draw Graph google.charts.load('current', {'packages':['corechart']}); google.charts.setOnLoadCallback(drawChart); function drawChart() { //Chart stuff.... Doesn't matter //It's programmed to Draw Line with defaultData and globalResult }; var chart = new google.visualization.LineChart(document.getElementById('curve_chart')); chart.draw(data, options); //Swap Value here: defaultData = globalResult; } }) I tried to swap defaultData and globalResult after the Chart is drawn, But some how it always drawing a new chart when swapping data, thus it causes interruption on the graph (like another line just died in the middle of the drawing, left half of the line hanging out there). If I trying to put these outside of the function drawChart, it will draw 2 same line with another dies in the middle. And I also cannot place this outside of $.get() scope cause that the chart won't be drawn. How do I fix that?
WhiteHat
2#
the load statement (google.charts.load) will wait until the document is ready, before executing the callback, or promise it returns... as such, no need for --> $(document).ready load google first using the promise, then create the chart and save the reference for later use, which will allow you to draw the same chart with any data recommend setup similar to following... let globalResult = []; let defaultData = ["None", 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200]; google.charts.load('current', { packages: ['corechart'] }).then(() => { // save reference to chart here var chart = new google.visualization.LineChart(document.getElementById('curve_chart'));$('#input').on("change", (evt) => { let text = $('#input').val(); // the {text: text} sends a parameter named text with the // value of what was typed in the textbox$.get("/display", {text: text}) .done((data) => { globalResult = data['result']; \$('#input').val(''); // reset the textbox //Chart stuff.... chart.draw(data, options); //Swap Value here: defaultData = globalResult; }); }); }); | {"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": 0.16316519677639008, "perplexity": 12296.692128247847}, "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/1512948594665.87/warc/CC-MAIN-20171217074303-20171217100303-00741.warc.gz"} |
https://www.lmfdb.org/Character/Dirichlet/4000/ | # Properties
Modulus 4000 Structure $$C_{200}\times C_{4}\times C_{2}$$ Order 1600
Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(4000)
pari: g = idealstar(,4000,2)
## Character group
sage: G.order() pari: g.no Order = 1600 sage: H.invariants() pari: g.cyc Structure = $$C_{200}\times C_{4}\times C_{2}$$ sage: H.gens() pari: g.gen Generators = $\chi_{4000}(877,\cdot)$, $\chi_{4000}(1057,\cdot)$, $\chi_{4000}(2751,\cdot)$
## First 32 of 1600 characters
Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.
orbit label order primitive -1 1 3 7 9 11 13 17 19 21 23 27
$$\chi_{4000}(1,\cdot)$$ 4000.a 1 No $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4000}(3,\cdot)$$ 4000.cy 200 Yes $$1$$ $$1$$ $$e\left(\frac{23}{200}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{23}{100}\right)$$ $$e\left(\frac{139}{200}\right)$$ $$e\left(\frac{71}{200}\right)$$ $$e\left(\frac{61}{100}\right)$$ $$e\left(\frac{77}{200}\right)$$ $$e\left(\frac{63}{200}\right)$$ $$e\left(\frac{23}{25}\right)$$ $$e\left(\frac{69}{200}\right)$$
$$\chi_{4000}(7,\cdot)$$ 4000.bl 20 No $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$i$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{4000}(9,\cdot)$$ 4000.cn 100 No $$1$$ $$1$$ $$e\left(\frac{23}{100}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{23}{50}\right)$$ $$e\left(\frac{39}{100}\right)$$ $$e\left(\frac{71}{100}\right)$$ $$e\left(\frac{11}{50}\right)$$ $$e\left(\frac{77}{100}\right)$$ $$e\left(\frac{63}{100}\right)$$ $$e\left(\frac{21}{25}\right)$$ $$e\left(\frac{69}{100}\right)$$
$$\chi_{4000}(11,\cdot)$$ 4000.db 200 Yes $$-1$$ $$1$$ $$e\left(\frac{139}{200}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{39}{100}\right)$$ $$e\left(\frac{77}{200}\right)$$ $$e\left(\frac{3}{200}\right)$$ $$e\left(\frac{49}{50}\right)$$ $$e\left(\frac{111}{200}\right)$$ $$e\left(\frac{9}{200}\right)$$ $$e\left(\frac{81}{100}\right)$$ $$e\left(\frac{17}{200}\right)$$
$$\chi_{4000}(13,\cdot)$$ 4000.de 200 Yes $$-1$$ $$1$$ $$e\left(\frac{71}{200}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{71}{100}\right)$$ $$e\left(\frac{3}{200}\right)$$ $$e\left(\frac{67}{200}\right)$$ $$e\left(\frac{97}{100}\right)$$ $$e\left(\frac{29}{200}\right)$$ $$e\left(\frac{51}{200}\right)$$ $$e\left(\frac{17}{50}\right)$$ $$e\left(\frac{13}{200}\right)$$
$$\chi_{4000}(17,\cdot)$$ 4000.ct 100 No $$-1$$ $$1$$ $$e\left(\frac{61}{100}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{11}{50}\right)$$ $$e\left(\frac{49}{50}\right)$$ $$e\left(\frac{97}{100}\right)$$ $$e\left(\frac{29}{100}\right)$$ $$e\left(\frac{16}{25}\right)$$ $$e\left(\frac{33}{50}\right)$$ $$e\left(\frac{63}{100}\right)$$ $$e\left(\frac{83}{100}\right)$$
$$\chi_{4000}(19,\cdot)$$ 4000.dc 200 Yes $$-1$$ $$1$$ $$e\left(\frac{77}{200}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{77}{100}\right)$$ $$e\left(\frac{111}{200}\right)$$ $$e\left(\frac{29}{200}\right)$$ $$e\left(\frac{16}{25}\right)$$ $$e\left(\frac{173}{200}\right)$$ $$e\left(\frac{187}{200}\right)$$ $$e\left(\frac{33}{100}\right)$$ $$e\left(\frac{31}{200}\right)$$
$$\chi_{4000}(21,\cdot)$$ 4000.dd 200 Yes $$1$$ $$1$$ $$e\left(\frac{63}{200}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{63}{100}\right)$$ $$e\left(\frac{9}{200}\right)$$ $$e\left(\frac{51}{200}\right)$$ $$e\left(\frac{33}{50}\right)$$ $$e\left(\frac{187}{200}\right)$$ $$e\left(\frac{153}{200}\right)$$ $$e\left(\frac{27}{100}\right)$$ $$e\left(\frac{189}{200}\right)$$
$$\chi_{4000}(23,\cdot)$$ 4000.cv 100 No $$1$$ $$1$$ $$e\left(\frac{23}{25}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{21}{25}\right)$$ $$e\left(\frac{81}{100}\right)$$ $$e\left(\frac{17}{50}\right)$$ $$e\left(\frac{63}{100}\right)$$ $$e\left(\frac{33}{100}\right)$$ $$e\left(\frac{27}{100}\right)$$ $$e\left(\frac{61}{100}\right)$$ $$e\left(\frac{19}{25}\right)$$
$$\chi_{4000}(27,\cdot)$$ 4000.cy 200 Yes $$1$$ $$1$$ $$e\left(\frac{69}{200}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{69}{100}\right)$$ $$e\left(\frac{17}{200}\right)$$ $$e\left(\frac{13}{200}\right)$$ $$e\left(\frac{83}{100}\right)$$ $$e\left(\frac{31}{200}\right)$$ $$e\left(\frac{189}{200}\right)$$ $$e\left(\frac{19}{25}\right)$$ $$e\left(\frac{7}{200}\right)$$
$$\chi_{4000}(29,\cdot)$$ 4000.da 200 Yes $$1$$ $$1$$ $$e\left(\frac{93}{200}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{93}{100}\right)$$ $$e\left(\frac{199}{200}\right)$$ $$e\left(\frac{161}{200}\right)$$ $$e\left(\frac{19}{25}\right)$$ $$e\left(\frac{157}{200}\right)$$ $$e\left(\frac{183}{200}\right)$$ $$e\left(\frac{47}{100}\right)$$ $$e\left(\frac{79}{200}\right)$$
$$\chi_{4000}(31,\cdot)$$ 4000.cl 50 No $$-1$$ $$1$$ $$e\left(\frac{43}{50}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{18}{25}\right)$$ $$e\left(\frac{49}{50}\right)$$ $$e\left(\frac{18}{25}\right)$$ $$e\left(\frac{1}{25}\right)$$ $$e\left(\frac{7}{50}\right)$$ $$e\left(\frac{4}{25}\right)$$ $$e\left(\frac{19}{50}\right)$$ $$e\left(\frac{29}{50}\right)$$
$$\chi_{4000}(33,\cdot)$$ 4000.cq 100 No $$-1$$ $$1$$ $$e\left(\frac{81}{100}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{31}{50}\right)$$ $$e\left(\frac{2}{25}\right)$$ $$e\left(\frac{37}{100}\right)$$ $$e\left(\frac{59}{100}\right)$$ $$e\left(\frac{47}{50}\right)$$ $$e\left(\frac{9}{25}\right)$$ $$e\left(\frac{73}{100}\right)$$ $$e\left(\frac{43}{100}\right)$$
$$\chi_{4000}(37,\cdot)$$ 4000.de 200 Yes $$-1$$ $$1$$ $$e\left(\frac{81}{200}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{81}{100}\right)$$ $$e\left(\frac{133}{200}\right)$$ $$e\left(\frac{37}{200}\right)$$ $$e\left(\frac{67}{100}\right)$$ $$e\left(\frac{19}{200}\right)$$ $$e\left(\frac{61}{200}\right)$$ $$e\left(\frac{37}{50}\right)$$ $$e\left(\frac{43}{200}\right)$$
$$\chi_{4000}(39,\cdot)$$ 4000.cx 100 No $$-1$$ $$1$$ $$e\left(\frac{47}{100}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{47}{50}\right)$$ $$e\left(\frac{71}{100}\right)$$ $$e\left(\frac{69}{100}\right)$$ $$e\left(\frac{29}{50}\right)$$ $$e\left(\frac{53}{100}\right)$$ $$e\left(\frac{57}{100}\right)$$ $$e\left(\frac{13}{50}\right)$$ $$e\left(\frac{41}{100}\right)$$
$$\chi_{4000}(41,\cdot)$$ 4000.cw 100 No $$1$$ $$1$$ $$e\left(\frac{33}{100}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{33}{50}\right)$$ $$e\left(\frac{19}{100}\right)$$ $$e\left(\frac{41}{100}\right)$$ $$e\left(\frac{3}{25}\right)$$ $$e\left(\frac{17}{100}\right)$$ $$e\left(\frac{23}{100}\right)$$ $$e\left(\frac{7}{50}\right)$$ $$e\left(\frac{99}{100}\right)$$
$$\chi_{4000}(43,\cdot)$$ 4000.by 40 No $$1$$ $$1$$ $$e\left(\frac{1}{40}\right)$$ $$-1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{40}\right)$$
$$\chi_{4000}(47,\cdot)$$ 4000.cr 100 No $$1$$ $$1$$ $$e\left(\frac{79}{100}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{29}{50}\right)$$ $$e\left(\frac{18}{25}\right)$$ $$e\left(\frac{33}{100}\right)$$ $$e\left(\frac{81}{100}\right)$$ $$e\left(\frac{23}{50}\right)$$ $$e\left(\frac{37}{50}\right)$$ $$e\left(\frac{57}{100}\right)$$ $$e\left(\frac{37}{100}\right)$$
$$\chi_{4000}(49,\cdot)$$ 4000.be 10 No $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$-1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{4000}(51,\cdot)$$ 4000.cc 40 No $$-1$$ $$1$$ $$e\left(\frac{29}{40}\right)$$ $$i$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{40}\right)$$
$$\chi_{4000}(53,\cdot)$$ 4000.cz 200 Yes $$-1$$ $$1$$ $$e\left(\frac{113}{200}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{100}\right)$$ $$e\left(\frac{9}{200}\right)$$ $$e\left(\frac{101}{200}\right)$$ $$e\left(\frac{41}{100}\right)$$ $$e\left(\frac{87}{200}\right)$$ $$e\left(\frac{153}{200}\right)$$ $$e\left(\frac{13}{25}\right)$$ $$e\left(\frac{139}{200}\right)$$
$$\chi_{4000}(57,\cdot)$$ 4000.i 4 No $$-1$$ $$1$$ $$-1$$ $$-i$$ $$1$$ $$i$$ $$-1$$ $$i$$ $$i$$ $$i$$ $$i$$ $$-1$$
$$\chi_{4000}(59,\cdot)$$ 4000.dc 200 Yes $$-1$$ $$1$$ $$e\left(\frac{51}{200}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{51}{100}\right)$$ $$e\left(\frac{193}{200}\right)$$ $$e\left(\frac{27}{200}\right)$$ $$e\left(\frac{8}{25}\right)$$ $$e\left(\frac{99}{200}\right)$$ $$e\left(\frac{181}{200}\right)$$ $$e\left(\frac{79}{100}\right)$$ $$e\left(\frac{153}{200}\right)$$
$$\chi_{4000}(61,\cdot)$$ 4000.dd 200 Yes $$1$$ $$1$$ $$e\left(\frac{9}{200}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{9}{100}\right)$$ $$e\left(\frac{87}{200}\right)$$ $$e\left(\frac{93}{200}\right)$$ $$e\left(\frac{19}{50}\right)$$ $$e\left(\frac{141}{200}\right)$$ $$e\left(\frac{79}{200}\right)$$ $$e\left(\frac{61}{100}\right)$$ $$e\left(\frac{27}{200}\right)$$
$$\chi_{4000}(63,\cdot)$$ 4000.cs 100 No $$1$$ $$1$$ $$e\left(\frac{43}{100}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{43}{50}\right)$$ $$e\left(\frac{37}{50}\right)$$ $$e\left(\frac{61}{100}\right)$$ $$e\left(\frac{27}{100}\right)$$ $$e\left(\frac{8}{25}\right)$$ $$e\left(\frac{2}{25}\right)$$ $$e\left(\frac{19}{100}\right)$$ $$e\left(\frac{29}{100}\right)$$
$$\chi_{4000}(67,\cdot)$$ 4000.df 200 Yes $$1$$ $$1$$ $$e\left(\frac{107}{200}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{100}\right)$$ $$e\left(\frac{51}{200}\right)$$ $$e\left(\frac{139}{200}\right)$$ $$e\left(\frac{99}{100}\right)$$ $$e\left(\frac{93}{200}\right)$$ $$e\left(\frac{167}{200}\right)$$ $$e\left(\frac{39}{50}\right)$$ $$e\left(\frac{121}{200}\right)$$
$$\chi_{4000}(69,\cdot)$$ 4000.da 200 Yes $$1$$ $$1$$ $$e\left(\frac{7}{200}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{100}\right)$$ $$e\left(\frac{101}{200}\right)$$ $$e\left(\frac{139}{200}\right)$$ $$e\left(\frac{6}{25}\right)$$ $$e\left(\frac{143}{200}\right)$$ $$e\left(\frac{117}{200}\right)$$ $$e\left(\frac{53}{100}\right)$$ $$e\left(\frac{21}{200}\right)$$
$$\chi_{4000}(71,\cdot)$$ 4000.cm 100 No $$-1$$ $$1$$ $$e\left(\frac{29}{100}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{29}{50}\right)$$ $$e\left(\frac{47}{100}\right)$$ $$e\left(\frac{83}{100}\right)$$ $$e\left(\frac{14}{25}\right)$$ $$e\left(\frac{21}{100}\right)$$ $$e\left(\frac{49}{100}\right)$$ $$e\left(\frac{8}{25}\right)$$ $$e\left(\frac{87}{100}\right)$$
$$\chi_{4000}(73,\cdot)$$ 4000.cp 100 No $$-1$$ $$1$$ $$e\left(\frac{31}{50}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{6}{25}\right)$$ $$e\left(\frac{91}{100}\right)$$ $$e\left(\frac{37}{50}\right)$$ $$e\left(\frac{43}{100}\right)$$ $$e\left(\frac{63}{100}\right)$$ $$e\left(\frac{47}{100}\right)$$ $$e\left(\frac{71}{100}\right)$$ $$e\left(\frac{43}{50}\right)$$
$$\chi_{4000}(77,\cdot)$$ 4000.cz 200 Yes $$-1$$ $$1$$ $$e\left(\frac{179}{200}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{79}{100}\right)$$ $$e\left(\frac{147}{200}\right)$$ $$e\left(\frac{183}{200}\right)$$ $$e\left(\frac{3}{100}\right)$$ $$e\left(\frac{21}{200}\right)$$ $$e\left(\frac{99}{200}\right)$$ $$e\left(\frac{4}{25}\right)$$ $$e\left(\frac{137}{200}\right)$$
$$\chi_{4000}(79,\cdot)$$ 4000.cg 50 No $$-1$$ $$1$$ $$e\left(\frac{37}{50}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{12}{25}\right)$$ $$e\left(\frac{8}{25}\right)$$ $$e\left(\frac{12}{25}\right)$$ $$e\left(\frac{43}{50}\right)$$ $$e\left(\frac{19}{25}\right)$$ $$e\left(\frac{47}{50}\right)$$ $$e\left(\frac{23}{25}\right)$$ $$e\left(\frac{11}{50}\right)$$ | {"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": 0.9051642417907715, "perplexity": 117.02452259397732}, "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/1575540482038.36/warc/CC-MAIN-20191205190939-20191205214939-00475.warc.gz"} |
https://www.physicsforums.com/threads/interpreting-magnitude-of-hspices-fft-output-of-mixed-signals.261886/ | # Interpreting magnitude of HSPICE's FFT-output of mixed signals
1. Oct 5, 2008
### prasfft
I ran a time-domain simulation in HSPICE & I am trying to analyze the frequency content of the transient current draw...(FYI- I have the power systems "impedance vs. frequency" curve, and my aim is to determine the noise voltage on my power rail given its impedance now)
So I run FFT (current-waveform,t_start, t_stop, NP) using the in-built calculator...
Now how does one interpret the resulting spectral density curve?
Is the magnitude (on Y-axis) the real amplitude of current at that frequency i.e. can I just take that amplitude and multiply it by impedance Z at that frequency to calculate the noise voltage...??
I'd highly appreciate if some one can lend insight into this...thanks a bunch
Can you offer guidance or do you also need help?
Draft saved Draft deleted
Similar Discussions: Interpreting magnitude of HSPICE's FFT-output of mixed signals | {"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": 0.926533043384552, "perplexity": 3636.0331272958756}, "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/1512948567042.50/warc/CC-MAIN-20171215060102-20171215080102-00637.warc.gz"} |
http://projecteuler.net/problem=303 | ## Multiples with small digits
### Problem 303
Published on Saturday, 25th September 2010, 10:00 pm; Solved by 1738
For a positive integer n, define f(n) as the least positive multiple of n that, written in base 10, uses only digits 2.
Thus f(2)=2, f(3)=12, f(7)=21, f(42)=210, f(89)=1121222.
Also, .
Find . | {"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": 0.8268110156059265, "perplexity": 7913.425592590545}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368696382917/warc/CC-MAIN-20130516092622-00013-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/compute-sum-of-a-power-series.602666/ | # Compute sum of a power series
1. May 3, 2012
### blak97
1. The problem statement, all variables and given/known data
Explicitly compute the function g defined by:
g(x) = $\Sigma$n2x2n from n=1 to infinity
I was thinking something along the lines of differentiating$\Sigma$ x2n twice
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
2. May 3, 2012
### micromass
Staff Emeritus
Yes. So what do you get??
Similar Discussions: Compute sum of a power series | {"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": 0.9468771815299988, "perplexity": 2599.457445332058}, "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-2017-43/segments/1508187823067.51/warc/CC-MAIN-20171018180631-20171018200631-00776.warc.gz"} |
http://uah.edu/science/departments/math/undergraduate-students/290-main/science/science-mathematical-science/3484-ma-244 | # Courses
## MA 244, Introduction to Linear Algebra
### Course Description and Goals
This is an introductory course in linear algebra primarily intended for students in mathematics, science, and engineering. Topics include
• systems of linear equations and their solution by Gaussian elimination
• vectors in Rn and the inner product operation
• the algebra of matrices and the determinant of a matrix
• eigenvalues and eigenvectors of matrices
• similarity and diagonalization of matrices
• abstract vector spaces
• linear independence, span, basis, and dimension
• linear transformations on vector spaces and their associated matrices and subspaces
• special properties of symmetric matrices
• applications, particularly to geometry and calculus
• the use of the MATLAB computer algebra system
Goals include
• a basic understanding of the special language, notation, and point of view of linear algebra
• a basic understanding of the key concepts of linear independence, span, basis, and dimension
• an improved ability to think abstractly, in particular a basic understanding of an abstract algebraic structure defined by a set of axioms
• the ability to solve basic computational problems involving matrices and systems of linear equations.
• the ability to construct simple proofs
• a basic understanding of the central importance of linear algebra in other areas of mathematics
• an improved ability to read, write, speak, and think in mathematical terms
### Alabama General Studies Curriculum
MA 244 is an AGSC approved course. The standard AGSC number is Math 237.
3 Semester Hours
### Grading System
This course is graded A, B, C, D, F. The grade typically depends on a combination of class tests, homework, MATLAB assignments, quizzes, and a comprehensive final exam. | {"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": 0.9162005186080933, "perplexity": 1464.4649114563742}, "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-2015-35/segments/1440646249598.96/warc/CC-MAIN-20150827033049-00147-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://www.birs.ca/events/2014/5-day-workshops/14w5001/videos/watch/201406051333-Cheng.html | ## Video From 14w5001: The Future of Trace Formulas
Thursday, June 5, 2014 13:33 - 14:42
Trace formula for Lie algebras and Poisson summation formula for the Harish-Chandra transform | {"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": 0.8416691422462463, "perplexity": 2071.485602354683}, "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/1603107876500.43/warc/CC-MAIN-20201021122208-20201021152208-00237.warc.gz"} |
https://www.physicsoverflow.org/7395/can-users-claim-posts-from-unknowntose | # Can users claim posts from UnknownToSE?
+ 1 like - 0 dislike
162 views
I have noticed that even though the user "UnknownToSE" is meant only for users who no more exist on SE, it is being automatically applied for users who do exist on SE, including Danu, Trimok, and Jonathan Gleason.
Is it possible for administrators to manually assign the posts to the correct user accounts? If so, how?
asked Mar 14, 2014 in Bug
edited Mar 16, 2014
No, actually not yet. However, if that happens, there seems to be a bug in the import plugin. Could you give me one or two links to posts, where this happens so that I may check the reason for this error?
@polarkernel E.g. /6120#a6158, /5335, /7285
OK, I see. These are users that have already been imported from SE.TP. After detection of the user name collision, a comparison of the email addresses on SE.P and SE.TP did not provide a match, they use a new email address now. I have treated these users as unknown cases and now I see that it would be better to add "(SE)" to the user name and enable a later account merge. Shall I change the plugin to do this?
A repair of the posts already imported is only possible directly in the database. If there are not yet many of them, I can do this manually.
@polarkernel I think the plug-in should be modified that way. As for changing the posts directly in the database, there are 25 answers and 9 questions like that at the momment.
The new version of the plugin is on now. I will search for the wrong accounts and correct them. Note that like this these users are not verified at all.
All corrections of UnknownToSE should be done. Additionally, there have been more than 100 comments to change, very annoying. Please put an eye on this case in future imports. With the new plugin version this should no more happen, but ...
Just in case, alarm me immediately.
@polarkernel Thank you.
Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor) Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ys$\varnothing$csOverflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register. | {"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": 0.22734227776527405, "perplexity": 1441.6586743621642}, "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-2019-51/segments/1575540482954.0/warc/CC-MAIN-20191206000309-20191206024309-00097.warc.gz"} |
https://quantumgeometrydynamics.com/the-measurement-of-physical-properties-and-frames-of-reference/ | # The Measurement of Physical Properties and Frames of Reference
Note: the following is a section of Introduction to Quantum-Geometry Dynamics
According to QGD:
• ${{m}_{a}}$, the mass of an object $a$, is equal to the number of $preon{{s}^{\left( + \right)}}$ that compose it;
• ${{E}_{a}}$ , its energy, is equal to its mass multiplied by the fundamental momentum of the $preo{{n}^{\left( + \right)}}$; that is: where ${{\vec{c}}_{i}}$ is the momentum vector of a $preo{{n}^{\left( + \right)}}$ and $c=\left\| {{{\vec{c}}}_{i}} \right\|$is the fundamental momentum, then ${{E}_{a}}=\sum\limits_{i=1}^{{{m}_{a}}}{\left\| {{{\vec{c}}}_{i}} \right\|}={{m}_{a}}c$.
• ${{\vec{P}}_{a}}$ , the momentum vector of an object, is equal to the vector sum of all the momentum vectors of its component $preon{{s}^{\left( + \right)}}$ or ${{\vec{P}}_{a}}=\sum\limits_{i=1}^{{{m}_{a}}}{{{{\vec{c}}}_{i}}}$ and${{P}_{a}}$ , its momentum, is the magnitude of its momentum vector. That is: ${{P}_{a}}=\left\| {{{\vec{P}}}_{a}} \right\|=\left\| \sum\limits_{i=1}^{{{m}_{a}}}{{{{\vec{c}}}_{i}}} \right\|$ and finally
• ${{v}_{a}}$ , its speed, is the ratio of its momentum over its mass or ${{v}_{a}}=\frac{{{P}_{a}}}{{{m}_{a}}}=\frac{\left\| \sum\limits_{i=1}^{{{m}_{a}}}{{{{\vec{c}}}_{i}}} \right\|}{{{m}_{a}}}$.
All the properties above are intrinsic which implies that they are qualitatively and quantitatively independent of the frame of reference against which they are measured. We must however make the essential distinction between the measurement of a property of an object and its actual intrinsic property.
Take for instance the speed of light which we have derived from the fundamental description of the properties of mass and momentum and shown to be constant. That is: ${{v}_{\gamma }}=\frac{{{P}_{\gamma }}}{{{m}_{\gamma }}}$ and since, for momentum vectors of photons all point in the same direction we have ${{P}_{\gamma }}={{E}_{\gamma }}$ and $\displaystyle {{v}_{\gamma }}=\frac{{{P}_{\gamma }}}{{{m}_{\gamma }}}=\frac{{{E}_{\gamma }}}{{{m}_{\gamma }}}=\frac{{{m}_{\gamma }}c}{{{m}_{\gamma }}}=c$.
If we were to experimentally measure the speed of light, or more precisely, the speed of photons, we would set up instruments within an agreed upon frame of reference. We would map the space in which the measurement apparatus is set and though the property of speed is intrinsic, thus independent of the frame of reference, the measurement of the property is dependent on the frame of reference. But if, as we know, the speed of light has been observed to be independent of the frame of reference, then how can this be reconciled with QGD’s intrinsic speed?
Before moving forward with the experiment it is important to consider what it is that our apparatus actually measures. Speed is conventionally defined as the ratio of displacement over time, that is $v=\frac{d}{t}$ where $d$ the distance is and $t$ is time. Space and time here are considered physical dimensions and as a consequence the conventional definition of speed is never questioned.
Distance can be measured by something as primitive as a yard stick and its physicality is hard to argue with. Time and its physicality pose serious problems. Time is assumed to be measurable using a clock of some sort but, it is easily shown that clocks are simply cyclic and periodic systems linked to counting devices and they do not measured time but merely count the number of repetitions of arbitrarily chosen states of these systems.
So conventional speed in general, and that of light in particular, is simply the distance in conventional units something travels divided by the number of cycles a clock goes through during its travel. Therefore the conventional definition of speed, which is the ratio of the distance travelled by an object over the number of cycles, is not the objects speed, but of the distance travelled between two cycles. That goes for the speed of photons.
There is a relation between conventional speed and intrinsic speed and we find that the conventional speed of a photon is proportional to its intrinsic speed, that is $\frac{d}{t}\propto {{v}_{\gamma }}$, but while conventional speed is relational (and not physical since time itself is not physical) , the intrinsic speed is physical since it is derived from momentum and mass, both of which are measurable, hence physical.
Now going back to frames of reference, let us assume a room moving at an intrinsic speed ${{v}_{a}}$. A source of photons is placed at the very centre of the room which photons are detected by detectors placed on the walls, floor and ceiling. The source and detectors are linked are in turn linked to a clock by wires of the same length. The clock registers the emission and the reception of the photons in such a way that we can calculate the conventional speed of photons. For now, we will assume that the direction of motion of the room is along the $x$ axis.
QGD predicts that even though the intrinsic speed of photons is reference frame independent, their one way conventional speed to detector ${{D}_{{{x}_{1}}}}$ will be larger than their one way conventional speed at the detector ${{D}_{{{x}_{2}}}}$. The relativity theory predicts that the conventional speed of photons will be the same at both detectors independently of ${{v}_{a}}$. So all that is needed to test which theory gives the correct prediction is to make one way measurements of the conventional speed of photons. Problem is; all measurements of the speed of light are two way measurements and since any possible contribution of ${{v}_{a}}$ to the conventional speed of photons traveling in one direction is cancelled out when it is reflected in the other direction. In other words since both QGD and the relativity theory predicts the two way measurements will be equal at ${{D}_{{{x}_{1}}}}$ and ${{D}_{{{x}_{2}}}}$ such experiments cannot distinguish between QGD and the relativity theory.
However, a similar experiment which measures not speed but momentum can distinguish between the theories. The photons at detector ${{D}_{{{x}_{2}}}}$ will be redshifted while those at ${{D}_{{{x}_{1}}}}$ would be blueshifted. Both theories predict ${{P}_{{{D}_{{{x}_{1}}}}}}>{{P}_{{{D}_{{{x}_{2}}}}}}$but their predictions for the other detectors are different.
Assuming that the room’s motion is align with the $x$ axis*, the relativity theory predicts that ${{P}_{{{D}_{{{x}_{1}}}}}}>{{P}_{{{D}_{{{y}_{1}}}}}}={{P}_{{{D}_{{{y}_{2}}}}}}={{P}_{{{D}_{{{z}_{1}}}}}}={{P}_{{{D}_{{{z}_{2}}}}}}>{{P}_{{{D}_{{{x}_{2}}}}}}$. For the same experiment the QGD theory predicts ${{P}_{{{D}_{{{x}_{1}}}}}}={{P}_{{{D}_{{{y}_{1}}}}}}={{P}_{{{D}_{{{y}_{2}}}}}}={{P}_{{{D}_{{{z}_{1}}}}}}={{P}_{{{D}_{{{z}_{2}}}}}}>{{P}_{{{D}_{{{x}_{2}}}}}}$.
If QGD’s prediction is verified, then the intrinsic of the frame of reference can be calculated using the equations we introduced earlier to describe the redshift effect. That is; from our description of the redshift effect, we know that $\displaystyle {{P}_{\gamma }}=\Delta {{P}_{{{D}_{{{x}_{1}}}}}}$ then we have $\displaystyle \frac{c-{{v}_{a}}}{c}{{m}_{\gamma }}={{P}_{\gamma }}-\frac{{{v}_{a}}}{c}={{P}_{{{D}_{{{x}_{1}}}}}}-\frac{{{v}_{a}}}{c}={{P}_{{{D}_{{{x}_{2}}}}}}$and $\displaystyle {{v}_{a}}=\left( {{P}_{{{D}_{{{x}_{1}}}}}}-{{P}_{{{D}_{{{x}_{2}}}}}} \right)c$.
Once the intrinsic speed of a reference system is known, then it can be taken into account when estimating the physical properties of light emitting objects from within it.
QGD’s description of the redshift effect implies distinct predictions for all observations based on redshifts measurement but I would like to bring attention to one direct consequence which has been confirmed by observations; the observed flatness of the orbital speed of stars around their galactic centers .
* The alignment with the $x$ axis is found by rotating that detector assembly so that the ${{D}_{{{x}_{2}}}}$ detector measures the lowest momentum (largest redshift). | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 42, "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": 0.9814522862434387, "perplexity": 263.3086511424971}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056974.30/warc/CC-MAIN-20210920010331-20210920040331-00091.warc.gz"} |
https://howlingpixel.com/wiki/Orrery | # Orrery
An orrery is a mechanical model of the solar system that illustrates or predicts the relative positions and motions of the planets and moons, usually according to the heliocentric model. It may also represent the relative sizes of these bodies; but since accurate scaling is often not practical due to the actual large ratio differences, a subdued approximation may be used instead. Though the Greeks had working planetaria, the first orrery that was a planetarium of the modern era was produced in 1704, and one was presented to Charles Boyle, 4th Earl of Orrery – whence came the name. They are typically driven by a clockwork mechanism with a globe representing the Sun at the centre, and with a planet at the end of each of the arms.
A small orrery showing earth and the inner planets
## History
### Early versions
Antikythera mechanism (main fragment), ca. 125 BC
Carlo G Croce, reconstruction of Dondi's Astrarium, originally built between 1348 and 1364 in Padova
Astronomical clock (Venus-Mercury side), Eberhard Baldewein et al., Marburg-Kassel, 1563–1568 - Mathematisch-Physikalischer Salon, Dresden - DSC08057
The Antikythera mechanism, discovered in 1900 in a wreck off the Greek island of Antikythera and extensively studied, exhibited the diurnal motions of the Sun, Moon, and the five known planets. It has been dated between 150 and 100 BC. The Antikythera hand driven mechanism is now considered one of the first orreries, but for many decades was ignored as it was thought to be far too complex to be genuine.[1] It was geocentric and used as a mechanical calculator designed to calculate astronomical positions.
According to Cicero, the Roman philosopher who was writing in the first century BC, Posidonius constructed a planetary model.
In 1348, Giovanni Dondi built the first known clock driven mechanism which displays the ecliptical position of Moon, Sun, Mercury, Venus, Mars, Jupiter and Saturn according to the complicated ptolemeic planetary theories.[2][3] The clock itself is lost, but Dondi left a complete description of the astronomic gear trains of his clock.
As late as 1650, P. Schirleus built a geocentric planetarium with the Sun as a planet, and with Mercury and Venus revolving around the Sun as its moons.[4]
At the court of William IV, Landgrave of Hesse-Kassel two complicated astronomic clocks were built in 1561 and 1563-1568, which show on four sites the ecliptical position of Sun, Mercury, Venus, Mars, Jupiter and Saturn, the Moon, Sun and Dragon (Nodes of the Moon) according to Ptolemy, a Calendar, the Sunrise and Sunset and an automated celestial sphere with an animated Sun symbol which, for the first time on a celestial globe, show the real position of the sun, including the equation of time.[5][6] The clocks are now on display in Kassel at the Astronomisch-Physikalisches Kabinett and in Dresden at the Mathematisch-Physikalischer Salon.
In De revolutionibus orbium coelestium, published in Nuremberg in 1543, Nicolaus Copernicus challenged the Western teaching of a geocentric universe in which the Sun revolved daily around the Earth. He observed that some Greek philosophers had proposed a heliocentric universe. This simplified the apparent epicyclic motions of the planets, making it feasible to represent the planets' paths as simple circles. This could be modelled by the use of gears. Tycho Brahe's improved instruments made precise observations of the skies (1576–1601), and from these Johannes Kepler (1621) deduced that planets orbited the Sun in ellipses. In 1687 Isaac Newton explained the cause of elliptic motion in his theory of gravitation.[7]
### Modern orreries
The Orrery inside the Sphaera Copernicana, designed by Joseph of Gottorp and build by Andreas Bösch, 1653
Clock makers George Graham and Thomas Tompion built the first modern orrery around 1704 in England.[8] Graham gave the first model, or its design, to the celebrated instrument maker John Rowley of London to make a copy for Prince Eugene of Savoy. Rowley was commissioned to make another copy for his patron Charles Boyle, 4th Earl of Orrery, from which the device took its name in English.[9] This model was presented to Charles' son John, later the 5th Earl of Cork and 5th Earl of Orrery. Independently, Christiaan Huygens published details of a heliocentric planetary machine in 1703, which he built while resident in Paris between 1665 and 1681. He calculated the gear trains needed to represent a year of 365.242 days, and used that to produce the cycles of the principal planets.[4]
Joseph Wright's painting A Philosopher giving a Lecture on the Orrery in which a lamp is put in place of the Sun (ca. 1766), which hangs in Derby Museum and Art Gallery, depicts a group listening to a lecture by a natural philosopher. The Sun in a brass orrery provides the only light in the room. The orrery depicted in the painting has rings, which give it an appearance similar to that of an armillary sphere. The demonstration was thereby able to depict eclipses.[10]
To put this in chronological context, in 1762 John Harrison's marine chronometer first enabled accurate measurement of longitude. In 1766, astronomer Johann Daniel Titius first demonstrated that the mean distance of each planet from the Sun could be represented by the following progression:
${\displaystyle {\frac {4+0}{10}},{\frac {4+3}{10}},{\frac {4+6}{10}},{\frac {4+12}{10}},{\frac {4+24}{10}},{\frac {4+48}{10}},.....}$
That is, 0.4, 0.7, 1.0, 1.6, 2.8, 5.2 ... The numbers refer to astronomical units, the mean distance between Sun and Earth, which is 1.496 × 10⁸ km (93 × 10⁶ miles). The Derby Orrery does not show mean distance, but demonstrated the relative planetary movements.
Eisinga's Planetarium was built from 1774 to 1781 by Eise Eisinga in his home in Franeker, in the Netherlands. It displays the planets across the width of a room's ceiling, and has been in operation almost continually since it was created.[11] This orrery is a planetarium in both senses of the word: a complex machine showing planetary orbits, and a theatre for depicting the planets' movement. Eisinga house was bought by the Dutch Royal family who gave him a pension.
A 1766 Benjamin Martin Orrery, used at Harvard
In 1764, Benjamin Martin devised a new type of planetary model, in which the planets were carried on brass arms leading from a series of concentric or coaxial tubes. With this construction it was difficult to make the planets revolve, and to get the moons to turn around the planets. Martin suggested that the conventional orrery should consist of three parts: the planetarium where the planets revolved around the Sun, the tellurion (also tellurian or tellurium) which showed the inclined axis of the Earth and how it revolved around the Sun, and the lunarium which showed the eccentric rotations of the Moon around the Earth. In one orrery, these three motions could be mounted on a common table, separately using the central spindle as a prime mover.[1]
## Explanation
All orreries are planetariums or planetaria (alternative plural). The term orrery has only existed since 1714. A grand orrery is one that includes the outer planets known at the time of its construction. The word planetarium has been captured, and now usually refers to hemispherical theatres in which images of the night sky are projected onto an overhead surface. Planetariums (orreries) can range widely in size from hand-held to room-sized. An orrery is used to demonstrate the motion of the planets, while a mechanical device used to predict eclipses and transits is called an astrarium.
An orrery should properly include the Sun, the Earth and the Moon (plus optionally other planets). A model that only includes the Earth, the Moon and the Sun is called a tellurion or tellurium, and one which only includes the Earth and the Moon is a lunarium. A jovilabe is a model of Jupiter and its moons.[12]
Planet Avg. Distance
from Sun
Diameter Mass Density No. of moons Orbital period (years) Inclination
to ecliptic
Axial tilt Rotational period (sidereal)
Mercury 0.39 AU 0.38 Earth diameter 0.05 Earth mass 5.5 g/cm³ 0 0.24 7.0 0 59 days
Venus 0.72 0.95 0.82 5.3 0 0.62 3.4 177 -243 days
Earth 1.00 1.00 1.00 5.5 1 1.00 0 23 23.9 hours
Mars 1.52 0.53 0.11 3.9 2 1.88 1.9 25 24.5 hours
Jupiter 5.20 11.21 317.9 1.3 69 11.9 1.3 3 10 hours
Saturn 9.54 9.45 95.2 0.7 62 29.5 2.5 27 11 hours
Uranus 19.2 4.01 14.5 1.3 27 84 0.8 98 -17 hours
Neptune 30.1 3.88 17.1 1.6 14 165 1.8 28 16 hours
A planetarium will show the orbital period of each planet and the rotation rate, as shown in the table above. A tellurion will show the earth with the moon revolving around the sun. It will use the angle of inclination of the equator from the table above to show how it rotates around its own axis. It will show the earth's moon, rotating around the earth.[13] A lunarium is designed to show the complex motions of the moon as it revolves around the earth.
Orreries are usually not built to scale. Human orreries, where humans move about as the planets, have also been constructed, but most are temporary. There is a permanent human orrery at Armagh Observatory in Northern Ireland, which has the six ancient planets, Ceres, and comets Halley and Encke. Uranus and beyond are also shown, but in a fairly limited way.[14] Another is at Sky's the Limit Observatory and Nature Center in Twentynine Palms, CA. This is a true to scale (20 billion to one), true to position (accurate to within four days) human orrery. The first four planets are relatively close to one another, but the next four require a certain amount of hiking in order to visit them.[15]
A normal mechanical clock could be used to produce an extremely simple orrery with the Sun in the centre, Earth on the minute hand and Jupiter on the hour hand; Earth would make 12 revolutions around the Sun for every 1 revolution of Jupiter. Note however that Jupiter's actual year is 11.86 Earth years long, so this particular example would lose accuracy rapidly. A real orrery would be more accurate and include more planets, and would perhaps make the planets rotate as well.
## Projection orreries
Many planetariums (buildings) have a projection orrery, which projects onto the dome of the planetarium a Sun with either dots or small images of the planets. These usually are limited to the planets from Mercury to Saturn, although some include Uranus. The light sources for the planets are projected onto mirrors which are geared to a motor which drives the images on the dome. Typically the Earth will circle the Sun in one minute, while the other planets will complete an orbit in time periods proportional to their actual motion. Thus Venus, which takes 224.7 days to orbit the Sun, will take 37 seconds to complete an orbit on an orrery, and Jupiter will take 11 minutes, 52 seconds.
Some planetariums have taken advantage of this to use orreries to simulate planets and their moons. Thus Mercury orbits the Sun in 0.24 of an Earth year, while Phobos and Deimos orbit Mars in a similar 4:1 time ratio. Planetarium operators wishing to show this have placed a red cap on the Sun (to make it resemble Mars) and turned off all the planets but Mercury and Earth. Similar tricks can be used to show Pluto and its five moons.
## Notable orreries
An orrery made by Robert Brettell Bate, circa 1812. Now in Thinktank, Birmingham Science Museum.
Shoemaker John Fulton of Fenwick, Ayrshire, built three between 1823 and 1833. The last is in Glasgow's Kelvingrove Art Gallery and Museum.
The Franeker Planetarium built by a wool carder named Eise Eisinga in his own living room, in the small city of Franeker in Friesland, is in fact an orrery. It was constructed between 1774 and 1781. The "face" of the model looks down from the ceiling of a room, with most of the mechanical works in the space above the ceiling. It is driven by a pendulum clock, which has 9 weights or ponds. The planets move around the model in real time.[16]
An innovative concept is to have people play the role of the moving planets and other Solar System objects. Such a model, called a human orrery, has been laid out with precision at the Armagh Observatory.[14]
## In popular culture
• A large orrery is a key feature in the climactic scene of the film Lara Croft: Tomb Raider (2001). In the 2015 game "Rise of the Tomb Raider", Lara traverses through the orrery of the legendary city of Kitezh while searching for the Divine Source.
• An orrery is used to determine when total eclipses occur in Pitch Black.
• The orrery is an artificial construct consisting of life-sized planets and a sun in Green Lantern: New Guardians.[17]
• An orrery is among the scientific things Tarzan looks on in Tarzan (1999 movie).
• The third level of Fireproof Games' popular smartphone game The Room occurs in and around a Talisman Co. Heliocentric Orrery.
• An orrery is one of the rooms in Andrew Plotkin's interactive fiction game The Dreamhold. It contains multiple items vital to completing the game.
• An orrery can be seen on board the spaceship Juggernaut in Prometheus.
• A complex orrery is used in a pivotal scene of The Dark Crystal.
• In Prince of Persia: The Forgotten Sands, the Prince manoeuvers through a gigantic water-powered orrery to get to the other side of one of the palace's towers; it is inaccurately named "the Astrolabe" in-game.
• The construction system Meccano is a popular tool for construction highly accurate orreries. Model 391, the first Meccano Orrery, was described in the June 1918 Meccano Manual.[18][19]
## References
1. ^ a b Calvert, H.R. (1967). Astronomy: Globes Orreries and other Models. London: H.M.S.O. ASIN B001A9C9SQ.
2. ^ King, Henry C.; Millburn, John R. (1978). Geared to the stars : the evolution of planetariums, orreries, and astronomical clocks. Toronto: University of Toronto Press. pp. 28–41. ISBN 0-8020-2312-6.
3. ^ Lloyd, H. Alan (1958). Some Outstanding Clocks Over Seven Hundred Years. London: Leonard Hill Books Limited. pp. 9–24.
4. ^ a b Brewster, David (1830). "Planetary Machines". The Edinburgh Encyclopedia. 16. Edinburgh: William Blackwood et al. p. 624. Retrieved 2011-06-08.
5. ^ Lloyd, Alan (1958). Some Outstanding Clocks Over Seven Hundred Years. Leonard Hill Books Limited. pp. 46–57.
6. ^ Poulle, Emmanuel; Sändig, Helmut; Schardin, Joachim; Hasselmeyer, Lothar (2008). Die Planetenlaufuhr : ein Meisterwerk der Astronomie und Technik der Renaissance geschaffen von Eberhard Baldewein 1563 - 1568 (1ª ed.). Stuttgart: Dt. Gesellschaft für Chronometrie. ISBN 978-3-89870-548-6.
7. ^ Ronan, Colin (1992) [First published 1981]. The Practical Astronomer. London: Bloomsbury Books. pp. 108–112. ISBN 1-85471-047-8.
8. ^ Carlisle, Rodney (2004). Scientific American Inventions and Discoveries, p. 189. John Wiley & Songs, Inc., New Jersey. ISBN 0-471-24410-4.
9. ^ "orrery". Oxford English Dictionary (3rd ed.). Oxford University Press. September 2005. (Subscription or UK public library membership required.)
10. ^ "Revolutionary Players". Search.revolutionaryplayers.org.uk. Retrieved 2010-02-09.
11. ^ "Welcome - Planetarium Friesland". www.planetarium-friesland.nl.
12. ^ Pentz, M.J. (1971). The Earth, Its Shape, Internal Structure and Composition. OU_S100_22. Bletchley: Open University Press. ISBN 978-0-335-02034-8.
13. ^ "Adler Planetarium:Research Collections". 1300 South Lake Shore Drive • Chicago IL 60605: Adler Planetarium. 2010. Retrieved 22 June 2011.
14. ^ a b "Armagh Observatory Human Orrery".
15. ^ "Sky's the Limit Observatory and Nature Center Human Orrery".
16. ^ Sixma, H (November 1934). "The Franeker Planetarium". Popular Astronomy. SAO/NASA ADS. XLII (9): 489–495. Bibcode:1934PA.....42..489S. Retrieved 2011-06-22.
17. ^ New Guardians #4-6 (Dec 2011 - Feb 2012)
18. ^ "Model 391, Meccano Orrery".
19. ^ Whiting, Michael (2007). "Orrery Developments:The Use of Meccano in Constructing Planetaria". Bulletin of the Scientific Society (94). Retrieved 2017-05-03. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "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": 0.5513551831245422, "perplexity": 4100.476576779138}, "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/1512948583808.69/warc/CC-MAIN-20171216045655-20171216071655-00592.warc.gz"} |
https://www.physicsforums.com/threads/relative-velocity-of-accelerating-and-non-accelerating-particles.777349/ | # Relative velocity of accelerating and non accelerating particles
Tags:
1. Oct 21, 2014
### Hijaz Aslam
Q. Two particles start simultaneously from the same point and move along two straight lines, one (particle A) with uniform velocity v and other (particle B) with a uniform acceleration a. If $\alpha$ is the angle between the lines of motion of two particles then the least value of relative velocity will be at time given by:
(a) $vsin\alpha/a$ (b) $vcos\alpha/a$ (c) $vtan\alpha/a$ (d) $vcot\alpha//a$
My text gives the answer as (b) $vcos\alpha/a$ . I think they reached at the answer as follows:
At an instant (the instant when the relative velocity is minimum; lets say) V=at, therefore $vcos\alpha-V=0$ where 0 is the shortest relative velocity (assumed). Therefore $vcos\alpha=at$ or $t=vcos\alpha/a$.
But this answer seems unconvincing. It is not necessary that for the relative velocity to be minimum the component of velocity of the 'A' (which attains a constant velocity) should be equal to the velocity of the 'B' (which has the constant acceleration) at a particular instant. Can anyone provide the precise solution?
2. Oct 21, 2014
### Staff: Mentor
Hello Hijaz Aslam. In future be sure to use the posting template for homework questions. It's a Physics Forum rule.
Can you write an expression for the relative speed versus time (or more simply, the square of the relative speed)? If so, how does one usually go about minimizing a function?
3. Oct 21, 2014
### Hijaz Aslam
I am afraid, I didn't get what you said. Can you be more precise please?
4. Oct 21, 2014
### Staff: Mentor
Suppose particle A's line lies along the x-axis and particle B's line is at angle α to the x-axis. Both particles start out at the origin. Can you write expressions for the x and y components of the velocities of both particles?
If you can, then can you find the components of the relative velocity vector?
5. Oct 21, 2014
### Hijaz Aslam
Yes, I think at the instant when the relative velocity is least we have the velocity of particle 'B' as : $(atcos\alpha)\hat{i}+(atsin\alpha)\hat{j}$
And the relative velocity of 'B' with reference to 'A' is given by $v_{BA}=v_{B}-v_{A}$ so we have: $v_{BA}=(atcos\alpha-v)\hat{i}+(atsin\alpha)\hat{j}$
And the magnitude $|v_{BA}|=a^{2}t^{2}-2avtcos\alpha+v^{2}$. Solving the quadratic to find time gives: $t=(cos\alpha\pm isin\alpha)/av$. NOW WHAT?
Am I correct so far?
6. Oct 21, 2014
### Staff: Mentor
Actually what you have is the square of the magnitude of the relative velocity. Which is perfectly fine! When one is minimized then so it the other.
Rather than solve for the time, what you want to do is find when this magnitude is minimized, right? How do you go about finding where a function has a minimum?
7. Oct 21, 2014
### Hijaz Aslam
Of course we differentiate it (silly me, I forgot the minimum part) , then equate it to zero ie : $2a^2t+2av-2a^2tcos\alpha-2avcos\alpha=0$
=> $at+v-atcos\alpha-vcos\alpha=0$ , simplifying we get $at+v=0$ or $t=-v/a$. And Wallah!! That's a wrong answer :( Am I wrong somewhere?
(BTW I didn't consider the denominator of the differential coefficient, because of course it gets transported into the right hand side which is zero. And isn't the acceleration constant? So we don't have to consider the D.C of 'a'. Do we? ).
Last edited: Oct 21, 2014
8. Oct 21, 2014
### Staff: Mentor
I'm not following how you arrive at your derivative with respect to time of the squared magnitude.
You have $| V_{BA} |^2 = a^2 t^2 - 2 a v cos(\alpha) t + v^2$ to start with. What's the derivative w.r.t. time?
9. Oct 21, 2014
### haruspex
I don't see how you got that from differentiating your expression for the square of the relative velocity.
With regard to the textbook explanation, the thing to notice is that the relative velocity perpendicular to B's path is constant, so it reduces to minimising the component parallel to B's path.
10. Oct 21, 2014
### Hijaz Aslam
gneill - I have use $|V_{BA}|=\sqrt(a^2t^2-2avtcos\alpha+v^2)$ itself. See differentiating $|V_{BA}|$ w.r.t we have:
$(2a^2t-2avcos\alpha-2a(dv/dt)tcos\alpha+2v(dv/dt))/2\sqrt(a^2t^2-2avtcos\alpha+v^2)$$(2a^2t-2avcos\alpha-2a^2tcos\alpha+2av)/2\sqrt(a^2t^2-2avtcos\alpha+v^2)$ . To find the minimum of this value (which is $|V_{BA}|$), we equate it to zero, so we have: $2a^2t-2avcos\alpha-2a^2tcos\alpha+2av$ . I have skipped the above steps. (NOTE: I've differentiated the above presuming that the acceleration is constant. Is that assumption correct?) (I've also used $dv/dt=a$)
11. Oct 21, 2014
### Staff: Mentor
You've made your life unnecessarily complicated by including the square root Minimize f(x)2 and you minimize f(x) too.
Note that a and v are not related to each other in this problem, and that both are constants, not variables. Certainly $dv/dt$ is not a.
12. Oct 21, 2014
### Hijaz Aslam
Oh my.. blimey.....I've never made such a blunder in my learning career, I don't know what's got into my head lately. Of course v is a constant and...OMG how did I even think about it: Of course yes so you have $2a^2t-2avcos\alpha=0$ that is $t=v/acos\alpha$. Thank you very much gneill, my brain's all shut down. Sorry for wasting your time with such a silly mistake. Thank you gneill. (I really appreciate your method of squeezing out the answer from the questioner itself, it made me understand the whole concept myself. And I like that TARDIS D.P..I am a Whovian :D ) Thanks again.
And one more thing (I'm sorry) : Is that solution I gave in the beginning which takes $vcos\alpha=at$ and then proving that $t=vcos\alpha/a$ a reliable one? Or is it just coincidentally correct?
13. Oct 21, 2014
### Hijaz Aslam
haruspex - Do you mean that we can arrive at the answer by taking : $vcos\alpha=at$ and hence $t=vcos\alpha/a$? Can you please explain what you've mentioned?
14. Oct 21, 2014
### Staff: Mentor
You're welcome. I'm a big fan of The Doctor too.
Offhand I can't think of a good obvious argument for assuming $vcos(\alpha)=at$ means the relative velocity is minimized, other than it follows from the correct solution
15. Oct 22, 2014
### haruspex
As I wrote in post #9, it's valid because the rel velocity perpendicular to B's path is constant, so it's just a matter of minimising the component parallel to B's path.
In fact, the problem can be generalised in a couple of ways. If the variable speed is w=w(t) then the minimum rel velocity occurs when $vcos(\alpha)=w(t)$.
Neither is it specific to velocity and acceleration. The same equations apply if you drop the d/dt down a level, i.e. change velocities to displacements and accelerations to velocities (in which context, the answer is rather more obvious).
16. Oct 22, 2014
### Hijaz Aslam
haruspex - Do you mean the relative velocity perpendicular to B or A? Please consider the above diagram.
17. Oct 22, 2014
### haruspex
Perpendicular to B's path, as I wrote. What is the component of the relative velocity in that direction? Is it not constant?
18. Oct 22, 2014
### Hijaz Aslam
Alright, Yes as B doesn't have any components towards its perpendicular, Component of relative velocity in its perpendicular direction is constant. Alright so the only velocity in consideration is the one parallel to B. Got it!
So we can't say that $atcos\alpha=v$ gives the minimum relative velocity because, the perpendicular relative velocity of 'A' is not constant. Isn't it?
19. Oct 22, 2014
### Hijaz Aslam
gneill - harupex above has got an explanation for the method I've mention in the beginning. It's far simpler. Your method made the concepts clear for me though. :) Thanks
20. Oct 22, 2014
### haruspex
That's right, the situation is not symmetric.
Draft saved Draft deleted
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https://forum.gamsworld.org/viewtopic.php?t=10837 | ## Error 171: Domain violation for set
Problems with syntax of GAMS
Gulsum
User
Posts: 3
Joined: 9 months ago
### Error 171: Domain violation for set
Dear all,
As a student on dissertation stage, I am working on a model for cost minimization in train shunting.
As a brief clarification of model; there are arriving train units, departing train units and shunting lines on which are used for coupling and decoupling of train units. Mathematical model was first described by Schrijver.
Attachments
MinShuntingCost_MathematicalModel.pdf
MinShuntingCost.gms
bussieck
Moderator
Posts: 367
Joined: 3 years ago
### Re: Error 171: Domain violation for set
If you want to use GAMS at a dissertation level, you need to invest more in learning the tool. Your errors are of very fundamental nature:
1. You need to make some sets subsets of i adn j:
Code: Select all
itoj(i) 'arriving train units to be assigned to departing train units'/i7,i17,i27/
jtoi(j) 'departing train units to be matched with arriving train units'/j2,j12,j22/
2. The construct ord(j)-'1' makes no sense in GAMS. But you pdf does not help much either. The J_i and the I_j seem critical in your description. It's a nice set notation. In GAMS you often do this as maps Ji(j,i). Perhaps this is what you tried with the itoj and jtoi.
If you give a proper reference to Lex paper or provide the pdf of the relevant part of the paper there is a chance that someone here can help. I only found https://homepages.cwi.nl/~lex/files/Pla ... Tracks.pdf but can find little overlap with your pdf.
-Michael
Gulsum
User
Posts: 3
Joined: 9 months ago
### Re: Error 171: Domain violation for set
Dear Micheal,
As you mentioned, I have a lot to learn in GAMS. I am quite beginner.
And for second one, your understanding about subsets is correct. With ord(j)-'1' expression, I am trying to check the previous train unit in subsets in order to avoid any crossing. I provide a little bit clarification about crossing in train shunting as in attached file.
BRs
Gulsum
Attachments
Clarification About Crossing in Train Shunting.pdf
bussieck
Moderator
Posts: 367
Joined: 3 years ago
### Re: Error 171: Domain violation for set
There are big differences in the algebra in your write-up and the GAMS model, e.g. equation 6. I think I understand what the math does, but your equation does not implement the math and you try to make some arguments why the GAMS algebra also prevents crossing (true or not) but it does not implement the math! Your write-up is also missing the definition of some symbols (e.g. \tau_i, I guess this is the time the trains leaves or arrives) and is sloppy with symbol names (e.g. WL as train length in the text, but the algebra has l_i). I suggest that you do a proper mathematical write-up of the problem have a tables with the data in word and then try to implement exactly this math in GAMS. If you run into trouble with that I am sure you will find some help here.
-Michael
Gulsum
User
Posts: 3
Joined: 9 months ago
### Re: Error 171: Domain violation for set
Dear Micheal,
Thanks for your help, I will recheck the mathematical model then focus on GAMS model.
BRs
Gulsum | {"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": 0.8534316420555115, "perplexity": 2071.563841702056}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251789055.93/warc/CC-MAIN-20200129071944-20200129101944-00549.warc.gz"} |
https://mathematica.stackexchange.com/questions/157909/plotting-regionintersection | Plotting RegionIntersection
A new feature added in Mathematica 11.2 gives the ability to easily plot region intersection (see this post, scroll down to 3D Computational Geometry).
However, I can't seem to understand how to find the intersection of following objects:
contourRegionPlot3D[region_, {x_, x0_, x1_}, {y_, y0_, y1_}, {z_, z0_, z1_},
opts : OptionsPattern[]] := Module[{reg, preds},
reg = LogicalExpand[region && x0 <= x <= x1 && y0 <= y <= y1 && z0 <= z <= z1];
preds = Union@Cases[reg, _Greater | _GreaterEqual | _Less | _LessEqual, -1];
Show @ Table[ContourPlot3D[
Evaluate[Equal @@ p], {x, x0, x1}, {y, y0, y1}, {z, z0, z1},
RegionFunction -> Function @@ {{x, y, z}, Refine[reg, p] && Refine[! reg, ! p]},
opts], {p, preds}]]
shift = {1.2, 1, 1};
heart = ImplicitRegion[((y - shift[[1]])^2 + (9 (x - shift[[2]])^2)/ 4 + (z -
shift[[3]])^2 - 1)^3 - (y - shift[[1]])^2 (z - shift[[3]])^3 - (9 (x -
shift[[2]])^2 (z - shift[[3]])^3)/80 < 0, {x, y, z}];
heartPlot = RegionPlot3D[
heart,
PlotRange -> {{-0.5, 2.5}, {-2.5, 2.5}, {-0.5, 2.5}},
PlotPoints -> 30,
PlotStyle -> Directive[lightBlue, Opacity[0.4]]
];
arcRegion = 1.4 < x^2 + y^2 < 1.6 && 1.4 < z < 1.6 && 1 \[Pi]/64 < ArcTan[x, y] < 27 \[Pi]/64;
arcRegionPlot = contourRegionPlot3D[arcRegion, {x, 0.1, 2}, {y, 0.1, 2}, {z, 1.2, 1.8}];
RegionIntersection[
heartPlot // DiscretizeGraphics,
arcRegionPlot // DiscretizeGraphics
]
And here's what I get as an output:
What am I doing wrong here? I know that those 2 regions for sure intersect:
• Without going into details, I suspect problems with the dimensionality of regions (surface vs. volume). Do you want to treat them as volumes? Oct 16 '17 at 12:46
• @Szabolcs, Frankly, I'm not sure. What I want is to have a nice annular tunnel cut through the heart. Oct 16 '17 at 12:48
• I wouldn't expect much consistency in dimensionality from DiscretizeGraphics. Graphics are just for looks. When you do an intersection then a surface and a volume are very different. I would try RegionIntersection or RegionDifference on the ImplicitRegion objects, then use BoundaryDiscretizeRegion with explicit bounds on the result. Oct 16 '17 at 12:55
• @Szabolcs, I've updated my question according to your suggestion. It works but produces some unwanted visual artifacts. Any ideas how to get rid of them? Oct 16 '17 at 13:41
• Decrease MaxCellMeasure? Try different Method values? Oct 16 '17 at 13:45
Following @Szabolcs's advice, here's what I could accomplish:
lightBlue = RGBColor[0.593454, 0.888609, 0.918547];
shift = {1.2, 1, 1};
heart = ImplicitRegion[((y - shift[[1]])^2 + (9 (x - shift[[2]])^2)/ 4 + (z -
shift[[3]])^2 - 1)^3 - (y - shift[[1]])^2 (z - shift[[3]])^3 - (9 (x -
shift[[2]])^2 (z - shift[[3]])^3)/80 < 0, {x, y, z}];
heartPlot = RegionPlot3D[
heart,
PlotRange -> {{-0.5, 2.5}, {-2.5, 2.5}, {-0.5, 2.5}},
PlotPoints -> 100,
PlotStyle -> Directive[lightBlue, Opacity[0.4]]
];
arcRegionImplicit = ImplicitRegion[1.4^2 < x^2 + y^2 < 1.6^2 && 1.4 < z < 1.6 && 0 < ArcTan[x, y] < \[Pi]/2, {x, y, z}];
Show[
heartPlot,
RegionPlot3D[BoundaryDiscretizeRegion[RegionIntersection[heart, arcRegionImplicit], MaxCellMeasure -> 0.001]]
]
With the following result: | {"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": 0.15440361201763153, "perplexity": 5965.199144826022}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300289.37/warc/CC-MAIN-20220117031001-20220117061001-00072.warc.gz"} |
https://kakila.bitbucket.io/emumore/posts/polyonymous-algorithms.html | # Polyonymous Algorithms
One core idea of emulation is to represent the ensemble of outputs of a complicated simulator in a reduced basis. The battle-horse algorithm to do this is the famous PCA, a.k.a POD, a.k.a SVD, a.k.a EOF, a.k.a. EBD, a.k.a. KLD, a.k.a. …
Really, this algorithm has a different name in each community that uses it! I did not invest much time in finding whether this is due to simultaneous discoveries, or due to researchers not looking into other communities to see what already exist (i.e. re-inventing the wheel and calling it differently), or due to mischievous re-naming to get published. In case of the first there is nothing to do but wait (and hope) for unification. The second is something shouldn’t be common anymore, specially in the age of the internet. The third and last is unforgivable, it is more common than what I would like to accept, and is caused by the stupid pressure to publish a lot (instead of good stuff). I believe that the true cause is a mix of all three.
Anyways, I hope new researchers, with young blood, are more careful, ethical, and worry less about piling up disposable articles.
As I said at the beginning, one very useful approach to accelerate a complicated simulator is to try to represent the ensemble of outputs in a reduced basis. Generally this is something of the form
where $$\mathbf{y}(t,\mathbf{\lambda})$$ is the output of the simulator, here assumed to depend on time and some parameter vector $$\mathbf{\lambda}$$. In the Ansatz above, we try to put the time dependence in some parameter independent basis $$\varphi_i(t)$$, which is hopefully small. The dependence on the parameters is present only in the coefficients of the basis. Put in words, we try to represent any output of the simulator as a linear combination of a fixed basis. In this representation, we need to learn only the parameter dependence of the basis coefficients. We learn this dependence from outputs of the simulator obtained with different parameters, i.e.e the training data. When the basis is small this can provide a boost in the calculation time of outputs at new parameter values. The size of the basis is related to the complexity of the signals the simulator generates, more complex outputs require more basis elements to generate a good representation.
## SVD decomposition
A very efficient way of obtaining the basis $$\varphi_i(t)$$ is by applying the Singular Value Decomposition (SVD) to the so called snapshots matrix (or data matrix) $$\mathbb{Y}$$ which contains the recorded simulation outputs in its columns
This way of obtaining the basis is equivalent to:
• Principal Components Analysis (PCA): well know in machine learning and statistics and used for dimensionality reduction.
• Proper Orthogonal Decomposition (POD): popular in structural mechanics, physics, and theory of differential equations.
• Karhunen-Loève Decomposition (KLD): also well known in statistics.
• Empirical Orthogonal Functions (EOF): popular among wind and solar power researchers.
The list is really long and it gets longer the more I read from different research fields.
Of course there are other decomposition algorithms that are not equivalent to SVD. For example there is Nonnegative Matrix Factorization (NMF), Independent Component Analysis, Anechoic Mixing Models, my own work on kinematic chains using the Dynamic Decomposition Method1, and the many decompositions used in Compressed Sensing. All these other methods are also valid approaches for emulation. They can be particularly useful if we have prior information about the basis, or if we want the basis to have a given property for the sake of interpretability of the decomposition (this is seldom required in emulation since the objective is just to accelerate the simulator and not much more).
A very simple example is implemented in the script s_svd_ode.m (available in the repository), where the motion of the pendulum is reduced to an interpolation problem. The parameter vector contains the initial angle of the pendulum and the initial speed. In this example only 4 basis elements are needed to emulate the pendulum with an error of about 1%. you can see the surfaces of these coefficients int he plots below
We presented a concrete example of application of SVD and MNF in our publication2, under the name Data-driven emulation.
Similar ideas are applied in model order reduction (we will post about the difference between model order reduction and emulation soon), you can read about them in Reduced Basis Method for PDEs3 and in POD for dynamical systems 4.
# References
1. Carbajal, J. P. (2012). Harnessing Nonlinearities: Generating Behavior from Natural Dynamics. University of Zürich. https://doi.org/10.5167/uzh-66463
2. Carbajal, J. P., Leitão, J. P., Albert, C., & Rieckermann, J. (2017). Appraisal of data-driven and mechanistic emulators of nonlinear simulators: The case of hydrodynamic urban drainage models. Environmental Modelling & Software, 92, 17–27. http://doi.org/10.1016/j.envsoft.2017.02.006. Arxiv: https://arxiv.org/abs/1609.08395
3. Quarteroni, A., Manzoni, A., & Negri, F. (2015). Reduced Basis Methods for Partial Differential Equations: An Introduction. Springer International Publishing.
4. Volkwein, S. (2013). Proper orthogonal decomposition: Theory and reduced-order modelling. Lecture Notes, University of Konstanz. http://www.math.uni-konstanz.de/numerik/personen/volkwein/teaching/POD-Book.pdf | {"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": 0.7684782147407532, "perplexity": 987.1809759968176}, "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/1550247484648.28/warc/CC-MAIN-20190218033722-20190218055722-00496.warc.gz"} |
https://dsp.stackexchange.com/questions/23035/low-pass-filter-with-minimal-ringing | # low pass filter with minimal ringing
I am trying to filter out some square wave signal to within a limited band (1/4 or 1/8 of the original), I realized that there's a lot of ringing in the wave when I use my filter (elliptical), I also tried Butterworth, and others (given in Matlab fir1, and classic iir filters) but the only filter that seems to give no ringing is Gaussian. So my question is, how should I go about designing a LPF with minimal ringing? (preferred characteristics: minimal pass band ripple, stop band of more than -50dB, relatively fast roll off). Also as I am trying to implement this in a DSP, low order filters such as IIR types are preferred.
Thank you for any help.
• if the poles are real, not complex-conjugate, then the impulse response (and step response) does not ring. this means, for a biquad IIR, that the Q must be no greater than 1/2. but you won't get the roll-off you want with low Q, i'm afraid. whether it's IIR or FIR, a sharp transition means ringing at the frequency of approximately that of the sharp transition. – robert bristow-johnson Apr 28 '15 at 19:33
• @Robert Are there any optimal IIR filters where we can optimize for Order, Transition band, PB & SB ripples like Parks-McClellan for FIR filters? – Naveen Apr 28 '15 at 22:33
• oh i dunno. i thought Prony was a method to design the impulse response of an IIR to be what you want. as far as frequency-domain design with brick-walls and the transition band and PB and SB, i guess you might want to look into Elliptical filters. they be pretty ugly in the time-domain (like horribly non-constant group delay). oh, and there is Greg Berchin's FDLS for frequency-domain design. – robert bristow-johnson Apr 28 '15 at 22:39
• ringing need not happen at high frequencies. unless you're using Planck units (or some other natural system of units), frequency is relative anyway. ringing is caused by an imaginary component in your poles. with real coefficients and real signal values in your filter, poles and zeros are either purely real or the come in complex-conjugate pairs. if the latter, your impulse response will have an exponentially-damped sinusoid in it. having as rapid step response as possible without ringing usually has real poles coincident on top of each other. – robert bristow-johnson Apr 29 '15 at 23:26
• well, if your FIR is long enough, you can make your FIR $h[n]$ be whatever you want, including something that rings (as long as the FIR is, note the "F"). with an IIR, it theoretically rings forever (if the poles are complex-conjugate) hence the "I" in IIR. – robert bristow-johnson May 1 '15 at 18:38 | {"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": 0.6055145263671875, "perplexity": 1684.2902080755384}, "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-2019-22/segments/1558232261326.78/warc/CC-MAIN-20190527045622-20190527071622-00175.warc.gz"} |
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# Inequalities and Roots
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25 Jul 2013, 20:26
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Expert's post
gmatter0913 wrote:
Hi Karishma,
I tried the problem x-1 < sqrt (7-x) as below:
As 7-x is under sqrt, it is +ve. Therefore, 7-x>=0 ; x<=7 ----->(1)
x-1 can be -ve or +ve
When x-1<=0; x<=1 --------> (2)
When x-1>=0; x>=1 --------> (3)
As both sides are +ve, we can square both the sides
(x-1)^2 < 7-x
x^2 -x -6<0
(x-3)(x+2)<0
-2<x<3 ------------>(4)
The answer to this problem is (x<3). I am not sure how to arrive at that from hereon. Could you please help me?
You have done the process correctly. Now you need to understand what this implies.
You got x <= 7
Case 1: x-1< 0
When x-1< 0; x < 1
Note that when x-1 is negative, it will always be less than $$\sqrt{(7-x)}$$
So whenever x<1, the inequality will always hold.
Case 2: x-1 >= 0
If x-1 is non negative, we can square the inequality.
From this, you get -2<x<3.
The inequality holds in this range.
From the two cases, we see that the inequality holds for the range x < 3.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Senior Manager Joined: 12 Mar 2010 Posts: 383 Concentration: Marketing, Entrepreneurship GMAT 1: 680 Q49 V34 Followers: 2 Kudos [?]: 176 [0], given: 87 Re: Inequalities and Roots [#permalink] ### Show Tags 26 Jul 2013, 01:05 Hi Karishma, I have one more doubt on my solution posted earlier. Quote: I tried the problem x-1 < sqrt (7-x) as below: As 7-x is under sqrt, it is +ve. Therefore, 7-x>=0 ; x<=7 ----->(1) x-1 can be -ve or +ve When x-1<=0; x<=1 --------> (2) When x-1>=0; x>=1 --------> (3) As both sides are +ve, we can square both the sides (x-1)^2 < 7-x x^2 -x -6<0 (x-3)(x+2)<0 -2<x<3 ------------>(4) Shouldn't this be 1<=x<3 (as x>=1 is the pre-supposed condition to square them) Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7191 Location: Pune, India Followers: 2174 Kudos [?]: 14058 [1] , given: 222 Re: Inequalities and Roots [#permalink] ### Show Tags 26 Jul 2013, 03:23 1 This post received KUDOS Expert's post gmatter0913 wrote: Hi Karishma, I have one more doubt on my solution posted earlier. Quote: I tried the problem x-1 < sqrt (7-x) as below: As 7-x is under sqrt, it is +ve. Therefore, 7-x>=0 ; x<=7 ----->(1) x-1 can be -ve or +ve When x-1<=0; x<=1 --------> (2) When x-1>=0; x>=1 --------> (3) As both sides are +ve, we can square both the sides (x-1)^2 < 7-x x^2 -x -6<0 (x-3)(x+2)<0 -2<x<3 ------------>(4) Shouldn't this be 1<=x<3 (as x>=1 is the pre-supposed condition to square them) Most certainly. The only reason I don't care about the values from -2 to 1 is that these values are already covered in the first case. We know they already hold for the inequality. We only get 1 to 3 extra values and that's what we care about. In a stand alone question, the presupposed condition must be satisfied (x <= 7 AND x >= 1) _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199
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Re: Inequalities and Roots [#permalink] 12 Mar 2016, 17:59
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Display posts from previous: Sort by | {"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": 0.4725833535194397, "perplexity": 8953.204593985654}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501173872.97/warc/CC-MAIN-20170219104613-00577-ip-10-171-10-108.ec2.internal.warc.gz"} |
http://www.gradesaver.com/the-book-thief/q-and-a/what-is-liesel-memingers-moral-177313 | # What is Liesel Meminger's moral?
Could you give me textual evidence of how you created the answer and where it is located? Thank you | {"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": 0.9589373469352722, "perplexity": 3918.0791869776667}, "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-2017-17/segments/1492917118851.8/warc/CC-MAIN-20170423031158-00353-ip-10-145-167-34.ec2.internal.warc.gz"} |
http://tex.stackexchange.com/questions/30141/error-in-built-output | # Error in built output
This is difficult for me with all these $signs. Now, where is the problem in the following MWE? \documentclass{article}% \usepackage{amsmath}% \usepackage{amsfonts}% \usepackage{amssymb}% \usepackage{graphicx} \usepackage{comment} \begin{document} \varphi_{nk}(x,y) = \left\{ \begin{array}{c l} 1 &$x_{k}\succ_{n} y_{k}$\\ 1/2 &$x_{k} \sim_{n} y_{k}$\\ 0 &$x_{k}\prec_{n} y_{k}$\end{array} \right. So \textit{n} is \varphi_{n}(x,y)= \sum_{k}\varphi_{nk} \end{document} Also a more general question related to Tex.sx. How can I copy the code to the question box, without having to press space bar 4 times for each line to indent it? As a follow up, in case I would like to insert the word 'if' in every case (piece) of the function above, how can I do so? Eg ...1/2 & if$x_{k}\succ_{n} y_{k}$ doesn't seem to work as the 'if' is conjoined. - Re "question box" (code sample): Highlight the code and click the "code" button (with "{}" on it). – lockstep Oct 1 '11 at 9:23 For questions about the site, please visit TeX - LaTeX Meta. – Stefan Kottwitz Oct 1 '11 at 9:23 ## 2 Answers Don't use $ within an array environment, since the array environment is completely in math mode.
\documentclass{article}
\usepackage{amsmath}%
\usepackage{amsfonts}%
\usepackage{amssymb}%
\begin{document}
$\varphi_{nk}(x,y) = \left\{ \begin{array}{c l} 1 & x_{k}\succ_{n} y_{k}\\ 1/2 x_{k} \sim_{n} y_{k}\\ 0 & x_{k}\prec_{n} y_{k} \end{array} \right.$
So $n$ is $\varphi_{n}(x,y)= \sum_{k}\varphi_{nk}$.
\end{document}
• Use math expressions such as \varphi_{nk}(x,y) in math mode, either within text (inline) such as by $...$ or $$...$$ or in displayed mode, such as by $...$ in my example.
• Don't use empty lines before or after such displayed math formulas.
• Don't use \textit for simulating math mode.
Have a look at the Mathmode tag wiki for links to tutorials, useful packages and resources on this site.
-
You should read Math mode (H. Voß). With $...$ you always use the inline math.
You example can be modified with the cases-environment:
\documentclass{article}%
\usepackage{amsmath}%
\usepackage{amsfonts}%
\usepackage{amssymb}%
\usepackage{graphicx}
\usepackage{comment}
\begin{document}
$$\varphi_{nk}(x,y) = \left\{ \begin{array}{c l} 1 & x_{k}\succ_{n} y_{k}\\ 1/2 & x_{k} \sim_{n} y_{k}\\ 0 & x_{k}\prec_{n} y_{k} \end{array} \right.$$
So \textit{n} is$\varphi_{n}(x,y)= \sum_{k}\varphi_{nk}$
$$\varphi_{nk}(x,y) = \begin{cases} 1 & x_{k}\succ_{n} y_{k}\\ 1/2 & x_{k} \sim_{n} y_{k}\\ 0 & x_{k}\prec_{n} y_{k} \end{cases}$$
So \textit{n} is$\varphi_{n}(x,y)= \sum_{k}\varphi_{nk}$
\end{document}
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https://www.physicsforums.com/threads/femtoampere-op-amp-in-luggage-will-it-be-degraded-by-luggage-screening-xrays.562370/#post-3682537 | # Femtoampere op amp in luggage - will it be degraded by luggage screening xrays?
• Thread starter Dmytry
• Start date
• #1
510
1
Somewhat unusual question:
Do you think LMP7721MA would get degraded by xrays used for luggage screening? It is an electrometer opamp with extremely low input bias current:
http://www.national.com/pf/LM/LMP7721.html#Overview [Broken]
Normally the electronics is not affected by the xrays but this chip is far from usual.
Last edited by a moderator:
## Answers and Replies
• #2
5,573
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Femtoamp are mostly CMOS front end, look into whether CMOS is X-ray sensitive. I use femtoamp before, I don't recall any warning. If you cannot find info on CMOS in X-ray and if there is no warning on data sheet, it should not be a problem. If you worry more, call or email to the manufacturer and ask. If you still worry, carry with you on the plane.
• #3
jim hardy
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it's nmos that's most sensitive.
generally speaking electronics is tougher than living things.
a computer with cmos will take a couple thousand rads.
i have never tested one of those nmos electrometer ic's
but would be astonished if you were able to measure a degradation in its performance
after any sane x-ray.
surely they get x-rayed in shipment sometimes.
try an experiment - run a roll of photographic film through a scanner and have it developed. if it's not fogged, the dose was in low millirads like <10mr...
i once subjected my TI99 computer to 1000 rads. itr ran fine during and after the exposure.
that's best i can do.
maybe somebody in a nuke plant could test one for you - i put the TI99 in our HP department's calibrator and gave it two hours at 500R/hr, running a memory test loop..
old jim
• #4
1,681
3
It will probably be fine since the low input current is achieved by active means. The typical OpAmp is degraded by thousands or tens of thousands of gamma rads. 1000 gamma rads is 100% fatal dose.
I would be very surprised if this device were degraded in any measurable way.
• #5
jim hardy
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1000 gamma rads is 100% fatal dose.
for humans.
most electronics between 10,000 & 100,000.
• #6
5,573
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Hey Jim, did you look at the LMP7721 spec.? I must be getting old!!! This one has low voltage noise down to 30nV/sqrt(Hz) at 10 Hz(below 10nV/sqrt(Hz)) at about 500Hz, GBW of 17MHz, over 10V/uS and less than 2mA supply current!!!! Only draw back if you can call it is low supply voltage limit.
In my days, you'll be lucky to get 10fA input bias current, slow as snail, and quite high noise. This is not for the weak of heart!!!
It did not say the input transistor. But if it is CMOS, then op won't have a problem. But I doubted because I never seen a CMOS with such low flicker noise at 10Hz..........Which again............in my days!!!
• #7
jim hardy
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no question i'm obsolete.
last electrometer opamp i used was OPA128 for integrate/hold stage in analog controller.
which was astounding to me in 2002...... it'd hold to a millivolt overnight with just 1uf.
this one looks better by almost an order of magnitude.
(interestingly, the 128 datasheet mentions its use in rad-hardened equipment. it must be pretty stout in that regard. that'd be desirable for something you'd use in a radiation meter for measuring ion chamber current. i'd wager the 7721 is rad-stout also)
the tools available today's youth are amazing.
i guess that's why we're allotted threescore and ten - the world changes so much we'd be a drag on it.
next twenty years will see English language become more precise in its everyday use, to keep up with the computers.
old jim, still clinging to Fortran.
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• #8
5,573
203
When I was doing electronmeter amp, OPAs were still belong to Burr Brown!!!! There goes to show how long has it been for me!!! I guess I am slightly newer on programming......PASCAL!!! :rofl:
I just refused to learn C++ anymore, I just don't have the interest. I had software engine did all the programmings.
Before, we never looked at big manufacturers like National, Motorola and Ti because their stuffs are mostly of lower spec. All the most exotic ones are like PMI, Comlinear ( still remember this? They specialize on high speed op-amps), Burr Brown( low bias current), Apex( high voltage) etc. Now I notice they are got bought out by Analog Devices, National etc. I don't remember who bought out Apex, I know they got bought out by another big company.
Last edited:
• #9
510
1
Ya that's some amazing op-amp... my concerns are also for the plastic packaging vs radiation.
Anyhow, I calculated that the background radiation over 10 years should give it a dose of 0.3E-6 *24*365*10 = 0.026 Gy , and i'd reasonably assume that it won't degrade in 10 years...
I can't find the luggage screening doses though. Also, the effects are not precisely same for x-rays and natural background radiation. x-rays fog film a lot more effectively (at doses where the natural radiation will trigger a few grains in the film, x-ray can trigger every grain). I guess hand luggage should be safe enough.
I am indeed planning to make a radiation detector with it, but only meant to be used near background radiation level (or i'd use something waaay less sensitive)
• #10
jim hardy
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Ya that's some amazing op-amp... my concerns are also for the plastic packaging vs radiation.
Anyhow, I calculated that the background radiation over 10 years should give it a dose of 0.3E-6 *24*365*10 = 0.026 Gy , and i'd reasonably assume that it won't degrade in 10 years...
I can't find the luggage screening doses though. Also, the effects are not precisely same for x-rays and natural background radiation. x-rays fog film a lot more effectively (at doses where the natural radiation will trigger a few grains in the film, x-ray can trigger every grain). I guess hand luggage should be safe enough.
I am indeed planning to make a radiation detector with it, but only meant to be used near background radiation level (or i'd use something waaay less sensitive)
i think that were airport scanners high level there'd be lots more shielding around them than i have noticed.
i paid careful attention to PCB layout, guarding my input tracks as advised in datasheet appnotes and keeping them short and far away from power traces even on other layers. Polypropylene capacitors work well for low leakage applications and are cheaper than polycarbonate, or at least they were a few years ago.
good luck with your project. What are you using for a detector? ion chamber? GM tube? something new?
old jim
• #11
510
1
i think that were airport scanners high level there'd be lots more shielding around them than i have noticed.
i paid careful attention to PCB layout, guarding my input tracks as advised in datasheet appnotes and keeping them short and far away from power traces even on other layers. Polypropylene capacitors work well for low leakage applications and are cheaper than polycarbonate, or at least they were a few years ago.
good luck with your project. What are you using for a detector? ion chamber? GM tube? something new?
old jim
Just an ion chamber, i'm hoping to be able to detect individual cosmic ray tracks. Yes, the guard line is very important there... i'll connect guard to two n/c wires on the package as well. Also i'm thinking of bending the input pins upwards and hanging the sensitive circuitry in the air. The circuit will be in a small metal box inside the ionization chamber, with wire sticking out. I'll use the capacitance of the ionisation chamber as the capacitor.
I actually have 4 of those chips so I plan to build several different circuits. In one i want to use very high value resistor, in other a mechanical switch to discharge the capacitor. I can use a tiny galvanometer as actuator for the switch. I'll be discharging actively (connecting the negating input of amplifier to the amplifier's output).
One really sweet thing about this opamp is that it got back-to-back diodes between inputs. I.e. you can have this ultra sensitive input hanging in the air and use it as a fairly robust electroscope, and it won't get zapped.
• #12
5,573
203
Just an ion chamber, i'm hoping to be able to detect individual cosmic ray tracks. Yes, the guard line is very important there... i'll connect guard to two n/c wires on the package as well. Also i'm thinking of bending the input pins upwardsGood idea. Guard trace only put the potential close to the input, but any residue of flux will still create a conduction path. We also use ultra sound freon bath for cleaning the boards. and hanging the sensitive circuitry in the air. The circuit will be in a small metal box inside the ionization chamber, with wire sticking out. I'll use the capacitance of the ionisation chamber as the capacitor.
I actually have 4 of those chips so I plan to build several different circuits. In one i want to use very high value resistor, in other a mechanical switch to discharge the capacitor. I can use a tiny galvanometer as actuator for the switch. I'll be discharging actively (connecting the negating input of amplifier to the amplifier's output).
One really sweet thing about this opamp is that it got back-to-back diodes between inputs. I.e. you can have this ultra sensitive input hanging in the air and use it as a fairly robust electroscope, and it won't get zapped.
Don't trust the back to back diode inside the opamp that much. They are very weak.
• #13
jim hardy
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air insulation works and is suggested in some application notes.
sounds like a fun project.
I can use a tiny galvanometer as actuator for the switch....
darn - i just looked at a mil-style sealed -50 0 +50 microamp galvanometer in a surplus store yesterday... had two contact outputs and was only ten bucks. It was at "Pappy's" surplus near Goldsboro NC.... if i'd known you needed one i'd have got it.
• #14
510
1
Don't trust the back to back diode inside the opamp that much. They are very weak.
I'll connect some 100K..1M resistor in series. That should do it. With the ionisation chamber the issue is that the input may get shorted onto 100v supply.
The guards are really neat idea. I'm going to make guarded posts inside the ion chamber and suspend inner electrode using a fishing mono-filament tied to those posts... if i end up using micro-controller in this meter, I can make it vary voltage on the guard to measure guard-to-input resistance (and contact voltage) and compensate for it.
Re: galvanometer, i was thinking of the kind that used to be common as audio level indicators. I have various old soviet electronics for really cheap. It's not critical, I can make electromagnet that'd short the connection, or reed switch. Thinking about it, with those back to back diodes it is not important to keep input shorted when the device is turned off, so i would use normally-open switch that i'd close momentarily to zero the input. So the power consumption of the switch will be low in any case. I'll put the switch between the output and negating input (which will be connected to the inner electrode in ion chamber). Eventually I want to use microcontroller to process the data and do the switching as needed, and send the data to computer for logging, as well as display digital readout (and the standard deviation for the noise so i know if something is statistically significant).
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• #15
5,573
203
I'll connect some 100K..1M resistor in series. That will do it. Use a longer body resistor so static HV less likely to creep over the body surface.That should do it. With the ionisation chamber the issue is that the input may get shorted onto 100v supply.
The guards are really neat idea. I'm going to make guarded posts inside the ion chamber and suspend inner electrode using a fishing mono-filament tied to those posts... if i end up using micro-controller in this meter, I can make it vary voltage on the guard to measure guard-to-input resistance (and contact voltage) and compensate for it.
Re: galvanometer, i was thinking of the kind that used to be common as audio level indicators. I have various old soviet electronics for really cheap. It's not critical, I can make electromagnet that'd short the connection, or reed switch. Thinking about it, with those back to back diodes it is not important to keep input shorted when the device is turned off, so i would use normally-open switch that i'd close momentarily to zero the input. So the power consumption of the switch will be low in any case. I'll put the switch between the output and negating input (which will be connected to the inner electrode in ion chamber). Eventually I want to use microcontroller to process the data and do the switching as needed, and send the data to computer for logging, as well as display digital readout (and the standard deviation for the noise so i know if something is statistically significant).
One other thing you did not mention whether the input go through coax like some of the electronmeters. You need to use rigid coax if possible. Even double shield coax will create noise from vibration even if you don't move it. In our spectrometer, the vibration of the vacuum pumps causing problem and we had to switch to rigid coax.
• #16
jim hardy
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""I'll put the switch between the output and negating input... ."
as yungman said, input is not bulletproof so put a resistor to limit current when close switch.
old jim
• #17
510
1
One other thing you did not mention whether the input go through coax like some of the electronmeters. You need to use rigid coax if possible. Even double shield coax will create noise from vibration even if you don't move it. In our spectrometer, the vibration of the vacuum pumps causing problem and we had to switch to rigid coax.
I'll be placing the circuit inside the ion chamber can... i want to keep it simple and i won't be measuring high dose rates so I don't need to keep electronics safely away from the chamber.
edit: A question though: how do you deal with huge input capacitance when you have coax? Sounds like it would massively increase the time constant.
resistor: yes, of course. I'll not even have anything connect directly to input I think, not interested in high frequency operation, and it'll be convenient to just solder the resistor straight to the input leg in the air.
Though this chip specifies ESD protection for 2000v human body model and 200v machine model, which is fairly amazing for something like this.
• #18
5,573
203
I'll be placing the circuit inside the ion chamber can... i want to keep it simple and i won't be measuring high dose rates so I don't need to keep electronics safely away from the chamber.
edit: A question though: how do you deal with huge input capacitance when you have coax? Sounds like it would massively increase the time constant.
resistor: yes, of course. I'll not even have anything connect directly to input I think, not interested in high frequency operation, and it'll be convenient to just solder the resistor straight to the input leg in the air.
Though this chip specifies ESD protection for 2000v human body model and 200v machine model, which is fairly amazing for something like this.
They are all slow, your feedback resistor is going to be in 10EE11 Ω. The input cap not just slow things down, it create more noise as the apparent gain of the stage is $\frac {Z_f}{Z_{in}} \;\hbox{where }\; Z_{in} \;$ is from the input capacitance and decrease with frequency. As frequency going up, the closed loop gain of the op-amp rise and the output noise increase. Depend on the the speed requirement. The main way of dealing with this is a small cap across the feedback resistor. With this Z_f will decrease with frequency to keep the closed loop gain constant to keep the noise down. But yes, this will slow down the stage. Consider yourself lucky that this amp has 17MHz of GBW. We dealt with slow amp in old days.
One way is to put a voltage devider using lower value resistor at the output of the op-amp and the divider output connect the large feedback resistor to the summing junction. Same if you have a 1/10 divider, your feedback resistor can be decrease to 1/10. The problem with this is your offset error increase by 10 times and noise increase by `10 times at low frequency.
• #19
828
1
It will probably be fine since the low input current is achieved by active means.
Could you or someone else in here explain a little more about achieving the low input current by active means? How is this done more specifically?
All the different transitor and diodes I can find have leakage currents in the nano to micro amp range, so I am curious how it can be cut down to 1 or 2 femtoamps. Also, since this is done actively, wouldn't it reduce the bandwidth of the amplifier?
I was thinking about somehow using a current mirror to reduce the leakage current on a critical component, is this the method they use?
• #20
5,573
203
Don't know this specific amp, but they did use current source to compensate for bias current.
CMOS input bias current are below 1pA easily.
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http://mathhelpforum.com/calculus/32146-parametric-equation-cartesian-equation.html | # Math Help - Parametric Equation to Cartesian Equation
1. ## Parametric Equation to Cartesian Equation
Eliminate the parameter t to find a Cartesian equation for:
x = t^2
y = 8 + 4t
[x = Ay^2 + By + C]
2. Originally Posted by Del
Eliminate the parameter t to find a Cartesian equation for:
x = t^2
y = 8 + 4t
[x = Ay^2 + By + C]
Solve the y equation for t:
$y = 8 + 4t$
$4t = y - 8$
$t = \frac{y - 8}{4}$
Now insert this into the x equation:
$x = \left ( \frac{y - 8}{4} \right ) ^2$
Now just FOIL it out.
-Dan | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "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": 0.8420037031173706, "perplexity": 2639.687754256543}, "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-2016-30/segments/1469258918071.75/warc/CC-MAIN-20160723072838-00047-ip-10-185-27-174.ec2.internal.warc.gz"} |
http://math.stackexchange.com/users/23292/gspr | # gspr
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49 up 22 question | {"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": 0.8458452224731445, "perplexity": 20101.27522434117}, "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-2015-06/segments/1422121934081.85/warc/CC-MAIN-20150124175214-00119-ip-10-180-212-252.ec2.internal.warc.gz"} |
https://en.wikipedia.org/wiki/Scientific_inquiry | # Models of scientific inquiry
(Redirected from Scientific inquiry)
In the philosophy of science, models of scientific inquiry have two functions: first, to provide a descriptive account of how scientific inquiry is carried out in practice, and second, to provide an explanatory account of why scientific inquiry succeeds as well as it appears to do in arriving at genuine knowledge.
The search for scientific knowledge ends far back into antiquity. At some point in the past, at least by the time of Aristotle, philosophers recognized that a fundamental distinction should be drawn between two kinds of scientific knowledge—roughly, knowledge that and knowledge why. It is one thing to know that each planet periodically reverses the direction of its motion with respect to the background of fixed stars; it is quite a different matter to know why. Knowledge of the former type is descriptive; knowledge of the latter type is explanatory. It is explanatory knowledge that provides scientific understanding of the world. (Salmon, 2006, pg. 3)[1]
"Scientific inquiry refers to the diverse ways in which scientists study the natural world and propose explanations based on the evidence derived from their work."[2]
## Accounts of scientific inquiry
### Classical model
The classical model of scientific inquiry derives from Aristotle, who distinguished the forms of approximate and exact reasoning, set out the threefold scheme of abductive, deductive, and inductive inference, and also treated the compound forms such as reasoning by analogy.[citation needed]
### Logical empiricism
Wesley Salmon (1989)[1] began his historical survey of scientific explanation with what he called the received view, as it was received from Hempel and Oppenheim in the years beginning with their Studies in the Logic of Explanation (1948) and culminating in Hempel's Aspects of Scientific Explanation (1965). Salmon summed up his analysis of these developments by means of the following Table.
Laws / Explananda Particular Facts General Regularities
Universal Laws D-N
Deductive-Nomological
D-N
Deductive-Nomological
Statistical Laws I-S
Inductive-Statistical
D-S
Deductive-Statistical
In this classification, a deductive-nomological (D-N) explanation of an occurrence is a valid deduction whose conclusion states that the outcome to be explained did in fact occur. The deductive argument is called an explanation, its premisses are called the explanans (L: explaining) and the conclusion is called the explanandum (L: to be explained). Depending on a number of additional qualifications, an explanation may be ranked on a scale from potential to true.
Not all explanations in science are of the D-N type, however. An inductive-statistical (I-S) explanation accounts for an occurrence by subsuming it under statistical laws, rather than categorical or universal laws, and the mode of subsumption is itself inductive instead of deductive. The D-N type can be seen as a limiting case of the more general I-S type, the measure of certainty involved being complete, or probability 1, in the former case, whereas it is less than complete, probability < 1, in the latter case.
In this view, the D-N mode of reasoning, in addition to being used to explain particular occurrences, can also be used to explain general regularities, simply by deducing them from still more general laws.
Finally, the deductive-statistical (D-S) type of explanation, properly regarded as a subclass of the D-N type, explains statistical regularities by deduction from more comprehensive statistical laws. (Salmon 1989, pp. 8–9).[1]
Such was the received view of scientific explanation from the point of view of logical empiricism, that Salmon says "held sway" during the third quarter of the last century (Salmon, p. 10).[1]
## Choice of a theory
During the course of history, one theory has succeeded another, and some have suggested further work while others have seemed content just to explain the phenomena. The reasons why one theory has replaced another are not always obvious or simple. The philosophy of science includes the question: What criteria are satisfied by a 'good' theory. This question has a long history, and many scientists, as well as philosophers, have considered it. The objective is to be able to choose one theory as preferable to another without introducing cognitive bias.[3] Several often proposed criteria were summarized by Colyvan.[4] A good theory:
1. Is elegant (Formal elegance; no ad hoc modifications)
2. Contains few arbitrary or adjustable elements (simplicity/parsimony)
3. Agrees with and explains all existing observations (unificatory/explanatory power)
4. Makes detailed predictions about future observations that can disprove or falsify the model if they are not borne out.
5. Is fruitful: the emphasis by Colyvan is not only upon prediction and falsification, but also upon a theory's seminality in suggesting future work.
Stephen Hawking supported items 1–4, but did not mention fruitfulness.[5] On the other hand, Kuhn emphasizes the importance of seminality.[6]
The goal here is to make the choice between theories less arbitrary. Nonetheless, these criteria contain subjective elements, and are heuristics rather than part of scientific method.[7] Also, criteria such as these do not necessarily decide between alternative theories. Quoting Bird:[8]
They [such criteria] cannot determine scientific choice. First, which features of a theory satisfy these criteria may be disputable (e.g. does simplicity concern the ontological commitments of a theory or its mathematical form?). Secondly, these criteria are imprecise, and so there is room for disagreement about the degree to which they hold. Thirdly, there can be disagreement about how they are to be weighted relative to one another, especially when they conflict.
— Alexander Bird, Methodological incommensurability
It also is debatable whether existing scientific theories satisfy all these criteria, which may represent goals not yet achieved. For example, explanatory power over all existing observations (criterion 3) is satisfied by no one theory at the moment.[9]
Whatever might be the ultimate goals of some scientists, science, as it is currently practiced, depends on multiple overlapping descriptions of the world, each of which has a domain of applicability. In some cases this domain is very large, but in others quite small.[10]
— E.B. Davies, Epistemological pluralism, p. 4
The desiderata of a "good" theory have been debated for centuries, going back perhaps even earlier than Occam's razor,[11] which often is taken as an attribute of a good theory. Occam's razor might fall under the heading of "elegance", the first item on the list, but too zealous an application was cautioned by Albert Einstein: "Everything should be made as simple as possible, but no simpler."[12] It is arguable that parsimony and elegance "typically pull in different directions".[13] The falsifiability item on the list is related to the criterion proposed by Popper as demarcating a scientific theory from a theory like astrology: both "explain" observations, but the scientific theory takes the risk of making predictions that decide whether it is right or wrong:[14][15]
It must be possible for an empirical scientific system to be refuted by experience." "Those among us who are unwilling to expose their ideas to the hazard of refutation do not take part in the game of science.
— Karl Popper, The logic of scientific discovery, p. 18 and p. 280
Thomas Kuhn argued that changes in scientists' views of reality not only contain subjective elements, but result from group dynamics, "revolutions" in scientific practice which result in paradigm shifts.[16] As an example, Kuhn suggested that the heliocentric "Copernican Revolution" replaced the geocentric views of Ptolemy not because of empirical failures, but because of a new "paradigm" that exerted control over what scientists felt to be the more fruitful way to pursue their goals.
## Aspects of scientific inquiry
### Deduction and induction
Deductive logic and inductive logic are quite different in their approaches.
#### Deduction
Deductive logic is the reasoning of proof, or logical implication. It is the logic used in mathematics and other axiomatic systems such as formal logic. In a deductive system, there will be axioms (postulates) which are not proven. Indeed, they cannot be proven without circularity. There will also be primitive terms which are not defined, as they cannot be defined without circularity. For example, one can define a line as a set of points, but to then define a point as the intersection of two lines would be circular. Because of these interesting characteristics of formal systems, Bertrand Russell humorously referred to mathematics as "the field where we don't know what we are talking about, nor whether or not what we say is true". All theorems and corollaries are proven by exploring the implications of the axiomata and other theorems that have previously been developed. New terms are defined using the primitive terms and other derived definitions based on those primitive terms.
In a deductive system, one can correctly use the term "proof", as applying to a theorem. To say that a theorem is proven means that it is impossible for the axioms to be true and the theorem to be false. For example, we could do a simple syllogism such as the following:
1. Arches National Park lies within the state of Utah.
2. I am standing in Arches National Park.
3. Therefore, I am standing in the state of Utah.
Notice that it is not possible (assuming all of the trivial qualifying criteria are supplied) to be in Arches and not be in Utah. However, one can be in Utah while not in Arches National Park. The implication only works in one direction. Statements (1) and (2) taken together imply statement (3). Statement (3) does not imply anything about statements (1) or (2). Notice that we have not proven statement (3), but we have shown that statements (1) and (2) together imply statement (3). In mathematics, what is proven is not the truth of a particular theorem, but that the axioms of the system imply the theorem. In other words, it is impossible for the axioms to be true and the theorem to be false. The strength of deductive systems is that they are sure of their results. The weakness is that they are abstract constructs which are, unfortunately, one step removed from the physical world. They are very useful, however, as mathematics has provided great insights into natural science by providing useful models of natural phenomena. One result is the development of products and processes that benefit mankind.
#### Induction
Learning about the physical world requires the use of inductive logic. This is the logic of theory building. It is useful in such widely divergent enterprises as science and crime scene detective work. One makes a set of observations, and seeks to explain what one sees. The observer forms a hypothesis in an attempt to explain what he/she has observed. The hypothesis will have implications, which will point to certain other observations that would naturally result from either a repeat of the experiment or making more observations from a slightly different set of circumstances. If the predicted observations hold true, one feels excitement that they may be on the right track. However, the hypothesis has not been proven. The hypothesis implies that certain observations should follow, but positive observations do not imply the hypothesis. They only make it more believable. It is quite possible that some other hypothesis could also account for the known observations, and may do better with future experiments. The implication flows in only one direction, as in the syllogism used in the discussion on deduction. Therefore, it is never correct to say that a scientific principle or hypothesis/theory has been proven. (At least, not in the rigorous sense of proof used in deductive systems.)
A classic example of this is the study of gravitation. Newton formed a law for gravitation stating that the force of gravitation is directly proportional to the product of the two masses and inversely proportional to the square of the distance between them. For over 170 years, all observations seemed to validate his equation. However, telescopes eventually became powerful enough to see a slight discrepancy in the orbit of Mercury. Scientists tried everything imaginable to explain the discrepancy, but they could not do so using the objects that would bear on the orbit of Mercury. Eventually, Einstein developed his theory of general relativity and it explained the orbit of Mercury and all other known observations dealing with gravitation. During the long period of time when scientists were making observations that seemed to validate Newton's theory, they did not, in fact, prove his theory to be true. However, it must have seemed at the time that they did. It only took one counterexample (Mercury's orbit) to prove that there was something wrong with his theory.
This is typical of inductive logic. All of the observations that seem to validate the theory, do not prove its truth. But one counter-example can prove it false. That means that deductive logic is used in the evaluation of a theory. In other words, if A implies B, then not B implies not A. Einstein's theory of General Relativity has been supported by many observations using the best scientific instruments and experiments. However, his theory now has the same status as Newton's theory of gravitation prior to seeing the problems in the orbit of Mercury. It is highly credible and validated with all we know, but it is not proven. It is only the best we have at this point in time.
Another example of correct scientific reasoning is shown in the current search for the Higgs boson. Scientists on the Compact Muon Solenoid experiment at the Large Hadron Collider have conducted experiments yielding data suggesting the existence of the Higgs boson. However, realizing that the results could possibly be explained as a background fluctuation and not the Higgs boson, they are cautious and waiting for further data from future experiments. Said Guido Tonelli:
We cannot exclude the presence of the Standard Model Higgs between 115 and 127 GeV because of a modest excess of events in this mass region that appears, quite consistently, in five independent channels [...] As of today what we see is consistent either with a background fluctuation or with the presence of the boson.
A brief overview of the scientific method would then contain these steps as a minimum:
1. Make a set of observations regarding the phenomenon being studied.
2. Form a hypothesis that might explain the observations. (Inductive Step)
3. Identify the implications and outcomes that must follow, if the hypothesis is to be true.
4. Perform other experiments or observations to see if any of the predicted outcomes fail.
5. If any predicted outcomes fail, the hypothesis is proven false since if A implies B, then not B implies not A. (Deductive Logic) It is then necessary to change the hypothesis and go back to step 3. If the predicted outcomes are confirmed, the hypothesis is not proved, but rather can be said to be consistent with known data.
When a hypothesis has survived a sufficient number of tests, it may be promoted to a scientific theory. A theory is a hypothesis that has survived many tests and seems to be consistent with other established scientific theories. Since a theory is a promoted hypothesis, it is of the same 'logical' species and shares the same logical limitations. Just as a hypothesis cannot be proven but can be disproved, that same is true for a theory. It is a difference of degree, not kind.
Arguments from analogy are another type of inductive reasoning. In arguing from analogy, one infers that since two things are alike in several respects, they are likely to be alike in another respect. This is, of course, an assumption. It is natural to attempt to find similarities between two phenomena and wonder what one can learn from those similarities. However, to notice that two things share attributes in several respects does not imply any similarities in other respects. It is possible that the observer has already noticed all of the attributes that are shared and any other attributes will be distinct. Argument from analogy is an unreliable method of reasoning that can lead to erroneous conclusions, and thus cannot be used to establish scientific facts.
## Sources
1. ^ a b c d Wesley C. Salmon (2006). Four decades of scientific explanation (Reprint of Salmon, W.C. 1989. In, Scientific Explanation, eds. P. Kitcher and W.C. Salmon, volume XIII of Minnesota Studies in the Philosophy of Science ed.). University of Pittsburgh Press. ISBN 9780822959267.
2. ^ National Research Council (1996). National Science Education Standards. Washington, DC: The National Academies Press. p. 23. doi:10.17226/4962.
3. ^ Thomas Kuhn formally stated this need for the "norms for rational theory choice". One of his discussions is reprinted in Thomas S Kuhn (2002-11-01). "Chapter 9: Rationality and Theory Choice". In James Conant, John Haugeland (ed.). The Road since Structure: Philosophical Essays, 1970–1993 (2nd ed.). University of Chicago Press. pp. 208 ff. ISBN 0226457990.
4. ^ Mark Colyvan (2001). The Indispensability of Mathematics. Oxford University Press. pp. 78–79. ISBN 0195166612.
5. ^ Stephen Hawking; Leonard Mlodinow (2010). "What is reality?". The Grand Design. Random House Digital, Inc. p. 51. ISBN 0553907077. See also: model-dependent realism.
6. ^ Thomas S Kuhn (1966). The structure of scientific revolutions (PDF) (3rd ed.). University of Chicago Press. p. 157. ISBN 0226458083. That decision must be based less on past achievement than on future promise.
7. ^ For example, Hawking/Mlodinow say (The Grand Design, p. 52) "The above criteria are obviously subjective. Elegance, for example, is not something easily measured, but it is highly prized among scientists." The idea of 'too baroque' is connected to 'simplicity': "a theory jammed with fudge factors is not very elegant. To paraphrase Einstein, a theory should be as simple as possible, but not simpler".(The Grand Design, p. 52) See also: Simon Fitzpatrick (April 5, 2013). "Simplicity in the Philosophy of Science". Internet Encyclopedia of Philosophy. and Baker, Alan (Feb 25, 2010). Edward N. Zalta (ed.). "Simplicity". The Stanford Encyclopedia of Philosophy (Summer 2011 Edition).
8. ^ Bird, Alexander (Aug 11, 2011). Edward N. Zalta (ed.). "§4.1 Methodological Incommensurability". The Stanford Encyclopedia of Philosophy (Spring 2013 Edition).
9. ^ See Stephen Hawking; Leonard Mlodinow (2010). The Grand Design. Random House Digital, Inc. p. 8. ISBN 0553907077. It is a whole family of different theories, each of which is a good description of observations only in some range of physical situations...But just as there is no map that is a good representation of the earth's entire surface, there is no single theory that is a good representation of observations in all situations.
10. ^ E Brian Davies (2006). "Epistemological pluralism". PhilSci Archive.
11. ^ Occam's razor, sometimes referred to as "ontological parsimony", is roughly stated as: Given a choice between two theories, the simplest is the best. This suggestion commonly is attributed to William of Ockham in the 14th-century, although it probably predates him. See Baker, Alan (February 25, 2010). "Simplicity; §2: Ontological parsimony". The Stanford Encyclopedia of Philosophy (Summer 2011 Edition). Retrieved 2011-11-14.
12. ^ This quote may be a paraphrase. See MobileReference (2011). Famous Quotes from 100 Great People. MobileReference. ISBN 1611980763. MobilReference is a Boston-based e-book publisher.
13. ^ Baker, Alan (Feb 25, 2010). Edward N. Zalta (ed.). "Simplicity". The Stanford Encyclopedia of Philosophy (Summer 2011 Edition).
14. ^ Karl Popper. "Science: Conjectures and refutations" (PDF). Texas A&M University The motivation & cognition interface lab. Archived from the original (PDF) on 2013-09-09. Retrieved 2013-01-22. This lecture by Popper was first published as part of the book Conjectures and Refutations and is linked here.
15. ^ Karl Raimund Popper (2002). The logic of scientific discovery (Reprint of translation of 1935 Logik der Forchung ed.). Routledge/Taylor & Francis Group. pp. 18, 280. ISBN 0415278430.
16. ^ Thomas S Kuhn (1966). The structure of scientific revolutions (PDF) (3rd ed.). University of Chicago Press. ISBN 0226458083. | {"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": 0.867675244808197, "perplexity": 1175.3895949253808}, "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-2020-05/segments/1579250591763.20/warc/CC-MAIN-20200118023429-20200118051429-00425.warc.gz"} |
http://flr-project.org/FLBEIA/reference/create.biol.arrays.html | This function generates an FLBiol object, given the data inputs as arrays. Supported formats are Excel (xls and xlsx) and R format (RData).
create.biol.arrays(filename, name = NA, ages, hist.yrs, sim.yrs,
fbar = NULL, mean.yrs, excel = TRUE, unit = list())
## Arguments
filename A character vector with the name of the files containing the stock data. Supported formats are Excel (xls and xlsx) and R format (RData). In case of using R format, the information must be stored in data object (consisting in a list with the different elements). The following information is compulsory: abundances in numbers at age (n), mean weight at age (wt), maturity (mat), natural mortality (m), moment of the year when spawning occurs in percentage (spwn), fishing mortality at age (f) and catch in numbers at age (caa). For the rest of information, if not provided, default values are set. For example, fecundity (fec) is set to 1, landings and discard in numbers at age (laa and daa) are set to cca and 0, respectively. Finally for weights, if missing, weights at age for landings (wl) and discards (wd) are set to the weights in the population and weights at age for catch (wc) are set to the weighted mean of the weights of landings and discards. A character (optional) with the name of the stock. A numeric vector with the age classes of stock. A vector with the historical years. A vector with the simulation years. A numeric vector with the age range (min,max) to be used for estimating average fishing mortality. A vector with the years used to compute the mean to condition the parameters in the projection period. Logical. TRUE (default), if the data is provided in an Excel file and FALSE, if an RData object is used instead. A list with the units of the different elements included in filename. Unitless objects must be set to '' or character(1). This parameter is only required if excel==FALSE. When using Excell files the units are taken from the first row and column (cell A1) of each sheet. If the cell is empty then units are set to NA, in case of an unitless object then 1 must be inputed into cell A1.
## Value
An FLBiol.
FLBiol, create.fleets.arrays | {"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": 0.4159024655818939, "perplexity": 3078.129623312654}, "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/1664030337906.7/warc/CC-MAIN-20221007014029-20221007044029-00071.warc.gz"} |
http://cstheory.stackexchange.com/questions/10781/tractability-of-mutual-information-augmented-ensemble-classification-algorithms | Tractability of mutual information-augmented ensemble classification algorithms
I am seeking to augment random forest classification using Shannon-Weaver mutual information as a metaheuristic to partition candidate datasets. Specifically, I am trying to determine if such an approach is both tractable and offers an improved convergence time over bruteforce methods and random forest classification on its own without a major reduction in classification.
Suppose we have a collection of data sets, $K$, that contains rows $\{k1, k2, ..., kn\}$. Each of these rows carries an unknown language $L$ in the context of an unknown, uniformly-applied noise function. Our hypothesis is that at least some subset of these data rows share information: that is, for some rows, $I(kx,ky) > 0$ for ${kx,ky} \in K$. Additionally, we hypothesize that multivariate mutual information $I(kx,ky,...) \not= 0$ for some set of multivariate relations. That is, that our graph contains compositions that are more informative in the context of multiply-chained relationships, or contain some XOR-shaped relationship.
If we attempt to bruteforce this space, because mutual information is commutative, we require n-binomial-n time and space. That is to say, to compute the mutual information of all combinations within collection $D$, we require $\sum\limits_{x=1}^n\binom{n}{x}$ time, assuming for simplicity that the comparison of each row is an $O(1)$ operation.
We would then prune output data set using a fixed cutoff value, $v$, retaining only connections where $I(kx,...) > v$. We would then sort this set in descending order of the number of terms and use this to construct an undirected graph, by connecting features that share positive mutual information and forming branches when multivariate mutual information is negative.
The obvious reduction to this complexity, at an error-bound cost in robustness, is to use random forest analysis. I wish to simplify this computation further, by computing the pairspace mutual information for each pair of rows, then using a cutoff value similar to $v$, construct sets that only contain the participating nodes of each of these graphs. These sets would then be fed into our random forest classifier to determine the shape of the graphs, at an expected reduced time for convergence.
Is this approach tractable? Even if so, are there better approaches to the pruning stage of this problem?
-
This question is extremely cross-disciplinary and research level. As a result, I felt this to be the most correct StackExchange for it to live within, ousting even Stats.SE. – MrGomez Mar 21 '12 at 1:57
It's debatable. you might get some feedback here, but it sounds like you're looking for practical experience with the heuristics, and stats.SE might be slightly better on that front. This might be one of the few instances where simultaneous cross posting isn't a bad thing – Suresh Venkat Mar 21 '12 at 2:13
@SureshVenkat Thank you. I've done so: stats.stackexchange.com/questions/25039/… – MrGomez Mar 21 '12 at 21:09 | {"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": 0.5563949346542358, "perplexity": 656.4667407348127}, "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-2015-35/segments/1440644064869.18/warc/CC-MAIN-20150827025424-00075-ip-10-171-96-226.ec2.internal.warc.gz"} |
http://mathhelpforum.com/calculus/45258-integration.html | 1. ## Integration
Find ∫x tan inverse (x^2) dx, for x from 0 to 1.
2. $\displaystyle\int_0^1 x\arctan x^2dx=\int_0^1\left(\frac{x^2}{2}\right)'\arctan x^2dx=$
$\displaystyle=\frac{x^2}{2}\arctan x^2|_0^1 -\int_0^1\frac{x^3}{1+x^4}dx=$
$\displaystyle\frac{\pi}{8}-\frac{1}{3}\ln(1+x^4)\left|_0^1\right.=\frac{\pi}{ 8}-\frac{1}{3}\ln 2$
3. Hello! Thank you for helping, may I know how did you get from
$\displaystyle\frac{x^2}{2}\arctan x^2|_0^1 -\int_0^1\frac{x^3}{1+x^4}dx$ to $\displaystyle\frac{\pi}{8}-\frac{1}{3}\ln(1+x^4)\left|_0^1\right.$ ??
Thank you!
4. $\frac{x^{2}}{2}\arctan x^{2}\bigg|_{0}^{1}=\frac{1^{2}}{2}\arctan 1-\frac{0^{2}}{2}\arctan 0=\frac{\pi }{8}.$
Those are things you should know since you're evaluating definite integrals.
As for the last integral, it's an $\frac14$ instead an $\frac13.$
----
Just for fun: $\int_{0}^{1}{x\arctan x^{2}\,dx}=\int_{0}^{1}{\int_{0}^{x^{2}}{\frac{x}{ 1+y^{2}}\,dy}\,dx}=\int_{0}^{1}{\int_{\sqrt{y}}^{1 }{\frac{x}{1+y^{2}}\,dx}\,dy},$ hence $\int_{0}^{1}{x\arctan x^{2}\,dx=\frac{1}{2}\int_{0}^{1}{\frac{1-y}{1+y^{2}}\,dy}=}\frac{\pi }{8}-\frac{\ln 2}{4}.$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "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": 0.8587648272514343, "perplexity": 2083.2865034130796}, "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-2016-40/segments/1474738660887.60/warc/CC-MAIN-20160924173740-00129-ip-10-143-35-109.ec2.internal.warc.gz"} |
https://infoscience.epfl.ch/record/184312 | Infoscience
Journal article
# Analysis of the resonant components in (B)over-bar(s)(0) -> J/psi pi(+)pi(-)
The decay (B) over bar (0)(s) -> J/psi pi(+)pi(-) can be exploited to study CP violation. A detailed understanding of its structure is imperative in order to optimize its usefulness. An analysis of this three-body final state is performed using a 1.0 fb(-1) sample of data produced in 7 TeV pp collisions at the LHC and collected by the LHCb experiment. A modified Dalitz plot analysis of the final state is performed using both the invariant mass spectra and the decay angular distributions. The pi(+)pi(-) system is shown to be dominantly in an S-wave state, and the CP-odd fraction in this (B) over bar (0)(s) decay is shown to be greater than 0.977 at 95% confidence level. In addition, we report the first measurement of the J/psi pi(+)pi(-) branching fraction relative to J/psi phi of (19.79 +/- 0.47 +/- 0.52)%. | {"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": 0.9590568542480469, "perplexity": 1822.411262148756}, "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-2017-17/segments/1492917122720.81/warc/CC-MAIN-20170423031202-00529-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/a-function-with-no-derivative.555894/ | # A Function with no Derivative?
1. Dec 1, 2011
### FeDeX_LaTeX
Hi,
Is there any function defined such that it is non-differentiable at every point?
Of course, cusps and asymptotic graphs aren't differentiable at those points, but what about one that can't be differentiated anywhere? I know there are crazy functions like defining some function to be 0 if x is rational and 1 if x is irrational.
Thanks.
2. Dec 1, 2011
### Office_Shredder
Staff Emeritus
There are in fact functions which are continuous at every point and differentiable nowhere. They're pretty complicated. One example:
http://en.wikipedia.org/wiki/Weierstrass_function
One example that's maybe easier to explain intuitively is Brownian motion. The basic idea is that you have an object that's moving up or down at random. Then f(t) is the height of the object at time t. Then the height of the object is continuous, but over arbitrarily small time intervals it changes whether it's moving up or down, so the derivative is not defined
3. Dec 1, 2011
### FeDeX_LaTeX
Thanks for the reply. I have heard of the Weierstrass function but did not know it was differentiable nowhere. Thanks for this.
I sort of get what you mean by the Brownian motion example.
How would one plot a graph of the function I alluded to, where f(x) = 0 if x is rational and f(x) = 1 if x is irrational?
Last edited: Dec 1, 2011
4. Dec 1, 2011
### Number Nine
You wouldn't. The best you could do is plot a grossly simplified kind-of sort-of approximation with a discrete number of values on a small interval.
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https://www.physicsforums.com/threads/a-few-questions-about-feynmans-qed-lecture.902595/ | # A few questions about Feynman's QED Lecture
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• #1
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Hello,
Apologies if this has been asked before. After watching Feynman’s QED lectures on the probabilities of different paths that photons can take towards a photomultiplier, a few questions came up in me.
Let’s take the simple scenario in which a photon emitter is faced straight towards a photomultiplier, without any mirrors or glass whatsoever. The photon emitter sends just one photon out. As Feynman stated, that photon can take different paths until it reaches the photomultiplier and you can calculate the probabilities of these paths that the photon would take.
Also as stated, the probability that the photon would take a certain range of more or less straight paths is higher than the probability of it taking a certain range of bent paths.
My questions:
1. Do the probabilities of all possible paths that a photon could take on its way to the photomultiplier together equal 100%?
2. If someone puts a photon detector directed at a certain range of paths, will the probability of the photon taking that range of certain paths be 100% minus the probability of all the possible paths other than that certain range?
3. If the answer to question 2 is yes, does this mean that statistically, if one repeats the experiment from question 2 a 100 times, the detector would go off a number of times according to that probability?
Another question came up when, after watching the lecture, I read further that this one photon actually takes all these possible paths simultaneously. This got me confused because if that’s true, how then can a photon take certain paths based on probabilities while it actually doesn’t have any preference and takes all these paths simultaneously?
4. Does this probability scenario merely arise when one repeats the experiment while using photon detectors directed at a certain range of possible paths?
5. Or is probability merely another term for intensity?
• #2
jfizzix
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The probability of taking a particular path is the square of the probability amplitude to do so. This is where the quantumness of quantum physics comes from.
The probability amplitude that a photon emitted at point A will arrive at point B is the sum over the probability amplitudes to take all possible paths beginning at A and ending at B.
Then, the probability (density) that a photon comes from A and ends at B is the square of the sum of these amplitudes.
Since emitters and detectors are not single points, it is important to point out, that this amplitude calculation gives you the conditional probability density of a photon arriving at point B given that it originated at point A. (They're densities, because there are a continuum of possible points to choose from and to sum over to get total probabilities).
Finally, to get the probability that the photon will arrive on a particular area of the detector, given that it originated in some other area on the source, you need to know the probability density of where photons will be emitted from the source, which could be found out experimentally.
As for whether the photon really takes these paths simultaneously, all we really know is that this method of calculation works very well to predict the probabilities that we measure.
Probabilities are not just another term for intensity. In particular, if just one photon hits a detector at a given point, the intensity distribution will just have that one point. Over time, as you gather more and more counts, your intensity distribution becomes smoorther and converges to one particular form, which will be the probability distribution. One can predict the ultimate intensity distribution from the probability distribution, and one can estimate a probability distribution from a given intensity distribution with varying levels of success.
• #3
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Probabilities are not just another term for intensity. In particular, if just one photon hits a detector at a given point, the intensity distribution will just have that one point. Over time, as you gather more and more counts, your intensity distribution becomes smoorther and converges to one particular form, which will be the probability distribution. One can predict the ultimate intensity distribution from the probability distribution, and one can estimate a probability distribution from a given intensity distribution with varying levels of success.
One other question; imagine a photon emitter shooting just one photon at a glass with such a thickness that it gives a probability of 4% reflection towards a photomultiplier. Does this mean that if you repeat this experiment a 100 times, every time with just one photon, that the photomultiplier would detect a photon 4 times total statistically speaking?
As for whether the photon really takes these paths simultaneously, all we really know is that this method of calculation works very well to predict the probabilities that we measure.
I'm really curious about this, since this does show in some way that a photon doesn't really have a preference based on probability. Which is weird since it is based on probability when you repeat the experiment several times and look at the intensity distribution. I'm talking about shooting just one photon every time.
• #4
Nugatory
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I'm really curious about this, since this does show in some way that a photon doesn't really have a preference based on probability. Which is weird....
You have to stop listening to your classical intuition. The weirdness goes away (or at least is replaced by a different weirdness) if you think in terms of the probability of a photon appearing at a given spot, instead of moving from the source to that spot.
• #5
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One other question; imagine a photon emitter shooting just one photon at a glass with such a thickness that it gives a probability of 4% reflection towards a photomultiplier. Does this mean that if you repeat this experiment a 100 times, every time with just one photon, that the photomultiplier would detect a photon 4 times total statistically speaking?
Yes.
I'm really curious about this, since this does show in some way that a photon doesn't really have a preference based on probability. Which is weird since it is based on probability when you repeat the experiment several times and look at the intensity distribution. I'm talking about shooting just one photon every time.
This is one of things that is hard to understand. One could ask how individual photons decide whether to be reflected or transmitted. But this is a simplisitic way of looking at it. The photon is closer to being an excitation of a field (that is everywhere already) than a classical 'corpuscule'.
[beaten to it]
• #6
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You have to stop listening to your classical intuition. The weirdness goes away (or at least is replaced by a different weirdness) if you think in terms of the probability of a photon appearing at a given spot, instead of moving from the source to that spot.
Ah I see now. This makes the whole concept of a photon taking all possible paths at the same time a bit wrong. Since, given your explanation, the photon would be going only one particular way based on the path you've decided to calculate the probability of. Such that, you can only observe a photon taking different paths by repeating the experiment and not just by executing the experiment just once. Am I making sense?
Also, is the probability of a photon taking a particular path calculated by multiplying the probabilities of finding the photon at the different spots on that path?
• #7
PeterDonis
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given your explanation, the photon would be going only one particular way based on the path you've decided to calculate the probability of
No. The photon does not take one path. It does not take all paths. What it is doing has no analogue at all in the classical terminology you are trying to use.
you can only observe a photon taking different paths by repeating the experiment
You never observe the photon taking a path. This experiment does not do that at all, no matter how many times you run it.
You apparently did not grasp what Nugatory meant by "you have to stop using your classical intuition". Any talk of the photon "taking a path" is classical intuition. Stop using it.
• #8
Nugatory
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Since, given your explanation, the photon would be going only one particular way based on the path you've decided to calculate the probability of. Such that, you can only observe a photon taking different paths by repeating the experiment and not just by executing the experiment just once. Am I making sense?
It would be better to drop the idea that a photon takes any path. I used the word "appears" quite deliberately in the post you're quoting; the calculation is giving us the probability that a photon will be detected when we put the detector at a given location but says nothing about what's happening or has happened anywhere else. We cannot safely say that the photon at the detector is the same photon ("same" is a tricky concept when applied to quantum particles) as the one that was emitted, nor that it moved on any path through the space between source and detector.
• #9
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No. The photon does not take one path. It does not take all paths. What it is doing has no analogue at all in the classical terminology you are trying to use.
You never observe the photon taking a path. This experiment does not do that at all, no matter how many times you run it.
You apparently did not grasp what Nugatory meant by "you have to stop using your classical intuition". Any talk of the photon "taking a path" is classical intuition. Stop using it.
I didn't mean to say that it really does take one or all paths. What I meant is that WE (mistakingly) consider it taking one particular path by calculating the probabilities of different spots on the path that we choose to think the photon is taking.
As for repeating the experiment to see different "paths" let's say we theoretically put photon detectors on all the possible spots between the photon emitter and the photomultiplier. When repeating the experiment several times, won't each try give a different pattern of certain photon detectors going off? Those patterns being based on the probabilities of the different spots where the photon would appear? Since the photon "collapses" when detectors are in place, it won't make 2 or more detectors go off at once. And that would make us THINK that it has taken one particular path based on the probabilities of the spots.
Just like Feynman said that a photon detector sometimes detects a photon that is at an "off-edge" spot and on other times it doesn't.
• #10
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It would be better to drop the idea that a photon takes any path. I used the word "appears" quite deliberately in the post you're quoting; the calculation is giving us the probability that a photon will be detected when we put the detector at a given location but says nothing about what's happening or has happened anywhere else. We cannot safely say that the photon at the detector is the same photon ("same" is a tricky concept when applied to quantum particles) as the one that was emitted, nor that it moved on any path through the space between source and detector.
I have not worded my intention of using paths well. I've rephrased it in my above post. This explantion of yours does give it a whole different view. Which also fits for the double slit experiment when 1 photon is involved I think.
• #11
PeterDonis
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WE (mistakingly) consider it taking one particular path by calculating the probabilities of different spots on the path that we choose to think the photon is taking
But we don't do that, at least not in the version of the experiment we've been talking about, where the only photon detection is at the final photomultiplier. We only calculate the amplitude for the photon to reach a photomultiplier at a given location. We don't calculate amplitudes for the photon to reach spots somewhere in space between the source and the photomultiplier.
let's say we theoretically put photon detectors on all the possible spots between the photon emitter and the photomultiplier
Then we are running a different experiment, which will be modeled differently in the math. Now we have to compute amplitudes for each detector to fire, and square each one individually to get a probability for that detector to fire. And the probability for the photomultiplier to detect a photon will no longer be the square of a single amplitude; it will be the sum of squares of a lot of amplitudes, one for each in-between detector firing. For example, suppose we have ten detectors in between the source and the photomultiplier, placed so that only one will fire for any given photon. Then the probability for the photon to reach the photomultiplier is the sum of squares of ten amplitudes--the amplitude for the photon to reach the photomultiplier given that detector #1 fires (times the probability that detector #1 fires), the amplitude for the photon to reach the photomultiplier given that detector #2 fires (times the probability that detector #2 fires), etc. And the final prediction for the probability of the photon reaching the photomultiplier will be different than the prediction from the original experiment, with no photon detectors.
In short, this new experiment, while it will give you lots of interesting data, tells you nothing useful about what is or is not happening in the original experiment.
• #12
jfizzix
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One other question; imagine a photon emitter shooting just one photon at a glass with such a thickness that it gives a probability of 4% reflection towards a photomultiplier. Does this mean that if you repeat this experiment a 100 times, every time with just one photon, that the photomultiplier would detect a photon 4 times total statistically speaking?
I'm really curious about this, since this does show in some way that a photon doesn't really have a preference based on probability. Which is weird since it is based on probability when you repeat the experiment several times and look at the intensity distribution. I'm talking about shooting just one photon every time.
To answer your first question, the most likely outcome of 100 runs of this experiment is 4 detections (at 19.9 percent probability), but the probabilities of getting 3 detections (19.7 percent), 5 detections (15.6 percent), and others are quite significant. This is part of my favorite version of the law of large numbers. As the number of trials grows large, the probability that your string of outcomes resembles the probability distribution to any fixed tolerance approaches 1. So, for a large enough number of trials, the probability of having less than 3% detections, or more than 5% detections approaches zero (it's below 10 percent for 1000 trials, below $10^{-4}$ percent for 10,000 trials, and below, well, $10^{-9}$ percent for a million trials) .
You can prepare a single photon to be in any quantum state you wish, and you can measure its detection (or lack thereof). Those are what you know, and can control. What happens between creation and detection is not measured and can only be speculated about. What we can predict reliably is what the intensity distribution would look like if we measured the photon between the emitter and the detector, but such a measurement would be another experiment with another detection.
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• #13
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And the final prediction for the probability of the photon reaching the photomultiplier will be different than the prediction from the original experiment, with no photon detectors.
So if I understand this correctly. Suppose we calculate the probability of a certain area of paths of 1 photon between the source and photomultiplier (without any photon detectors in between) according to Feyman, and that probability turns out to be 4%. Now if I put photon detectors only in that certain area of paths between the source and the photomultiplier, filling that area all up, and I repeat the experiment 100 times, there won't be 4 out of those 100 cases in which, cumulatively, all the photon detectors in that area have fired?
To answer your first question, the most likely outcome of 100 runs of this experiment is 4 detections (at 19.9 percent probability), but the probabilities of getting 3 detections (19.7 percent), 5 detections (15.6 percent), and others are quite significant. This is part of my favorite version of the law of large numbers. As the number of trials grows large, the probability that your string of outcomes resembles the probability distribution to any fixed tolerance approaches 1. So, for a large enough number of trials, the probability of having less than 3% detections, or more than 5% detections approaches zero (it's below 10 percent for 1000 trials, below 10−410−410^{-4} percent for 10,000 trials, and below, well, 10−910−910^{-9} percent for a million trials) .
This is interesting to read. Isn't this the standard statistical behavior of chances though? That the chance for something would be focused in a narrower range after more and more repeats?
You can prepare a single photon to be in any quantum state you wish, and you can measure its detection (or lack thereof). Those are what you know, and can control. What happens between creation and detection is not measured and can only be speculated about. What we can predict reliably is what the intensity distribution would look like if we measured the photon between the emitter and the detector, but such a measurement would be another experiment with another detection.
Yes, I was indeed asking about the (intensity) distribution when one repeats the experiment each time with 1 photon. I thought that the probabilities of the different areas in that distribution, calculated in Feynman's way without photon detectors, would agree with the distribution of probabilities of photon detectors firing at those areas.
• #14
PeterDonis
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Suppose we calculate the probability of a certain area of paths of 1 photon between the source and photomultiplier (without any photon detectors in between) according to Feyman, and that probability turns out to be 4%. Now if I put photon detectors only in that certain area of paths between the source and the photomultiplier, filling that area all up, and I repeat the experiment 100 times, there won't be 4 out of those 100 cases in which, cumulatively, all the photon detectors in that area have fired?
Of all the runs in which the photon reaches the photomultiplier, 4% of them will have one of the photon detectors firing. But the fraction of all runs in which the photon reaches the photomultiplier will be different with the detectors present than without them.
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• #15
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Of all the runs in which the photon reaches the photomultiplier, 4% of them will have one of the photon detectors firing. But the fraction of all runs in which the photon reaches the photomultiplier will be different with the detectors present than without them.
This cleared it up for me. Thank you.
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2K | {"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": 0.9719027280807495, "perplexity": 424.7248179719743}, "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-2021-25/segments/1623487634576.73/warc/CC-MAIN-20210617222646-20210618012646-00637.warc.gz"} |
https://proofwiki.org/wiki/Definition:Game_Theory | # Definition:Game Theory
## Definition
Game theory is the branch of discrete mathematics which studies mathematical models of conflict and cooperation between intelligent rational decision-makers.
Problems in game theory are a special case of those of linear programming.
## Historical Note
The origins of the mathematical discipline of game theory can be traced to Ernst Zermelo's 1913: Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels ("On an Application of Set Theory to the Theory of the Game of Chess") (Proceedings of the Fifth International Congress of Mathematicians Vol. 2: 501 – 504).
Another early landmark was Émile Borel's 1921: La Théorie du Jeu et les Équations Intégrales à Noyau Symétrique (C.R. Acad. Sci. Vol. 173: 1304 – 1308).
He also stated, but failed to prove, a special case of the Fundamental Theorem of Games in his paper of 1927: Sur les systèmes de formes linéaires à déterminant symétrique gauche et la théorie générale du jeu (C.R. Acad. Sci. Vol. 184: 52 – 54).
The proof was given in a lecture by John von Neumann, documented as 1928: Zur Theorie der Gesellschaftspiele (Math. Ann. Vol. 100: 295 – 320).
The field was properly established by John von Neumann and Oskar Morgenstern in their Theory of Games and Economic Behaviour of $1944$, as a result of their observation that certain problems in economics were identical with those of games of strategy.
As the field evolved, it became apparent that this new discipline had a considerable number of wide-ranging applications.
## Also see
• Results about game theory can be found here. | {"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": 0.4499817490577698, "perplexity": 2070.775127599779}, "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/1566027315681.63/warc/CC-MAIN-20190820221802-20190821003802-00021.warc.gz"} |
http://randomwits.com/blog/make-money-stock1 | # Random Wits
Life is too short for a diary
## Random
$random stuff ├── tags ├── bookshelf ├── resources ├── quotes ├── habits └── about me + say Hello Thu 08 Apr 2021 ### How to Make(Or Lose) Money in Stocks Part1 Recently I finished watching web-series Scam 1992. It’s based on story of Harshad Mehta, a famous Indian stockbrocker who made fortunes in stocks. Despite his iconic success & failure, the series rekindled my interest in world of “stocks”. I guess the famous dialogue “Risk Hai Toh Ishq Hai” has stuck with me. I still consider myself a novice when it comes to stocks. There’s a no magic bullet to make money in stocks. However you can leverage scripts to reduce time to accumulate information. I’ll share one such approach in helping you to buy or sell stocks. Lets say you want to buy or sell some stocks. You can use some website to track them everyday (too tedious). Or you can use some API (like yahoofinance) to get this information. However free API usually have some time lag. We will using python in getting our current stock prices directly from google. # Setup before you begin Open your favourite terminal to create directory $ mkdir $stocks$ cd $_ We will be using poetry to manage our library depedencies. Create a default pyproject.toml file like this $ poetry init
Keep pressing enter to keep the defualt configuration
Next we will create a text file, stocks.csv. This will list all the stocks that we need to track. For this example I am using aaple and microsoft.
ticker,sell,sell,buy
aapl,0,125,0,0
msft,0,0,230,0
Here let me briefly expalin the columns:
1. ticker : stock ticker symbol
2. sell: the price at which you want to sell stock
"Investing should be more like watching paint dry or watching grass grow. If you want excitement, take $800 and go to Las Vegas." - Paul Samuelson Next create python file, stocks/main.py import pandas as pd from io import BytesIO from reportlab.platypus import SimpleDocTemplate, Paragraph, PageBreak from reportlab.lib.styles import getSampleStyleSheet, ParagraphStyle from reportlab.lib.units import mm from reportlab.lib.pagesizes import letter from reportlab.platypus.tables import Table, TableStyle from reportlab.lib import colors from reportlab import platypus from reportlab.lib.styles import ParagraphStyle as PS from selenium import webdriver from selenium.webdriver.common.keys import Keys from selenium.webdriver.chrome.options import Options from selenium.webdriver.common.action_chains import ActionChains from reportlab.platypus import Image as Image2 import logging Next we will open our favourite Web browser to type aapl stocks We will then right click and use inspect the web page Here we are looking for jsname with value vWLAgc So our algorithm is like this for every stock 1. get current price of stock 2. Prints if the current price is greater than my desired selling price 3. Prints if the current price is smaller then my desired buying prices I’ll be using reportlab library to generate pdf for my output. Run this command using $ poetry run python stock/main.py | {"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": 0.22634193301200867, "perplexity": 8718.104253084764}, "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-2021-25/segments/1623487614006.8/warc/CC-MAIN-20210614232115-20210615022115-00625.warc.gz"} |
https://www.perimeterinstitute.ca/video-library/collection/perimeter-institute-quantum-discussions?page=16&qt-seminar_series=1 | # Perimeter Institute Quantum Discussions
This series consists of weekly discussion sessions on foundations of quantum Theory and quantum information theory. The sessions start with an informal exposition of an interesting topic, research result or important question in the field. Everyone is strongly encouraged to participate with questions and comments.
## Seminar Series Events/Videos
Currently there are no upcoming talks in this series.
## Discrete Phase Space and Minimum-Uncertainty States
Wednesday Mar 28, 2007
Speaker(s):
Consider a discrete quantum system with a d-dimensional state space. For certain values of d, there is an elegant information-theoretic uncertainty principle expressing the limitation on one's ability to simultaneously predict the outcome of each of d+1 mutually unbiased--or mutually conjugate--orthogonal measurements. (The allowed values of d include all powers of primes, and at present it is not known whether any value of d is
Scientific Areas:
## Classical interaction cannot replace a quantum message
Wednesday Mar 21, 2007
Speaker(s):
We give a communication problem between two players, Alice and Bob, that can be solved by Alice sending a quantum message to Bob, for which any classical interactive protocol requires exponentially more communication.
Scientific Areas:
## Multi-level, multi-party singlets as ground states and their role in entanglement distribution
Wednesday Mar 07, 2007
Speaker(s):
We show that singlets composed of multiple multi-level quantum systems can naturally arise as the ground state of a physically-motivated Hamiltonian. The Hamiltonian needs to be one which simply exchanges the states of nearest neighbours in any graph of interacting d-level quantum systems (qudits) as long as the graph also has d sites. We point out that local measurements on some of these qudits, with the freedom of choosing a distinct measurement basis at each qudit randomly from an infinite set of bases, project the remainder onto a singlet state.
Scientific Areas:
## An extended, quartic quantum theory and a generalised theory of quantum information processing
Wednesday Feb 21, 2007
Speaker(s):
We propose an extended quantum theory, in which the number of degrees of freedom K behaves as FOURTH power the number N of distinguishable states. As the simplex of classical N--point probability distributions can be embedded inside a higher dimensional convex body of mixed quantum states, one can further increase the dimensionality constructing the set of extended quantum states. The embedding proposed corresponds to an assumption that the physical system described in N dimensional Hilbert space is coupled with an auxiliary subsystem of the same dimensionality.
Scientific Areas:
## Quantum Simulations of Quantum and Classical Systems
Monday Jan 22, 2007
Speaker(s):
If a large quantum computer (QC) existed today, what type of physical problems could we efficiently simulate on it that we could not simulate on a conventional computer? In this talk, I argue that a QC could solve some relevant physical "questions" more efficiently. First, I will focus on the quantum simulation of quantum systems satisfying different particle statistics (e.g., anyons), using a QC made of two-level physical systems or qubits.
Scientific Areas:
## Geometric measure of entanglement and its applications to multi-partite states and quantum phase transitions
Wednesday Jan 17, 2007
Speaker(s):
A multi-partite entanglement measure is constructed via the distance or angle of the pure state to its nearest unentangled state.
Scientific Areas:
## Quantum Kolmogorov complexity
Wednesday Jan 10, 2007
Kolmogorov complexity is a measure of the information contained in a binary string. We investigate the notion of quantum Kolmogorov complexity, a measure of the information required to describe a quantum state. We show that for any definition of quantum Kolmogorov complexity measuring the number of classical bits required to describe a pure quantum state, there exists a pure n-qubit state which requires exponentially many bits of description. This is shown by relating the classical communication complexity to the quantum Kolmogorov complexity.
Scientific Areas:
## Experimental decoy state quantum key distribution
Wednesday Dec 13, 2006
Speaker(s):
Scientific Areas:
## Observable Entanglement measures
Wednesday Dec 06, 2006
Although entanglement constitutes one of the most remarkable differences between classical and quantum mechanics, and entanglement does have directly observable consequences, entanglement is not a regular observable like momentum or energy. It is rather a non-linear functional of a typically large set of such observables.
Scientific Areas:
## Quantum key distribution protocols with and without rotational
Wednesday Nov 29, 2006
We explore the role of rotational symmetry of quantum key distribution
(QKD) protocols in their security. Specifically, in the first part of the
talk, we consider a generalized QKD protocol with discrete rotational
symmetry. Note that, before our work, each QKD protocol seems to have a
different security proof. Given that the techniques of those proofs are
similar, it will be interesting to have a unified proof for QKD protocols
with symmetry (e.g., the BB84 protocol and the SARG04 protocol). This is
Scientific Areas:
## RECENT PUBLIC LECTURE
### Amber Straughn: A New Era in Astronomy: NASA’s James Webb Space Telescope
Speaker: Amber Straughn | {"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": 0.8004905581474304, "perplexity": 1230.2548472642811}, "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-2017-13/segments/1490218193716.70/warc/CC-MAIN-20170322212953-00349-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://doc.sagemath.org/html/en/reference/stats/sage/stats/distributions/discrete_gaussian_polynomial.html | # Discrete Gaussian Samplers for $$\ZZ[x]$$¶
This class realizes oracles which returns polynomials in $$\ZZ[x]$$ where each coefficient is sampled independently with a probability proportional to $$\exp(-(x-c)²/(2σ²))$$.
AUTHORS:
• Martin Albrecht, Robert Fitzpatrick, Daniel Cabracas, Florian Göpfert, Michael Schneider: initial version
EXAMPLES:
sage: from sage.stats.distributions.discrete_gaussian_polynomial import DiscreteGaussianDistributionPolynomialSampler
sage: sigma = 3.0; n=1000
sage: l = [DiscreteGaussianDistributionPolynomialSampler(ZZ['x'], 64, sigma)() for _ in range(n)]
sage: l = [vector(f).norm().n() for f in l]
sage: mean(l), sqrt(64)*sigma # abs tol 5e-1
(24.0, 24.0)
class sage.stats.distributions.discrete_gaussian_polynomial.DiscreteGaussianDistributionPolynomialSampler(P, n, sigma)
Discrete Gaussian sampler for polynomials.
EXAMPLES:
sage: from sage.stats.distributions.discrete_gaussian_polynomial import DiscreteGaussianDistributionPolynomialSampler
sage: p = DiscreteGaussianDistributionPolynomialSampler(ZZ['x'], 8, 3.0)()
sage: p.parent()
Univariate Polynomial Ring in x over Integer Ring
sage: p.degree() < 8
True
sage: gs = DiscreteGaussianDistributionPolynomialSampler(ZZ['x'], 8, 3.0)
sage: [gs() for _ in range(3)] # random
[4*x^7 + 4*x^6 - 4*x^5 + 2*x^4 + x^3 - 4*x + 7, -5*x^6 + 4*x^5 - 3*x^3 + 4*x^2 + x, 2*x^7 + 2*x^6 + 2*x^5 - x^4 - 2*x^2 + 3*x + 1]
__init__(P, n, sigma)
Construct a sampler for univariate polynomials of degree n-1 where coefficients are drawn independently with standard deviation sigma.
INPUT:
EXAMPLES:
sage: from sage.stats.distributions.discrete_gaussian_polynomial import DiscreteGaussianDistributionPolynomialSampler
sage: p = DiscreteGaussianDistributionPolynomialSampler(ZZ['x'], 8, 3.0)()
sage: p.parent()
Univariate Polynomial Ring in x over Integer Ring
sage: p.degree() < 8
True
sage: gs = DiscreteGaussianDistributionPolynomialSampler(ZZ['x'], 8, 3.0)
sage: [gs() for _ in range(3)] # random
[4*x^7 + 4*x^6 - 4*x^5 + 2*x^4 + x^3 - 4*x + 7, -5*x^6 + 4*x^5 - 3*x^3 + 4*x^2 + x, 2*x^7 + 2*x^6 + 2*x^5 - x^4 - 2*x^2 + 3*x + 1]
__call__()
Return a new sample.
EXAMPLES:
sage: from sage.stats.distributions.discrete_gaussian_polynomial import DiscreteGaussianDistributionPolynomialSampler
sage: sampler = DiscreteGaussianDistributionPolynomialSampler(ZZ['x'], 8, 12.0)
sage: sampler().parent()
Univariate Polynomial Ring in x over Integer Ring
sage: sampler().degree() <= 7
True | {"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": 0.6189684271812439, "perplexity": 6327.898748533028}, "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/1637964363149.85/warc/CC-MAIN-20211205065810-20211205095810-00137.warc.gz"} |
https://eskesthai.net/2015/05/05/the-mera-lattice/ | ## The Mera Lattice
There are reasons this information is meaningful to me and I hope to explain myself shortly.
Consistency Conditions for an AdS/MERA Correspondence
The Multi-scale Entanglement Renormalization Ansatz (MERA) is a tensor network that provides an efficient way of variationally estimating the ground state of a critical quantum system. The network geometry resembles a discretization of spatial slices of an AdS spacetime and “geodesics” in the MERA reproduce the Ryu-Takayanagi formula for the entanglement entropy of a boundary region in terms of bulk properties. It has therefore been suggested that there could be an AdS/MERA correspondence, relating states in the Hilbert space of the boundary quantum system to ones defined on the bulk lattice. Here we investigate this proposal and derive necessary conditions for it to apply, using geometric features and entropy inequalities that we expect to hold in the bulk. We show that, perhaps unsurprisingly, the MERA lattice can only describe physics on length scales larger than the AdS radius. Further, using the covariant entropy bound in the bulk, we show that there are no conventional MERA parameters that completely reproduce bulk physics even on super-AdS scales. We suggest modifications or generalizations of this kind of tensor network that may be able to provide a more robust correspondence. See: http://arxiv.org/abs/1504.06632
*** | {"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": 0.9424030780792236, "perplexity": 554.0376017573773}, "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-2022-05/segments/1642320303717.35/warc/CC-MAIN-20220121222643-20220122012643-00255.warc.gz"} |
http://mathhelpforum.com/advanced-algebra/85138-isomorphism-normal-subgroups.html | # Thread: Isomorphism in normal subgroups
1. ## Isomorphism in normal subgroups
Let G = Z4 + U(4), H = <(2,3)> and K = <(2,1)>. Show that G/H is not isomorphic to G/K.
2. Originally Posted by o&apartyrock
Let $G = \mathbb{Z}_4 \oplus U(4), \ H = <(2,3)>$ and K = <(2,1)>. Show that G/H is not isomorphic to G/K.
Hint: note that both G/H and G/K have 4 elements. show that every non-identity element of G/K has order 2 and find an element of G/H which has order 4.
this is not a part of solution but the above also proves that $G/K \cong \mathbb{Z}_2 \oplus \mathbb{Z}_2$ and $G/H \cong \mathbb{Z}_4.$
3. How is it that G/H and G/k both have 4 element? My calculations show them having 8 elements each, since Z4 + U(4) has 8 elements. Am I incorrect?
4. Originally Posted by o&apartyrock
How is it that G/H and G/k both have 4 element? My calculations show them having 8 elements each, since Z4 + U(4) has 8 elements. Am I incorrect?
H and K have 2 elements. so |G/K|=|G|/|K|=8/2 = 4. same for G/H.
5. ## LaGrange
Do you have LaGrange's Thorem yet?
$|G/H|=\frac{|G|}{|H|}$
As you noted $|G|=|\mathbb{Z}_4 \oplus U_4|=8$
Direct computation shows $|H|=|<2,3>|=|\{(2,3) , (0,1) \}|= 2$
Similarly,
$|K|=|<2,1>|=|\{(2,1) , (0,1) \}|= 2$
So you see by the above,
$|G/H|=\frac{|G|}{|H|}=\frac{8}{2}=4$
$|G/H|=\frac{|G|}{|K|}=\frac{8}{2}=4$
Follow NCA's hints to see why $H \not \cong K$
6. Ah I see. Simple mistake on my part. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "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": 0.8825664520263672, "perplexity": 1861.083188618896}, "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-2016-40/segments/1474738662022.71/warc/CC-MAIN-20160924173742-00137-ip-10-143-35-109.ec2.internal.warc.gz"} |
https://asmedigitalcollection.asme.org/appliedmechanics/article-abstract/42/2/478/387678/Multiparameter-Quadratic-Eigenproblems?redirectedFrom=fulltext | This paper contains an analytical theory for the study of the eigensystem of a multi-parameter quadratic eigenproblem. Previous work in this general area has focused mainly on first order eigenproblems. In the present work, eigenvalues and eigenvectors are expressed in the form of infinite series in which parameters entering the elements of various matrices play the roles of independent variables, and it is shown how the coefficients may be evaluated. The methods of derivation are given in sufficient detail to allow extension to either higher derivatives or higher order eigenproblems. Among the results presented are formulae for the second derivatives of eigenvectors, which have not been presented previously. Formulae applicable to special cases of first order eigenproblems are given also.
This content is only available via PDF. | {"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": 0.9161406755447388, "perplexity": 313.1659432150515}, "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-2019-43/segments/1570987787444.85/warc/CC-MAIN-20191021194506-20191021222006-00123.warc.gz"} |
https://puzzling.stackexchange.com/questions/53159/lined-to-the-nines?noredirect=1 | Lined to the nines
Each line in the following list of equalities may be made true by moving, according to a common rule, the numbers at the left of the = equals sign in that line.
What is the value of X in X 11 10 9 = 11?
0 1 2 3 4 5 6 7 8 9 = 0
1 2 3 4 5 6 7 8 9 = 1
2 3 4 5 6 7 8 9 = 2
3 4 5 6 7 8 9 = 3
4 5 6 7 8 9 = 4
5 6 7 8 9 = 5
6 7 8 9 = 6
7 8 9 = 7
8 9 = 8
10 9 = 9
11 10 9 = 10
X 11 10 9 = 11
12 11 10 9 = 12
10 11 12 11 10 9 = 13
.
.
.
... including, in case it’s not obvious, ...
10 11 12 13 14 15 16 17 18 19 20 19 18 17 16 15 14 13 12 11 10 9 = 153
.
.
.
No symbols or markings need to be added and the numbers may move left, right, up and down as long as they remain whole, separate, and to the left of the = equals sign.
The rule for moving numbers is so simple that it can be stated in an English sentence of 9 words or fewer. Understanding the result, though, requires remembering a convention familiar to a vast majority of mathematicians and taught to even more students who do not go on to pursue that field.
This list of lines begins with = 0 but has no end and, incidentally, the entry for each line has infinitely many alternatives. The present equations were chosen to emphasize some patterns into which the value for X fits in a surprising way.
(Note: This puzzle’s presentation was overhauled in April, 2020, and many comments from 2017 no longer apply exactly.)
• Does "to a unique integer result" mean (1) that each line's result is well-defined or (2) that all the lines' results are different? Jul 5 '17 at 11:21
• Thanks once again, @Gareth, edited. I was trying to avert unintended utterly simple solutions, like every line = C.
– humn
Jul 5 '17 at 11:30
• I was looking for an 'x' in the first line (line 1). It's actually lower-case 'L'. Jul 5 '17 at 12:02
• @humn No problem :) . Upper-case line references is a good idea in this question, actually. Jul 5 '17 at 12:10
• Thank you for a great puzzle idea or two, @Paul Karam! Something to seem so simple that it's almost impossible.
– humn
Jul 7 '17 at 17:08
The composition is
A string of right-associative $$x_y$$ operations, where $$y$$ is the base to which $$x$$ is expressed. The RHS is expressed in base 10 (the familiar '10', as opposed to the one where 'every base is base 10' :) ).
With an ascending string of single-digit numbers, the whole string reduces to the left-most operand because we start on the right and each pair reduces to the left operand. For example,
$$3_4 = 3$$.
The given examples all check out, including the monster that evaluates to 153.
We can start with [12 11 10 9] = 12, as given, then continue with:
$$13_{12}$$ = 12 + 3 = 15
$$14_{15}$$ = 15 + 4 = 19
...
$$10_{153}$$ = 153
Now, we have the following reduction since [11 10 9] = 10:
$$X_{[11,10,9]} = X_{10}$$
which we are told evaluates to 11.
Therefore $$X=11$$.
$$\require{begingroup}\begingroup \def\b#1{_{\large\,#1}} \begin{array}{rcl} 0\b{1\b{2\b{3\b{4\b{5\b{6\b{7\b{8\b9}}}}}}}} & = & 0 \\ 1\b{2\b{3\b{4\b{5\b{6\b{7\b{8\b9}}}}}}} & = & 1 \\ 2\b{3\b{4\b{5\b{6\b{7\b{8\b9}}}}}} & = & 2 \\ 3\b{4\b{5\b{6\b{7\b{8\b9}}}}} & = & 3 \\ 4\b{5\b{6\b{7\b{8\b9}}}} & = & 4 \\ 5\b{6\b{7\b{8\b9}}} & = & 5 \\ 6\b{7\b{8\b9}} & = & 6 \\ 7\b{8\b9} & = & 7 \\ 8\b9 & = & 8 \\ 10\b9 & = & 9 \\ 11\b{10\b9} & = & 10 \\ {\large\bf 11}\b{11\b{10\b9}} & = & 11 \\ 12\b{11\b{10\b9}} & = & 12 \\ 10\b{11\b{12\b{11\b{10\b9}}}} & = & 13 \\ & \vdots \\ 10\b{11\b{12\b{13\b{14\b{15\b{16\b{17\b{18\rlap{\b{19\b{20\b{19\b{18\b{17\b{16\b{15\b{14\b{13\b{12\b{11\b{10\b9}}}}}}}}}}}}}}}}}}}}} & = & 153 \\ & \vdots \\ \end{array} \endgroup$$
• One for the road. :) Apr 12 '20 at 16:34
• And a picture as a chaser
– humn
Apr 16 '20 at 17:48
Note: The puzzle’s presentation has been revised since the time of this posting. The version from that time is appended to this answer.
Lines $$i$$ and $$j$$ are the only other pair presented where consecutive rows have the same number of elements. There, the left-most digit is incremented by 2. Otherwise, the number in each column stays the same as the preceding row, except that new numbers can be introduced to the left. The rules for the new numbers isn't sought by this puzzle, and $$x$$ can be determined by the simple rule observed for lines $$i$$ and $$j$$.
Applying that simple rule to lines $$l$$ and $$m$$,
the increment-by-two rule gives us $$12 = m + 2$$, so $$m = 10$$.
Version of the puzzle when this answer was posted
Each of the following line a through line n evaluates, by one utterly simple secret rule, to a well-defined unique-from-each-other integer result. The resulting column of integers has an equally simple pattern.
line a: 0 1 2 3 4 5 6 7 8 9
line b: 1 2 3 4 5 6 7 8 9
line c: 2 3 4 5 6 7 8 9
line d: 3 4 5 6 7 8 9
line e: 4 5 6 7 8 9
line f: 5 6 7 8 9
line g: 6 7 8 9
line h: 7 8 9
line i: 8 9
line j: 10 9
line k: 11 10 9
line l: X 11 10 9
line m: 12 11 10 9
line n: 10 11 12 11 10 9
What is the value of X in line l?
(And what utterly simple rule applies to all lines?)
The l in line l is lowercase L, not numbercase one.
This sequence continues forward infinitely but not backward.
• Thank you for following one of my false leads. I'm trying to learn how to balance genuine clues and red herrings. Another puzzle was nothing but herrings.
– humn
Jul 8 '17 at 23:44
• Apologies, Lawrence, I neglected to acknowledge that your rule does work, yet an even simpler rule produced these lines
– humn
Jul 22 '17 at 23:46
• @humn I’m glad I did. I had about a 17h day today if I’ve counted my hours correctly, and this is such a nice surprise to find as I’m unwinding from the long day. Thanks again, and have a happy Easter. :) Apr 12 '20 at 15:59
• Perhaps solving this puzzle was a nice palate cleanser for you, @Lawrence, and when I say that an answer gets a bounty, it gets its own bounty. It's the principle, not the points. Again, I am grateful for your helping me realize that the original presentation was too coyly ambiguous. What if I append a snapshot to the solution, as I did to your previous answers, but this time of the rearranged numbers to go along with your more-complete-than-I'd-hoped analysis?
– humn
Apr 16 '20 at 15:32
• @humn Solving the years-long puzzle was certainly satisfying. Feel free to edit as you wish. :) Apr 16 '20 at 15:48
Note: The puzzle’s presentation has been revised since the time of this posting. The version from that time is appended to this answer.
Rule: adjacent elements on each line differ by 1.
The only element adjacent to $$x$$ is 11. So if $$x \ne 12$$ by line $$m$$, we have $$x=10$$.
Version of the puzzle when this answer was posted
Each of the following line a through line n evaluates, by one utterly simple secret rule, to a well-defined unique-from-each-other integer result. The resulting column of integers has an equally simple pattern.
line a: 0 1 2 3 4 5 6 7 8 9
line b: 1 2 3 4 5 6 7 8 9
line c: 2 3 4 5 6 7 8 9
line d: 3 4 5 6 7 8 9
line e: 4 5 6 7 8 9
line f: 5 6 7 8 9
line g: 6 7 8 9
line h: 7 8 9
line i: 8 9
line j: 10 9
line k: 11 10 9
line l: X 11 10 9
line m: 12 11 10 9
line n: 10 11 12 11 10 9
What is the value of X in line l?
(And what utterly simple rule applies to all lines?)
The l in line l is lowercase L, not numbercase one. | {"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": 23, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5304600596427917, "perplexity": 726.4209118389826}, "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-2021-39/segments/1631780057447.52/warc/CC-MAIN-20210923195546-20210923225546-00498.warc.gz"} |
http://www.mtosmt.org/issues/mto.04.10.2/mto.04.10.2.burns_woods.html?q=mto/issues/mto.04.10.2/mto.04.10.2.burns_woods.html | # Authenticity, Appropriation, Signification: Tori Amos on Gender, Race, and Violence in Covers of Billie Holiday and Eminem *
## Lori Burns and Alyssa Woods
KEYWORDS: popular music analysis, voice, gender, race, violence, authenticity
ABSTRACT: This paper studies alternative artist Tori Amos’s cover versions of two original performances by Billie Holiday and Eminem. The narrative perspectives and musical structures of the original songs offer great potential to explore questions of authenticity, appropriation, and intertextuality, and Amos’s distinctive revisions of the songs encourage reflection on her Signifyin(g) practices. The song “Strange Fruit” marked a shift in Billie Holiday’s musical style and social consciousness. Her recording (1939) of this emotionally powerful song about the lynching of a black man is upheld as the benchmark (“authentic”) version of that song. Over five decades later (1994), Tori Amos expresses a powerful commitment to the style and social message of Holiday’s original, yet her musical presentation is not merely historical tribute; rather, Amos Signifies on the older text to offer a contemporary statement on race and violence. Eminem’s song, “‘97 Bonnie and Clyde” (1999) exposes the problematic theme of violence against women. In her version (2001), Tori Amos appropriates Eminem’s lyrics, but casts a new perspective over the narrative by assuming the voice of the murdered woman. This paper analyzes the originals and covers using an interpretive framework that focuses on the voice as the site and vehicle of an artist’s Signifyin(g) expression.
Volume 10, Number 2, June 2004
[1] Recent studies in popular music explore the problematic attribution of “authenticity” to an artist’s musical work.(1) Such an attribution might be an evaluation of the sincerity of the artist, or a judgment concerning purity of musical style. Sometimes an entire genre is evaluated on the basis of its authenticity, for instance, when folk is associated with the authentic and pop with the synthetic. The concept of “authenticity” becomes ever more germane when the analyst is considering an artist’s borrowing of another artist’s original material. In a simplistic evaluation of such “cover” songs, the original material might be described as authentic and the cover an appropriation, yet the interpretive process ought never to be that simple.
[2] The evaluation of an artist’s authenticity relies heavily upon the subjective perspective of both artist and listener. Allan Moore identifies three possible perspectives on musical authenticity—the perspective of originator (the unmediated expression), that of appropriator (the borrowing of another artist’s material), and that of listener (the reception of the expression as genuine).(2) Moore recognizes intersections among these three categories, for instance, an appropriation of another artist’s work may still be considered “authentic” as long as the borrowed material is presented with “sincerity.” Such attributions of genuineness, honesty, authenticity, suggest a unified statement, perhaps one could even say single-voiced utterance, which by definition does not admit of contradiction, irony, sarcasm.
[3] The interpretation of a univocal utterance is not in keeping with a postmodern approach to cultural and artistic expression. Indeed, a postmodern conception of art would embrace a multi-voiced, intertextual expression and an interpretive approach that would eschew an attribution of fixed meaning. Richard Middleton understands intertextuality in the context of popular music such that “all texts make sense only through their relationships, explicit or implicit, with other texts.”(3) Although Middleton does not invoke the term “authenticity,” its value seems implicit when, for instance, in his analysis of a Miles Davis remix, he concludes that Davis emerges as more of an auteur in the remix.(4) Again in his analysis of a remixed Bob Marley song, Middleton asserts that the producer makes the music “sound more like itself,” whereupon he wonders “how this musical ‘self’ is being conceived and where it is located.”(5)
[4] These questions of authenticity, appropriation, and intertextuality are all implicitly connected to the more basic question of authorship. While Middleton certainly writes a convincing argument for the dismantling of the concept of author in the realm of produced popular music, we still wish to acknowledge the social positioning of the recording artist or singer. And while we recognize the problems associated with the assertion of authorial intentions in a postmodern theoretical framework, we are loath to dismiss the concept of an author’s voice, because of the strong social statements and political messages that can be found in popular song.
[5] An interpretive concept that acknowledges the self, the subjective social position, is “Signifyin(g).” The concept was developed by African-American literary and musical scholars as an interpretive tool for jazz, with its stylistic features of musical play, elaboration, variation, transformation.(6) Signifyin(g) is figurative, implicative speech that makes use of vernacular tropes and rhetorical devices.(7) Henry Louis Gates explains that the rhetorical devices themselves, the play of language, the manipulation of meaning, are the essence of Signifyin(g). The Signifyin(g) subject is referred to as the trickster, a master of technique, and the fascination with the expression is not that s/he signifies something, but that s/he “signifies in some way.(8) A natural corollary of this privileging of process over literal content would be the privileging of subject, the Signifier, over the signified. Thus, the process and the subjective voice are at the forefront of the Signifyin(g) expression.
[6] This conception of Signifyin(g) is valuable as we weigh the other terms that are active in the authenticity debate (authenticity and appropriation). Here follows a formulation of a question that could serve to reconcile these seemingly opposing terms: If an artist’s subjective process of Signifyin(g) on a text is a way of making a personal claim, is that not simultaneously an authentic expression of the self and an appropriation of the chosen text to serve that individual expression?
[7] Before we turn to our analytic examples, we would like to reflect on the music-theoretical enterprise of analyzing an artist’s vocal expressive practices. Since the music we have chosen for study is vocal music, with strong lyrical content, our primary analytic emphasis will be on the voice as signifier. We have developed an analytic approach that gives consideration to the space that the voice occupies, the perspectives that an artist’s voice might adopt in the different contexts that comprise a song, as well as the locality of the voice within the domains of text and music. The strategies for the socio-musical communication of popular song derive from nuances of vocal expression in relation to text delivery, including the gamut of expression founded in vocal quality, range, and production, to text pronunciation and articulation, to the manipulation of musical gestures and structures. The following are our four categories for the interpretation of the voice as the site and vehicle of a Signifyin(g) expression.
1. Voice as Subject in the Lyrical Narrative. The voice is situated as the speaking subject for the lyrics, adopting a particular narrative perspective. The singer might adopt the role of narrator (a third-person voice), or the role of a character (a first-person subject) in the lyrical narrative.(9) The subject is not necessarily fixed in a song performance—an artist’s voice may switch from one character’s subjective position to another, adopting more than one voice in the course of the song. Neither is the subject determined by the lyrical content alone, but rather is developed by the musical artist. That is, one artist might adopt a character stance for a given song, while another artist could assume a different voice in the story. The subjective position is a level of meaning for the listener to understand, based on that artist’s ability to adopt that voice, that is, to communicate a social stance, through the use of dramatic and musical techniques.
2. Voice as the Vehicle of Social Communication. The subject or character in a popular song narrative might communicate a social message, describe a situation, express an emotion. The lyrical narrative, with its potential for social affect and emotion, is transmitted by and through the vocal effects. Some of these effects might be considered to lie in the domain of dramatic presentation, achieved through pronunciation, accent, emphasis, as these are part of a system of socio-linguistic conventions. However, just as the subject of a song is not fixed, the social message of a song is open to interpretation. An artist uses such linguistic conventions to shape the meaning of the song, enhancing concepts or offering contradictory meanings.
3. Voice as Participant in the Musical Codes, Conventions, Styles. A singer presents the lyrics in the context of the musical content, in which we find in operation the connotations of style and gesture that are part of a long history of musical codes and conventions. Conventional meanings and style connotations contribute to the context-based musical framework for the song. The voice has an important role in the structure of form, phrase, rhythm, melody, harmony and texture, and will participate in that musical design and structure in a variety of ways, sometimes strongly directing the formal structure, and sometimes being relegated to an incidental role in that structure. Since popular music is a performance-based musical art, an artist can choose to manipulate content to greater or lesser degrees. Rhythmic, melodic, and phrase content are subject to change and variation, leading to potential Signifyin(g) practices in those domains. For instance, the singer could replace the tonal convention of dissonance resolution with an avoidance of closure, indicating a deviation from the norm.
4. Voice as Member of the Instrumental Ensemble. The singing voice participates in an active musical texture that features not only instruments but also, for recorded popular music, the production techniques that affect the sound. The musical content and structure of the song (form, harmony, melody, and rhythm, etc.) are transmitted or enacted through the instrumental ensemble. The voice presents itself in dialogue with the instruments, revealing a variety of musical relationships, the interplay of musical ideas conveying meaning that can be related to the socio-lyrical content.
[8] Our analyses provide reflections on authenticity, appropriation, intertextuality, and “Signifyin(g),” through these interpretive perspectives on the voice. Although these concepts may seem to exist only at a music-critical level, we present concrete music-theoretical techniques that bring musical content, structure, and design into the argument. We study here two recordings by Tori Amos of songs originally recorded by Billie Holiday and Eminem. Amos is well known not only for her original song compositions but also for her performance of cover songs. In addition to the Strange Little Girls album, which is a collection of covers, Amos has released many “singles” that feature remixes and covers. Some of her most famous covers appear on the Crucify EP (1992) where Amos reinterprets Nirvana’s “Smells Like Teen Spirit,” “Angie” by the Rolling Stones, and Led Zeppelin’s “Thank You.” The two Amos covers that we have chosen for this study are interesting for their thematic handling of race and violence within a particular social context. These songs take us from New York in 1939 to Detroit in 1999.
#### “Strange Fruit” (Lori Burns)
[9] Billie Holiday’s decision to perform “Strange Fruit”—a song about the lynching of a black man—at the racially integrated Greenwich Village Café Society in its 1939 opening season has been credited as a turning point in her performing career. The producer from her early recording period, John Hammond, captured the essence of this transitional moment of both acclaim and criticism with the following remarks: “The beginning of the end for Billie was ‘Strange Fruit,’ when she had become the darling of the left-wing intellectuals. . . I think she began taking herself seriously, and thinking of herself as very important.”(10) The political context and powerful social content of the song held very real consequences for Holiday—for instance, although she had a recording contract with Columbia, they refused to record “Strange Fruit.” Columbia did, however, release her to record it for Milt Gabler at Commodore in April of 1939.(11)
[10] Holiday’s singing style has been the focus of many critical remarks. With regard to this particular recording, Stuart Nicholson writes, “. . . she relies on the grain of her voice, hard and worldly-wise, and careful, dramatic enunciation that would have done credit to a classically trained actor, to exploit the unequivocal drama of the lyrics.”(12) Nicholson also captures the spirit of listener-evaluated authenticity with the claim that the song “was a landmark recording, but a very different kind than was perceived at the time. It was one of the first examples of a popular song becoming impossible to disentangle from a single, specific recording of it.”(13)
[11] Jazz critic Will Friedwald takes an interesting analytical stance on the recording that I would like to quote here and then develop:
Beginning with the overdramatic but startlingly effective ‘Strange Fruit’ (1939, Commodore), Holiday experiments with slightly suppressing her melodic embellishment as a means to turn lyrics into personal videos of the mind. . . [O]nly she can implant in your mind the horrifically powerful image of lynch mob victims hanging from the trees like so much strange fruit. One word from Holiday is worth a thousand pictures.(14)
[12] Without explicitly identifying the concept of cultural memory, Friedwald’s comment explores listener response through the development of a mental image, implicitly suggesting that a listener will conjure such images through his or her acquired cultural memories. The concept of cultural memory is a powerful rubric for the study of any music, but in particular, African-American music scholars have made explicit use of this concept in their commentaries on black music traditions. In The Power of Black Music, Samuel Floyd writes, “Cultural memory, obviously a subjective concept, seems to be connected with cultural forms—in the present case, music, where the ‘memory’ drives the music, and the music drives memory.”(15) In Race Music, Guthrie Ramsey writes about music as a means of accessing cultural memories, the access made possible because “cultural forms such as tales, stories, and music (especially the performative aspects of such) function as reservoirs in which cultural memories reside.”(16)
[13] In his remarks, Friedwald suggests that Holiday can “implant” a response in the listener’s mind. Contemporary feminists Marianne Hirsch and Valerie Smith develop a conception of cultural memory as based upon performative acts of transfer. Such an act of transfer is “an act in the present by which individuals and groups constitute their identities by recalling a shared past on the basis of common and therefore often contested norms, conventions, and practices.”(17) Since we may not have access to the original experience the transmission of history and cultural memory is considered by scholar James Young as “twice-behaved behavior.”(18) This conception of historical and cultural transmission resonates with the feminist belief that history is constructed and contested. Feminists tell us not to forget or suppress the past, but rather that we must contest such suppression with an “active remembering.”
[14] With these ideas about cultural memory in mind, I would like to consider our first interpretive perspective, that is, Holiday’s Voice as Subject in the Lyrical Narrative. Holiday adopts the voice of a narrator for this song. One might say that Holiday’s version is quite believable, or authentic, given her social, racial, and historical positioning. Why are we quick to identify her performance as authentic—the benchmark—according to Nicholson? Here is where Friedwald’s commentary is of assistance to us: Holiday succeeds at implanting in our minds the image of this horrific scene; it is her performative act of transfer—her own subjective positioning and historical context in relation to that cultural memory is an important vehicle in transmitting the meaning of this song. She conveys for us—witnesses, “behaves”—the past behavior that is the subject of “Strange Fruit.”
Example 1
(click to enlarge)
[15] As the Vehicle of the Social Communication, Holiday’s voice presents the lyrical drama through careful enunciation and word emphasis, developing the listener’s awareness of the scene. Lewis Allan’s song lyrics use the metaphors of fruit and nature to represent the hanging body in the tree, thus couching the horrible image in poetic terms. A transcription of the original melody, Holiday’s vocal line, and Amos’s vocal line for verse 1 are aligned in Example 1.(19) In lines 1 and 2 of verse 1, Holiday brings to the fore the words that describe a natural scene: trees, fruit, leaves, root. She ascribes to these words longer rhythmic values, directing the rhythmic flow to these words as anchors. In particular we notice this in line 2 where twice the expression “blood on the. . .” is passed over very quickly, thus de-emphasizing the word string that carries the human or social implications of the story. In line 3 Holiday draws out the words “swingin’” and “southern,” taking us a step closer to that human story; that is, these words suggest social contexts, whereas the emphasized words in lines 1 and 2 represent nature. Holiday’s emphasis on the nature words is achieved by durational values, but now in line 3 the emphasis comes through melodic elaboration and swung rhythms, clearly distinguishing the words “swingin’” and “southern” as carrying a particular musical style connotation. The final line 4 of the verse is offered as a direct communication of the lyrical statement. In both rhythmic and melodic presentation, this line is delivered with a straight feeling and a sense of resignation. “Hangin’” arrives with a relatively strong emphasis on beat 3. (It is important to note that these gestures in the Holiday version are not found in the sheet music. I will offer some comparative remarks between the original and Holiday’s version presently.)
[16] I interpret the overall shape of this first verse in the following way: Holiday begins by emphasizing the words that represent the natural scene, not giving the human reality of this story much emphasis; the human context does come forward in line 3 with more emphasis on the social words, which are set to a lilting melodic pattern; the final line states the situation fairly clearly, yet the object of the hanging is still metaphorically disguised as strange fruit.
[17] Let us return to the quotation of Friedwald with this analysis in mind. Friedwald’s commentary points to a kind of bare simplicity in the Holiday performance. I would like to connect this aesthetic of simplicity to a theoretical concept that has been developed in literary theory. In her article on “The Site of Memory,” Toni Morrison analyzes the narratives of slave autobiographies written in the mid-19th century, and identifies some common features in the literary intent and expression of these authors. One writing strategy that she explores is the understatement of atrocity as an important means of retaining an audience. Morrison states: “. . . it was extremely important for the writers of these narratives to appear as objective as possible—not to offend the reader by being too angry. . .(20) Morrison identifies her task in analyzing these texts as follows: “My job becomes how to rip that veil drawn over ‘proceedings too terrible to relate.’”(21) Morrison’s analysis illuminates the subject’s perspective, revealing a self-consciousness over the trauma that has been experienced, and a desire to express the history of the trauma in objective terms, in forms that control and contain the content.
[18] Holiday begins her tale with the veil drawn over, but does allow herself to express strong emotion as she comes to the close of the song. In order to illuminate her expression, in order to rip that veil, I will turn to a more detailed musical analysis, and at the same time, to our analytic perspectives on Holiday’s vocal Signifyin(g) practices.
[19] As a Member of the Instrumental Ensemble, Holiday is featured at the center of this arrangement. The song has a lengthy introduction, first featuring 27 seconds of a muted trumpet in a searching melodic solo against a non-rhythmic high-hat wash and harmony in the winds. This section comes to a close, followed by a 43-second piano solo, which establishes a somber and poignant mood in a slow swing style with the rhythmic pulse provided by the bass. By the time the voice enters, a great sense of expectation has been established, and she is well featured as the teller of the anticipated story. The piano continues in the texture, but at a lower level of activity; the bass has a quiet presence, as does the muted trumpet. The tempo of this song is very slow, at quarter pulse equals 58. It is, in fact, one of the few songs in Holiday’s repertoire with such a slow tempo. In that context, the song is marked as unique.
[20] As a Participant in the Musical Codes and Conventions, Holiday reveals herself, as always, to be an innovator in jazz singing. As mentioned earlier, she develops the song from its original form. That would be true of all singers of jazz standards, but given that Holiday had no other performances of this song from which to receive influences, she certainly places her own particular signature on the musical content and style. She manipulates and enhances the unadorned melody of the original song.
[21] I have already drawn attention to Holiday’s durational emphasis in lines 1 and 2, on the words trees, fruit, leaves, root. A voice-leading analysis tells us even more about the weight of those words: trees arrives on the tonic, B, fruit on C as the neighboring scale degree $\stackrel{ˆ}{2}$, and then those pitches repeated for leaves and root. In the original song, the melody consists almost solely of this $\stackrel{ˆ}{1}$ - $\stackrel{ˆ}{2}$ - $\stackrel{ˆ}{1}$ - $\stackrel{ˆ}{2}$ movement. There is one ornamental pitch, the third scale degree, heard over the dominant, at the verb “bear.” When Holiday elaborates the melody, she takes that ornamental scale degree $\stackrel{ˆ}{3}$ and extends it even higher to scale degree $\stackrel{ˆ}{4}$, the E. The verb “bear” is particularly poignant when we know the ultimate meaning of the song (tree bearing fruit becomes tree dropping dead fruit). This verb is presented on the active contrapuntal scale degree $\stackrel{ˆ}{4}$ (E), stepping down on the word “strange” to the scale degree $\stackrel{ˆ}{3}$ and then $\stackrel{ˆ}{2}$, the goal of the melodic motion. “Strange” is also given an unusual rhythmic setting, arriving on a very weak second half of beat 2, but then being held over as the first part of a swung triplet rhythm. My interpretive point here is that the words that emerge most prominently in the lyrical emphasis and musical structure of the song—trees and fruit—are in fact enhanced by the more active and poignant words even though these active moments are fleeting and always brought back into containment by the strong structural arrivals.
[22] Line 2 also features a pattern of elaborative pitches being presented on the “emotional” or “active” words of the line, moving to the structural pitches on the strong words from nature. In the original song, “blood on the leaves” was set to a repeated tonic, and “blood at the root” to a repeated second degree. Holiday elaborates this simple structure, putting the contrapuntally active pitches on the emotionally active words in the text. “Blood on the leaves” moves from a neighboring scale degree $\stackrel{ˆ}{2}$, down to the fifth degree (a deep pitch in Holiday’s range), and then to settle on the tonic. “Blood at the root” leans heavily on the minor third scale degree in repeated neighbor resolutions to scale degree $\stackrel{ˆ}{2}$.
[23] Line 3 emphasizes “swingin’” and “southern” using melodic and rhythmic patterning that departs dramatically from the feeling of structure and containment. Here the melody escapes. In the original song, the rising arpeggiation from scale degree $\stackrel{ˆ}{2}$ through $\stackrel{ˆ}{4}$ to $\stackrel{ˆ}{6}$ is the first dissonant melodic movement. The $\stackrel{ˆ}{6}$ settles to scale degree $\stackrel{ˆ}{5}$ on the word “breeze.” Holiday heightens the musical expression in this meaningful phrase. Her rhythmic articulation is one means, but melodically her line is noteworthy because of the way in which she exceeds the structure of the original melody, going one pitch beyond the neighbor note that was $\stackrel{ˆ}{6}$, rising up to a $\stackrel{ˆ}{7}$ before settling back to $\stackrel{ˆ}{5}$. The effect of this G - A - F is to dissipate the impact of the $\stackrel{ˆ}{6}$ neighbor to $\stackrel{ˆ}{5}$ and its resolution. The expectations that a listener might conventionally feel for a G - F resolution, are suspended once the higher note A enters the dissonant field. From that $\stackrel{ˆ}{7}$, Holiday simply falls back to the scale degree $\stackrel{ˆ}{5}$, interestingly enough, one that is supported in the bass by a leading tone, a cross relation with the $\stackrel{ˆ}{7}$ in the melody.
Example 2
(click to enlarge)
[24] Line 4 answers the elaborative melodic pattern of line 3 with a strict presentation of the structural notes. The pattern of freedom and containment that was felt in line 1 and then again in line 2 is offered at a larger level by the whole of line 3 followed by line 4. The sense of rigidity or containment is further enhanced in line 4 by the contrapuntal relationship between bass and voice—they are in octaves, a rather unusual presentation, and one that contributes to this sense of containment or control. The first verse establishes this struggle between strict and free, nature and humanity. That struggle is certainly the essence of the song’s lyrical and musical narrative. Based on Morrison’s discussion of cultural trauma and memory, the struggle to control one’s presentation of an extreme human tragedy was an important aspect of the African-American slave narrative. I will jump ahead to the final verse of the song, to illustrate a few points about Holiday’s struggle within that narrative. The original melody of the final verse, as well as Holiday’s and Amos’s vocal lines are transcribed in Example 2.
[25] The final verse features the same harmonic and melodic relationships that were established in verse 1, but with a prolongation of the dissonant melodic excursion. In the original song, line 1 of verse 3 is melodically equivalent to line 1 of the first verse. Line 2, however, borrows the melodic pattern of line 3—the dissonant arpeggiation from scale degree $\stackrel{ˆ}{2}$ to $\stackrel{ˆ}{6}$, which then resolves to 5. Line 3 of verse 3 then introduces something new—a climb to $\stackrel{ˆ}{7}$, resolving to $\stackrel{ˆ}{6}$. Line 4 abandons the dissonant upper register and outlines an ascending leap from the low tonic to the fifth, followed by a return through scale degrees $\stackrel{ˆ}{3}$ and $\stackrel{ˆ}{2}$ to $\stackrel{ˆ}{1}$. In sum, this final verse heightens the emotional expression that was contained in verse 1, and yet still manages to return to control for the close of the song.
[26] Holiday takes this material and develops the dissonant expression while still achieving the aesthetic of restraint. Although, as Friedwald points out, in the context of her other performances, we might interpret her melodic work as “suppressed melodic embellishment,” in the context of the original song, she does exceed the existing structure. Her greatest excess occurs in line 3 (“sun to rot”), where she elaborates scale degree $\stackrel{ˆ}{5}$ with its lower leading tone, and then ultimately where she treats the original $\stackrel{ˆ}{7}$ - $\stackrel{ˆ}{6}$ resolution (“trees to drop”) as the moment to release her outcry at the horrific scene of the hanging. She moves chromatically from the A flat ($\stackrel{ˆ}{7}$) down through G natural and G flat, but then returns to the A flat before sliding down to F (scale degree $\stackrel{ˆ}{5}$). The accompaniment here fades out, leaving a long moment of silence before her final line, which conforms to the original melody.
[27] I will turn now to the Amos, even though it is difficult to wrench oneself away from Holiday’s musical portrait of that powerful scene.
[28] How can a contemporary artist such as Tori Amos enter in to this historical narrative? How does she use her voice as a Subject in the Lyrical Narrative? We may not be able to see Amos as experiencing the same traumas of racism that Holiday experienced, but she does carry cultural memories and traumas authentic to her own experience and she has made such traumas a strong thematic feature of her work. Her work in general has revealed a contemporary social conscience regarding the boundaries and restrictions that are placed on women in certain social, cultural, and religious contexts. Her own cultural history (she is part Native-American Cherokee Indian) has raised her sensitivity to racism and gender discrimination. Many of her songs explore themes of power and what she herself refers to as patriarchal structures.
[29] Amos is a fine pianist and in this recording she accompanies herself.(22) Perhaps in keeping with the lengthy piano solo that introduces the Holiday version, Amos opens the song with a one-minute piano introduction. I will not discuss her instrumental Signifyin(g) practices here, but will restrict my comments to her vocal strategies. As the Vehicle of the Social Communication, Amos uses a wide variety of vocal techniques to convey emotions and meanings in her songs. She is not conventional in her singing presentation, but rather manipulates her vocal quality and intensity, and plays with rhythmic accentuation and diction to suggest and transmit meaning.
[30] A remarkable aspect of Amos’s delivery of the first verse is the distortion of the original ${\text{}}_{4}^{4}$ meter and slow tempo. She slows down the tempo even further, moving at about quarter = 44 at the very opening, increasing to 50 as the verse proceeds. The meter shifts between and among ${\text{}}_{4}^{4}$, ${\text{}}_{4}^{5}$, and ${\text{}}_{4}^{6}$, such that there is no consistent meter for the first verse. We are held in suspense, temporally, not knowing when her vocal and pianistic events will happen and what accent they might receive. There are occasional moments of metric and rhythmic normalization, which bring a sense of expectation, only to have such expectations immediately denied.
[31] The melody is parsed into individual gestures, the lack of continuity caused not only by the rests between vocal lines, but also by this rhythmic and metric unpredictability. The original melodic neighbor pattern between scale degrees $\stackrel{ˆ}{1}$ and $\stackrel{ˆ}{2}$ used as support for the nature words “tree, fruit, leaves, root” is still evident in her melody, but her angular patterns in the approach to those stable pitches, in combination with the unusual rhythmic accentuation, give emphasis to the active social words in the text and take away from the stable words from nature. If I return to the concept of restraint and freedom that I studied in the Holiday version, I would suggest here that Amos takes more liberties than Holiday, struggling against the controlling structure to a greater extent.
[32] Amos’s handling of the dissonant arpeggiation (verse 1, line 3) is noteworthy for its avoidance of the pitch (A) that was the goal of that gesture in the original song. She achieves, at the beginning of her line 3, a more conventional sense of ${\text{}}_{4}^{4}$ swing timing through the rhythmic accentuation in the piano, but that familiar musical feeling is short-lived when she creates a ${\text{}}_{4}^{5}$ bar in the next measure. Melodically, she overshoots the expected $\stackrel{ˆ}{6}$ by leaping to the $\stackrel{ˆ}{7}$ on “southern.” Holiday’s original overstepping of that line by moving up to $\stackrel{ˆ}{7}$ could arguably be the inspiration for Amos’s vocal gesture here. For the final line 4, Amos returns (as did Holiday) to emphasize the tonic in a rather unadorned melodic cadence, albeit in ${\text{}}_{4}^{6}$.
[33] I will once again skip ahead to the final verse of the song. In verse 3, Amos pushes against the structure of the original song to a greater extent than did Holiday. Holiday saved her most poignant gesture for the second half of line 3 (“for the trees to drop”), but Amos reaches that emotional height already at the end of line 2 (“for the wind to suck”). Amos’s premature climb to the peak of the melody requires her to sustain that climax for a longer period of musical time than Holiday. Holiday’s excursion was brief, checked under control immediately, a tempered outburst. Amos allows herself to linger in her outcry. Her actual melodic embellishments can be seen to derive directly from Holiday’s line, but with a greater degree of repetition and resulting emphasis on dissonance (the $\stackrel{ˆ}{4}$ neighbor to $\stackrel{ˆ}{5}$, the $\stackrel{ˆ}{6}$ and $\stackrel{ˆ}{7}$ gestures, and the chromatic slide from $\stackrel{ˆ}{7}$ to $\stackrel{ˆ}{5}$). Whereas Holiday offered a fairly conventional presentation of the final melodic line, Amos’s final rising glissando from the expected scale degree $\stackrel{ˆ}{5}$ to a sharp $\stackrel{ˆ}{4}$ is a remarkably unconventional gesture.
[34] How to interpret the vocal strategies of Holiday and Amos in relation to this particularly powerful text? The original song reveals the narrative of nature versus humanity, of restraint versus emotional response, of musical control versus containment. Holiday and Amos did not compose the song. They do compose, however, their own “authentic” versions of the song, that is, they Signify on the song, claiming it as their own, and transmitting its meaning to an audience. Based on the vocal Signifyin(g) practices that I have analyzed, I would categorize Holiday’s performance as that of a witness to the social scene, as someone historically connected to the context of the story, as revealed through strategies that are culturally prescribed (restraint in the telling of tragedy). I would categorize Amos’s version as an active remembering of a historical story by someone who carries cultural traumas from other contexts. Not being a witness on the scene, not being held to a standard of restraint, she takes greater liberties in declaring her outrage.
#### “‘97 Bonnie and Clyde” (Alyssa Woods)
[35] Rap artist Eminem’s solo albums are named after his different personas: The Slim Shady LP (1999) after his alter-ego, The Marshall Mathers LP (2000) after his birth name, and The Eminem Show (2002) after his stage name. The song that I will study here, “‘97 Bonnie and Clyde,” is from The Slim Shady LP.(23) Alter-ego Slim Shady emerges as a character through which Eminem is able to express social commentary in a first-person narrative that does not necessarily reflect his own personal views or actions. He uses the Slim Shady character to shock people by presenting them with views that most artists would or could not express. This alter-ego allows Eminem to be detached from the strong social issues that he expresses in his music. He says, “Slim Shady is just the evil thoughts that come into my head, the things I shouldn’t be thinking about. . . people should be able to determine when I am messing around.”(24) Eminem has a wide fan base, but receives a lot of negative media attention due to the offensive nature of his lyrics, which have been accused of encouraging hate crimes.
[36] In the song “‘97 Bonnie and Clyde,” Eminem uses the voice of alter-ego Slim Shady to express social commentary in a first-person narrative—Slim Shady describes how he has murdered his wife, kidnapped his infant daughter, and then justifies his actions as he disposes of her body in the river. Eminem’s song is loosely based on the Bill Withers and Grover Washington Jr. song “Just the Two of Us” (1980).(25) In Eminem’s song, “just the two of us” refers to “just me and my daughter,” the two who remain once the mother has been murdered. In the introduction we hear the narrator’s statements of love and affection for his daughter as well as his strong desire to be with her (“Nobody in this world is ever gonna keep you from me”). The first verse takes place as the narrator drives to the beach with his daughter. The listener begins to discover details of the murder as the narrator explains this late night trip to the beach to his daughter. The chorus consists of eight repetitions of the phrase, “Just the two of us,” the most obvious reference to the Withers/Washington original. In the second verse the narrator reveals more details of the crime as he attempts to explain the situation to his daughter in terms she might understand. After a second repetition of the chorus, the third verse describes the arrival at the beach and the disposal of the body in the water. After a final repetition of the chorus, the narrator once again declares his love for his daughter and reiterates that nobody will ever keep them apart.
[37] The title “‘97 Bonnie and Clyde” refers to Bonnie Parker and Clyde Barrom who were infamous criminals during the Great Depression.(26) With this title, Eminem invokes the early Americana story of the infamous criminals and places it into a 1997 context. By aligning his story of a father and daughter with the well-known characters of Bonnie and Clyde, Eminem implicates the daughter in the crime, and elevates her role in the narrative to a level—to a voice—that must be addressed. That is, by bringing an innocent child into the scene and act of violence, Eminem intensifies the implications of that domestic violence. If we consider the Voice as Subject in the Lyrical Narrative, Eminem adopts the role of the criminal father, but also raises our awareness of and gives a realistic presence to the daughter whose life will be forever affected by the crime.
[38] The realistic roles of father and daughter are enhanced by Eminem’s use of non-musical sound effects to place the listener into the scene, establishing the physical setting. During the first thirty-six seconds of the song, a remarkable length of time in the context of popular music, the listener hears the sounds of something heavy being dragged, a car being unlocked and something loaded into the trunk, passing traffic, and finally a car door being opened and closed, which is followed immediately by the introduction of the rhythm and vocals.
[39] Eminem reinforces the image of the child’s actual presence by including some vocal sounds of the infant—we hear baby words such as “yeah,” “no,” and “mama” in the background, and we imagine the position of that child in the car while the father drives, toting the mother’s body in the trunk. If we consider Eminem’s voice as the Vehicle of this Social Communication, we find him to be using vocal nuance and word diction that suggest an intimate relationship between father and child. We not only hear the child’s vocal interjections but also Eminem delivering some of the lyrics in the idiom of a child, for instance when he uses expressions such as “da-da,” and “free” as a substitute for “three.”
[40] At times Eminem, in the voice of the subject Slim Shady, trivializes and disguises the violence for the child. A few lyric quotations from the first verse will illustrate this nicely: “Oh where’s mama? She’s takin a little nap in the trunk”; “Don’t play with dada’s toy knife, honey, let go of it”; and “Don’t worry about that little boo-boo on her throat, it’s just a scratch.” This “simplification” of the crime scene continues throughout the song, and has the opposite effect of actually heightening the emotional impact of the violence. Perhaps the moment of greatest irony occurs in verse 3, when the narrator asks the child for help with the body (“Here you wanna tie a rope around this rock? We’ll tie it to her footsie then we’ll roll her off the dock”). We hear the child’s compliant interjection “yeah,” and we hear the splash as the body hits the water.
[41] It is in the introduction, chorus, and coda sections of the song that Slim Shady declares his love for his daughter. His claim that he will always be there for her, however, has an ironic effect in the story, since he admits in verse 2 that he is aware of the criminal punishment awaiting him (“There’s a place called heaven and a place called hell, a place called prison and a place called jail. And dada’s probably on his way to all of ‘em except one”).
[42] The lyrics of this song place a horrific act of violence into a narrative in which a child unwittingly participates in the actions that follow a murder. The violence of the described actions is contradicted by the naturalization of the events for the sake of the child. As a Participant in the Musical Codes and Conventions, Eminem invokes normative phrase and formal structures as the setting for this violence, thus creating a musical representation of that lyrical irony: the situation is presented as simple, comfortable, and normative, despite the actual violence that is occurring.
[43] The introduction and coda form the symmetrical outer shell of the song’s formal structure. There are three verses, each one paired with a statement of the chorus. The formal symmetry is further amplified by the balanced design of the internal phrasing. Each line of text is set to the same 1-bar rhythmic pattern (beat 1: dotted eighth - sixteenth; beats 2 and 3: eighth - quarter - eighth syncopation; beat 4: dotted eighth - sixteenth). Four lines of text are organized into a 4-bar phrase; each phrase ending is articulated by record scratching. Each verse has 16 lines of text, thus four 4-bar phrases. The continuity of rhythm provided by the repetitive pattern presents a sense of stability in the song. The chorus comprises eight lines of text supported by eight statements of the rhythmic pattern. The regular 4-bar phrasing from the verse is also present in the chorus, which can be parsed into two 4-bar phrases. Each two-bar sub-phrase is concluded with record scratching.
[44] As with most rap music, this song has a very regular rhythmic flow. Because the beat is constant throughout the song, any interruption of the background rhythm is considered to be significant. The rhythmic flow is interrupted at one critical moment, when the 1-bar pattern is absent for an entire line of text in verse 3 (“One-two-free-Wheeeee!”), the moment in the narrative when he throws the body into the water. This music includes the sound effect of a splash at the end of the phrase as the body supposedly hits the water. Such an interruption of regular rhythmic flow heightens the tension at this moment by suspending our sense of time. As a Member of the Instrumental Ensemble, Eminem’s voice has remained in constant balance in relation to the instrumental flow until this point. At this moment, however, the focus shifts to the voice because of the sudden change in textual rhythm—the voice draws out the three-count and the instrumental rhythm is discontinued.
[45] Eminem’s story of a father, an innocent child, and a murdered mother, asks the listener to witness (perhaps unwillingly) a particular course of actions that are described and carried out by Slim Shady. If we reflect on the question of authenticity, Eminem appears to distance himself as the originator of the expression. That is, his invocation of a different voice and subjective perspective permits him to disown the violent act, and instead to comment upon it as a social critic might. The interpretive concept of intertextuality allows for a multiplicity of voices to speak in this narrative—the persona of Slim Shady as perpetrator of the violent act, the father and the child, the victim, and Eminem as socio-musical commentator who engages the listener as witness to the crime. His Signifyin(g) on that story is presented through the medium of the genre of inner-city Detroit rap music, a genre that connotes the social contexts of race, poverty, violence, and hardship. At that level of musical connotation, a listener’s measurement of “authenticity” would likely be affected by the social context that Eminem’s work does not conform to the connotations of race and poverty. This is certainly one of the tensions that contributes to the social effects and meanings of Eminem’s work.
[46] Tori Amos is well known for expressing social and feminist issues in her music. Responding to the increasing level of violence in our culture, she released an album of cover songs in 2001 entitled Strange Little Girls.(27) Taking songs that were originally written and performed by men, Amos reinterprets the original material, adopting many different voices and perspectives over the course of the album.(28)
[47] Comparable to the Slim Shady character, the different personas that Amos adopts for each song allow her to provide a variety of perspectives on social issues, and permit her a degree of artistic detachment. Amos’s claim, “I’ve always found it fascinating how men say things, and how women hear them”(29) reveals her interest in the potential multiplicity of subjective perspectives. In the album of cover songs, she uses material originally performed by male artists, prepares and presents a new perspective for that material, and through the striking revisions, alerts the listener to different social meanings.
[48] Amos addresses the responsibility of an artist who writes about violence with the following remarks:
I would hear a lot of people say, ‘They’re only words, what is everybody going on about?’ That’s where I said I could pick up the gauntlet. I believe in freedom of speech, but you cannot separate yourself from your creation. We go back to the power of words, and words are like guns—Your fingerprints cannot be erased from your words; you only leave the scene of the crime covered in ink—Whether you choose the graciousness of Tom Waits or the brutality of ‘Bonnie and Clyde’ they’re equally powerful, and that’s what drove me.(30)
[49] What fingerprint does Amos leave on her version of this violent song? How does she Signify on this story, when she so clearly stands in opposition to its violent content? In the context of this “character” album, one of her most important decisions for the song had to have been the perspective that she would adopt in relation to the Slim Shady narrative. About this decision, she states: “I did not align with the character he represents. There was one person who definitely wasn’t dancing to this thing and that’s the woman in the trunk.”(31) Amos gives the murder victim a voice by offering the song text from her perspective. Without making substantial alterations to the lyrics, Amos achieves the effect of shifting the Subjective Voice in the Lyrical Narrative from murderer to murder victim.
[50] Amos’s contrived shift in narrative perspective from murderer to murdered casts new meaning over the lyrical content. She explains, “You’re hearing her listen to him tell their daughter lies.”(32) In other words, in her version of the song, the listener bears witness to the dead mother as she listens to her murderer’s justification of the murder.
[51] In her reinterpretation of “‘97 Bonnie and Clyde,” Amos remains true to Eminem’s lyrics. She makes some minor changes, and these do have an impact on the song’s meaning. In the introduction, Eminem’s statement, “And I’m always gonna be here for you no matter what happens” suggests that he is aware of his risked punishment for the crime of murder. Amos replaces the word “happens” with “happened.” The change in meaning here is subtle, but surely reveals the subjective stance of the mother: whereas Slim Shady is considering his future and the consequences of his actions, the murdered mother must acknowledge what has happened to her life.
[52] Amos makes two interesting cuts to the lyrics—words that would imply a future for the killer but not for the victim. She excludes the phrase “Just you and I” as well as the interjection “And when we ride” in the chorus, which Eminem recites between the repeated statements of “Just the two of us.” Whereas Amos cuts these lines, she adds two repetitions of the line “Me and my daughter” at the end of verse 2, delivering these repetitions in a much softer voice. In the context of the multiple voices that are engaged in this song text, we might hear the father’s voice in the first statement as an assertion, and the mother’s voice in the two repetitions with a sense of longing and loss.
[53] Amos’s recorded voice is an important Vehicle for the Communication of the mother’s feelings. To portray the victim’s voice, she explores a spoken vocal quality, reciting the text of the verses in a cold, quiet, and detached tone. She actually recorded her vocals from inside a box that did not allow her to move, which was created for the purpose of allowing her to relate psychologically to the dead mother.(33) In the final mix, her voice is very forward and highly compressed so that even her whispers suggest a close proximity to the listener. In addition to these production techniques Amos uses a variety of vocal strategies in order to convey emotion. For example, she emphasizes “mama” throughout the song by varying her intonation on the second syllable. By using the gentle nuances of expression that might imitate their intimate style of communication, Amos invokes both roles of mother and child. Sometimes emphasis is achieved by means of a colder tone. For instance the word “screamin’” in verse 3 is recited in a very low tone with no inflection and very hard diction on the “sc.” She uses a whisper in verse 2, in order to suggest fear at the line “But for now we’ll just say mama was real real bad.”
[54] There are moments in the song when Amos invokes the male voice of the father. To achieve this effect, she lowers her voice and delivers the text more aggressively. An example of this can be heard in verse 1: “Don’t play with dada’s toy knife, honey, let go of it.” At the end of verse 1, his anger towards her is evident in Amos’s vindictive tone of voice at the line “Mama’s messy isn’t she?”
[55] The handling of the body is obviously a critical moment in the song for Amos, as she is attempting to give voice to this murder victim. As the victim is thrown into the water, Amos gives a realistic gasp. From this point on, her voice gradually fades away and her breathing becomes more difficult until the last phrase (“Just the two of us”) is nothing but a whisper.
[56] In addition to these lyrical and vocal strategies, Amos creates drastic changes to the Eminem original in the domains of texture, form, tempo, rhythm, and phrase structure. In her manipulation of these elements, we are distinctly aware of her Voice as a Participant in the Musical Codes, Conventions and Styles, as well as a Member of the Instrumental Ensemble.
[57] Amos’s version is arranged for strings and piano, creating a dark and ominous backdrop for the voice, which is forward in the mix and highly compressed. The texture is unique in its wash of strings in interaction with this spoken, sometimes whispered, voice. The waves of sound in the strings are repetitive, yet irregular, creating a musical analogue for the water that is the ultimate destination for the victim’s body.
[58] The form of Amos’s version is abbreviated as she cuts the first 36 seconds of sound effects and omits the final statement of the chorus. Despite the abbreviated form, Amos’s version of the song is still longer. The total length of her version is 35 seconds longer. The difference in length can be attributed to the speed of the lyric delivery—Amos’s tempo is much slower than Eminem’s.
[59] Amos’s rhythmic presentation differs considerably from that of the original song. Like Eminem, she uses a repeated rhythmic pattern as a backdrop, but only for the introduction and chorus, whereas Eminem carried one throughout. During the verses, Amos’s version features a string line consisting of running sixteenth notes. These sixteenth notes are then taken over by the percussion in the chorus. In the third verse, a military drum is added to the texture, contributing to the intensity of the music, as it heads toward the lyrical climax of the song, when the body is dumped.
[60] The phrasing in Amos’s version is largely determined by a repeated pattern played by the strings, which is manipulated to create unusual phrase timing. The bass line is divided into three phrases, each of which begins with a descending g-minor arpeggiation pattern, but then ends with a different pitch (A, E, then C). This 3-phrase pattern then repeats three times in each verse. Amos thus disrupts the regularity and symmetry of Eminem’s 4 by 4 phrase patterning. Eminem’s text delivery is constructed to fit with these 4-bar phrases but Amos manipulates her delivery of the text to offset the lines with the beginnings and ends of phrases.
[61] The beginning of verse 2 is the first moment of phrase agreement between the strings and the voice. This synchronicity creates a momentary sense of regularity in the structuring of the song, but is not permitted to last. Amos disrupts the flow when she emphasizes the words “real, real, mad” to stretch out her line delivery. The phrases then remain out of sync for the remainder of the verse. Verse 3 begins with the voice and string phrases coinciding, but the phrasing is once again disrupted, this time signaling the textual climax of the song. When the body is thrown into the water, the line “one, two, three” is delivered over a longer span of time, suspending the phrase timing. As in verse 2, the vocal and string phrases then remain asynchronous for the remainder of the verse.
[62] An interesting moment of time expansion occurs at the end of the second verse. The repeated line “Me and my daughter” receives two full statements of the accompanying string phrase, followed by a long pause. This disruption draws attention to the lyrics, which I interpreted earlier as a moment of painful reflection for the murder victim.
[63] Amos’s desire to give voice to the victim is most clearly expressed in the chorus, the only part of the song that is given melodic phrasing for Amos to sing. It is also significant that the persistent, repeated string motive of the verse is replaced by a more melodic theme. These melodic elements create a considerable change in affect for the chorus, in which the mother laments the loss of her life with her daughter. Here I would argue that the chorus text “Just the two of us” is suggestive of the mother and daughter pairing as well as father and daughter. All of these elements contribute to a reading of the chorus as the mother’s expression of sorrow.
[64] The interpretive concept of intertextuality is useful as we reflect on the song lyrics and music of “‘97 Bonnie and Clyde.” As with Eminem’s original, Amos’s version invokes multiple voices within this song text: that of victim, child, perpetrator of violence, as well as social commentator. In addition, since this text was created in response to Eminem’s original, his voice as social commentator is also inherently present—as Amos adopts her own voice, as she Signifies on this text, we carry the cultural and musical memories of his voice as it was heard in the original song. As we remember his version, we hear in Amos’s version musical idioms and stylistic references that jog other cultural and musical memories. Although a singer-songwriter who usually accompanies herself at the piano, she crosses over, by means of the string ostinato, into a musical style with classical and possibly minimalist stylistic connotations. As she lifts the story out of its original rap context, she does not simply situate it within her own musical style context, but rather transcends the specificity of those stylistic connotations through the reference to a classical or minimalist genre.
#### Conclusions
[65] The original songs that we have analyzed here explore themes of violence and cultural trauma. These songs are performed by artists whose unique fingerprints are clearly stamped on their artistic statements, who convey powerful and “authentic” subjective positions, and who succeed in transmitting messages that evoke cultural memories. Amos binds these performances together, as the artist who “appropriates” such material, adapting it to her own subjective perspectives. Amos communicates a strong commitment to the musical expression and social messages of the original artists, yet her musical presentations are not merely historical tributes. Rather, she Signifies on the earlier texts, appropriating them to develop new perspectives, raising her own authentic voice to comment on gender, race and violence.
Lori Burns
The University of Ottawa
Department of Music
50 University Private
Ottawa, Ontario K1N 6N5
laburns@uottawa.ca
Alyssa Woods
The University of Michigan
School of Music
1100 Baits Drive
University of Michigan
Ann Arbor, MI 48109-2085
alywoods@umich.edu
### Footnotes
* A version of this paper was presented at the Society for Music Theory conference in Madison, Wisconsin, November 2003. A version of the section on Eminem’s “‘97 Bonnie and Clyde,” was presented at the conference Body Talk/Parler du corps, held at the University of Ottawa, November 2002.
A version of this paper was presented at the Society for Music Theory conference in Madison, Wisconsin, November 2003. A version of the section on Eminem’s “‘97 Bonnie and Clyde,” was presented at the conference Body Talk/Parler du corps, held at the University of Ottawa, November 2002.
1. See Mark Butler “Taking it Seriously: Intertextuality and Authenticity in Two Covers by the Pet Shop Boys,” Popular Music 22/1 (2003), 1–19; Johan Fornäs, “Listen to Your Voice! Authenticity and Reflexivity in Rock, Rap, and Techno Music,” in New Formations 24 (Winter, 1994), 155–173; Lawrence Grossberg, “The Media Economy of Rock Culture: Cinema, Postmodernity and Authenticity,” in Sound and Vision: The Music Video Reader, ed. Simon Frith, Andrew Goodwin, and Lawrence Grossberg (New York: Routledge, 1993), 185–209; and Allan Moore, “Authenticity as Authentication,” Popular Music 21/2 (2002), 209–223.
2. Moore (ibid.) uses the following terms to categorize these three perspectives: “first-person authenticity” is an original, unmediated expression (Moore, 213); “third-person authenticity” involves an appropriation of original material (215); and “second-person authenticity” takes into account the listener and his or her life values (220).
3. Richard Middleton, “Work-in(g)-Practice: Configurations of the Popular Music Intertext,” in The Musical Work: Reality or Invention, ed. Michael Talbot (Liverpool, Liverpool University Press, 2000), 61.
4. Ibid., 66.
5. Ibid., 67.
6. In The Power of Black Music (New York: Oxford University Press, 1995), Samuel Floyd dedicates a chapter to the subject of Signifyin(g), reviewing the origins of the term, and contextualizing the rhetorical principals for musical interpretation. Floyd credits Henry Louis Gates’s The Signifying Monkey: A Theory of African American Literary Criticism (New York: Oxford University Press, 1988) as the work that introduced this critical framework.
7. Gates, 52.
8. Ibid., 54.
9. I am stating the possibilities for narrative perspective here in rather basic terms, not really doing justice to the topic. For a more careful application of narrative theory to popular music analysis, please see Serge Lacasse, “Towards a Poetics of Phonography: The Narrative Function of the Vocal Scenography in Alanis Morissette’s ‘Front Row’ (1998),” Musurgia IX/2 (2002), and Lori Burns “Feminist Vocal Authority: Musical and Narrative Expressive Strategies in Alternative Female Rock Artists (1993–95),” in New Approaches to the Analysis of Pop and Rock Music, edited by John Covach and Mark Spicer (University of Michigan Press, forthcoming, 2006).
10. John Hammond, quoted in David Margolick, Strange Fruit: Billie Holiday, Café Society, and an Early Cry for Civil Rights (Philadelphia: Running Press, 2000), 78.
11. Billie Holiday, “Strange Fruit,” Frankie Newton, trumpet; Sonny White, piano (April 1939). Commodore 526.
12. Stuart Nicholson, Billie Holiday (Boston: Northeastern University Press, 1995), 114.
13. Ibid., 114.
14. Will Friedwald, Jazz Singing (New York: Da Capo Press, 1992), 131–32.
15. Floyd, 8.
16. Guthrie Ramsey, Race Music: Black Cultures from Bebop to Hip-Hop (Berkley and Los Angeles: University of California Press), 32–33.
17. Marianne Hirsch and Valerie Smith, “Gender and Cultural Memory,” Special Issue of Signs 28/1 (Autumn 2002), 5. On the subject of how history is transmitted, the authors refer the reader to Paul Connerton, How Societies Remember (New York: Cambridge University Press, 1989), 39; and James Young, “Toward a Received History of the Holocaust,” History and Theory 36/4 (1997), 41.
18. Hirsch and Smith, 9. In this regard, the authors refer us to Richard Schechner, Between Theater and Anthropology (Philadelphia: University of Pennsylvania Press, 1985).
19. The form of the original melody in Example 1 is based upon the published sheet music (words and music by Lewis Allan, Edward B. Marks Music Company, 1940). This score is our only source for the original composed version of the song. We can assert that the final published version of the song offers a form of blueprint for the song, a normative version that holds considerable value for any analyst. The “authenticity” of the sheet music is another research question. We do know that Abel Meeropol (Lewis Allan) worked with Holiday on the song in 1939, and we can assume that Holiday’s development of the song had some influence on the final publication. However, it is also the case that the sheet music version does not reflect the melodic and rhythmic presentation of the Holiday recording.
20. Toni Morrison, “The Site of Memory,” Inventing the Truth ed. William Zinsser (Boston: Houghton-Mifflin, 1987), 106.
21. Ibid., 110.
22. “Strange Fruit” appeared on a UK release with “Cornflake Girl,” “A Case of You,” “If 6 was 9,” Limited Edition CD (January 17, 1994), East West A7281.
23. Eminem, The Slim Shady LP, Aftermath Entertainment/Interscope Records (1999). CD 90287.
24. Karen Williams. Eminem: Life Story. Bauer Publishing Company, November 2002, 11.
25. Grover Washington Jr., Winelight (Elektra/Asylum, 1980). Another rap artist, Will Smith, also used the chorus of “Just the Two of Us” to record a song about his relationship with his son on the album Big Willie Style (1997). The song was also used in the movie Austin Powers: The Spy Who Shagged Me (1999) in a scene featuring Dr. Evil and his cloned son Mini-Me.
26. For accounts and critiques of the Bonnie and Clyde story, see E.R. Milner, The Lives and Times of Bonnie and Clyde (Carbondale and Edwardsville: Southern Illinois University Press, 1996), and Phillip W. Steele and Marie Barrow Scoma, The Family Story of Bonnie and Clyde (Gretna: Penguin Publishing Company, 2000).
27. Tori Amos, Strange Little Girls. Atlantic Recording Corporation, 2001. CD 83486.
28. Tori Amos performs each song on the album Strange Little Girls from the perspective of a different female character; these characters are identified on the promotional album liner photos through photos of Amos herself adopting different dress codes and styles Novelist Neil Gaiman wrote twelve stories that serve as mini biographies for the characters. The Neil Gaiman stories were provided in the Strange Little Girls tour program. These stories and the accompanying photos can be found at: Neil Gaiman, Tori Amos: Strange Little Girls, 2001. Available at www.strange-little-girls.com/stories.html.
29. Tori Amos, quoted by Darren Davis, “Tori Amos Covers Eminem And Slayer On New Album,” Launch (July 3, 2001), 1. Available at http://launch.yahoo.com/read/news.asp?contentID=200809.
30. Tori Amos, interviewed by Steve Hochman, “Tori Amos Offers a Woman’s-Eye View of Songs by Men ,” Los Angeles Times (July 1, 2001). Available at http://www.yessaid.com/interviews/01-07-01LATimes.html.
31. Tori Amos, reviewed and interviewed by Steffie Nelson, “Tori Amos: Personality Crisis,” (October 21 2001). Available at http://www.mtv.com/bands/a/amos_tori/News_Feature100601/index.jhtml.
32. Tori Amos, quoted by Teri van Horn in “Tori Amos Says Eminem’s Fictional Dead Wife Spoke to Her,” MTV News Archive (Sept. 28, 2001). Available at http://www.mtv.com/news/articles/1449422/20010928/story.jhtml.
33. Steffie Nelson, “Tori Amos: Personality Crisis.”
See Mark Butler “Taking it Seriously: Intertextuality and Authenticity in Two Covers by the Pet Shop Boys,” Popular Music 22/1 (2003), 1–19; Johan Fornäs, “Listen to Your Voice! Authenticity and Reflexivity in Rock, Rap, and Techno Music,” in New Formations 24 (Winter, 1994), 155–173; Lawrence Grossberg, “The Media Economy of Rock Culture: Cinema, Postmodernity and Authenticity,” in Sound and Vision: The Music Video Reader, ed. Simon Frith, Andrew Goodwin, and Lawrence Grossberg (New York: Routledge, 1993), 185–209; and Allan Moore, “Authenticity as Authentication,” Popular Music 21/2 (2002), 209–223.
Moore (ibid.) uses the following terms to categorize these three perspectives: “first-person authenticity” is an original, unmediated expression (Moore, 213); “third-person authenticity” involves an appropriation of original material (215); and “second-person authenticity” takes into account the listener and his or her life values (220).
Richard Middleton, “Work-in(g)-Practice: Configurations of the Popular Music Intertext,” in The Musical Work: Reality or Invention, ed. Michael Talbot (Liverpool, Liverpool University Press, 2000), 61.
Ibid., 66.
Ibid., 67.
In The Power of Black Music (New York: Oxford University Press, 1995), Samuel Floyd dedicates a chapter to the subject of Signifyin(g), reviewing the origins of the term, and contextualizing the rhetorical principals for musical interpretation. Floyd credits Henry Louis Gates’s The Signifying Monkey: A Theory of African American Literary Criticism (New York: Oxford University Press, 1988) as the work that introduced this critical framework.
Gates, 52.
Ibid., 54.
I am stating the possibilities for narrative perspective here in rather basic terms, not really doing justice to the topic. For a more careful application of narrative theory to popular music analysis, please see Serge Lacasse, “Towards a Poetics of Phonography: The Narrative Function of the Vocal Scenography in Alanis Morissette’s ‘Front Row’ (1998),” Musurgia IX/2 (2002), and Lori Burns “Feminist Vocal Authority: Musical and Narrative Expressive Strategies in Alternative Female Rock Artists (1993–95),” in New Approaches to the Analysis of Pop and Rock Music, edited by John Covach and Mark Spicer (University of Michigan Press, forthcoming, 2006).
John Hammond, quoted in David Margolick, Strange Fruit: Billie Holiday, Café Society, and an Early Cry for Civil Rights (Philadelphia: Running Press, 2000), 78.
Billie Holiday, “Strange Fruit,” Frankie Newton, trumpet; Sonny White, piano (April 1939). Commodore 526.
Stuart Nicholson, Billie Holiday (Boston: Northeastern University Press, 1995), 114.
Ibid., 114.
Will Friedwald, Jazz Singing (New York: Da Capo Press, 1992), 131–32.
Floyd, 8.
Guthrie Ramsey, Race Music: Black Cultures from Bebop to Hip-Hop (Berkley and Los Angeles: University of California Press), 32–33.
Marianne Hirsch and Valerie Smith, “Gender and Cultural Memory,” Special Issue of Signs 28/1 (Autumn 2002), 5. On the subject of how history is transmitted, the authors refer the reader to Paul Connerton, How Societies Remember (New York: Cambridge University Press, 1989), 39; and James Young, “Toward a Received History of the Holocaust,” History and Theory 36/4 (1997), 41.
Hirsch and Smith, 9. In this regard, the authors refer us to Richard Schechner, Between Theater and Anthropology (Philadelphia: University of Pennsylvania Press, 1985).
The form of the original melody in Example 1 is based upon the published sheet music (words and music by Lewis Allan, Edward B. Marks Music Company, 1940). This score is our only source for the original composed version of the song. We can assert that the final published version of the song offers a form of blueprint for the song, a normative version that holds considerable value for any analyst. The “authenticity” of the sheet music is another research question. We do know that Abel Meeropol (Lewis Allan) worked with Holiday on the song in 1939, and we can assume that Holiday’s development of the song had some influence on the final publication. However, it is also the case that the sheet music version does not reflect the melodic and rhythmic presentation of the Holiday recording.
Toni Morrison, “The Site of Memory,” Inventing the Truth ed. William Zinsser (Boston: Houghton-Mifflin, 1987), 106.
Ibid., 110.
“Strange Fruit” appeared on a UK release with “Cornflake Girl,” “A Case of You,” “If 6 was 9,” Limited Edition CD (January 17, 1994), East West A7281.
Eminem, The Slim Shady LP, Aftermath Entertainment/Interscope Records (1999). CD 90287.
Karen Williams. Eminem: Life Story. Bauer Publishing Company, November 2002, 11.
Grover Washington Jr., Winelight (Elektra/Asylum, 1980). Another rap artist, Will Smith, also used the chorus of “Just the Two of Us” to record a song about his relationship with his son on the album Big Willie Style (1997). The song was also used in the movie Austin Powers: The Spy Who Shagged Me (1999) in a scene featuring Dr. Evil and his cloned son Mini-Me.
For accounts and critiques of the Bonnie and Clyde story, see E.R. Milner, The Lives and Times of Bonnie and Clyde (Carbondale and Edwardsville: Southern Illinois University Press, 1996), and Phillip W. Steele and Marie Barrow Scoma, The Family Story of Bonnie and Clyde (Gretna: Penguin Publishing Company, 2000).
Tori Amos, Strange Little Girls. Atlantic Recording Corporation, 2001. CD 83486.
Tori Amos performs each song on the album Strange Little Girls from the perspective of a different female character; these characters are identified on the promotional album liner photos through photos of Amos herself adopting different dress codes and styles Novelist Neil Gaiman wrote twelve stories that serve as mini biographies for the characters. The Neil Gaiman stories were provided in the Strange Little Girls tour program. These stories and the accompanying photos can be found at: Neil Gaiman, Tori Amos: Strange Little Girls, 2001. Available at www.strange-little-girls.com/stories.html.
Tori Amos, quoted by Darren Davis, “Tori Amos Covers Eminem And Slayer On New Album,” Launch (July 3, 2001), 1. Available at http://launch.yahoo.com/read/news.asp?contentID=200809.
Tori Amos, interviewed by Steve Hochman, “Tori Amos Offers a Woman’s-Eye View of Songs by Men ,” Los Angeles Times (July 1, 2001). Available at http://www.yessaid.com/interviews/01-07-01LATimes.html.
Tori Amos, reviewed and interviewed by Steffie Nelson, “Tori Amos: Personality Crisis,” (October 21 2001). Available at http://www.mtv.com/bands/a/amos_tori/News_Feature100601/index.jhtml.
Tori Amos, quoted by Teri van Horn in “Tori Amos Says Eminem’s Fictional Dead Wife Spoke to Her,” MTV News Archive (Sept. 28, 2001). Available at http://www.mtv.com/news/articles/1449422/20010928/story.jhtml.
Steffie Nelson, “Tori Amos: Personality Crisis.”
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http://codeofthedamned.com/index.php/Alchemy: | ## Steganography
Send feedback »
A software library provides no value if it does not simplify the task of creating your application. At the very least we would like to show that the library contains all of the tools required to complete the intended goal. Ideally, the library is complete, easy to use, and is efficient. The only way to learn how well the library is designed and implemented is to use it.
Furthermore, it is useful and sometimes necessary to provide an exemplar for others to see how the library is intended to be used. The Steganography sample program included with Alchemy is this exemplar. I chose steganography to demonstrate that Alchemy is much more useful than the serialization of data for networking. In the process of developing this application I discovered some pain-points with the library and added tools to Alchemy to eliminate this pain.
## Steganography
What is steganography?
Steganography is the hiding of messages within plain-sight. This should not be confused with "Stenography," which is the recording of dictation. Steganography can be performed in may ways. Normal words can be given special meaning and included within a message that appears to be mundane. The location of words relative to others in the message can have a significant meaning. The second letter of every other word can be extracted to form the message. The possibilities are endless.
The form of steganography that I have implemented with Alchemy embeds a text message within a bitmap image. This can be achieved by taking advantage of the fact that the low-order bits for the color channels in an image affect the final color much less compared to the high-order bits.
The table below shows a sample for each color channel, with and without the two lower-bits set. The row with binary indicates the values of the four lower-bits for each 8-bit color. For demonstration purposes, the alpha channel is represented with grayscale.
Red Green Blue Alpha FF FC FF FC FF FC FF FC 1111 1100 1111 1100 1111 1100 1111 1100
Compare this to the result if we substitute only the single high-bit for each color channel:
Red Green Blue Alpha 7F FF 7F FF 7F FF 7F FF 0111 1111 0111 1111 0111 1111 0111 1111
The only caveat is the image should have a sufficient amount of entropy, otherwise the noise added by the encoded data may become visible; if not to a human, then most certainly to computer searching for such anomalies. Photographs with a range of gradients are good candidates for this form of steganography.
## Why Use Steganography as a Sample?
Through the development of the base set of features for Alchemy, I focused solely on the serializing of data for network data transfer protocols. However, Alchemy is a flexible serialization library that is not restricted to network communication. Portable file formats also require serialization capabilities similar to the capabilities found in Alchemy. To this end, loading and storing a bitmap from a file is a good serialization task; bitmaps are relatively easy to acquire, and the format is simple enough to be implemented in a small sample program.
I wanted to keep the program simple. Writing a portable network communication program is not simple; especially since Alchemy does not provide functionality directly related to network communication. I also felt that if I were to use a network related exemplar, potential user of Alchemy would assume it can only be used for network related tasks. Moreover, I did not want to add extra support code to the application that would hide or confuse the usage of Alchemy.
## Strategy
In keeping with simplicity, the sample program requires 32-bit bitmaps. For this type of encoding, there are four color channels (Red, Green, Blue, and Alpha) for each pixel, where each channel is one-byte in size. We will encode a one-byte of data within each pixel. To accomplish this, we will assign two-bits of the encoded byte into the two lower-bits of each color channel. This results in a 25% encoding rate within the image.
Consider an example where we combine the orange color 0xFF9915 with the letter i, 0x69:
Channel 1 Channel 2 Channel 3 Channel 4 Input 0xFF 0x99 0x15 0x00 Value 1111 1111 1001 1001 0001 0101 0000 0000 Data 01 10 10 01 Result 1111 1101 1001 1010 0001 0110 0000 0001 Output 0xFD 0x9A 0x16 0x01
This is not a very complex encoding strategy. However, it will allow me to demonstrate the serialization of data for both input and output, as well as the packed-data bit (bit-field) functionality provided by Alchemy.
## Bitmap Format
The bitmap file format has many different definitions. The variety of formats are a result of its inception on IBM's OS/2 platform, migration to Windows, and evolution through the years. Additionally, the format allows for an index 8-bit color table, Run-Length Encoded (RLE) compression, gamma correction, color profiles and many other features.
The sample application simply uses the bitmap format introduced with Windows 3.0. It contains a file header that indicates the file is of type BITMAP, a bitmap information section, and the pixel data. The Alchemy definitions for each section are found below. These definitions provide the fundamental structure for the data; the goal was to provide a table-based definition that looks very similar to the definition of a struct. This declaration is also for generating the majority of the serialization logic for Alchemy:
The bitmap file header is a short constructor that is only 14-bytes large. The first two bytes will contain the letters "BM" to indicate that this is a bitmap. The length of the file, and the offset to the first pixel data are also encoded in this structure:
C++
// ************************************************************* ALCHEMY_STRUCT(bitmap_file_header_t, ALCHEMY_DATUM(uint16_t, type), ALCHEMY_DATUM(uint32_t, length), ALCHEMY_DATUM(uint16_t, reserved_1), ALCHEMY_DATUM(uint16_t, reserved_2), ALCHEMY_DATUM(uint32_t, offset) )
The bitmap information section is 40-bytes of data that defines the dimensions and color-depth of the encoded bitmap:
C++
// ************************************************************* ALCHEMY_STRUCT(bitmap_info_header_t, ALCHEMY_DATUM(uint32_t, size), ALCHEMY_DATUM(int32_t, width), ALCHEMY_DATUM(int32_t, height), ALCHEMY_DATUM(uint16_t, planes), ALCHEMY_DATUM(uint16_t, bit_depth), ALCHEMY_DATUM(uint32_t, compression), ALCHEMY_DATUM(uint32_t, sizeImage), ALCHEMY_DATUM(int32_t, x_pixels_per_meter), ALCHEMY_DATUM(int32_t, y_pixels_per_meter), ALCHEMY_DATUM(uint32_t, color_count), ALCHEMY_DATUM(uint32_t, important_color) )
### Bitmap Information
This is a utility definition to combine the information header and the color data from the buffer for convenience:
C++
// ************************************************************* ALCHEMY_STRUCT(bitmap_info_t, ALCHEMY_DATUM(bitmap_info_header_t, header), ALCHEMY_ALLOC(byte_t, header.sizeImage, pixels) )
### Pixel Definition
This is a convenience structure to access each color-channel independently in a pixel:
C++
// ************************************************************* ALCHEMY_STRUCT(rgba_t, ALCHEMY_DATUM(byte_t, blue), ALCHEMY_DATUM(byte_t, green), ALCHEMY_DATUM(byte_t, red), ALCHEMY_DATUM(byte_t, alpha) )
## Alchemy Declarations
### Storage Buffer
Alchemy supports both static and dynamic memory management for its internal buffers; dynamic allocation is the default. However, the storage policy can easily be changed to a static policy with a new typedef. The definition below shows the static buffer definitions used by the sample program:
C++
namespace detail { typedef Hg::basic_msg hg_file_t; typedef Hg::basic_msg hg_info_t; }
### Alchemy Message
For convenience, we also pre-define a type for the message format type.
C++
typedef Hg::Message< detail::hg_file_t> file_t; typedef Hg::Message< detail::hg_info_t> info_t;
## Bitmap Abstraction
As I mentioned previously, I wanted to keep this sample application as simple as possible. One of the things that I was able to do is encapsulate the bitmap data details into the following Bitmap abstraction. This class provides storage for a loaded bitmap, loads and stores the contents, and provides a generic processing function on each pixel:
C++
class Bitmap { public: bool Load (const std::string &name); bool Store(const std::string &name); void process( std::string &msg, pixel_ftor ftor); private: std::string m_file_name; file_t m_file_header; info_t m_info; };
The processing function takes a function-pointer as an argument that specifies the processing operation to be performed each time the function is called. This is the definition for that function-pointer.
C++
typedef void (*pixel_ftor) ( Hg::rgba_t& pixel, Hg::byte_t& data);
This section shows the implementation for both the Load and Store operations of the bitmap. The implementation uses the Standard C++ Library to open a file, and read or write the contents directly into the Hg::Message type with the stream operators.
C++
// ************************************************************* bool Bitmap::Load (const std::string &name) { m_file_name = name; std::ifstream input(m_file_name, std::ios::binary); if (input.bad()) { return false; } input >> m_file_header; const size_t k_info_len = 0x36ul; if (k_info_len != m_file_header.offset) { return false; } input >> m_info; return true; }
And the implementation for Store:
C++
// ************************************************************ bool Bitmap::Store (const std::string &name) { std::ofstream output(name, std::ios::binary); if (output.bad()) { return false; } output << m_file_header; output << m_info; return true; }
### Process
I mentioned at the beginning that it is important to implement programs that perform real-work with your libraries to verify that your library is easy to use and provides the desired functionality as expected. With my first pass implementation of this program, both of those qualities were true for Alchemy, except the performance was quite slow. The cause turned out to be the load and initialization of every single pixel into my implementation for Hg::packed_bits.
The problem is that the bytes that represent the pixel data are normally read into an array as a bulk operation. Afterwards, the proper address for each pixel is indexed, rather than reading the data into an independent object that represents the pixel. When I recognized this, I came up with the idea for the data_view<T> construct. This allows a large buffer to be loaded as raw memory, and a view of the data can be mapped to any type desired, even a complex data structure such as the rgba_t type that I defined.
The data_view is an object that provides non-owning access to the underlying raw buffer. If this sounds familiar that is because it is very similar to the string_view construct that is slated for C++17. It was shortly after I implemented data_view that discovered that string_view existed. So I was a bit shocked, and delighted when I realized how similar the concepts and implementations are to each other. It was a bit of validation that I had chosen a good path to solve this problem.
I plan to write an entry that describes the data_view in detail at a later time. Until then, if you would like to learn more about the approach, I encourage you to check out its implementation in Alchemy, or the documentation for the string_view object.
The purpose of process is to sequentially execute the supplied operation on a single message byte and source image pixel. This is continued until the entire message has been processed, or there are no more available pixels.
C++
// ************************************************************* void Bitmap::process( std::string &msg, pixel_ftor ftor) { auto t = Hg::make_view(m_info.pixels.get()); auto iter = t.begin(); // Calculate the number of bytes that can be encoded or extracted // from the image and ensure the the message buffer is large enough. size_t length = t.end() - iter; msg.resize(length); for (size_t index = 0; iter != t.end(); ++iter, ++index) { ftor(*iter, (Hg::byte_t&)(msg[index])); } }
## Weave and Extract
These are the two functions that provide the pixel-level operations to encode a message byte into a pixel with the strategy that was previously mentioned. Weave combines the message byte with the supplied pixel, and Extract reconstructs the message byte from the pixel.
I am investigating the possibility of implementing a union-type for Alchemy. If I end up doing this I will most likely revisit this sample and provide an alternative implementation that incorporates the Hg::packed_bits type. This will completely eliminate the manual bit-twiddling logic that is present in both of these functions:
C++
// ************************************************************* void weave_data ( Hg::rgba_t& pixel, Hg::byte_t& data) { using Hg::s_data; s_data value(data); pixel.blue = (pixel.blue & ~k_data_mask) | (value.d0 & k_data_mask); pixel.green = (pixel.green & ~k_data_mask) | (value.d1 & k_data_mask); pixel.red = (pixel.red & ~k_data_mask) | (value.d2 & k_data_mask); pixel.alpha = (pixel.alpha & ~k_data_mask) | (value.d3 & k_data_mask); }
Extract implementation:
C++
// ************************************************************* void extract_data ( Hg::rgba_t& pixel, Hg::byte_t& data) { using Hg::s_data; s_data value; value.d0 = (pixel.blue & k_data_mask); value.d1 = (pixel.green & k_data_mask); value.d2 = (pixel.red & k_data_mask); value.d3 = (pixel.alpha & k_data_mask); data = value; }
## The Main Program
The main program body is straight-forward. Input parameters are parsed to determine if an encode or decode operation should be performed, as well as the names of the files to use.
C++
// ************************************************************* int main(int argc, char* argv[]) { if (!ParseCmdParams(argc, argv)) { PrintHelp(); return 0; } string message; sgraph::Bitmap bmp; bmp.Load(input_file); if (is_encode) { message = ReadFile(msg_file); bmp.process(message, weave_data); bmp.Store(output_file); } else { bmp.process(message, extract_data); WriteFile(output_file, message); } return 0; }
## Results
To demonstrate the behavior of this application I ran sgraph to encode the readme.txt file from its project. Here is the first portion of the file:
========================================================================
CONSOLE APPLICATION : sgraphy Project Overview
========================================================================
AppWizard has created this sgraphy application for you.
This file contains a summary of what you will find in each of the files that
Into this image:
This is the result image:
For comparison, here is a sample screen-capture from a Beyond Compare diff of the two files:
## Summary
I implemented a basic application that performs steganography to demonstrate how to use the serialization features of my library, Alchemy. I chose a unique application like this to make the demonstration application a bit more interesting and to show the library can be used for much more than just serialization of data for network transfer.
## Rvalue References Applied
Send feedback »
A continuation of a series of blog entries that documents the design and implementation process of a library. The library is called, Network Alchemy[^]. Alchemy performs automated data serialization with compile-time reflection. It is written in C++ using template meta-programming.
My previous entry was a condensed overview on rvalue references. I described the differences between value expressions and types. I also summarized as much wisdom as I could collect regarding how to effectively use move semantics and perfect-forwarding. After I completed the essay, I was eager to integrate move semantics for my serialization objects in Alchemy. This entry is a journal of my experience optimizing my library with rvalue references.
Full story »
## Alchemy: PackedBits (BitLists Mk3)
Send feedback »
A continuation of a series of blog entries that documents the design and implementation process of a library. The library is called, Network Alchemy[^]. Alchemy performs low-level data serialization with compile-time reflection. It is written in C++ using template meta-programming.
My second attempt to create a bit-field type was more successful. The size of the container only grew linearly with each sub-field that was added, and the implementation was cleaner. However, I showed an image of what this implementation looked like in the debugger and it was very in convenient. The thing I was concerned with the most was the pitiful performance that was revealed by my benchmark tests.
This entry describes my discoveries and the steps that I took to re-invent the bit-field type in Alchemy for the third time. This is also the current implementation in use by Alchemy, which is about 10% faster than hand-coded collection of packed-bits.
Full story »
## Alchemy: Benchmarks and Optimizations
Send feedback »
A continuation of a series of blog entries that documents the design and implementation process of a library. The library is called, Network Alchemy[^]. Alchemy performs automated data serialization with compile-time reflection. It is written in C++ using template meta-programming.
Benchmark testing and code profiling is a phase that can often be avoided for the majority of development. That is, if you develop wisely. Selecting appropriate data structures and algorithms for the task at hand. Avoiding pre-mature optimization is about not getting caught up on the minute details before you even have a working system. That doesn’t mean to through out good decision making altogether. Well I have reached the point in Alchemy, where I have a feature-set that is rich enough to make this a useful library. This entry chronicles my discoveries for how well Alchemy performs and the steps I have taken to find and improve the areas where improvement has been required.
Full story »
## Alchemy: Array / Vector Serialization
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A continuation of a series of blog entries that documents the design and implementation process of a library. The library is called, Network Alchemy[^]. Alchemy performs low-level data serialization with compile-time reflection. It is written in C++ using template meta-programming.
The alterations required up to this point have been relatively minor to integrate arrays and vectors into Alchemy. That does not mean that the solutions were clean and simple from the beginning. The exercise for integrating the serialization support of these containers was quite challenging. These containers became especially challenging because of the possibilities they created for flexibility with data management
Full story »
## Alchemy: Vectors
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A continuation of a series of blog entries that documents the design and implementation process of a library. The library is called, Network Alchemy[^]. Alchemy performs low-level data serialization with compile-time reflection. It is written in C++ using template meta-programming.
It's time to break some barriers that have existed within Alchemy since its inception, message with fixed sizes. While the storage policy concept that I use with the message buffer allows Alchemy to dynamically allocate memory for messages, the current structure of the library only allows messages whose size is known at compile-time.
There is already so much value in what Alchemy is capable of accomplishing, even with the static size limitation. However, the only way for Alchemy to expand and reach its potential, is to remove this limitation and provide support for dynamically sized messages. This entry will demonstrate the changes that were required to achieve this goal.
Full story »
## Alchemy: Arrays
Send feedback »
A continuation of a series of blog entries that documents the design and implementation process of a library. The library is called, Network Alchemy[^]. Alchemy performs low-level data serialization with compile-time reflection. It is written in C++ using template meta-programming.
Once Alchemy was functional and supported a fundamental set of types, I had other development teams in my department approach me about using Alchemy on their product. Unfortunately, there was one type I had not given any consideration to up to this point, arrays. This group needed the ability to have variable sized messages, where the array payload started at the last byte of the fixed-format message. At that point, I had no clean solution to help deal with that problem.
Full story »
## Alchemy: Proxy Fields
Send feedback »
A continuation of a series of blog entries that documents the design and implementation process of a library. The library is called, Network Alchemy[^]. Alchemy performs low-level data serialization with compile-time reflection. It is written in C++ using template meta-programming.
After I had completed my initial targetted set of features for Alchemy, demonstrated the library to my colleagues, and received the initial round of feedback, I was ready to correct some mistakes. The completion of nested structures in my API was very challenging for many reasons. This required each object to know entirely too much about the other constructs in the system. I was very motivated to find an elegant and effective solution because the next feature I decided to tackle would be very challenging, support for arrays. I turned to Proxies to solve this problem.
Full story »
## Alchemy: Nested Types
Send feedback »
A continuation of a series of blog entries that documents the design and implementation process of a library. The library is called, Network Alchemy[^]. Alchemy performs low-level data serialization with compile-time reflection. It is written in C++ using template meta-programming.
I am almost done describing the first set of features that I was targeting when I set out to create Alchemy. The only remaining feature to be documented is the ability to have nested types. Basically, structs within structs. This entry describes the approach that I took as well as some of the challenges that I had to conquer in order to create a usable solution.
Full story »
## Alchemy: BitLists Mk2
Send feedback »
A continuation of a series of blog entries that documents the design and implementation process of a library. The library is called, Network Alchemy[^]. Alchemy performs low-level data serialization with compile-time reflection. It is written in C++ using template meta-programming.
With my first attempt at creating Alchemy, I created an object that emulated the behavior of bit-fields, yet still resulted in a packed-bit format that was ABI compatible for portable wire transfer protocols. You can read about my design and development experiences regarding the first attempt here Alchemy: BitLists Mk1[^].
My first attempt truly was the epitome of Make it work. Because I didn't even know if what I was attempting was possible. After I released it, I quickly received feedback regarding defects, additional feature requests, and even reported problems with it's poor performance. This pass represents the Make it right phase.
Full story »
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https://learn.saylor.org/mod/url/view.php?id=11855 | ## Understanding the Ethics of Public Speaking
Read this chapter, which discusses ethical communication. Attempt the exercises at the end of each section, as well as the chapter exercises. | {"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": 0.8006273508071899, "perplexity": 1113.6719707618918}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320301341.12/warc/CC-MAIN-20220119125003-20220119155003-00686.warc.gz"} |
https://www.physicsforums.com/threads/moment-of-inertia-help-needed.15105/ | # Moment of inertia help needed
1. Feb 24, 2004
### ilikephysics
I'm really having problems understanding how to do moment of inertia. Can someone please help me with this problem? Explain it to me please. Thanks so much.
Question:
Find the moment of inertia of a box of sides a, b, and c, mass M, and uniform density for rotations about an axis passing through its center and perpendicular to the two faces of sides a and b.
Find the moment of inertia for rotations about an axis passing along one edge of length c.
2. Feb 25, 2004
### ilikephysics
3. Feb 25, 2004
### paul11273
I think this question sounds a little vague. Can you clairfy it a little better?
Also, show some work that you have done so we can see where you are having trouble. That will also help us (atleast me) visualize what is going on.
4. Feb 25, 2004
### HallsofIvy
Staff Emeritus
The "moment of inertia" of an object around an axis of rotation is the integral of (distance of each point from the axis of rotation)2 times the density. The integral is taken over the volume of the object. The fact that this is not circularly symmetric makes it a little harder. Take the (uniform) density to be the constant δ Set up a coordinate system so that center of one "a by b" face is at (0,0,0) and the center of the other face is at (0,0,c). Then the distance from a point (x,y,z) to the nearest point on the axis of rotation, (0, 0, z), is &radic:(x2+ y2and its square is, of course, simply x2+y2. The moment of inertia is:
$$\int_{x=-a/2}^{a/2}\int_{y=-b/2}^{b/2}\int_{z=0}^{c} \delta(x^2+ y^2)dzdydx$$ | {"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": 0.8795623183250427, "perplexity": 398.06642455557954}, "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-2016-44/segments/1476988719286.6/warc/CC-MAIN-20161020183839-00561-ip-10-171-6-4.ec2.internal.warc.gz"} |
http://arminstraub.com/talk/secantseries-halifax | arminstraub.com
# Talk: Trigonometric Dirichlet series and Eichler integrals (Dalhousie)
Trigonometric Dirichlet series and Eichler integrals (Dalhousie)
Date: 2014/10/20
Occasion: Number Theory and Experimental Mathematics Day
Place: Dalhousie University
## Abstract
This talk is motivated by the secant Dirichlet series $$\psi_s(\tau) = \sum_{n = 1}^{\infty} \frac{\sec(\pi n \tau)}{n^s}$$, recently introduced and studied by Lalín, Rodrigue and Rogers as a variation of results of Ramanujan. We review some of its properties, which include a modular functional equation when $$s$$ is even, and demonstrate that the values $$\psi_{2 m}(\sqrt{r})$$, with $$r > 0$$ rational, are rational multiples of $$\pi^{2 m}$$. These properties are then put into the context of Eichler integrals of Eisenstein series of higher level. In particular, we determine the period polynomials of such Eichler integrals and indicate that they appear to give rise to unimodular polynomials, an observation which complements recent results by Conrey, Farmer and Imamoglu as well as El-Guindy and Raji on zeros of period polynomials of Hecke eigenforms in the case of level $$1$$. This talk is based on joint work with Bruce C. Berndt. | {"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": 0.954698920249939, "perplexity": 632.0875982851727}, "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-2017-17/segments/1492917118740.31/warc/CC-MAIN-20170423031158-00266-ip-10-145-167-34.ec2.internal.warc.gz"} |
http://stats.stackexchange.com/questions/45401/how-to-validate-diagnose-a-gamma-glm-in-r | # How to validate & diagnose a gamma GLM in R?
I am fitting a generalized linear model in R with the log link and I need to validate and diagnose my model. I have never worked with the GLM in the past.
• Is there an article or any references I can look for that would help me learn how to diagnose the model?
• Does anyone have any tips for me on how to do this or even just how to get started?
• What is the difference between the deviance and $r^2$?
• Can we calculate the SS error in the GLM?
(The best way for me to understand is to give formulas and explain what they are used for.)
-
Just out of curiosity, why are you using gamma? (It's a less frequently used model.) Can you say a little about your situation, data, and goals? Also, is there something specific that you are worried about (do you think there may be a certain problem w/ your model), or are you just wanting to do your due diligence? – gung Dec 15 '12 at 16:55
Faraway's Extending the linear model (...) has some GLM diagnostics in 6.4 (page 135). – Roman Luštrik Dec 16 '12 at 10:00
-Look at Chapter 6 or Section 6.3.4 in the book "Statistical Models in S" by Chambers and Hastie. Also you many want to check the package boot and function "glm.diag.plots" (Diagnostics plots for generalized linear models). Here are some code with gamma family and the plots from the help file.
library(boot)
data(leuk, package = "MASS")
leuk.mod <- glm(time ~ ag-1+log10(wbc), family = Gamma(log), data = leuk)
leuk.diag <- glm.diag(leuk.mod)
glm.diag.plots(leuk.mod, leuk.diag)
These plots are (upper left: residual vs linear predictor, upper right: normal scores plots of standardized deviance residuals, Lower left: approximate Cook statistics against leverage, Lower right: the plot of Cook statistic)
- See Introduction to Generalized Linear Models
- Have a look at the above reference, pages 42 and 44 to see the difference of deviance and $r^2$.
- The following code shows how to find SSE (but normally you don't need it!)
#Create a data set
counts <- c(18,17,15,20,10,20,25,13,12)
outcome <- gl(3,1,9)
treatment <- gl(3,3) | {"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": 0.5529171824455261, "perplexity": 1388.6177472297522}, "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-2015-48/segments/1448398468971.92/warc/CC-MAIN-20151124205428-00148-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://periodictable.readthedocs.io/en/latest/guide/formula_grammar.html | $$\renewcommand\AA{\text{Å}}$$
Chemical Composition¶
Some properties are available for groups of elements. Groups are specified as a chemical formula string and either density or cell volume for the crystal structure. While it does not provide any information about molecular structure, a formula does provide complete control over chemical composition.
A formula string is translated into a formula using periodictable.formulas.formula():
• Formula strings consist of counts and atoms, where individual atoms are represented by periodic table symbol. The atoms are case sensitive, so “CO” is different from “Co”. Here is an example of calcium carbonate:
>>> from periodictable import formula
>>> print(formula("CaCO3"))
CaCO3
• Formulas can contain multiple groups separated by space or plus or by using parentheses. Whole groups can have a repeat count. The following are equivalent definitions of hydrated calcium carbonate:
>>> print(formula("CaCO3+6H2O"))
CaCO3(H2O)6
>>> print(formula("CaCO3 6H2O"))
CaCO3(H2O)6
>>> print(formula("CaCO3(H2O)6"))
CaCO3(H2O)6
• Parentheses can nest, e.g., in polyethylene glycol:
>>> print(formula("HO ((CH2)2O)6 H"))
HO((CH2)2O)6H
• Isotopes are represented by index, such as O[18] = 18O:
>>> print(formula("CaCO[18]3+6H2O"))
CaCO[18]3(H2O)6
• Ions are represented by charge, such as O{2-} = O2-:
>>> print(formula("P{5+}O{2-}4"))
P{5+}O{2-}4
If charge is +/- 1 then the number is optional:
>>> print(formula("Na{+}Cl{1-}"))
Na{+}Cl{-}
When specifying both charge and isotope, isotope comes first:
>>> print(formula("Fe[56]{2+}"))
Fe[56]{2+}
Even though the charge is on the individual atoms, the entire formula has a charge:
>>> print(formula("P{5+}O{2-}4").charge)
-3
• Counts can be integer or decimal:
>>> print(formula("CaCO3+(3HO1.5)2"))
CaCO3((HO1.5)3)2
• Formula density can be specified using the special ‘@’ tag:
>>> print(formula("NaCl@2.16").density)
2.16
Density gives the isotopic density of the compound, so for example, D2O could be specified using:
>>> print("%.3f"%formula("D2O@1.112").density)
1.112
It can also be specified using the natural density of the compound, assuming the isotopes substitution does not change the unit cell volume:
>>> print("%.3f"%formula("D2O@1n").density)
1.112
Density applies to the entire formula, so for example a D2O-H2O 2:1 mixture (not by mass or by volume) would be:
>>> print("%.3f"%formula("2D2O + H2O@1n").density)
1.074
• Mass fractions use %wt, with the final portion adding to 100%:
>>> print(formula("10%wt Fe // 15% Co // Ni"))
FeCo1.4214Ni7.13602
Only the first item needs to specify that it is a mass fraction, and the remainder can use a bare %.
• Volume fractions use %vol, with the final portion adding to 100%:
>>> print(formula("10%vol Fe // Ni"))
FeNi9.68121
Only the first item needs to specify that it is a volume fraction, and the remainder can use a bare %.
Volume fraction mixing is only possible if the densities are known for the individual components, which will require the formula density tag if the component is not an element. A density estimate is given for the mixture but in general it will not be correct, and should be set explicitly for the resulting compound.
• Specific mass can be giving with count follwed by mass units:
>>> print(formula("5g NaCl // 50mL H2O@1"))
NaCl(H2O)32.4407
Density will be required for materials given by volume. Mass will be stored in the total_mass attribute of the resulting formula.
• Multilayers can be specified by thickness:
>>> print(formula("1 um Si // 5 nm Cr // 10 nm Au"))
Si119.99CrAu1.41722
Density will be required for each layer. Thickness will be stored in the total_thickness attribute of the resulting formula. Thickness can be converted to total_volume by multiplying by cross section, and to total_mass by multiplying that by density.
• Mixtures can nest. The following is a 10% salt solution by weight mixed 20:80 by volume with D2O:
>>> print(formula("20%vol (10%wt NaCl@2.16 // H2O@1) // D2O@1n"))
NaCl(H2O)29.1966(D2O)122.794
• Empty formulas are supported, e.g., for air or vacuum:
>>> print(formula())
<BLANKLINE>
>>> formula()
formula('')
The grammar used for parsing formula strings is the following:
formula :: compound | mixture | nothing
mixture :: quantity | percentage
quantity :: count unit part ('//' count unit part)*
percentage :: count '%wt|%vol' part ('//' count '%' part)* '//' part
part :: compound | '(' mixture ')'
compound :: group (separator group)* density?
group :: count element+ | '(' formula ')' count
element :: symbol isotope? ion? count?
symbol :: [A-Z][a-z]*
isotope :: '[' number ']'
ion :: '{' number? [+-] '}'
density :: '@' count
count :: number | fraction
number :: [1-9][0-9]*
fraction :: ([1-9][0-9]* | 0)? '.' [0-9]*
separator :: space? '+'? space?
unit :: mass | volume | length
mass :: 'kg' | 'g' | 'mg' | 'ug' | 'ng'
volume :: 'L' | 'mL' | 'uL' | 'nL'
length :: 'cm' | 'mm' | 'um' | 'nm'
Formulas can also be constructed from atoms or other formulas:
• A simple formula can be created from a bare atom:
>>> from periodictable import Ca, C, O, H
>>> print(formula(Ca))
Ca
• More complex structures will require a sequences of counts and fragments. The fragment itself can be a structure:
>>> print(formula( [ (1,Ca), (1,C), (3,O), (6,[(2,H),(1,O)]) ] ))
CaCO3(H2O)6
• Structures can also be built with simple formula math:
>>> print(formula("CaCO3") + 6*formula("H2O"))
CaCO3(H2O)6
• Formulas can be easily cloned:
>>> print(formula( formula("CaCO3+6H2O")))
CaCO3(H2O)6
Density¶
Density can be specified directly when the formula is created, or updated within a formula. For isotope specific formulas, the density can be given either as the density of the formula using naturally occurring abundance if the unit cell is approximately the same, or using the density specific to those isotopes used.
This makes heavy water density easily specified as:
>>> D2O = formula('D2O',natural_density=1)
>>> print("%s %.4g"%(D2O,D2O.density))
D2O 1.112
Density can also be estimated from the volume of the unit cell, either by using the covalent radii of the constituent atoms and assuming some packing factor, or by knowing the lattice parameters of the crystal which makes up the material. Standard packing factors for hcp, fcc, bcc, cubic and diamond on uniform spheres can be used if the components are of about the same size. The formula should specify the number of atoms in the unit cell, which is 1 for cubic, 2 for bcc and 4 for fcc. Be sure to use the molecular mass (M.molecular_mass in g) rather than the molar mass (M.mass in u = g/mol) in your calculations.
Because the packing fraction method relies on the covalent radius estimate it is not very accurate:
>>> from periodictable import elements, formula
>>> Fe = formula("2Fe") # bcc lattice has 2 atoms per unit cell
>>> Fe.density = Fe.molecular_mass/Fe.volume('bcc')
>>> print("%.3g"%Fe.density)
6.55
>>> print("%.3g"%elements.Fe.density)
7.87
Using lattice parameters the results are much better:
>>> Fe.density = Fe.molecular_mass/Fe.volume(a=2.8664)
>>> print("%.3g"%Fe.density)
7.88
>>> print("%.3g"%elements.Fe.density)
7.87
Mixtures¶
Mixtures can be created by weight or volume ratios, with the density of the result computed from the density of the materials. For example, the following is a 2:1 mixture of water and heavy water:
>>> from periodictable import formula, mix_by_volume, mix_by_weight
>>> H2O = formula('H2O',natural_density=1)
>>> D2O = formula('D2O',natural_density=1)
>>> mix = mix_by_volume(H2O,2,D2O,1)
>>> print("%s %.4g"%(mix,mix.density))
(H2O)2D2O 1.037
Note that this is different from a 2:1 mixture by weight:
>>> mix = mix_by_weight(H2O,2,D2O,1)
>>> print("%s %.4g"%(mix,mix.density))
(H2O)2.2234D2O 1.035
Except in the simplest of cases, the density of the mixture cannot be computed from the densities of the components, and the resulting density should be set explicitly.
Derived values¶
Once a formula has been created, it can be used for summary calculations. The following is an example of hydrated quartz, which shows how to compute molar mass and neutron/xray scattering length density:
>>> import periodictable
>>> SiO2 = periodictable.formula('SiO2')
>>> hydrated = SiO2 + periodictable.formula('3H2O')
>>> print('%s mass %s'%(hydrated,hydrated.mass))
SiO2(H2O)3 mass 114.13014
>>> rho,mu,inc = periodictable.neutron_sld('SiO2+3H2O',density=1.5,wavelength=4.75)
>>> print('%s neutron sld %.3g'%(hydrated,rho))
SiO2(H2O)3 neutron sld 0.849
>>> rho,mu = periodictable.xray_sld(hydrated,density=1.5,
... wavelength=periodictable.Cu.K_alpha)
>>> print('%s X-ray sld %.3g'%(hydrated,rho))
SiO2(H2O)3 X-ray sld 13.5
Biomolecules¶
The periodictable.fasta module can be used to load and manage bio molecules. These can be used to compute molecular weights, approximate volumes and scattering for various lipids and proteins. In addition it supports labile hydrogen calculations, allowing you to compute the neutron scattering length density of the molecule in the presence of D2O as a solvent, assuming all labile hydrogens are substituted. | {"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": 0.8272197246551514, "perplexity": 5557.13766484242}, "config": {"markdown_headings": false, "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-2021-31/segments/1627046154408.7/warc/CC-MAIN-20210802234539-20210803024539-00646.warc.gz"} |
http://aux.planetmath.org/topicsinalgebraictopology | # topics in algebraic topology
## Primary tabs
Keywords:
homology and cohomology theory, fundamental functor, fundamental groupoid functor, groupoid category, algebroid category, crossed complexes, complex modules, homology groups and groupoids. homotopy theory, groupoids, categorical algebra, topological categ
Synonym:
category theory, algebraic geometry, topology and groupoids
Type of Math Object:
Topic
Major Section:
Reference | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 8, "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": 0.8902007937431335, "perplexity": 24960.495928666936}, "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-2017-39/segments/1505818695066.99/warc/CC-MAIN-20170926051558-20170926071558-00650.warc.gz"} |
https://projecteuclid.org/search_result?type=index&q.a.author=H.M.%20Srivastava | ## Keyword »
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### A class of Frobenius-type Eulerian polynomials
Srivastava, H.M., Boutiche, M.A., and Rahmani, M.
Rocky Mountain Journal of Mathematics Volume 48, Number 3 (2018), 1003-1013.
Journal article
### Advances on Integrodifferential Equations and Transforms
Srivastava, H. M., Yang, Xiao-Jun, Baleanu, Dumitru, Nieto, Juan J., and Hristov, Jordan
Abstract and Applied Analysis Volume 2015, Special Issue, (2015).
Journal article
### Corrigendum to “Krasnosel’skii Type Hybrid Fixed Point Theorems and Their Applications to Fractional Integral Equations”
Srivastava, H. M., Bedre, Sachin V., Khairnar, S. M., and Desale, B. S.
Abstract and Applied Analysis Volume 2015, Special Issue, (2015).
Journal article
### Independent Component Analysis Based on Information Bottleneck
Ke, Qiao, Zhang, Jiangshe, Srivastava, H. M., Wei, Wei, and Chen, Guang-Sheng
Abstract and Applied Analysis Volume 2015, (2015).
Journal article
### $q$-Extension of a Multivariable and Multiparameter Generalization of the Gottlieb Polynomials in Several Variables
CHOI, Junesang and SRIVASTAVA, H. M.
Tokyo Journal of Mathematics Volume 37, Number 1 (June 2014), 111-125.
Journal article
### Local Fractional Sumudu Transform with Application to IVPs on Cantor Sets
Srivastava, H. M., Golmankhaneh, Alireza Khalili, Baleanu, Dumitru, and Yang, Xiao-Jun
Abstract and Applied Analysis Volume 2014, (2014).
Journal article
### A Local Fractional Integral Inequality on Fractal Space Analogous to Anderson’s Inequality
Wei, Wei, Srivastava, H. M., Zhang, Yunyi, Wang, Lei, Shen, Peiyi, and Zhang, Jing
Abstract and Applied Analysis Volume 2014, (2014).
Journal article
### Modelling Fractal Waves on Shallow Water Surfaces via Local Fractional Korteweg-de Vries Equation
Yang, Xiao-Jun, Hristov, Jordan, Srivastava, H. M., and Ahmad, Bashir
Abstract and Applied Analysis Volume 2014, (2014).
Journal article
### Krasnosel’skii Type Hybrid Fixed Point Theorems and Their Applications to Fractional Integral Equations
Srivastava, H. M., Bedre, Sachin V., Khairnar, S. M., and Desale, B. S.
Abstract and Applied Analysis Volume 2014, Special Issue, (2014).
Journal article
### Some Further Generalizations of Hölder's Inequality and Related Results on Fractal Space
Chen, Guang-Sheng, Srivastava, H. M., Wang, Pin, and Wei, Wei
Abstract and Applied Analysis Volume 2014, Special Issue, (2014).
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https://indico.cern.ch/event/848732/contributions/4524339/ | # The 16th International Workshop on Tau Lepton Physics (TAU2021) (Virtual Edition)
September 27, 2021 to October 1, 2021
Indiana University
America/Indiana/Indianapolis timezone
## Monte Carlo Event Generator updates with tau pair events at Belle II energies
Sep 29, 2021, 2:45 PM
20m
Virtual (Indiana University)
### Virtual
#### Indiana University
Oral contribution Tau2021 Abstracts
### Speaker
Zbigniew Andrzej Was (Polish Academy of Sciences (PL))
### Description
The Monte Carlo for lepton pair production and tau decays consist
of KKMC for lepton pair production, Tauola for tau lepton decays and
Photos for radiative corrections in decays.
An effort for adaptation of the system for precision data to be collected
at Belle II experiment lead to extension of phase space generation modules
both in Photos and Tauola to enable decays and/or radiative corrections
with emission of additional light lepton pairs. The phase-space and matrix
element parts are separated, that is why extension is useful for
processes where lepton pair is produced through narrow resonances,
like dark photon or dark scalar candidates.
List of tau decays is enriched with multitude of exotic decay channels useful for
new physics searches. The hadronic currents parameterizations of main decay channels
is prepared for basic simulation in the experiment. The basis for future
work on precise fits of hadronic currents including Machine Learning
is retained, but development of necessary software solutions is left for
the forthcoming years.
Programs are now available in stand-alone format or through the Basf2 system of
Belle II software as well.
### Primary authors
Swagato Banerjee (University of Louisville (US)) Zbigniew Andrzej Was (Polish Academy of Sciences (PL)) | {"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": 0.9231334328651428, "perplexity": 16587.384253310924}, "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/1652662545548.56/warc/CC-MAIN-20220522125835-20220522155835-00259.warc.gz"} |
https://dmoj.ca/problem/thogsfortnite2 | Thog's Fortnite 2
View as PDF
Points: 17 (partial)
Time limit: 5.0s
Java 15.0s
Memory limit: 64M
Java 128M
Authors:
Problem types
Allowed languages
Ada, Assembly, Awk, Brain****, C, C#, C++, COBOL, CommonLisp, D, Dart, F#, Forth, Fortran, Go, Groovy, Haskell, Intercal, Java, JS, Kotlin, Lisp, Lua, Nim, ObjC, OCaml, Octave, Pascal, Perl, PHP, Pike, Prolog, Racket, Ruby, Rust, Scala, Scheme, Sed, Swift, TCL, Text, Turing, VB, Zig
Thog is an avid TF2 (Thog's Fortnite 2) player, and he loves unlocking achievements in TF2; it was his love for TF2 that allowed him to discover alternate dimensions, as well as interdimensional portals to travel between them (the Nobel Prize was, unfortunately, not a TF2 achievement). To his delight, every dimension contains a different TF2!
When using a portal, Thog takes minutes to travel from dimension to (note: the reversed connection from to would take minutes). Additionally, the TF2 in dimension has available achievements for Thog to receive, which he can only achieve once: the achievement requires minutes to complete and adds points to Thog's global TF2 account.
Before Thog can start using his new technology, rival TF2 players sabotaged interdimensional travel, forcing Thog to spend at most minutes in the dimension. To make things worse, Thog's mom is coming home in minutes, and she will force Thog to drop what he is doing and write his infamous Yahoo answer.
Help Thog find out the maximum amount of points while still starting and returning to his home (at the dimension) within minutes!
(Note: DMOJ and Thog are not affiliated with Fortnite.)
Input Specification
The first line will contain and , the maximum number of minutes Thog can spend across all dimensions and the number of dimensions (which are labelled from to ).
The next lines will contain , , and , the maximum number of minutes Thog can spend in the dimension, the number of achievements in the dimension, and the number of minutes it takes to travel to the dimension.
Before each next dimension line is printed, the next lines directly after the dimension will contain and , the number of minutes Thog needs to spend to acquire the achievement option and the number of points received from completing the achievement option.
The next lines will contain and , a portal that allows Thog to travel between the dimension and the dimension (0-indexed).
(Important note: the connections will always form a tree from the root dimension 0.)
Output Specification
Output the maximum number of points Thog can achieve in minutes (starting from his home at dimension 0).
Sample Input 1
50 1
70 4 0
20 7
35 5
15 10
4 6
Sample Output 1
23
Explanation for Sample Output 1
The maximum number of points Thog can achieve in 50 minutes is 23: he collects 7 points in 20 minutes, 10 points in 15 minutes, and 6 points in 4 minutes (the other achievement (5 points in 35 minutes) would push him over the maximum time he can spend in his initial dimension and the time he can spend collecting points).
Sample Input 2
100 2
80 4 0
20 10
70 40
80 50
30 20
70 2 1
40 10
20 40
0 1
Sample Output 2
80
Explanation for Sample Output 2
The maximum number of points Thog can achieve in 100 minutes is 80: he collects 40 points in 70 minutes, then he goes to dimension 1 in 1 minute and collects 40 points in 20 minutes, then he returns to his initial dimension in 0 minutes (which is the guaranteed travel time to his home in all test cases).
Sample Input 3
150 3
60 3 0
50 10
30 20
10 30
100 2 5
100 20
30 50
20 1 10
20 20
0 1
0 2
Sample Output 3
120
Explanation for Sample Output 3
The maximum number of points Thog can achieve in 150 minutes is 120: he collects 20 points in 30 minutes and 30 points in 10 minutes from his initial dimension, then he goes to dimension 1 in 5 minutes and collects 50 points in 30 minutes, then he goes to the dimension 2, taking 10 minutes (0 minutes to his home and 10 minutes to the third dimension), and collects 20 points in 20 minutes, then he returns home (from the third dimension) in 0 minutes.
Sample Input 4
100 5
60 3 0
50 10
30 20
40 30
100 2 5
100 20
30 50
20 1 10
20 20
50 2 10
10 50
50 10
100 1 5
50 10
0 1
0 2
1 3
3 4
Sample Output 4
130
Explanation for Sample Output 4
The maximum number of points Thog can achieve in 100 minutes is 130: he collects 30 points in 40 minutes from his initial dimension, then he goes to dimension 1 in 5 minutes and collects 50 points in 30 minutes, then he goes to the third dimension in 10 minutes and collects 50 points in 10 minutes, then he returns home in 5 minutes (back to dimension 1, then dimension 0). | {"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": 0.18998031318187714, "perplexity": 2265.3575439367064}, "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-2021-25/segments/1623487607143.30/warc/CC-MAIN-20210613071347-20210613101347-00603.warc.gz"} |
https://planetmath.org/propertiesofthemultiplicativeorderofaninteger | # properties of the multiplicative order of an integer
###### Definition.
Let $m>1$ be an integer and let $a$ be another integer relatively prime to $m$. The order of $a$ modulo $m$ (or the multiplicative order of $a\mod m$) is the smallest positive integer $n$ such that $a^{n}\equiv 1\mod m$. The order is sometimes denoted by $\operatorname{ord}a$ or $\operatorname{ord}_{m}a$.
###### Proposition.
Let $m$ be a positive integer and suppose that $(a,m)=1$.
1. 1.
$a^{s}\equiv 1\mod m$ if and only if $\operatorname{ord}a$ divides $s$. In particular, $\operatorname{ord}a$ divides $\phi(m)$, where $\phi$ is the Euler phi function.
2. 2.
$a^{s}\equiv a^{t}\mod m$ if and only if $s\equiv t\mod\operatorname{ord}a$.
3. 3.
If $\operatorname{ord}a=d$ then $\displaystyle\operatorname{ord}a^{k}=\frac{d}{\gcd(k,d)}$ for any $k\geq 1$.
4. 4.
If $\operatorname{ord}a=d$ and $e$ is a positive divisor of $d$ then $a^{d/e}$ has exact order $e$.
5. 5.
Suppose $\operatorname{ord}a=h$ and $\operatorname{ord}b=k$ with $\gcd(h,k)=1$. Then $\operatorname{ord}(ab)=hk$.
Title properties of the multiplicative order of an integer PropertiesOfTheMultiplicativeOrderOfAnInteger 2013-03-22 16:20:44 2013-03-22 16:20:44 alozano (2414) alozano (2414) 4 alozano (2414) Theorem msc 11-00 msc 13M05 msc 13-00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 32, "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": 0.9868878722190857, "perplexity": 220.48164885153628}, "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/1570987838289.72/warc/CC-MAIN-20191024012613-20191024040113-00128.warc.gz"} |
https://www.quizover.com/physics-k12/section/case-3-all-friction-states-by-openstax | # 10.6 Induced motion on rough incline plane (Page 3/3)
Page 3 / 3
The components of forces parallel to contact surface (excluding friction) is :
$\begin{array}{l}\sum {F}_{x}=F\mathrm{cos}{30}^{0}-mg\mathrm{sin}{45}^{0}\\ ⇒{F}_{\mathrm{net}}=10\phantom{\rule{2pt}{0ex}}X\phantom{\rule{2pt}{0ex}}\frac{\surd 3}{2}-5\phantom{\rule{2pt}{0ex}}X\phantom{\rule{2pt}{0ex}}10\phantom{\rule{2pt}{0ex}}X\phantom{\rule{2pt}{0ex}}\frac{1}{\surd 2}=-26.7\phantom{\rule{2pt}{0ex}}N\\ ⇒{F}_{\mathrm{net}}<0\end{array}$
It means that the block has tendency to move in the downward direction. The friction, therefore, is in up direction. Now, this completes the force system on the block as shown here.
An additional external force with component parallel to contact up the incline, does not guarantee upward motion. The force of gravity can still be greater than the component of applied additional external force parallel to the contact surface.
Now, our next task is to know the state of friction. To know the state of friction, we need to compare the net force component parallel to contact with maximum static friction. Now, maximum friction force is :
$\begin{array}{l}{F}_{s}={\mu }_{s}N=0.55N\end{array}$
In order to evaluate maximum static friction, we need to know normal force on the block. It is clear from the free body diagram that we can find normal force, "N" by analyzing force in y-direction. As there is no motion in vertical direction, the components in this direction form a balanced force system.
$\begin{array}{l}\sum {F}_{y}=N+F\mathrm{sin}{30}^{0}-mg\mathrm{cos}{45}^{0}=0\\ ⇒N=mg\mathrm{cos}{45}^{0}-F\mathrm{sin}{30}^{0}\\ ⇒N=5x10x\frac{1}{\surd 2}-10x\frac{1}{2}\\ ⇒N=30.36\phantom{\rule{2pt}{0ex}}\mathrm{Newton}\end{array}$
The maximum friction force is :
$\begin{array}{l}⇒{F}_{s}={\mu }_{s}N=0.55x30.36=16.7\phantom{\rule{2pt}{0ex}}N\end{array}$
Thus magnitude of net component parallel to contact surface (26.7) is greater than maximum static friction (16.7 N). Thus, body will slide down and friction will be equal to kinetic friction. Hence,
$\begin{array}{l}⇒{F}_{F}={F}_{k}={\mu }_{k}N=0.53x30.36=16.1\phantom{\rule{2pt}{0ex}}N\end{array}$
## Case 2 : friction equal to maximum static friction
In this case, net force parallel to contact surface is equal to maximum static friction.
$\begin{array}{l}{F}_{F}={F}_{s}={\mu }_{s}N\end{array}$
Problem : A block of 10 kg rests on a rough incline of angle 45°. The block is tied to a horizontal string as shown in the figure. Determine the coefficient of friction between the surfaces, if tension in the string is 50 N. Consider g = 10 $\phantom{\rule{2pt}{0ex}}m/{s}^{2}$ .
Solution : Here, block is stationary. We need to know the motional tendency, had the string were not there.
It is given that the string is taught with a tension of 50 N. Clearly, the block would have moved down had it not been held by the string is taut. The direction of friction, therefore, is upwards. Further, the system is static with taut string. It means that friction has reached maximum static friction. Otherwise, how would have block moved down if not held by the string. Hence, the forces on the block form a balanced force system, including maximum static friction acting upward.
$\begin{array}{l}\sum {F}_{x}=mg\mathrm{sin}{45}^{0}-{\mu }_{s}N-T\mathrm{cos}{45}^{0}=0\\ ⇒{\mu }_{s}N=10x10x\frac{1}{\surd 2}-50x\frac{1}{\surd 2}=50\frac{1}{\surd 2}\end{array}$
and
$\begin{array}{l}\sum {F}_{y}=N-mg\mathrm{cos}{45}^{0}-T\mathrm{sin}{45}^{0}=0\\ ⇒N=10x10x\frac{1}{\surd 2}+50x\frac{1}{\surd 2}=150\frac{1}{\surd 2}\end{array}$
$\begin{array}{l}⇒{\mu }_{s}=\frac{1}{3}\end{array}$
## Case 3 : all friction states
Problem : A block attached with a spring (of spring constant “k”) is placed on a rough horizontal plate. The spring is in un-stretched condition, when plate is horizontal. The plate is, then, raised with one end gradually as shown in the figure. Analyze friction and extension of the spring as angle (θ) increases to 90°.
Solution : In the initial stages, spring does not apply any force as block remains stationary because of friction. The friction acts in up direction as there is no applied external force due to spring. The magnitude of friction is equal to the component of weight along the incline. The friction and extension in the spring (x) for different ranges of angle “θ” are given here. Note that ${\mathrm{tan}}^{-1}\left({\mu }_{s}\right)$ is equal to angle of repose. This is the angle of inclination of the plate with horizon, when block begins to move down.
(i) For $\theta <{\mathrm{tan}}^{-1}\left({\mu }_{s}\right)$
$\begin{array}{l}⇒{f}_{s}=mg\mathrm{sin}\theta \phantom{\rule{2pt}{0ex}};\phantom{\rule{2pt}{0ex}}x=0\end{array}$
(ii) For $\theta ={\mathrm{tan}}^{-1}\left({\mu }_{s}\right)$
Till the angle does not reach the value equal to angle of repose, there is no motion of the block.
$\begin{array}{l}⇒{F}_{s}={\mu }_{s}mg\mathrm{cos}\theta \phantom{\rule{2pt}{0ex}};\phantom{\rule{2pt}{0ex}}x=0\end{array}$
(iii) For $\theta >{\mathrm{tan}}^{-1}\left({\mu }_{s}\right)$
The block starts sliding down. The direction of friction is up along the incline. As the spring stretches, it applies spring force to counteract the net downward force to again bring the block to rest. Before, the block is brought to a stop, the acceleration of the block (“a”) is :
$\begin{array}{l}\sum {F}_{x}=mg\mathrm{cos}\theta -{\mu }_{s}mg\mathrm{cos}\theta -kx=ma\\ ⇒a=\frac{mg\mathrm{cos}\theta -{\mu }_{s}mg\mathrm{cos}\theta -kx}{m}\end{array}$
When the block is brought to a stop, the extension in the string ${x}_{0}$ is obtained as under :
$\begin{array}{l}\sum {F}_{x}=mg\mathrm{cos}\theta -{\mu }_{s}mg\mathrm{cos}\theta -k{x}_{0}=0\\ ⇒k{x}_{0}=mg\mathrm{sin}\theta -{\mu }_{k}mg\mathrm{cos}\theta \\ ⇒{x}_{0}=\frac{mg\mathrm{sin}{\theta }_{0}-{\mu }_{s}mg\mathrm{cos}{\theta }_{0}}{k}\end{array}$
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
can nanotechnology change the direction of the face of the world
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how did you get the value of 2000N.What calculations are needed to arrive at it
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A balloon is released from the ground which rises vertically up with acceleration 1.4m/sec^2.a ball is released from the balloon 20 second after the balloon has left the ground. The maximum height reached by the ball from the ground is
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the body travels the distance of d=( 14+- 0.2)m in t=( 4.0 +- 0.3) s calculate it's velocity with error limit find Percentage error
Explain it ?Fy=?sN?mg=0?N=mg?s | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 19, "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": 0.7632017135620117, "perplexity": 612.1524090813026}, "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-2018-09/segments/1518891812978.31/warc/CC-MAIN-20180220145713-20180220165713-00028.warc.gz"} |
https://forum.support.xerox.com/t5/FreeFlow-Core/Save-Export-to-EPS/m-p/229262 | cancel
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FreeFlow User
## Save/Export to EPS
Jump to solution
Hello all! We use Freeflow to feed many different print devices in our plant. One is a direct UV printer. It has a crappy RIP that will only properly recognize spot colors if it is given an EPS file. So far, we just manually convert the Freeflow output PDF to EPS using Acrobat and sometimes Illustrator.
I would love to automate this conversion, but so far any of the command line or other easily scriptable kits for converting PDFs to EPS rasterize the vector graphics as part of their conversion. Or at least, that's all I have been able to find.
Does anyone have any suggestions? I would love if export to EPS (but retain vectors) were an option for Freeflow, but I can certainly understand why the focus is on a PDF workflow. I'm fine with doing some programming around save destinations and hot folders to make this happen, but can anyone point me in the direction of a good library or scriptable application that would maintain the vector output?
I'm even open to doing this with Acrobat since we pay for it anyway, but I cannot find decent documentation on how to script it.
25 Replies
Highlighted
FreeFlow Production Workflow Moderator
## Re: Save/Export to EPS
Jump to solution
Hi,
Have you tested Ghostscript? https://www.ghostscript.com/download/gsdnld.html. I just did a quick test and it seems like you can retain the vectors with it.
Download and install Ghostscript and import the attached workflow to FreeFlow Core. You need FreeFlow Core version 5.4 to be able to import it. If not, create a workflow and place an External Process in it. The External Process then uses the attached batch file that will convert incoming pdf to eps using Ghostscript and save the eps to folder c:\out\ with the name <filename.pdf>.eps.
"C:\Program Files\gs\gs9.50\bin\gswin64c.exe" -dNOPAUSE -dNOCACHE -dBATCH -sDEVICE=eps2write -sOutputFile=c:\out\%~nx1.eps %1
/Stefan
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FreeFlow User
## Re: Save/Export to EPS
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Stefan that's perfect. I'm not sure how I missed Ghostscript. Thanks for your help!
Highlighted
FreeFlow Production Workflow Moderator
## Re: Save/Export to EPS
Jump to solution
Highlighted
FreeFlow Production Workflow Moderator
## Re: Save/Export to EPS
Jump to solution
It is actually possible to use Acrobat to do this. It is a bit trickier than the above methods but could give more flexibility because you can use the printer driver of your choice. The attached Powershell script will watch folder C:\in for pdf files and when a pdf files arrives, Acrobat will print the pdf using the Windows printer defined to C:\out\<filename.pdf>.eps. I have used a printer driver for Xerox iGen5 but some other PostScript printer driver could be used. Make sure you set the printer driver PostScript option to print to "Encapsulated PostScript (EPS)" instead of the default "Optimize for Speed".
Stefan
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Frequent Member
## Re: Save/Export to EPS
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Hello,
Im trying to do this by Powershell script and Acrobat (Pro not reader). I can run script, when i add file to "in" it is adding it to print queue but then nothing happended. It is stuck in print queue. I have tied everything and dont have ide what to do next...
Highlighted
Frequent Member
## Re: Save/Export to EPS
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OK, I manage to make it save a proper out.ps but cannot force script to change name to imputed_file_name.eps
Highlighted
FreeFlow Production Workflow Moderator
## Re: Save/Export to EPS
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Try the attached.
Highlighted
Frequent Member
## Re: Save/Export to EPS
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It is working ! great thank You very much ! :)
As i can see, You have commented one line and added 2 delays?
How I can now integrate it with Core? By External node? $FFin$ as "in" folder and $FFout$ as "out" folder?
Highlighted
FreeFlow Production Workflow Moderator
## Re: Save/Export to EPS
Jump to solution
I had some issue launching Acrobat with a script from within FFCore so I did this outside FFCore instead. You could give it a try, but then you need to create a batch file that calls the PowerShell script and passes the argument %1 for the incoming file to be run with Acrobat from the batch file to the Powershell script $args[0] to$FFin$in an External process. You also need to disable the file system watcher ($fsw) in the PowerShell script as this can/should only be run once to keep watching the folder as long as PowerShell runs the script.
As you already have this setup outside of FFCore, the simplest way is to place a Save component in a FFCore workflow and save the pdf to C:\in\.
Stefan | {"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": 0.6634920835494995, "perplexity": 4960.624161818841}, "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/1606141197593.33/warc/CC-MAIN-20201129093434-20201129123434-00307.warc.gz"} |
http://mathoverflow.net/questions/20949/sum-of-product-of-fourier-series | ## Sum of product of Fourier series
I want to compute the following product
$$\frac{1}{N}\sum_{t=1}^{N}\left(\sum_{s=-\infty}^{\infty}a_{s}\exp(2\pi is\frac{t}{N}\right)\left(\sum_{z=-\infty}^{\infty}a_{z}\exp(-2\pi iz\frac{t}{N})\right)$$ If $N\rightarrow\infty$ we can approximate it with integral: $$\int_{0}^{1}\left(\sum_{s=-\infty}^{\infty}a_{s}\exp(2\pi isx\right)\left(\sum_{z=-\infty}^{\infty}a_{z}\exp(2\pi izx)\right)dx=\sum_{s=-\infty}^{\infty}a_{s}\sum_{z=-\infty}^{\infty}a_{z}\int_{0}^{1}\exp(2\pi i(s-z))dx$$ Hence $s=z$ and we have $$\sum_{s=-\infty}^{\infty}a_{s}^{2}$$
On the other hand this product is equal to: $$\frac{1}{N}\left(\sum_{s=-\infty}^{\infty}a_{s}\right)\left(\sum_{z=-\infty}^{\infty}a_{z}\right)\sum_{t=1}^{N}\exp(2\pi i(s-z)\frac{t}{N}=\sum_{w=-\infty}^{\infty}\sum_{s=-\infty}^{\infty}a_{s}a_{s+Nw}$$
We have $$\sum_{s=-\infty}^{\infty}a_{s}^{2}+\sum_{w=-\infty,w\neq0}^{\infty}\sum_{s=-\infty}^{\infty}a_{s}a_{s+Nw}$$
Now I don't see why the second term will disappear.
Which is correct?
-
There is an error somewhere in your penultimate formula. Could you please re-edit? Also, is this an isolated calculation or exercise? if not, could you give us a bit more background context (for instance, why you're interested)? – Yemon Choi Apr 10 2010 at 19:37
You are taking limits as $N\to\infty$. In the sum $\sum_{w\ne0}a_{s+Nw}$ the terms thin out as $N$ increases. Assuming $a_n\to0$ quickly enough as $n\to\pm\infty$ then $\sum_{w\ne0}a_{s+Nw}$ will tend to $0$. – Robin Chapman Apr 10 2010 at 20:02
Following Robin's comment, you need some hypotheses on the decay of your coefficients in order for the Fourier series to converge. – S. Carnahan Apr 10 2010 at 20:11
Yemon Choi, thanks, I have re-edited. I have obtained this expression, while solving some least square problem. And I use Fourier series of basis functions. – WBT Apr 10 2010 at 20:17
Robin Chapman, Scott Carnahan In my case Fourier coefficients $a_s=sinc(s)^p$ function. But still, I am confused about the limits. Because $s->\infty$, hence $s+Nw$ can be small, depending in which order I'll take limits. – WBT Apr 10 2010 at 20:25
show 1 more comment | {"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": 0.9609553813934326, "perplexity": 558.8913653321666}, "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/1368705069221/warc/CC-MAIN-20130516115109-00094-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://mathonline.wikidot.com/linear-operators-on-linear-spaces | Linear Operators on Linear Spaces
# Linear Operators on Linear Spaces
Definition: Let $X$ and $Y$ be linear spaces over $\mathbb{R}$ (or $\mathbb{C}$). A function $T : X \to Y$ is said to be a Linear Operator from $X$ to $Y$ if it satisfies the following properties: 1) $T(x + y) = T(x) + T(y)$ for all $x, y \in X$. (Additivity) 2) $T(\lambda x) = \lambda T(x)$ for all $x \in X$ and for all $\lambda \in \mathbb{R}$ (or $\mathbb{C}$). (Homogeneity) The set of all linear operators from $X$ to $Y$ is denoted $\mathcal L (X, Y)$.
It is common to use the notation "$Tx$" instead of "$T(x)$" to denote the image of $x$ under $T$.
For example, let $X = \mathbb{R}$ and $Y = \mathbb{R}$ and consider the function $T : \mathbb{R} \to \mathbb{R}$ defined for all $x \in \mathbb{R}$ by:
(1)
\begin{align} \quad T(x) = 2x \end{align}
Then $T$ is a linear operator from $\mathbb{R}$ to $\mathbb{R}$ since for all $x, y \in \mathbb{R}$ we have that:
(2)
\begin{align} \quad T(x + y) = 2(x + y) = 2x + 2y = T(x) + T(y) \end{align}
And for all $x \in \mathbb{R}$ and for all $\lambda \in \mathbb{R}$ we have that:
(3)
\begin{align} \quad T(\lambda x) = 2(\lambda x) = \lambda (2x) = \lambda T(x) \end{align}
Definition: Let $X$ and $Y$ be normed linear spaces over $\mathbb{R}$ (or $\mathbb{C})$. A linear operator $T : X \to Y$ is said to be a Bounded Linear Operator if there exists an $M \in \mathbb{R}$, $M \geq 0$ such that for every $x \in X$ we have that $\| T(x) \| \leq M \| x \|$. The set of all bounded linear operators from $X$ to $Y$ is denoted $\mathcal B(X, Y)$.
Note that we can only consider bounded linear operators if both $X$ and $Y$ are normed linear spaces.
From the example above, we see that with the standard Euclidean norm of the absolute value on $X = Y = \mathbb{R}$, that $T : \mathbb{R} \to \mathbb{R}$ defined for all $x \in \mathbb{R}$ by $T(x) = 2x$ is a bounded linear operator since for all $x \in \mathbb{R}$:
(4)
\begin{align} \quad \| T(x) \| = |T(x)| = |2x| = 2|x| = 2\|x \| \end{align}
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http://people.cs.aau.dk/~normark/schemedoc/getting-started-from-command-prompt.html | # Using SchemeDoc from an operating sytem command prompt
This tutorial will guide you through the steps of using SchemeDoc from a command prompt.
You cannot use this approach if LAML is configured to use DrScheme. You are recommended to configure LAML to use MzScheme.
1. SchemeDoc installation.
You must first install SchemeDoc (or the full LAML system) relative to your platform (such as Windows), operating system (such as Windows XP) and Scheme System (such as DrScheme).
On Windows: If you organize the Scheme and SchemeDoc software as recommended, this is an easy step.
If at all possible for you, you should add the LAML bin directory to the path environment variable of your operating system.
On windows, this is done via the menus Start > Programs > Accessories > Command Prompt
Navigate to the directory in which your Scheme stuff is located.
3. Make and run a LAML script which procduces the docmentation.
The script should normally be in the same directory as your Scheme source file. The example script ex.sdoc makes the documetation of the Scheme source file ex.scm.
From the command prompt, run the script by
` laml ex.sdoc`
If you could not add the laml bin directory to the operating system path you have to write something like
` C:\programs\laml\bin\laml ex.sdoc`
4. Enjoy the result.
The resulting HTML file is available in the same directory as your source file.
In our case it is ex.html. A couple of other auxiliary files do also appear (not important to you).
The steps above have been tested with MzScheme 370 on Windows 2000, LAML (full) version 32.1.
The steps above have also been tested with MzScheme 209 on Linux with LAML (full) version 32.1.
The steps above have also been tested with MzScheme 209 on Windows XP with SchemeDoc version 32.1. | {"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": 0.8465108275413513, "perplexity": 5979.572938734706}, "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-2014-42/segments/1414637905639.57/warc/CC-MAIN-20141030025825-00177-ip-10-16-133-185.ec2.internal.warc.gz"} |
http://kb.osu.edu/dspace/handle/1811/18849 | # CAVITY RINGDOWN SPECTROSCOPY WITH A CW $CO_{2}$-LASER, MICROWAVE-MODULATED SIDEBAND SYSTEM
Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/18849
Files Size Format View
1998-MI-11.jpg 106.8Kb JPEG image
Title: CAVITY RINGDOWN SPECTROSCOPY WITH A CW $CO_{2}$-LASER, MICROWAVE-MODULATED SIDEBAND SYSTEM Creators: Bucher, C. R.; Lehmann, K. K.; Fraser, G. T.; Plusquellic, D. F. Issue Date: 1998 Publisher: Ohio State University Abstract: This work reports the first observation of a ringdown decay from an empty resonator using a $< 0.5$ MHz linewidth, cw, carbon dioxide laser with $\sim 1$ mW of microwave sidebands separated 8 GHz to 18 GHz from the $CO_{2}$ carrier frequency. The resonator consists of a Fabry-Perot interferometer with two highly reflective mirrors $(R\sim 99.5\%)$ separated by 1.2 m providing an optical pathlength for absorption of 420 m and a theoretical ringdown time of 800 ns. At present, the lack of availability of highly reflective mid-infrared mirrors places an upper limit on the ringdown time. One of the benefits of using an extremely high resolution laser is that a single mode of the cavity can be selectively monitored. Future investigations with the experimental system include saturation spectroscopy of unstable chemical species, such as ozone, for accurate concentration determination. Description: Author Institution: Department of Chemistry, Princeton University; Optical Technology Division, National Institute of Standards and Technology URI: http://hdl.handle.net/1811/18849 Other Identifiers: 1998-MI-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": 0.4429751932621002, "perplexity": 5494.1303833488555}, "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-2016-07/segments/1454701174607.44/warc/CC-MAIN-20160205193934-00250-ip-10-236-182-209.ec2.internal.warc.gz"} |
https://mathematicsleadership.wordpress.com/tag/teaching-strategies/ | # Differentiated Instruction: Engaging Students at a Whole New Level
Differentiated instruction provides insight into the students’ level of engagement with the subject. For example, one student from my Algebra II class had struggled with the material covered during the first semester. Her scores on tests and quizzes ranged from 60% to 80%. She submitted most of her homework. When I spoke to the student, she said that she wanted to understand the material better, but she did not know how to study. We tried several methods, and nothing worked. I investigated further and discovered that she really loved creating art on the computer. So, I introduced her to several programs online (e.g. Blender , Desmos, and Scratch by MIT) that she could use to explore three-dimensional modeling. She got excited and started working on them instantly. After a week, she found herself struggling to make some of the objects the right size or place them in the right position. That is when I introduced her to the mathematics used in three-dimensional modeling. Instantly, she wanted to learn as much as she could about graphing two- and three-dimensional equations. What I learned from this experience was that engagement is crucial to the learning process. The only way that this could have been this successful was by consistently engaging the student using the methods listed above. By working closely with students and helping them explore the material in their own way (i.e. differentiated learning), we can facilitate the learning process more effectively.
Scratch is a free programming language where you can create your own interactive stories, games, and animations.
Graph functions, plot tables of data, evaluate equations, explore transformations, and much more – for free!
Blender is a professional free and open-source 3D computer graphics software product used for creating animations.
# Planning and Implementing Differentiated Instruction
There are a number of methods that I use to determine if my instructional design is responsive to the needs of each student as they access the Common Core State Standards. First, I hold daily class meetings to check in with the students. I have been holding these meetings since the beginning of the year and have found them very successful. Second, I hold one-on-one meetings with each of the students every two weeks. This allows me time to ask questions and learn more about the student’s level of understanding and level of interest. Third, I host online office hours using Google Docs to give students the option of asking questions or expressing their concerns through text rather than through voice. Fourth, I have students maintain progress journals, where they reflect on their learning. Since these are their journals, I allow them to fill them out how they choose. This also allows me to see how they are processing their learning.
# Creating a Culture That Engages Students in Learning
The school culture significantly impacts student learning and achievement in a variety of ways. By providing a safe learning environment, the students will be encouraged to develop personally, socially, and academically, at a pace that is consistent with their needs. By setting high expectations and providing rigorous academic opportunities, the students will be engaged in more meaningful learning. By providing the students with personal and academic supports, they will be able to develop strong connections with the staff and the school.
In the midst of all this, it is important for a teacher to understand his/her role. From the first day of school (or before the first day), the teacher has already begun creating a culture for teaching and learning. Usually, it is expected that teachers design and decorate their classroom. For some, this may mean rearranging their student desks in a way that best fits the teacher’s pedagogical style. For others, it may mean designing their walls and distributing supplies. Creating a syllabus and discussing it the first week of school sets the tone in many ways. From the first week to the first month, every moment spent teaching, is as much a moment of teaching as it is a moment of modeling, coaching, and leading.
One area that I think is especially important for teachers to exercise their role in creating a culture of teaching and learning is in their level of energy. For example, I love mathematics. At first, the students would chuckle at my excitement over the problems that I would challenge them with, but soon, they felt the same excitement. Interestingly, many of them doubted themselves in the beginning and refused to work on the challenging problems. Now, they wouldn’t have it any other way. In fact, in a recent class meeting, the students reflected on their level of confidence and efficacy and noted how much it has improved over the past few months.
# Lesson Planning: Integrating English Language Development with Mathematics
The lesson planning process is just that, a process. At one point, I thought that I could follow a checklist, fill in the blanks, and the result would be a solid lesson plan. I thought that maybe if I included a few strategies that addressed the learning needs of EL students and students with special needs, that I would have developed a higher quality lesson plan, but even that was not so. Developing a high quality lesson plan requires more than filling out a checklist. In mathematics, for example, the lessons follow a sequence that ultimately ties into a main concept. Knowing this, it would be beneficial to integrate the collaborative model into the lesson through problem-based learning as students connect what they have learned and apply this to a number of challenges. Through a model that thrives on communication and social interaction, it would not only help students develop their critical thinking skills, but provide them with a language-rich environment for improving their English language proficiency. According to Shahzia Pirani-Mellstrom (n.d.), “Due to this interaction students not only advance their language skills, but also learn how to be better critical thinkers by examining material together and sharing various perspectives.” This is particularly important in mathematics, where students easily grasp the calculations, but struggle with the language used to explain the concepts and read the problems given to them. By increasing the amount of time students spend communicating and collaborating with their peers, they are simultaneously developing their critical thinking skills and their English language proficiency.
Considering the diversity of students that are represented in many of our classrooms, it is important to include strategies of English language development that focus on reading, writing, speaking, and listening. Even though mathematics may not seem to be the most likely subject for including English language development, it does provide an excellent means for developing English language proficiency and mathematical fluency. Using collaborative models that thrive on problem-based and project-based learning are ideal ways of engaging students through social interaction, while providing a way to formatively assess the students’ understanding of the material. Time management is another crucial aspect of designing an effective lesson plan, “An accurate allocation of time for activities during lesson planning is critical for the lesson plan’s successful implementation” (Serdyukov & Ryan, 2008, p. 122).
In my lesson plan, I was planning to address the concept of percentages by teaching students some of the strategies for decoding the language of percentages and then working in collaborative groups to create their own posters for explaining how to use these strategies depending on the problem given. At the end of the lesson, they would have the opportunity to share their posters with the rest of the class and discuss why they chose to provide the explanations they did. Considering the time management piece of the lesson, I am still debating whether the students would be able to complete the posters in time to share their results with the class. Again, this is why managing time is so essential to the quality of a lesson plan.
References
Pirani-Mellstrom, S. (Interviewee). (n.d.). Successful teaching practices in action: Project-based learning for English language learners. [Interview Transcript]. Retrieved from http://ediv.alexanderstreet.com.ezproxy.nu.edu/View/1641205
Serdyukov, P. & Ryan, M. (2008). Writing effective lesson plans. Pearson: United States
# Project Based Learning: Day 6
Instead of starting class with a Check-In meeting, I decided to start class with a collaborative activity. I had all the students silently redesign the room to accommodate a class meeting. They were not allowed to talk to each other, but they could write notes to each other and use hand signals. The caveat was that they could not make a sound or else they lost the challenge. I did this to drive home the importance of communication and collaboration. They completed the challenge and did so successfully. After starting the meeting we reflected on the activity and they all really enjoyed it, especially what they learned from it.
The night before, I asked students to respond to the following two questions:
• Imagine a unique and creative way that you could document all that you’ve experienced and learned throughout the Project Based Learning process. Describe, draw, and/or design your idea in order to present it to the class on Tuesday. Use any medium that you wish, as long as your idea is unique and creative.
• Research different PBL activities online and find (5) unique project ideas that you would have a lot of fun doing. Your (5) project must be described in your own words (i.e. copying from the internet will not be acceptable). If you found the project idea online, provide the url somewhere in your description. To receive full credit, your (5) project ideas must be different from everyone else’s. How you all decide to compare project ideas, I’ll leave that up to. If you decide to create a document of some sort on Google, I’d ask that you share that with me.
I had all the students take a seat and share one of their project ideas. I premised this by telling them not to present their idea, but to sell us on their idea. In other words, I wanted them to consider us to be their potential investors and they had to convince us to invest in their idea. Even though they listed five project ideas for their homework assignment, I had them share one of those ideas so that I could model how the students to question or comment on each other’s ideas. As we went around the room, I engaged each student with questions to further explore their ideas.
After going around the room once, the students gained a better idea not only of how to sell their ideas, but also how to respond to the other student’s presentations. I gave them a few minutes to review their four other project ideas before having them share these ideas with the class. The students who seemed to struggle most with this part of the activity were encouraged by their peers to share whatever came to mind. Taking whatever the student said, the class brainstormed the idea to give the student something to explore.
At this point, the students were curious why we spent so much time recording and sharing five unique project ideas. This is when I introduced them to the Genius Hour (related to the 80/20 principle). Essentially, Genius Hour is a time set aside in the schedule for the students to actively pursue their own interests and explore their passions. While most of my students were absolutely excited about the idea, I noticed that a few students seemed a little stressed out about it. They felt that it lacked the structure of a regular classroom. They were also concerned that whatever they chose to pursue would not meet my expectations. I realize that much of this stems from their response to years of learning within structured environments. So, I structured it a little more for these students to help scaffold their transition to this other type of learning.
We had about 10 minutes left. For last night’s homework, I asked the students to brainstorm different ways they could document their Project Based Learning experience. I felt that they could probably share out some of their ideas and they could vote on the best way.
Some of the ideas they suggested were:
• Picture poster/wall
• Scrapbook (tangible or virtual)
• PowerPoint presentation
• Class PBL website
• Class PBL blog
• Notebook (similar to a Lab Notebook)
After discussing the merits of each idea, the class made two decisions. First, a small group of interested students would develop a class PBL website, documenting each group’s progress. This small group would attend weekly website develop workshops that I would host during their lunch period. Second, each student would be given the freedom to choose how they document their Project Based Learning experience. The only restriction is that they must consistently update it and somehow show me their updates.
So far, everything has been working out great with these past few days dedicated to introducing the students to Project Based Learning. I’ll be researching Genius Hour and developing a guide for that as I go. Stay tuned for updates on that! Also, if you have any ideas or suggestions for rolling out a successful Genius Hour session, please share!
Here are some of the websites that I’ve been using to research about Genius Hour.
# Alternative Assessments: Multiple-Choice Tests
Have you ever given a multiple-choice test and wondered whether restricting your students’ creativity to a small number of available options truly assessed their comprehension of a concept? I have, but I didn’t toss the multiple-choices out. Call me an optimist, but I always try to find the benefit of something.
I asked myself, “What could possibly be the benefit of giving a multiple-choice test?” The last time I created a multiple-choice test, I found it far more involved than creating other types of assessments. Once I typed out the question, I knew the correct answer and struggled to write three more false answers for a total of four possible answers. So, I wondered if I could harness some of that critical thinking that went into creating the multiple-choice test. What if I could take a different approach to this type of test that required a higher level of critical thinking? I thought for a while about it and decided to create a complete multiple-choice test, but without the questions.
That’s right! I gave my students a multiple-choice test with four answer choices (with the correct answer marked) for each question, but without the questions. Using the answer choices provided, they had to figure out what the question could have been. The first time that I tried it, the students seemed extremely engaged in the different way of thinking. What I liked about it was that it really got them to critically think about the material before writing down a question.
What alternative assessments have you created to inspire critical thinking?
# Multiple Intelligences: A Different Type of Survey
In years past, I tried using a Multiple Intelligences Inventory like the surveys that many of us have seen, but found it to be counterintuitive. Instead, I use centers as a way of assessing and identifying my students’ needs. At the beginning of the school year, I arranged the classroom into centers with different types of math activities for them to explore. For example, one center focused on visual learners by engaging the students in an art activity involving mathematics. Another center focused on linguistics learners and involved word problems and logic puzzles. A third center focused on kinesthetic learners and had manipulatives for the students to explore mathematical concepts. At each of these centers, I had activities for the students to engage in independently (i.e. intrapersonal learners) or with a friend (i.e. interpersonal learners). By allowing the students to choose the center and activity they would like to participate, I was able to assess their style of learning as well as their learning needs.
In one class that I did this, I learned that many of my students appealed to the center that involved art, while a small number of them appealed to the center that involved word problems and logic puzzles. For this class, I approached mathematics from a more visual perspective, while providing the students with resources online for them to engage in further reading. I had students complete daily math journals where they had to summarize their learning by writing or illustrating their thoughts. I also provided the students with the means to solve problems visually (e.g. bar diagrams) or linguistically (e.g. written explanations).
In another class, I found that many of my students were absolutely uninterested in the logic games. Interestingly, this was my Geometry class, which addresses deductive and inductive logic throughout most of the course. After reflecting on the students’ needs, I decided to steer away from the traditional axiomatic approach to Geometry, and embraced a more project-based approach. Many of these students were interpersonal, linguistics, and bodily-kinesthetic learners. Therefore, I designed a variety of activities for them to explore the concepts of Geometry while collaborating in groups on projects that they designed and built.
For more information on the application of Multiple Intelligences Theory in Mathematics Education:
# Rethinking the Order of Operations (i.e. PEMDAS)
I was talking to my students the other day about the Order of Operations (i.e. PEMDAS). I quickly reviewed the Order of Operations as we worked through several algebraic expressions. Then, I asked my students why we followed the Order of Operations. They said, “It’s just what we’re supposed to follow.” I decided to investigate this further and I asked them, “But why does the Order of Operations follow the order that it does?” They didn’t know.
Why do we follow the order that makes up the Order of Operations? I asked several other people and got the same response — their teacher told them it’s what they were supposed to follow. Welcome to the era of education that focused primarily on the product. Why study the reason behind the Order of Operations, when teaching students that they’re supposed to follow it works? That is like asking, “Why teach an archer about trajectory physics, when you could just teach the archer to hit a specific target?”
So, I entertained the challenge of understanding the Order of Operations further with my students. I wrote PEMDAS vertically on my marker board and analyzed the directionality of each operation.
• Parentheses only refers to embedded operations, so we left that aside.
• Exponents were essentially a form of multiplication, since $x^2$ is equivalent to $x \cdot x$.
• Multiplication and Division are usually computed together from left to right. I stopped my students at this point to consider the two different operations. Could multiplication be computed bidirectionally? Yes. What about division? If we think of division as multiplication, then $\frac x 2$ could be written as $x \cdot \frac 1 2$ (i.e. multiplying x by the multiplicative inverse of 2).
• Addition and Subtraction are much like Multiplication and Division. While addition could be computed bidirectionally, subtraction won’t allow for it. Fortunately, we are able to write subtraction as the addition of an additive inverse. For example, $5-3$ could be written as $5 + (-3)$.
Therefore, instead of PEMDAS, we have PMA. This simplifies things a little, but it doesn’t answer the question why we follow the order of PEMDAS (even if it’s written as PMA).
Let’s visualize a situation where PEMDAS would be needed. In the above picture, we have four stacks of squares with nine circles in each square, a single square with nine circles in it, and four circles by themselves. If we had to put this in an expression, we could write it as $4(3^2) + 3^2 + 4$. If we had to add up all of the blue circles, how would we do it? Would you want to count all the circles one-by-one? This may be a little time-consuming. What if we computed each of the squares as nine circles (from $3^2 = 9$). Then, if one square equals nine circles, four squares must equal 36 circles. Thus, 36 circles + 9 circles + 4 circles. Interestingly, we just followed PEMDAS. Wait! I don’t remember bringing PEMDAS into this. It seems that the reason for PEMDAS is right in front of us.
Four squares of nine circles + one square of nine circles + four circles
4 ( 9 circles) + 9 circles + 4 circles
36 circles + 9 circles + 4 circles
Basically, we had to convert the original expression into an expression that allowed for addition to happen with quantities of similar terms. There was no way to add a square with four circles. Instead, we had to convert the square to nine circles to allow for addition to be possible. Ultimately, PEMDAS follows PMA, ranking the operations in priority from the embedded operation (P), to multiplication (M), and then to addition (A). If addition is the final operation performed, then all quantities must be similar in order to be added. Likewise, if multiplication is the final operation performed, then all quantities must be similar in order to be multiplied.
In summary, we follow the Order of Operations to allow for multiplication and addition with quantities of similar terms.
# Classroom Management: Social Contracts
Along with involving students in the selection of topics to be covered, I would also involve them in developing behavior guidelines for the class. According to Marzano, Marzano, and Pickering (2009, p. 13), “Probably the most obvious aspect of effective classroom management involves the design and implementation of classroom rules and procedures.” In their book, Discipline with Dignity, Curwin, Mendler, and Mendler (2008, p. 68) agree with the importance of involving student in the development of the classroom rules and procedures, introducing their view of the classroom rules and procedures as a social contract, “The social contract is an agreement between teacher and students about the values, rules, and consequences for classroom behavior.” Using a social contract would not only increase student responsibility, but it would also affect their academic achievement.
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We introduce differentiability for functions of several variables and find tangent planes.
### Differentiability
Previously in your calculus experience, we often asked the question, “Is this function differentiable?” When looking at $f: \R \to \R$, the answer to that question was the same as the answer to,“Does the derivitive exist?” Now that we are working with multivariable functions, we’ve already seen that there is more than one derivative we can define at any given point, giving us different information about the surface. Therefore, we need a different strategy. Another way we could have answered whether a function $f: \R \to \R$ was differentiable was to ask whether there exists a tangent line (that is, a linear approximation) to the function at that point. This idea we can generalize to higher dimensions.
Recall, for $f: \R \to \R$, we say a function is differentiable if the limit exists. This is equivalent to saying that
where $\l (x)$ is the equation of the tangent line to $f$ at $a$.
Let’s use this same idea to define differentiability in higher dimensions.
In $\R ^2$, we can interpret this definition as saying that a function $F$ is differentiable at a vector $\vec {a}$ if there is a plane $L(\vec {x})$ at that point such that $F$ approaches $L(\vec {x})$ faster than $\vec {x}$ approaches $\vec {a}$. In this case, we call this plane the tangent plane. We interpret this differentiability as, if one “zooms in” on the graph of $F$ at $(\vec {a}, F(\vec {a}))$ sufficiently, it looks more and more like the tangent plane.
You can use this interactive to visualize a tangent plane.
How do we interpret this definition in higher dimensions? If we zoom in on a differentiable curve $f:\R \to \R$, we will see $f$ approach its tangent line. If we zoom in on a differentiable surface $F:\R ^2 \to \R$, we will see $F$ approach its tangent plane. Similarly, if we zoom in on a differentiable surface $F:\R ^n \to \R$, we should expect to see $F$ approach a flat surface $L(x)$ which looks like $\R ^n$.
Keep in mind that this statement of differentiability is much stronger than just saying the partial derivatives of $F$ exist at $\vec {a}$. Because this is a limit in a higher dimension, we are saying this limit must exist and be equal for every path by which $\vec {x}$ could approach $\vec {a}$, not just the paths along the axes. Because of this, it is very difficult to use this definition to show that a function is differentiable. Thankfully we have the following theorem.
In words, this theorem is saying that if all of the partial derivatives are all continuous on all of $S$, then $F$ is differentiable on $S$. Notice how much easier this is to use than the definition! This theorem assures us that essentially all functions that we see in the course of our studies here are differentiable on their natural domains.
Remember, we were trying to generalize the concept of differentiability for $f:\R \to \R$? Our concept of differentiability for $f:\R \to \R$ had a lot of nice properties. Many of these properties also hold for differentiability in higher dimensions. In particular, here are a few examples.
Since most of the functions we see in this course are differentiable on their domains, they are also continuous.
A note of caution: differentiability in higher dimensions is a much more subtle notion. For instance, it is possible for a function $F$ to be differentiable yet some partials may not be continuous. It is also possible for all the partial derivatives to exist at a point and the function still fail to be continuous, let alone differentiable, at that point. Such strange behavior of functions is a source of delight for many mathematicians. | {"extraction_info": {"found_math": true, "script_math_tex": 68, "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": 0.9415557980537415, "perplexity": 105.20733601655401}, "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/1618038088245.37/warc/CC-MAIN-20210416161217-20210416191217-00241.warc.gz"} |
https://www.geraldbelton.com/post/connecting-r-to-an-oracle-database/ | # Connecting R to an Oracle Database
R is a very popular language for doing analytics, and particularly statistics, on your data. There are a number of R functions for reading in data, but most of them take a delimited text file (such as .CSV) for input. That's great if your existing data is in a spreadsheet, but if you have large amounts of data, it's probably stored in a relational database. If you work for a large company, chances are that it is an Oracle database.
The most efficient way to access an Oracle database from R is using the RODBC package, available from CRAN. If the RODBC package is not installed in your R environment, use the install.packages("RODBC") command to install it. ODBC stands for Open DataBase Connectivity, an open standard application programming interface (API) for databases. ODBC was created by the SQL Access Group and first released in September, 1992. Although Microsoft Windows was the first to provide an ODBC product, versions now exist for Linux and Macintosh platforms as well. ODBC is built-in to current versions of Windows. If you are using a different operating system, you'll need to install on OBDC driver manager.
Before you can access a database from R, you'll need to create a Data Source Name, or DSN. This is an alias to the database, which provides the connection details. In Windows, you create the DSN using the ODBC Source Administrator. This tool can be found in the Control Panel. In Windows 10, it's under System and Security -> Administrative Tools -> ODBC Data Sources. Or you can just type "ODBC" in the search box. On my system, it looks like this:
As you can see, I already have a connection to an Oracle database. To set one up, click Add, and you'll get this box:
Select the appropriate driver (in my case, Oracle in OraDB12Home1) and click the Finish button. A Driver Configuration box opens:
For "Data Source Name," you can put in almost anything you want. This is the name you will use in R when you connect to the database.
The "Description" field is optional, and again, you can put in whatever you want.
TNS Service Name is the name that you (or your company data base administrator) assigned when configuring the Oracle database. And "User ID" is your ID that you use with the database.
After you fill in these fields, click the "Test Connection" button. Another box pops up, with the TNS Service Name and User ID already populated, and an empty field for your password. Enter your password and click "OK." You should see a "Connection Successful" message. If not, check the Service Name, User ID, and Password.
Now you are ready to connect R to the database.
Here's the R code that you need:
library(RODBC)
# Create a connection to the database called "channel"
# Query the database and put the results into the data frame
# "dataframe"
dataframe <;- sqlQuery(channel, "
SELECT *
FROM
SCHEMA.DATATABLE")
# When finished, it's a good idea to close the connection
odbcClose(channel)
First, I don't like the idea of having a password appear, unencrypted, in the R program. One possible solution is to prompt the user for the password before creating the connection:
pswd <- readline("Input Password: ")
channel <- odbcConnect("DATABASE", uid="USERNAME", pwd=pswd)
This will enable the connection to be made without compromising the security of the password.
Second, the sqlQuery will pass to Oracle whatever is inside the quotation marks. This is the workhorse function of the RODBC package. The term ‘query’ includes any valid SQL statement including table creation, updates, etc, as well as ‘SELECT’s.
Finally, I should mention that R works with data that is loaded into the computer's memory. If you try to load a really huge database into memory all at once, it will a) take a very long time, and b) possibly fail due to exceeding your computer's memory capacity. Of course, relational database systems like Oracle are the natural habitat of very large data sets, so that may be your motivation for connecting R to Oracle in the first place. Carefully constructed SQL Queries will let Oracle do the work of managing the data, and return just the data that R needs for performing analytics.
Writing SQL Queries is beyond the scope of this blog post. If you need help with that, there are plenty of free tutorials on the web, or you might find this book helpful: Oracle 12c for Dummies | {"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": 0.18330931663513184, "perplexity": 1670.798438729722}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057421.82/warc/CC-MAIN-20210923104706-20210923134706-00266.warc.gz"} |
https://brilliant.org/problems/will-you-integrate-it-2015-times-vi/ | Will you integrate it 2015 times? - VI
Calculus Level 2
A function $f : \mathbb{R} \rightarrow \mathbb{R}$ is at least $2015$ times differentiable. $f(x)$ is differentiated 2015 times to get $g(x) = \dfrac{ d^{2015} }{dx^{2015} } \big[ f(x) \big]$.
True or False
If $f(x)$ is an odd function, then $g(x) = g(-x)$ for all values of $x$.
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http://www.koreascience.or.kr/article/ArticleFullRecord.jsp?cn=JMGHBV_2016_v33n4_303 | Development of Temperature Measurement System Using Fiber Optics Linear Transmittance Filter with Fiber Bragg Grading Sensor
Title & Authors
Development of Temperature Measurement System Using Fiber Optics Linear Transmittance Filter with Fiber Bragg Grading Sensor
Nam, Kwang Sik; Choi, Jin Gyu; Zhao, Shang; Kim, Jea Ki; Choi, Ho Min; Lee, Seok Soon;
Abstract
The fiber optical temperature sensing device was developed by using a Fiber Bragg Grading (FBG) sensor and a linear transmittance optical filter. The temperature change causes change in the FBG sensor reflectance wavelength and the reflectance wavelength from FBG sensor is transmitted to a linear transmittance filter so that the optical signal value is determined by the wavelength. The temperature can be measured by the optical signal value by passing FBG reflectance wavelength to the linear transmittance filter. Using the developed system, temperature ranges from $\small{10^{\circ}C}$ to $\small{50^{\circ}C}$ were measured and the measured data were almost linear.
Keywords
Fiber optic;Fiber bragg grating;Linear transmittance filter;
Language
Korean
Cited by
References
1.
Lee, K.-W., Rhim, H.-C., and Seo, T.-S., "Strain Measurement of Steel Roof Truss Using FBG Sensor during Construction of Reverse Shell Shaped Reinforced Concrete Structure," Journal of the Korean Society for Nondestructive Testing, Vol. 31, No. 4, pp. 335-342, 2011.
2.
Lee, K. H. and Kim, D. H., "Shape Monitoring of Composite Cantilever Beam by Using Fiber Bragg Grating Sensors," Transaction of the Korean Society of Mechanical Engineers: A, Vol. 37, No. 7, pp. 833-839, 2013.
3.
Chung, W. S. and Kang, D. H., "Application of FBG Sensors for Monitoring of Railroad Bridge," Magazine of the Korean Concrete Institute, Vol. 24, No. 3, pp. 25-25, 2012.
4.
Kim, H.-Y., Kang, D., Lee, J.-H., and Kim, D.-H., "Characteristics of Thermal Coefficient of Fiber Bragg Grating for Temperature Measurement," Transactions of the Korean Society of Mechanical Engineers: A, Vol. 37, No. 8, pp. 999-1005, 2013.
5.
Zhao, C.-L., Demokan, M., Jin, W., and Xiao, L., "A Cheap and Practical FBG Temperature Sensor Utilizing a Long-Period Grating in a Photonic Crystal Fiber," Optics Communications, Vol. 276, No. 2, pp. 242-245, 2007.
6.
Kersey, A. D., Davis, M. A., Patrick, H. J., LeBlanc, M., Koo, K., et al., "Fiber Grating Sensors," Journal of Lightwave Technology, Vol. 15, No. 8, pp. 1442-1463, 1997.
7.
Othonos, A. and Kalli, K., "Fiber Bragg Gratings: Fundamentals and Applications in Telecommunications and Sensing," Artech House, 1st Ed., pp. 28-50, 1999.
8.
Park, H.-J., Lee, J.-H., and Song, M.-H., "Distributed Fiber-Optic Temperature Sensor Network for Protection of Electric Power Systems," Journal of the Korean Institute of Illuminating and Electrical Installation Engineers, Vol. 20, No. 5, pp. 64-71, 2006. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 2, "/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": 0.25628426671028137, "perplexity": 9501.30376580169}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608633.44/warc/CC-MAIN-20170526032426-20170526052426-00094.warc.gz"} |
https://msollami.com/tutorials/2013/12/27/nks-primer | A Primer on a New Kind of Science
A New Kind of Science (NKS) is probably the worst named intellectual framework of all time. Egotistical as it sounds, Wolfram's book really does contain some paradigm shifting ideas and I'll try to explain them in rapid broad strokes.
Background
Every year since 2003, Stephen Wolfram and his group of instructors from Wolfram Research organize a summer school, and in 2010 and 2011 I participated as a student and instructor, respectively. Since 2003, more than 250 people have participated, some of whom continued developing their 3-week research projects as their Master’s or Ph.D theses or publications.
The basic subject of NKS is the study of simple abstract rules, that is, elementary computer programs. In 1988 Wolfram discovered a class of one-dimensional cellular automata which he called the elementary cellular automata (ECA). Simple programs are capable of a remarkable range of behavior, NKS argues that this is evidence that simple programs are enough to capture the essence of almost any complex system.
Generally speaking, NKS has three forms:
1. The experimental science and enumeration of simple programs
2. The technological application of interesting simple programs
3. A razor for thinking of the universe in computational terms
The central thesis of NKS posits two ideas: that the nature of computation must be explored experimentally, and that the results of these experiments have great relevance to understanding the natural world (which is assumed to be digital).
Edward Fredkin and Konrad Zuse pioneered the idea of a computable universe. In physics and cosmology, digital physics is a collection of theoretical perspectives based on the premise that the universe is, at heart, describable by information, and is therefore computable. The computational universe is the space of all computer programs.
Mapping and mining the computational universe
In order to study simple rules and their often complex behavior, Wolfram believes it is necessary to systematically explore all of these computational systems and document what they do. Traditional wisdom holds that real world is complex but that in formal systems on paper everything is simple. Rule 30 and other systems show that this is not the case. The richness of the world can be faithfully reproduced in formal systems, and in simple programs at that.
The randomness displayed in Rule 30 is a completely deterministic one. Indeed, in NKS randomness almost always refers to the outcome of a deterministic process. A synonym is ’complexity’. Now, there exist are three mechanisms for randomness:
1. Randomness from initial conditions
2. Randomness from the environment
3. Intrinsic randomness generation
Sensitive dependence on initial conditions in deterministic nonlinear systems has been well studied since Henri Poincaré introduced the three-body problem by in 1890. Randomness from the environment is not a true source of randomness, because the environment is just another system. That is, the external environment of one system is the internal environment of a larger system. The third type of randomness was investigated by Wolfram and encountered on numerous occasions in his exploration of the computational universe. A common question is “why wasn’t intrinsic randomness discovered earlier?” Page 48 replies: “Indeed, even very early in the history of traditional mathematics there were already signs of the basic phenomenon of complexity. One example known for well over two thousand years concerns the distribution of prime numbers: the rules for generating primes are simple, yet their distribution seems in many respects random. However almost without exception mathematical work on primes has concentrated not on this randomness, but rather on proving the presence of various regularities in the distribution.”
The NKS strategy for exploring the computational universe can be summarized as follows:
1. Identify a computational system to explore
2. Devise an enumeration scheme for your system
3. Construct an efficient implementation of your system
4. Carry out a visual exploration of the space of system behavior
5. Use machine learning to build detectors and filters for programmatic searching
6. Investigate in more detail specific features and properties of selected rules
Computational irreducibility
Loosely speaking, a process is computationally irreducible [p 737-750] if it cannot be computed by a faster process. An example of reducibility is Rule 90. Given the initial condition, and the coordinates of some cell, there is a quick procedure [p 608-609] to determine whether the cell will be black or white. On the other hand, irreducibility means that there can be no way to predict how a system will behave except by going through almost as many steps of computation as the evolution of the system itself. [p 739] Rule 150 is computationally reducible because there exists a program that computes the color of a cell on row T faster than the automaton itself can compute it. Rule 30 is computationally irreducible because (as far as anyone knows) there is no such ”shortcut” program. But we must ask if intrinsic randomness and computational irreducibility are the same thing. I think that computational irreducibility implies intrinsic randomness generation. But intrinsic randomness generation does not imply computational irreducibility, because one can imagine modifying rule 30 to slow it down. Wolfram posits a conjecture on computational irreducibility:
Theorem - Let WorstTime(T, n) be the longest time that Turing machine T takes to halt over all inputs of length ≤ n on which it does halt. (See computations of this, pp. 761, 763.) T is reducible if some Turing machine U with the same inputs and outputs which has
WorstTime(U, n)/WorstTime(T,n) → 0 as n → ∞.
Then as the number of states grows infinite the fraction of reducible Turing machines vanishes.
The previous conjecture is an instance of the more general Principle of Computational Equivalence (PCE). The principle states that systems found in the natural world can perform computations up to a maximal universal level of computational power. Most systems can attain this level and in principle can compute the same things as a universal Turing machine.
• Weak PCE: Almost every rule is either trivial or universal.
• Strong PCE: Almost every computation is either trivial or universal.
Irreducibility is present within the theory of graphs, for instance, the theory of finite cubic planar graphs is undecidable. Consider a Turing machine with a two way tape single head s1, s2, · · · , sn. Let the tape have a certain initial configuration and allow the machine to run. Assume the machine performs a finite computation and halts. The main idea is to code the printout of all such computations as finite cubic planar graphs. Notice that in order to do this for a given machine we need only a fixed number of configuration to code our information i.e. black, s1, s2, · · · , sn, head, lest end of the tape, right end of the tape and halt. The requirement that the graphs be cubic appears to offer no more difficulty than that of guaranteeing this fixed number of unambiguous configurations. Thus, we can identify certain vertices with squares of the tape while the others exist in configurations describing what is in those squares and how the machine moves.
Theorem - The theory of finite cubic planar graphs is undecidable.
Proof: Consider a Turing machine as above. For each possible beginning position of the tape consider the sentence in the language of graphs which says
[there exists (x1, ..., xn) where xi are in the configurations which represent this initial position] implies that [there exists (z1, ..., zm) where zi are in the halt configuration].
A solution to the decision problem for finite planar cubic graphs would imply a solution to the collection of all sentences (*), but these simply express the halting problem for the machine, thus proving the theorem. QED
Note that the PCE is not about functions or sets but rather concerns repeated application of some updating procedure to some state, and the history of states that results. In these terms, PCE states: For any updating procedure, either that procedure always yields simple results, or that procedure can be made to emulate any computation via an appropriate choice of initial conditions. Computation is therefore simply a question of translating input and outputs from one system to another. Consequently, most systems are computationally equivalent. Proposed examples of such systems are the workings of the human brain and the evolution of weather systems.
Originally, in 1936, Alan Turing proposed that all functions which could be effectively computed by a human could also be computed by a Turing Machine. (Of course, the converse is obviously true anything computed by a Turing Machine can be computed by a human.) Since that time, Turing Machines have become widely accepted as the formal definition of computation, and Turing’s claim that this definition conforms to our intuitive understanding of the concept of computation is known as the Church-Turing Thesis. Note that the Church-Turing Thesis cannot be definitively proved. It is an empirical claim supported by observation, like the Newton's Law of Gravity or the Laws of Quantum Mechanics. Just as it is conceivable that those laws could be proved wrong by future observations, so too could the Church-Turing Thesis be proved wrong by future observations.
In every system there is a threshold for complexity. And although it is often low, there are many things that fall below it and can therefore be reduced in one form or another. Traditional mathematics has very successfully explored what lies below this threshold. But most systems from traditional mathematics are in fact capable of showing irreducible complexity. In particular, the digits of real numbers, continued fractions, Diophantine equations, differential and difference equations, solvability by radicals etc... But phenomena such as the complexity of the digits of π were just considered meaningless rather than indicative of a general class behavior. The reasoning must have been something like this: “There is no reducible pattern in the digits of π therefore it cannot be understood, therefore it is meaningless, so let’s ignore it.” Instead, NKS says “But isn’t that interesting!” So given a particular computation, how then can we determine that the computation halts? We know there is no general procedure that can answer all such questions. Nevertheless, there is a partial solution: if a computation does halt, then can we always verify that it halts by explicitly performing the computation, and then waiting for it to halt? (Of course, if the computation never halts, then we will be waiting forever.) But could there be a more efficient procedure of which we are unaware? The ideas in A New Kind Of Science suggest that the answer is “no”. One of the central claims of A New Kind Of Science is that there exist computational systems whose behavior is computationally irreducible, meaning that there is no shorter way to determine the system’s behavior than by explicitly following its computation. If computationally irreducible systems do indeed exist, then there is, in general, no faster way to determine whether an arbitrary computation halts than to explicitly perform that computation.
Now, Cellular Automata are the primary system that is studied in A New Kind Of Science, so it is important for us to show that Cellular Automata are equivalent to Turing Machines in their computational power.
Definition - Whenever a system is equivalent to Turing machines in its computational power, we say that it is computationally universal
The name universal derives from the Church-Turing Thesis, which claims that Turing Machines can compute all that can in principle be computed. The technique that we use to show that one system is equivalent in computational power to another system is called emulation.
Above is a graphic that shows a Cellular Automaton emulating a particular Turing Machine. The essential idea behind the emulation is that
1. Identify the Turing Machine’s tape with the cellular automaton’s line of cells.
2. Identify the white and black cells in the Turing Machine with white and light-gray cells in the cellular automaton.
3. Identify the Turing Machine’s head with a single cell in the cellular automaton, where the color of the cell encodes the state of the head together with the color that the head is reading.
It is clear that the behavior of this cellular automaton corresponds directly to the behavior of the Turing machine. For example, if we conventionally declare that the Turing Machine halts when the head moves right of its initial position, then the corresponding cellular automaton should be considered to halt whenever the cell which simulates the head moves right of its initial position. Of course, there is nothing special about this particular Turing Machine. Any Turing Machine can be emulated by a cellular automaton using similar methods.
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https://en.wikipedia.org/wiki/Van_%27t_Hoff_factor | # van 't Hoff factor
The van 't Hoff factor i (named after Dutch chemist Jacobus Henricus van 't Hoff) is a measure of the effect of a solute upon colligative properties such as osmotic pressure, relative lowering in vapor pressure, boiling-point elevation and freezing-point depression. The van 't Hoff factor is the ratio between the actual concentration of particles produced when the substance is dissolved and the concentration of a substance as calculated from its mass. For most non-electrolytes dissolved in water, the van 't Hoff factor is essentially 1. For most ionic compounds dissolved in water, the van 't Hoff factor is equal to the number of discrete ions in a formula unit of the substance. This is true for ideal solutions only, as occasionally ion pairing occurs in solution. At a given instant a small percentage of the ions are paired and count as a single particle. Ion pairing occurs to some extent in all electrolyte solutions. This causes the measured van 't Hoff factor to be less than that predicted in an ideal solution. The deviation for the van 't Hoff factor tends to be greatest where the ions have multiple charges.
## Dissociated solutes
The degree of dissociation is the fraction of the original solute molecules that have dissociated. It is usually indicated by the Greek symbol ${\displaystyle \alpha }$. There is a simple relationship between this parameter and the van 't Hoff factor. If a fraction ${\displaystyle \alpha }$ of the solute dissociates into ${\displaystyle n}$ ions, then
${\displaystyle i=\alpha n+(1-\alpha )=1+\alpha (n-1).}$
For example, the dissociation
KCl ⇌ K+ + Cl
yields ${\displaystyle n=2}$ ions, so that ${\displaystyle i=1+\alpha }$
For dissociation in the absence of association, the van 't Hoff factor is:
${\displaystyle i>1}$
## Associated solutes
Similarly, if a fraction ${\displaystyle \alpha }$ of ${\displaystyle n}$ moles of solute associate to form one mole of an n-mer (dimer, trimer, etc.), then
${\displaystyle i=1-\left(1-{\frac {1}{n}}\right)\alpha .}$
For the dimerisation of acetic acid in benzene
2CH3COOH ⇌ (CH3COOH)2
2 moles of acetic acid associate to form 1 mole of dimer, so that
${\displaystyle i=1-\left(1-{\frac {1}{2}}\right)\alpha =1-{\frac {\alpha }{2}}.}$
For association in the absence of dissociation, the van 't Hoff factor is:
${\displaystyle i<1}$
## Physical significance of i
Dimerization of a carboxylic acid by formation of hydrogen bonds (shown as dotted lines)
The value of i is the actual number of particles in solution after dissociation divided by the number of formula units initially dissolved in solution and means the number of particles per formula unit of the solute when a solution is dilute.
## Relation to osmotic coefficient
This quantity can be related to the osmotic coefficient g by the relation:
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https://www.repository.cam.ac.uk/handle/1810/337325?show=full | dc.contributor.author Stokell, Benjamin dc.contributor.author Shah, Rajen dc.date.accessioned 2022-05-19T23:30:31Z dc.date.available 2022-05-19T23:30:31Z dc.date.issued 2022-06 dc.identifier.issn 0960-3174 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/337325 dc.description.abstract There are a variety of settings where vague prior information may be available on the importance of predictors in high-dimensional regression settings. Examples include ordering on the variables offered by their empirical variances (which is typically discarded through standardisation), the lag of predictors when fitting autoregressive models in time series settings, or the level of missingness of the variables. Whilst such orderings may not match the true importance of variables, we argue that there is little to be lost, and potentially much to be gained, by using them. We propose a simple scheme involving fitting a sequence of models indicated by the ordering. We show that the computational cost for fitting all models when ridge regression is used is no more than for a single fit of ridge regression, and describe a strategy for Lasso regression that makes use of previous fits to greatly speed up fitting the entire sequence of models. We propose to select a final estimator by cross-validation and provide a general result on the quality of the best performing estimator on a test set selected from among a number $M$ of competing estimators in a high-dimensional linear regression setting. Our result requires no sparsity assumptions and shows that only a $\log M$ price is incurred compared to the unknown best estimator. We demonstrate the effectiveness of our approach when applied to missing or corrupted data, and time series settings. An R package is available on github. dc.publisher Springer Science and Business Media LLC dc.rights Attribution 4.0 International dc.rights.uri https://creativecommons.org/licenses/by/4.0/ dc.subject stat.ME dc.subject stat.ME dc.subject stat.CO dc.subject stat.ML dc.subject 62J07 dc.title High-dimensional regression with potential prior information on variable importance dc.type Article dc.publisher.department Dept of Pure Mathematics And Mathematical Statistics dc.publisher.department Department of Pure Mathematics And Mathematical Statistics dc.date.updated 2022-05-19T10:02:06Z prism.publicationName Statistics and Computing dc.identifier.doi 10.17863/CAM.84739 dcterms.dateAccepted 2022-05-16 rioxxterms.versionofrecord 10.1007/s11222-022-10110-5 rioxxterms.version VoR dc.contributor.orcid Stokell, Benjamin [0000-0002-8365-715X] dc.contributor.orcid Shah, Rajen [0000-0001-9073-3782] dc.identifier.eissn 1573-1375 rioxxterms.type Journal Article/Review pubs.funder-project-id Engineering and Physical Sciences Research Council (EP/N031938/1) cam.issuedOnline 2022-06-14 cam.orpheus.success Tue Jun 21 09:21:04 BST 2022 - Embargo updated cam.orpheus.counter 3 cam.depositDate 2022-05-19 pubs.licence-identifier apollo-deposit-licence-2-1 pubs.licence-display-name Apollo Repository Deposit Licence Agreement
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http://mathoverflow.net/questions/60902/formulas-for-equidistant-curves?sort=newest | # Formulas for equidistant curves
Hello,
I'm trying to draw on the computer a curve that keeps always the same distance(given as parameter) from a given curve. I know the formula for the given curve. I tried moving perpendicular to the first derivative but in some cases when the curve is sharp there are a lot of points creating some problems. This problem happens when the moving the curve with a distance greater that the radius of the curve.
Is there a simple/standard way of drawing this kind of drawing?
To be more precise I'm using these formulas when obtaining the above result. It works fine as long as the curve has no "sharp turns". This is the case that bothers me.
Thank you,
Iulian
-
I don't know; but you are talking about the envelope of a family of circles. en.wikipedia.org/wiki/Envelope_(mathematics) may be of some help. – Charles Matthews Apr 7 '11 at 8:15
If you just want a good easy picture, the simplest thing to do, as sugggested by Charles Matthews' comment, is to draw lots of equal radius circles centered about points on the curve. Your eye and brain will see the envelope. You could also draw lots of disks, or just use a computer drawing program such as Adobe Illustrator, make two copies of the curve (for instance on different layers) and give the lower copy a large stroke-width and a light color. (You can start from a PDF file that contains the mathematical curve, open it in Illustrator or a similar program, and edit as above).
If you want a more mathematical description or construction, the equidistant curves for a smooth curve $\gamma$ depend on the cut locus for $\gamma$. The cut locus is the set of points where there is more than one closest point on $\gamma$, and it is closely related to the whole theory of Voronoi diagrams. You can compute a good approximation of it from a Voronoi diagram program or a convex hull program, if you lift the curve to the paraboloid $z = x^2 + y^2 \subset \mathbb R^3$. In the complement of the cut locus, there is a smooth map $(x, y) \to C(x, y)$ where $C(x,y)$ is the closest point on $\gamma$; it can be traced out implicitly, it's the inverse function to what you're already doing. For a generic smooth curve, the cut locus is a piecewise smooth tree, whose endpoints are centers of osculating circles where the curvature of $\gamma$ has a local maximum. (However, in general, the cut locus can be quite complicated and have infinitely many branches, even for a $C^\infty$ curve). The edges of the cut locus can be traced from these endpoints, using the implicit function theorem; the main difficulty is keeping track of enough information to get the correct combinatorics for the graph. It's equivalent to the problem of constructing the convex hull of a simple curve on the paraboloid above.
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What is multiplexing gain and where does it apply?
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what is multiplexing gain
pmonon said:
If you mean multiplexing gain in MIMO context...
When MIMO is proposed it is shown to achieve higher rate than SISO. How to measure the gain? Well, from Shannon theorem we know that for an SISO link, the capacity is given by log(1+SNR) and for the m by n MIMO system the capapcity is shown to be min(m,n)lolg(1+SNR). Then, it is now a convention to refer to min(m,n) as multiplexing gain. It can be interpreted as multiple streams are multiplexed in spatial domain.
While the above line of thought focuses on transmision rate, i.e., capacity, another line of work studies the diversity order provided by multiple antennas. The latter is initiated by Alamouti who shows that a 2 tx antenna system can achieve the same diversity as a 2 rx antenna system. The idea here is to use multiple antennas to compensate channel fading to make the link more reliable, as opposed to shooting for higher data rate. The above two lines of work was bridged by Lizhong Zheng and David Tse, who tell us that with an MIMO system we can achieve higher data rate, as well as achieve higher reliablity. However, that is a tradeoff between the two.
Note that the tradeoff study is focus on high SNR and slow fading channel.
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