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 Water-Vapor Maser Survey for Active Galactic Nuclei: A Megamaser in NGC 6926We made a survey of water-vapor maser emission for 93 AGNs with theNobeyama 45-m and Mopra 22-m telescopes from 1999 to 2002. A megamaserwas detected in a Seyfert 2 galaxy, NGC 6926, at a distance of 80Mpc, in2002 June. [Greenhill et al. (2003a) have also reported a detection ofthe megamaser at the close date.] The peak flux density was 110mJy, andthe total isotropic luminosity was 340 Lȯ. The masershows triply peaked spectrum, suggesting an edge-on disk. A narrow-linefeature of the maser components at VLSR = 6001 kms-1 was strongly variable with a time scale of a few tens ofdays, and the variation should be of intrinsic origin. We also showed apossibility of variability of water-vapor maser emission of a megamaserpreviously detected in a Seyfert/ultraluminous FIR galaxy, NGC 6240. Dark galaxies or tidal debris? Kinematical clues to the origin of massive isolated HI cloudsAn extended HI cloud (VIRGOHI21) with an HI mass of~108Msolar and no apparent optical counterpart wasrecently discovered in the Virgo cluster. In order to understand theorigin of physical properties of apparently isolated HI clouds likeVIRGOHI21, we numerically investigate physical properties of tidal HIdebris that were formed by galaxy-galaxy interactions in clusters ofgalaxies. Our hydrodynamical simulations demonstrate that tidal debriswith total HI masses of 108-109Msolarcan have (1) a wide spread of HI velocities (>200kms-1),(2) a small mass fraction of stars (~10 per cent), and (3) a mean B-bandsurface brightness of the stellar components fainter than 30magarcsec-2. These results suggest that VIRGOHI21, which liesat a projected distance of ~150 kpc from the one-armed, HI-rich spiralgalaxy M99 (NGC 4254), is tidal debris. We propose that the comparisonbetween the simulated and the observed velocity fields of HI cloudsallows us to better understand their nature and origin (e.g. whetherthey are just tidal debris or are dark galaxies' that have HI gas onlyand are embedded within dark matter haloes). Massive HI clouds with no optical counterparts as high-density regions of intragroup HI rings and arcsWe present a new scenario in which massive intragroup HI clouds are thehigh-density parts of large HI rings/arcs formed by dynamicalinteraction between galaxy groups and gas-rich, low surface brightness(LSB) galaxies with extended gas discs. Our hydrodynamical simulationsdemonstrate that the group tidal field is very efficient at strippingthe outer HI gas of the disc if the gaseous disc of the LSB galaxyextends 2-5 times further than the stellar disc. We find that a massive,extended leading stream' orbiting the centre of the group can form outof the stripped outer HI envelope, while the severely shrunken LSBgalaxy, whose stellar disc remains unaffected, continues on its path.The result is a relatively isolated, massive HI cloud with a ring- orarc-like shape, a very inhomogeneous density distribution(NHI~ 1.0 × 1017-1.1 × 1020atomcm-2), and, initially, no stellar content. Only thehigh-density peaks of the simulated intragroup HI ring/arc can bedetected in many current HI observations. These will appear asrelatively isolated HI islands' near the group centre. We also findthat star formation can occur within the ring/arc, if the total gas masswithin the intragroup ring/arc is very large (~4 × 109Msolar). We discuss these results in terms of existingobservations of intragroup gas (e.g. the Leo Ring and HIPASS J0731-69)and intergalactic HII regions. Local Structures as Revealed by HIPASSThe HI Parkes All-Sky Survey (HIPASS) gives an unprecedented view of thelocal large-scale structures in the southern sky. I will review theresults from the HIPASS Bright Galaxy Catalogue (BGC, Koribalski et al.2004) and the first version of the deep catalogue (HICAT, Meyer et al.2004) with particular emphasis on galaxy structures across the Zone ofAvoidance. Some previously hardly noticed galaxy groups stand out quitedistinctively in the HI sky distribution and several large-scalestructures are seen for the first time. Because HI surveyspreferentially detect late-type spiral and dwarf galaxies, theirdistribution is less clustered than that of optically selected galaxies.HI surveys also significantly enhance the connectivity of large-scalefilaments by filling in gaps populated by gas-rich galaxies. Ultraluminous X-Ray Sources in Nearby Galaxies from ROSAT High Resolution Imager Observations I. Data AnalysisX-ray observations have revealed in other galaxies a class ofextranuclear X-ray point sources with X-ray luminosities of1039-1041 ergs s-1, exceeding theEddington luminosity for stellar mass X-ray binaries. Theseultraluminous X-ray sources (ULXs) may be powered by intermediate-massblack holes of a few thousand Msolar or stellar mass blackholes with special radiation processes. In this paper, we present asurvey of ULXs in 313 nearby galaxies withD25>1' within 40 Mpc with 467 ROSAT HighResolution Imager (HRI) archival observations. The HRI observations arereduced with uniform procedures, refined by simulations that help definethe point source detection algorithm employed in this survey. A sampleof 562 extragalactic X-ray point sources withLX=1038-1043 ergs s-1 isextracted from 173 survey galaxies, including 106 ULX candidates withinthe D25 isophotes of 63 galaxies and 110 ULX candidatesbetween 1D25 and 2D25 of 64 galaxies, from which aclean sample of 109 ULXs is constructed to minimize the contaminationfrom foreground or background objects. The strong connection betweenULXs and star formation is confirmed based on the striking preference ofULXs to occur in late-type galaxies, especially in star-forming regionssuch as spiral arms. ULXs are variable on timescales over days to yearsand exhibit a variety of long term variability patterns. Theidentifications of ULXs in the clean sample show some ULXs identified assupernovae (remnants), H II regions/nebulae, or young massive stars instar-forming regions, and a few other ULXs identified as old globularclusters. In a subsequent paper, the statistic properties of the surveywill be studied to calculate the occurrence frequencies and luminosityfunctions for ULXs in different types of galaxies to shed light on thenature of these enigmatic sources. Star Formation in H I-selected Galaxies. II. H II Region PropertiesA sample of 69 galaxies with radial velocities less than 2500 kms-1 was selected from the H I Parkes All Sky Survey (HIPASS)to deduce details about star formation in nearby disk galaxies selectedwith no bias to optical surface brightness selection effects. Broadband(B and R) and narrowband (Hα) images were obtained for all ofthese objects. More than half of the sample galaxies are late-type,dwarf disks (mostly Sc and Sm galaxies). We have measured the propertiesof the H II regions on Hα continuum-subtracted images, using theHIIphot package developed by Thilker et al. All but one of the galaxiescontained at least one detectable H II region. Examination of theproperties of the H II regions in each galaxy revealed that thebrightest regions in higher surface brightness galaxies tend to be moreluminous than those in lower surface brightness galaxies. A higherfraction (referred to as the diffuse fraction) of the Hα emissionfrom lower surface brightness galaxies comes from diffuse ionized gas. HII region luminosity functions (LFs) co-added according to surfacebrightness show that the shapes of the LFs for the lowest surfacebrightness galaxies are different from those for typical spiralgalaxies. This discrepancy could be caused by the lowest surfacebrightness galaxies having somewhat episodic star formation or by themforming a relatively larger fraction of their stars outside of dense,massive molecular clouds. In general, the results imply that theconditions under which star formation occurs in lower surface brightnessgalaxies are different than in more typical, higher surface brightnessspiral galaxies. The Distribution of Bar and Spiral Arm Strengths in Disk GalaxiesThe distribution of bar strengths in disk galaxies is a fundamentalproperty of the galaxy population that has only begun to be explored. Wehave applied the bar-spiral separation method of Buta and coworkers toderive the distribution of maximum relative gravitational bar torques,Qb, for 147 spiral galaxies in the statistically well-definedOhio State University Bright Galaxy Survey (OSUBGS) sample. Our goal isto examine the properties of bars as independently as possible of theirassociated spirals. We find that the distribution of bar strengthdeclines smoothly with increasing Qb, with more than 40% ofthe sample having Qb<=0.1. In the context of recurrent barformation, this suggests that strongly barred states are relativelyshort-lived compared to weakly barred or nonbarred states. We do notfind compelling evidence for a bimodal distribution of bar strengths.Instead, the distribution is fairly smooth in the range0.0<=Qb<0.8. Our analysis also provides a first look atspiral strengths Qs in the OSUBGS sample, based on the sametorque indicator. We are able to verify a possible weak correlationbetween Qs and Qb, in the sense that galaxies withthe strongest bars tend to also have strong spirals. Magnetic fields in barred galaxies. IV. NGC 1097 and NGC 1365We present λ3.5 cm and λ6.2 cm radio continuum maps intotal and polarized intensity of the barred galaxies NGC 1097 (at2´´-15´´ resolution) and NGC 1365 (at9´´-25´´ resolution). A previously unknown radiogalaxy southwest of NGC 1097 is reported. Apart from a smooth faintenvelope and a bright central region, both galaxies exhibit radio ridgesroughly overlapping with the massive dust lanes in the bar region. Thecontrast in total intensity across the radio ridges is compatible withcompression and shear of an isotropic random magnetic field, where thegas density compression ratio is approximately equal to 4 and the cosmicray density is constant across the ridges. The contrast in polarizedintensity is significantly smaller than that expected from compressionand shearing of the regular magnetic field; this could be the result ofdecoupling of the regular field from the dense molecular clouds. Theregular field in the ridge is probably strong enough to reducesignificantly shear in the diffuse gas (to which it is coupled) andhence to reduce magnetic field amplification by shearing. Thiscontributes to the misalignment of the observed field orientation withrespect to the velocity vectors of the dense gas. Our observations, forthe first time, indicate that magnetic forces can control the flow ofthe diffuse interstellar gas at kiloparsec scales. The total radiointensity reaches its maximum in the circumnuclear starburst regions,where the equipartition field strength is about 60 μG, amongst thestrongest fields detected in spiral galaxies so far. The regular fieldin the inner region has a spiral shape with large pitch angle,indicating the action of a dynamo. Magnetic stress leads to mass inflowtowards the centre, sufficient to feed the active nucleus in NGC 1097. -We detected diffuse X-ray emission, possibly forming a halo of hot gasaround NGC 1097. Cosmic magnetic fields - as observed in the Universe, in galactic dynamos, and in the Milky WayCosmic magnetism has that exotic Je ne sais quoi''! Magnetism has beenobserved in various objects, located near the edge of the Universe andall the way down to the Milky Way's center. The observed magnetic fieldcan take the cell-type shape in randomly-oriented large blobs found inintracluster gas or outside of clusters of galaxies, the helix shape insynchrotron jets, the longitudinal shape in ram-pressured shocks inradio lobes near elliptical galaxies, the spiral shape of logarithmicarms in spiral galaxies, or the egg shape of an enlarged interstellarbubble. In strength, the magnetic field varies from 0.1 nG(cosmological), to 20 μG (galaxies, jets, superbubbles), and to 1 mGin the Milky Way filaments.Magnetism plays a small physical role in the formation of largestructures. It acts as a tracer of the dynamical histories ofcosmological and intracluster events, it guides the motion of theinterstellar ionised gas, and it aligns the charged dust particles.Batteries and dynamos are often employed in models to create and amplifyseed magnetic fields. Starting soon after the Big Bang (redshiftz>2000), this review covers the cosmological background surface(z~1100, distance ~4.3 Gpc), the epoch of first stars (z~20 distance~4.1 Gpc), the currently observable Universe (z~10, distance ~3.9 Gpc),superclusters of galaxies (size ~50 Mpc), intracluster gas (size ~10Mpc), galaxies (~30 kpc), spiral arms (~10 kpc), interstellarsuperbubbles (~100 pc), synchrotron filaments (~10 pc), and the MilkyWay's center. Bar-induced perturbation strengths of the galaxies in the Ohio State University Bright Galaxy Survey - IBar-induced perturbation strengths are calculated for a well-definedmagnitude-limited sample of 180 spiral galaxies, based on the Ohio StateUniversity Bright Galaxy Survey. We use a gravitational torque method,the ratio of the maximal tangential force to the mean axisymmetricradial force, as a quantitative measure of the bar strength. Thegravitational potential is inferred from an H-band light distribution byassuming that the M/L ratio is constant throughout the disc. Galaxiesare deprojected using orientation parameters based on B-band images. Inorder to eliminate artificial stretching of the bulge, two-dimensionalbar-bulge-disc decomposition has been used to derive a reliable bulgemodel. This bulge model is subtracted from an image, the disc isdeprojected assuming it is thin, and then the bulge is added back byassuming that its mass distribution is spherically symmetric. We findthat removing the artificial bulge stretch is important especially forgalaxies having bars inside large bulges. We also find that the massesof the bulges can be significantly overestimated if bars are not takeninto account in the decomposition.Bars are identified using Fourier methods by requiring that the phasesof the main modes (m= 2, m= 4) are maintained nearly constant in the barregion. With such methods, bars are found in 65 per cent of the galaxiesin our sample, most of them being classified as SB-type systems in thenear-infrared by Eskridge and co-workers. We also suggest that as muchas ~70 per cent of the galaxies classified as SAB-types in thenear-infrared might actually be non-barred systems, many of them havingcentral ovals. It is also possible that a small fraction of the SAB-typegalaxies have weak non-classical bars with spiral-like morphologies. The neutral hydrogen environments of the nearby galaxies WLM, NGC 1313 and Sextans A We have mapped the neutral gas content of the surroundings of threegalaxies on the outskirts of the Local Group - Wolf-Lundmark-Melotte(WLM), NGC 1313 and Sextans A - at high velocity resolution andbrightness sensitivity. We present high-quality HI spectra andparameters for the target galaxies, and find no unknown companion HIclouds nearer than ~100 kpc to the targets, despite reaching asensitivity of ~106 Msolar for narrow-linewidthobjects. Ram Pressure Effects on the Magnetic Field of NGC 2442The λ6 cm radio continuum emission from the barred galaxy NGC2442 displays several unusual features that are probably due to theinteraction of the galaxy with the intergalactic medium. HIPASS J0731-69: Tidal Debris, or Primordial Gas Cloud?We present follow-up high-resolution H I, deep optical, and molecularobservations of the intergalactic gas cloud HIPASS J0731-69, andre-examine the question of its origin in light of these new data. HI Tidal Tails, Bridges and CloudsThere is plenty of intergalactic H I gas without any obvious stellarcontent ranging from (1) extended gas envelopes around some normal andpeculiar galaxies, (2) tidal tails/bridges in interacting or merginggalaxy systems, (3) large-scale rings around early type galaxies, and(4) detached clouds at varying distances from associated galaxies, butthere are few or no isolated H I clouds.The HIPASS Bright Galaxy Catalog, which covers the whole southern sky,contains only one definite extragalactic H I cloud which is locatedclose to the galaxy NGC 2442 whereas it is sensitive to isolated H Iclouds with MHI > 106 × D2Mȯ. The space density of H I clouds is therefore about1/1000th that of galaxies with the same MHI. Star Formation in H I-Selected Galaxies. I. Sample CharacteristicsA sample of 69 galaxies with radial velocities of less than 2500 kms-1 was selected from the H I Parkes All-Sky Survey (HIPASS)and imaged in broadband B and R and narrowband Hα, to deducedetails about star formation in nearby disk galaxies while avoidingsurface brightness selection effects. The sample is dominated bylate-type, dwarf disks (mostly Sc and Sm galaxies) with exponential diskscale lengths of ~1-5 kpc. The HIPASS galaxies, on average, have lowerstar formation rates (SFRs), are bluer, and have lower surfacebrightness than an optically selected sample. H II regions were detectedin all but one of the galaxies. Many galaxies had as few as two to fiveH II regions. The galaxies' Hα equivalent widths, colors, and SFRsper unit of H I mass are best explained by young mean ages (~3-5 Gyr,according to Schmidt-law models) with star formation histories in whichthe SFRs were higher in the past. Comparison of the surface brightnesscoverage of the HIPASS galaxies with that of an optically selectedsample shows that such a sample may miss ~10% of the local galaxy numberdensity and could possibly miss as much as 3%-4% of the SFR density. Theamount lower surface brightness galaxies contribute to the totalluminosity density may be insignificant, but this conclusion is somewhatdependent on how the fluxes of these objects are determined. Oxygen and nitrogen abundances in nearby galaxies. Correlations between oxygen abundance and macroscopic propertiesWe performed a compilation of more than 1000 published spectra of H IIregions in spiral galaxies. The oxygen and nitrogen abundances in each HII region were recomputed in a homogeneous way, using the P-method. Theradial distributions of oxygen and nitrogen abundances were derived. Thecorrelations between oxygen abundance and macroscopic properties areexamined. We found that the oxygen abundance in spiral galaxiescorrelates with its luminosity, rotation velocity, and morphologicaltype: the correlation with the rotation velocity may be slightlytighter. There is a significant difference between theluminosity-metallicity relationship obtained here and that based on theoxygen abundances determined through the R23-calibrations.The oxygen abundance of NGC 5457 recently determined using directmeasurements of Te (Kennicutt et al. \cite{Kennicutt2003})agrees with the luminosity-metallicity relationship derived in thispaper, but is in conflict with the luminosity-metallicity relationshipderived with the R23-based oxygen abundances. The obtainedluminosity-metallicity relation for spiral galaxies is compared to thatfor irregular galaxies. Our sample of galaxies shows evidence that theslope of the O/H - MB relationship for spirals (-0.079± 0.018) is slightly more shallow than that for irregulargalaxies (-0.139 ± 0.011). The effective oxygen yields wereestimated for spiral and irregular galaxies. The effective oxygen yieldincreases with increasing luminosity from MB  -11 toMB  -18 (or with increasing rotation velocity fromVrot  10 km s-1 to Vrot  100km s-1) and then remains approximately constant. Irregulargalaxies from our sample have effective oxygen yields lowered by afactor of 3 at maximum, i.e. irregular galaxies usually keep at least1/3 of the oxygen they manufactured during their evolution.Appendix, Tables \ref{table:refero}, \ref{table:referV}, and Figs.\ref{figure:sample2}-\ref{figure:sample5} are only available inelectronic form at http://www.edpsciences.org} Magnetic fields in barred galaxies. III. The southern peculiar galaxy NGC 2442Observations of the southern peculiar galaxy NGC 2442with the Australia Telescope Compact Array in total and linearlypolarized radio continuum at λ6 cm are presented and comparedwith previously obtained Hα data. The distribution of polarizedemission, a signature of regular magnetic fields, reveals some physicalphenomena which are unusual among spiral galaxies. We find evidence fortidal interaction and/or ram pressure from the intergalactic mediumcompressing the magnetic field at the northern and western edges of thegalaxy. The radial component of the regular magnetic field in thenorthern arm is directed away from the centre of the galaxy, a findingwhich is in contrast to the majority of galaxies studied to date. Theoval distortion caused by the interaction generates a sudden jump of themagnetic field pattern upstream of the inner northern spiral arm,similar to galaxies with long bars. An unusual island'' of strongregular magnetic field east of the galaxy is probably the brightest partof a magnetic arm similar to those seen in some normal spiral galaxies,which appear to be phase-shifted images of the preceding optical arm.The strong magnetic field of the island'' may indicate a past phase ofactive star formation when the preceding optical arm was exposed to rampressure. Double-barred galaxies. I. A catalog of barred galaxies with stellar secondary bars and inner disksI present a catalog of 67 barred galaxies which contain distinct,elliptical stellar structures inside their bars. Fifty of these aredouble-barred galaxies: a small-scale, inner or secondary bar isembedded within a large-scale, outer or primary bar. I providehomogenized measurements of the sizes, ellipticities, and orientationsof both inner and outer bars, along with global parameters for thegalaxies. The other 17 are classified as inner-disk galaxies, where alarge-scale bar harbors an inner elliptical structure which is alignedwith the galaxy's outer disk. Four of the double-barred galaxies alsopossess inner disks, located in between the inner and outer bars. Whilethe inner-disk classification is ad-hoc - and undoubtedly includes someinner bars with chance alignments (five such probable cases areidentified) - there is good evidence that inner disks form astatistically distinct population, and that at least some are indeeddisks rather than bars. In addition, I list 36 galaxies which may bedouble-barred, but for which current observations are ambiguous orincomplete, and another 23 galaxies which have been previously suggestedas potentially being double-barred, but which are probably not. Falsedouble-bar identifications are usually due to features such as nuclearrings and spirals being misclassified as bars; I provide someillustrated examples of how this can happen.A detailed statistical analysis of the general population of double-barand inner-disk galaxies, as represented by this catalog, will bepresented in a companion paper.Tables \ref{tab:measured} and \ref{tab:deproj} are only available inelectronic form at http://www.edpsciences.org Quasars and active galaxies.Not Available First results from the HI Jodrell All Sky Survey: inclination-dependent selection effects in a 21-cm blind surveyDetails are presented of the HI Jodrell All Sky Survey (HIJASS). HIJASSis a blind neutral hydrogen (HI) survey of the northern sky (δ> 22°), being conducted using the multibeam receiver on theLovell Telescope (full width at half-maximum beamwidth 12 arcmin) atJodrell Bank. HIJASS covers the velocity range -3500 to 10 000 kms-1, with a velocity resolution of 18.1 km s-1 andspatial positional accuracy of ~2.5 arcmin. Thus far about 1115deg2 of sky have been surveyed. The average rms noise duringthe early part of the survey was around 16 mJy beam-1.Following the first phase of the Lovell Telescope upgrade (in 2001), therms noise is now around 13 mJy beam-1. We describe themethods of detecting galaxies within the HIJASS data and of measuringtheir HI parameters. The properties of the resulting HI-selected sampleof galaxies are described. Of the 222 sources so far confirmed, 170 (77per cent) are clearly associated with a previously catalogued galaxy. Afurther 23 sources (10 per cent) lie close (within 6 arcmin) to apreviously catalogued galaxy for which no previous redshift exists. Afurther 29 sources (13 per cent) do not appear to be associated with anypreviously catalogued galaxy. The distributions of peak flux, integratedflux, HI mass and cz are discussed. We show, using the HIJASS data, thatHI self-absorption is a significant, but often overlooked, effect ingalaxies with large inclination angles to the line of sight. Properlyaccounting for it could increase the derived HI mass density of thelocal Universe by at least 25 per cent. The effect that this will haveon the shape of the HI mass function will depend on how self-absorptionaffects galaxies of different morphological types and HI masses. We alsoshow that galaxies with small inclinations to the line of sight may alsobe excluded from HI-selected samples, since many such galaxies will haveobserved velocity widths that are too narrow for them to bedistinguished from narrow-band radio-frequency interference. This effectwill become progressively more serious for galaxies with smallerintrinsic velocity widths. If, as we might expect, galaxies with smallerintrinsic velocity widths have smaller HI masses, then compensating forthis effect could significantly steepen the faint-end slope of thederived HI mass function. The IRAS Revised Bright Galaxy SampleIRAS flux densities, redshifts, and infrared luminosities are reportedfor all sources identified in the IRAS Revised Bright Galaxy Sample(RBGS), a complete flux-limited survey of all extragalactic objects withtotal 60 μm flux density greater than 5.24 Jy, covering the entiresky surveyed by IRAS at Galactic latitudes |b|>5°. The RBGS includes629 objects, with median and mean sample redshifts of 0.0082 and 0.0126,respectively, and a maximum redshift of 0.0876. The RBGS supersedes theprevious two-part IRAS Bright Galaxy Samples(BGS1+BGS2), which were compiled before the final(Pass 3) calibration of the IRAS Level 1 Archive in 1990 May. The RBGSalso makes use of more accurate and consistent automated methods tomeasure the flux of objects with extended emission. The RBGS contains 39objects that were not present in the BGS1+BGS2,and 28 objects from the BGS1+BGS2 have beendropped from RBGS because their revised 60 μm flux densities are notgreater than 5.24 Jy. Comparison of revised flux measurements forsources in both surveys shows that most flux differences are in therange ~5%-25%, although some faint sources at 12 and 25 μm differ byas much as a factor of 2. Basic properties of the RBGS sources aresummarized, including estimated total infrared luminosities, as well asupdates to cross identifications with sources from optical galaxycatalogs established using the NASA/IPAC Extragalactic Database. Inaddition, an atlas of images from the Digitized Sky Survey with overlaysof the IRAS position uncertainty ellipse and annotated scale bars isprovided for ease in visualizing the optical morphology in context withthe angular and metric size of each object. The revised bolometricinfrared luminosity function, φ(Lir), forinfrared-bright galaxies in the local universe remains best fit by adouble power law, φ(L)~Lα, withα=-0.6(+/-0.1) and α=-2.2(+/-0.1) below and above thecharacteristic'' infrared luminosityL*ir~1010.5Lsolar,respectively. A companion paper provides IRAS High Resolution (HIRES)processing of over 100 RBGS sources where improved spatial resolutionoften provides better IRAS source positions or allows for deconvolutionof close galaxy pairs. The 1000 Brightest HIPASS Galaxies: The H I Mass Function and ΩHIWe present a new, accurate measurement of the H I mass function ofgalaxies from the HIPASS Bright Galaxy Catalog, a sample of 1000galaxies with the highest H I peak flux densities in the southern(δ<0deg) hemisphere. This sample spans nearly 4orders of magnitude in H I mass[log(MHI/Msolar)+2logh75=6.8-10.6] andis the largest sample of H I-selected galaxies to date. We develop abivariate maximum likelihood technique to measure the space density ofgalaxies and show that this is a robust method, insensitive to theeffects of large-scale structure. The resulting H I mass function can befitted satisfactorily with a Schechter function with faint-end slopeα=-1.30. This slope is found to be dependent on morphologicaltype, with late-type galaxies giving steeper slopes. We extensively testvarious effects that potentially bias the determination of the H I massfunction, including peculiar motions of galaxies, large-scale structure,selection bias, and inclination effects, and we quantify these biases.The large sample of galaxies enables an accurate measurement of thecosmological mass density of neutral gas:ΩHI=(3.8+/-0.6)×10-4h-175. Low surface brightness galaxies contributeonly ~15% to this value, consistent with previous findings. The 2MASS Large Galaxy AtlasWe present the largest galaxies as seen in the near-infrared (1-2μm), imaged with the Two Micron All Sky Survey (2MASS), ranging inangular size from 1' to 1.5d. We highlight the 100 largest in thesample. The galaxies span all Hubble morphological types, includingelliptical galaxies, normal and barred spirals, and dwarf and peculiarclasses. The 2MASS Large Galaxy Atlas provides the necessary sensitivityand angular resolution to examine in detail morphologies in thenear-infrared, which may be radically different from those in theoptical. Internal structures such as spirals, bulges, warps, rings,bars, and star formation regions are resolved by 2MASS. In addition tolarge mosaic images, the atlas includes astrometric, photometric, andshape global measurements for each galaxy. A comparison of fundamentalmeasures (e.g., surface brightness, Hubble type) is carried out for thesample and compared with the Third Reference Catalogue. We furthershowcase NGC 253 and M51 (NGC 5194/5195) to demonstrate the quality anddepth of the data. The atlas represents the first uniform, all-sky,dust-penetrated view of galaxies of every type, as seen in thenear-infrared wavelength window that is most sensitive to the dominantmass component of galaxies. The images and catalogs are availablethrough the NASA/IPAC Extragalactic Database and Infrared ScienceArchive and are part of the 2MASS Extended Source Catalog. Morphological classification of the OSU Bright Spiral Galaxy SurveyTo quantify the distribution of bar shapes in spiral galaxies, we haveanalysed 113 H-band and 89 B-band galaxy images from the Ohio StateUniversity Bright Spiral Galaxy Survey. Parameters measuring bar shapeand position along the Hubble sequence were obtained in each waveband.Evidence was found for a bimodality in the distribution of bar shape,implying that barred and unbarred galaxies are not just the extrema of asingle distribution, and that any evolution between these two statesmust occur on a rapid time-scale. Objective bar shapes measured in theH-band were found to be more closely related to visual classificationsthan B-band bar strengths, as the B-band images are somewhat compromisedby localized star formation, especially in later type systems. Galaxieswere found to be more centrally concentrated in the infrared. Later typegalaxies showed greater asymmetry in the optical than the infrared,presumably again owing to localized star formation, but on average thebar shapes in the two bands were found to be the same. The Luminosity-Metallicity Relation, Effective Yields, and Metal Loss in Spiral and Irregular GalaxiesI present results on the correlation between galaxy mass, luminosity,and metallicity for a sample of spiral and irregular galaxies havingwell-measured abundance profiles, distances, and rotation speeds.Additional data for low surface brightness galaxies from the literatureare also included for comparison. These data are combined to study themetallicity-luminosity and metallicity-rotation speed correlations forspiral and irregular galaxies. The metallicity-luminosity correlationshows its familiar form for these galaxies, a roughly uniform change inthe average present-day O/H abundance of about a factor of 100 over 11mag in B luminosity. However, the O/H-Vrot relation shows achange in slope at a rotation speed of about 125 km s-1. Atfaster Vrot, there appears to be no relation between averagemetallicity and rotation speed. At lower Vrot, themetallicity correlates with rotation speed. This change in behaviorcould be the result of increasing loss of metals from the smallergalaxies in supernova-driven winds. This idea is tested by looking atthe variation in effective yield, derived from observed abundances andgas fractions assuming closed box chemical evolution. The effectiveyields derived for spiral and irregular galaxies increase by a factor of10-20 from Vrot~5 to 300 km s-1, asymptoticallyincreasing to approximately constant yeff forVrot>~150 km s-1. The trend suggests thatgalaxies with Vrot<~100-150 km s-1 may lose alarge fraction of their supernova ejecta, while galaxies above thisvalue tend to retain metals. A Search for H2O Maser Emission in Southern Active Galactic Nuclei and Star-forming Galaxies: Discovery of a Maser in the Edge-on Galaxy IRAS F01063-8034We report the cumulative results of five surveys for H2Omaser emission at 1.35 cm wavelength in 131 active galactic nuclei(AGNs) and star-forming galaxies, conducted at the Parkes Observatorybetween 1993 and 1998. We detected one new maser, in the edge-on galaxyIRAS F01063-8034, which exhibits a single ~0.1 Jy spectral feature at4282+/-6 km s-1 (heliocentric) with an unusually large54+/-16 km s-1 half-power full width. The centroid velocityof the emission increased to 4319.6+/-0.6 km s-1 (38+/-2 kms-1 width) over the 13 days between discovery andconfirmation of the detection. A similarly broad-line width and largechange in velocity has been noted for the maser in NGC 1052, wherein jetactivity excites the emission. Neither optical spectroscopy,radio-infrared correlations, nor infrared colors provide compellingevidence of unusual activity in the nucleus of IRAS F01063-8034. Sincethe galaxy appears to be outwardly normal at optical and infraredwavelengths, detection of an H2O maser therein is unique. Themaser emission is evidence that the galaxy harbors an AGN that isprobably obscured by the edge-on galactic disk. The detection highlightsthe possibility that undetected AGNs could be hidden in other relativelynearby galaxies. No other maser emission features have been identifiedat velocities between 3084 and 6181 km s-1. The 1000 Brightest HIPASS Galaxies: Newly Cataloged GalaxiesThe H I Parkes All-Sky Survey (HIPASS) is a blind 21 cm survey forextragalactic neutral hydrogen, covering the whole southern sky. TheHIPASS Bright Galaxy Catalog (BGC) is a subset of HIPASS and containsthe 1000 H I-brightest (peak flux density) galaxies. Here we present the138 HIPASS BGC galaxies that had no redshift measured prior to theParkes multibeam H I surveys. Of the 138 galaxies, 87 are newlycataloged. Newly cataloged is defined as having no optical (or infrared)counterpart in the NASA/IPAC Extragalactic Database. Using the DigitizedSky Survey, we identify optical counterparts for almost half of thenewly cataloged galaxies, which are typically of irregular or Magellanicmorphological type. Several H I sources appear to be associated withcompact groups or pairs of galaxies rather than an individual galaxy.The majority (57) of the newly cataloged galaxies lie within 10° ofthe Galactic plane and are missing from optical surveys as a result ofconfusion with stars or dust extinction. This sample also includes newlycataloged galaxies first discovered by Henning et al. in the H I shallowsurvey of the zone of avoidance. The other 30 newly cataloged galaxiesescaped detection because of their low surface brightness or opticalcompactness. Only one of these, HIPASS J0546-68, has no obvious opticalcounterpart, as it is obscured by the Large Magellanic Cloud. We findthat the newly cataloged galaxies with |b|>10° are generally lowerin H I mass and narrower in velocity width compared with the totalHIPASS BGC. In contrast, newly cataloged galaxies behind the Milky Wayare found to be statistically similar to the entire HIPASS BGC. Inaddition to these galaxies, the HIPASS BGC contains four previouslyunknown H I clouds. A Catalog of H I-Selected Galaxies from the South Celestial Cap Region of SkyThe first deep catalog of the H I Parkes All Sky Survey (HIPASS) ispresented, covering the south celestial cap (SCC) region. The SCC areais ~2400 deg2 and covers δ<-62°. The average rmsnoise for the survey is 13 mJy beam-1. Five hundredthirty-six galaxies have been cataloged according to their neutralhydrogen content, including 114 galaxies that have no previous catalogedoptical counterpart. This is the largest sample of galaxies from a blindH I survey to date. Most galaxies in optically unobscured regions of skyhave a visible optical counterpart; however, there is a small populationof low-velocity H I clouds without visible optical counterparts whoseorigins and significance are unclear. The rms accuracy of the HIPASSpositions is found to be 1.9′. The H I mass range of galaxiesdetected is from ~106 to ~1011 Msolar.There are a large number of late-type spiral galaxies in the SCC sample(66%), compared with 30% for optically selected galaxies from the sameregion in the NASA Extragalactic Database. The average ratio of H I massto B luminosity of the sample increases according to optical type, from1.8 Msolar/Lsolar for early types to 3.2Msolar/Lsolar for late-type galaxies. The HI-detected galaxies tend to follow the large-scale structure traced bygalaxies found in optical surveys. From the number of galaxies detectedin this region of sky, we predict the full HIPASS catalog will contain~5000 galaxies, to a peak flux density limit of ~39 mJy (3 σ),although this may be a conservative estimate as two large voids arepresent in the region. The H I mass function for this catalog ispresented in a subsequent paper. The Visibility of Galactic Bars and Spiral Structure at High RedshiftsWe investigate the visibility of galactic bars and spiral structure inthe distant universe by artificially redshifting 101 B-band CCD imagesof local spiral galaxies from the Ohio State University Bright SpiralGalaxy Survey. These local galaxy images represent a much fairerstatistical baseline than the galaxy atlas images presented by Frei etal. in 1995, the most commonly used calibration sample for morphologicalwork at high redshifts. Our artificially redshifted images correspond toHubble Space Telescope I814-band observations of the localgalaxy sample seen at z=0.7, with integration times matching those ofboth the very deep northern Hubble Deep Field (HDF) data and the muchshallower HDF flanking field observations. The expected visibility ofgalactic bars is probed in two ways: (1) using traditional visualclassification and (2) by charting the changing shape of the galaxydistribution in `Hubble space,'' a quantitative two-parameterdescription of galactic structure that maps closely onto Hubble'soriginal tuning fork. Both analyses suggest that over two-thirds ofstrongly barred luminous local spirals (i.e., objects classified as SBin the Third Reference Catalogue) would still be classified as stronglybarred at z=0.7 in the HDF data. Under the same conditions, most weaklybarred spirals (classified SAB in the Third Reference Catalogue) wouldbe classified as regular spirals. The corresponding visibility of spiralstructure is assessed visually, by comparing luminosity classificationsfor the artificially redshifted sample with the corresponding luminosityclassifications from the Revised Shapley-Ames Catalog. We find that forexposure times similar to that of the HDF, spiral structure should bedetectable in most luminous (MB~M*) low-inclination spiralgalaxies at z=0.7 in which it is present. However, obvious spiralstructure is only detectable in ~30% of comparable galaxies in the HDFflanking field data using the Wide Field Planetary Camera 2. Our studyof artificially redshifted local galaxy images suggests that, whenviewed at similar resolution, noise level, and redshift-correctedwavelength, barred spirals are less common at z~0.7 than they are atz=0.0, although more data are needed to definitively rule out thepossibility that cosmic variance is responsible for much of this effect. Magnetic fields in barred galaxies. I. The atlasThe total and polarized radio continuum emission of 20 barred galaxieswas observed with the Very Large Array (VLA) at lambda 3, 6, 18 and 22cm and with the Australia Telescope Compact Array (ATCA) at lambda 6 cmand 13 cm. Maps at 30\arcsec angular resolution are presented here.Polarized emission (and therefore a large-scale regular magnetic field)was detected in 17 galaxies. Most galaxies of our sample are similar tonon-barred galaxies with respect to the radio/far-infrared fluxcorrelation and equipartition strength of the total magnetic field.Galaxies with highly elongated bars are not always radio-bright. Wediscuss the correlation of radio properties with the aspect ratio of thebar and other measures of the bar strength. We introduce a new measureof the bar strength, Lambda , related to the quadrupole moment of thebar's gravitational potential. The radio surface brightness I of thebarred galaxies in our sample is correlated with Lambda , I~Lambda0.4+/-0.1, and thus is highest in galaxies with a long barwhere the velocity field is distorted by the bar over a large fractionof the disc. In these galaxies, the pattern of the regular field issignificantly different from that in non-barred galaxies. In particular,field enhancements occur upstream of the dust lanes where the fieldlines are oriented at large angles to the bar's major axis. Polarizedradio emission seems to be a good indicator of large-scalenon-axisymmetric motions. Tables 3, 4 and Figs. 8-10, 13, 15, 16, 18 and22 are only available in electronic form at http://www.edpsciences.org
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Template for writing a PhD thesis in Markdown

# tompollard/phd_thesis_markdown

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# Template for writing a PhD thesis in Markdown

This repository provides a framework for writing a PhD thesis in Markdown. I used the template for my PhD submission to University College London (UCL), but it should be straightforward to adapt suit other universities too.

## Citing the template

If you have used this template in your work, please cite the following publication:

Tom Pollard et al. (2016). Template for writing a PhD thesis in Markdown. Zenodo. http://dx.doi.org/10.5281/zenodo.58490

## Quickstart

If you're a mac user and you have conda and brew installed, run the following in your terminal to install and generate the example outputs:

# get texlive

# update tlmgr and packages
sudo tlmgr update --self

# make python venv and install pandoc
conda create -n phd -y python=3.7 pandoc
conda activate phd

# Install required python and texlive packages
make install

## Why write my thesis in Markdown?

Markdown is a super-friendly plain text format that can be easily converted to a bunch of other formats like PDF, Word and LaTeX. You'll enjoy working in Markdown because:

• it is a clean, plain-text format...
• ...but you can use LaTeX when you need it (for example, in laying out mathematical formula).
• it doesn't suffer from the freezes and crashes that some of us experience when working with large, image-heavy Word documents.
• comments, drafts of text, etc can be added to the document by wrapping them in <!-- -->
• it works well with Git, so keeping backups is straightforward. Just commit the changes and then push them to your repository.
• it is able to take advantage of autocompletion capabilities for figures and citations in several text editors (VSCode, Sublime, etc.)
• there is no lock-in. If you decide that Markdown isn't for you, then just output to Word, or whatever, and continue working in the new format.

## Are there any reasons not to use Markdown?

There are some minor annoyances:

• if you haven't worked with Markdown before then you'll find yourself referring to the style-guide fairly often at first.
• it isn't possible to add a short caption to tables and figures (figures are now fixed, thanks to @martisak). This means that /listoftables includes the long-caption, which probably isn't what you want. If you want to include the list of tables, then you'll need to write it manually.
• the style documents in this framework could be improved. The PDF and HTML (thanks @ArcoMul) outputs are acceptable, but HTML and Word needs work if you plan to output to this format.
• there is no straightforward way of specifying image size in the markdown right now, though this functionality is coming (see: #15) (Image size can now be specified. Thanks to @rudolfbyker for highlighting this).

## How is the template organised?

• Makefile => contains instructions for using Pandoc to produce the final thesis.
• output/ => directory to hold the final version.
• source/ => directory to hold the thesis content. Includes the references.bib file.
• scratch/ => directory to hold tables which can be converted between different formats.
• source/figures/ => directory to hold the figures.
• style/ => directory to hold the style documents.

## How do I get started?

1. Install the following software:
• A text editor, like Sublime, which is what you'll use write the thesis.
• A LaTeX distribution (for example, MacTeX for Mac users).
• Pandoc, for converting the Markdown to the output format of your choice.
• Pandoc plugins by running make install
• Git, for version control.
2. Fork the repository on Github
4. (Skip this step to use default UCL style) Configure style for your institution - see instructions below
5. Navigate to the directory that contains the Makefile and type "make pdf" (or "make html") at the command line to update the PDF (or HTML) in the output directory.
In case of an error (e.g. make: *** [pdf] Error 43), consult this article for possible fixes. Most importantly, make sure tlmgr is properly installed, then run install.sh
6. Edit the files in the 'source' directory, then goto step 5.

## How does it work?

The universal document converter pandoc does all the heavy lifting. For example:

1. make pdf (the code under pdf: ... in Makefile) runs pandoc which takes as input
1. the markdown files which contain the writing content: input/*.md
2. a yaml file with metadata: input/metadata.yml
3. a LaTeX template: style/template.tex
4. a LaTeX header: style/preamble.tex
5. a BibTeX file of your references: input/references.bib
6. a csl style file for citations: style/ref_format.csl
7. a bunch of options which change the output e.g. --number-sections
2. the output produced is:
1. the generated pdf: output/thesis.pdf
2. logs (which contain the .tex which was compiled): pandoc.pdf.log

Put simply, pandoc uses the latex template provided to create a .tex file, then compiles it. In detail, pandoc processes the input files in the following way (the file names in quotes aren't visible to you, but are named for the purpose of understanding):

1. Make replacements within the markdown files input/*.md e.g.:
• references to figures, captions, and sections are handled: @fig:my_fig -> \ref{fig:my_fig}
• equations are converted to LaTeX and numbered: $f(x) = ax^3 + bx^2 + cx + d$ {#eq:my_equation} -> $$f(x) = ax^3 + bx^2 + cx + d\label{eq:my_equation}$$
• citations are handled: [@Cousteau1963] -> (Cousteau Jacques & Dugan James 1963)
• see input/*.md for more examples!
2. Create "body.tex" by:
• converting all the *.md files in the order that they were stated in the pandoc call

# Troubleshooting

1. The first thing to try if the make * command fails is a simpler build, e.g. if make pdf failed, try make tex to see if that fails too.
2. If tex compilation is failing (i.e. make tex works but make pdf fails), try updating tex live and/or packages. For example, if you get the error make: *** [pdf] Error 43, have a look in pandoc.pdf.log for the error. If it is something like
l3backend-xdvipdfmx.def' not found

then try:

sudo tlmgr update --self
sudo tlmgr l3backend
# Full nuclear option - update *all* the packages! (takes about 10m)
# sudo tlmgr update --all
1. Try reinstalling everything from scratch (tip: check out .travis.yml)
2. Search the github issues and pull requests in this repo

# Contributing

Contributions to the template are encouraged! There are lots of things that could be improved, like:

• finding a way to add short captions for the tables, so that the lists of tables can be automatically generated.
• cleaning up the LaTeX templates, which are messy at the moment.
• improving the style of Word and TeX outputs.

Please fork and edit the project, then send a pull request.

Template for writing a PhD thesis in Markdown

## Packages 0

No packages published

format: plain


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# It Has Been Established that P : Einstein Was Q: Although a Great Scientist R : Weak in Arithmetic S : Right from His School Days the Proper Sequence Should Be - English Language

MCQ

In the question below, there is a sentence of which some parts have been jumbled up. Rearrange these parts which are labelled P, Q, R and S to produce the correct sentence. Choose the proper sequence.

It has been established that
P : Einstein was
Q: although a great scientist
R : weak in arithmetic
S : right from his school days
The proper sequence should be

• SRPQ

• QPRS

• QPSR

• RQPS

#### Solution

SRPQ

Concept: Para-jumbles (Entrance Exam)
Is there an error in this question or solution?


text:
SAMSON Elements

SAMSON Elements are modules for SAMSON, developed thanks to the SAMSON SDK, and distributed on SAMSON Connect. SAMSON Elements are what makes SAMSON useful: without any SAMSON Element, SAMSON cannot even create an atom, open a file, etc.

SAMSON Elements expose their functionality to SAMSON and other SAMSON Elements through a powerful introspection mechanism. This introspection mechanism makes it possible to save and load data graph objects without knowing their type, to reuse exposed functionality without having access to the source files or header files of the exposed SAMSON Element, to perform scripting, to pipeline tasks, etc.

The Element Generator can be used to generate a new SAMSON Element in a few clicks and help kickstart development.

# Element classes

A SAMSON Element contains one or more classes that provide functionality. Although any class may be exposed in a SAMSON Element, some classes, derived from classes provided in the SAMSON SDK, play a specific role in SAMSON.

## Apps

Apps are tools that may provide any type of functionality. An app may be e.g. a connector to an external executable or web service, may wrap previously developed code to integrate its functionality with SAMSON and other SAMSON Elements, or provide entirely new functionality based on the SAMSON Application Programming Interface. When SAMSON loads an app during startup, it includes it in the App menu and the App toolbar.

## Editors

Editors are classes that receive user interaction events (e.g. mouse and keyboard events) from SAMSON, which may be used to provide potentially complex editing functionality. For example, an editor may be a nanotube generator that lets users create a new nanotube model in a few clicks, a tool for deforming molecular structures while preserving local rigidity, a rectangle selection tool, a tool to apply a rigid-body transform to a model, etc. At startup, SAMSON positions editors in the Edit menu and the Editors toolbar.

One and only one editor is active at any time.

## Importers

Importers are classes dedicated to parsing files. Precisely, they implement an importFromFile function that may be called by s or other SAMSON Elements to parse files and, potentially, add nodes to SAMSON's data graph. An importer may be a PDB parser, an electron density parser, etc. Whenever a new importer is loaded at startup, SAMSON adds it to the list of available importers. Importers are used in particular when opening a new file from the File menu.

## Exporters

Exporters are classes dedicated to exporting content from the data graph to files. Precisely, they implement an exportToFile function that may be called by SAMSON or other SAMSON Elements to export to files. An exporter may be a PDB exporter, an XYZ exporter, etc. Whenever a new exporter is loaded at startup, SAMSON adds it to the list of available exporters, used in particular when exporting to a file from the File menu.

## Interaction models

Interaction models are one of the five categories of models in SAMSON (with structural models, dynamical models, visual models and property models). They are responsible for computing energies and forces and are used in SAMSON to perform various modeling and simulation tasks. They may rely on SAMSON's signals and slots mechanism to perform incremental calculations used in adaptive simulations. An interaction model may be e.g. a spring model, an elastic network model, an extended Hückel model, etc. When a new interaction model is loaded at startup, SAMSON stores it in a list of available interaction models, which may be used by SAMSON (e.g. when the user applies a new model to some data graph nodes), or other SAMSON Elements.

## Visual models

Visual models are one of the five categories of models in SAMSON (with structural models, dynamical models, interaction models and property models). Their sole purpose is to provide some visual representations in the SAMSON viewport. A visual model may be e.g. a secondary structure representation applicable to protein models, an electron density isosurface, a volume rendering of an electrostatics field, etc. When a new visual model is loaded at startup, SAMSON stores it in a list of available visual models, which may be used by SAMSON (e.g. when the user applies a new model to some data graph nodes), or other SAMSON Elements.

# Element categories

At the moment, a SAMSON Element may belong to one or more of the following categories:

• Assembly
• Biology
• Chemistry
• Developer
• Education
• Electronics
• General
• Materials
• Medicine
• Metrology
• Modeling
• Optics
• Particles
• Photonics
• Physics
• Simulation
• Toxicology
• Visualization

Note that, even though a SAMSON Element may contain several classes, all classes belonging to the same SAMSON Element have the same categories.

Categories are useful to arrange SAMSON Elements in the SAMSON user interface, as well as organize them on SAMSON Connect. Note that this categorization might evolve in the future.


text:
# Can someone explain to me what a function arrow is?

1. Dec 31, 2011

### IntegrateMe

Can someone explain to me what a "function arrow" is?

In particular, what this may mean:

I = [a, b]
f : I --> R

I'm just trying to understand what the arrow means.

Or if we have R --> R what that would mean.

Thank you!

2. Jan 1, 2012

### JHamm

Re: Can someone explain to me what a "function arrow" is?

The thing to the left of the arrow is the domain of the map f and the thing to the right is the range.
As an example a map which returns the square of all real numbers would be
$$f: \mathbb{R} \longrightarrow \mathbb{R}$$
A map which multiplies natural numbers by $\frac{12}{7}$ would be
$$f: \mathbb{N} \longrightarrow \mathbb{R}$$
And a map which takes a number from 1 to 4 and returns a complex number would be
$$f: [1, 4] \longrightarrow \mathbb{R}^2$$

3. Jan 1, 2012

### DavidAlan

Re: Can someone explain to me what a "function arrow" is?

It is just notation. It means that the map entails some correspondence between sets. In English, the arrow points to the possible set of outputs of the map. If your map takes as its domain some set and "points" to the set of complex numbers, then your map is "complex valued," meaning that it takes inputs that are elements of the set at the beginning of the arrow, and outputs elements of the complex numbers (i.e. numbers of the form a+ib).

For example, if f: R^2 --> C is defined by f(x,y)=x+iy then f turns elements of R^2 into "high school" complex numbers.

4. Jan 4, 2012

### IntegrateMe

Re: Can someone explain to me what a "function arrow" is?

JHamm,

If we use the example of:

f: R --> R

You said that it would return the square of all real numbers. But wouldn't it just return all real numbers, since the range, which is to the right, is R? The second one which involves 12/7 is also confusing me. Can you, or anyone for that matter, please clarify this for me.

Thanks for the help, guys, greatly appreciated.

Edit: Is this how you're describing the function f? For example, could I have said that f(x) = x^3 so that f: R --> R would actually return the cube of all real numbers?

Last edited: Jan 4, 2012
5. Jan 4, 2012

### Deveno

Re: Can someone explain to me what a "function arrow" is?

the usual notation is:

$$f: A \to B$$

what is meant by this is:

for any element a in the set A, f(a) is defined, and is an element of the set B. B is called the "co-domain" of f, and is not to be confused with the "range" of f (or the image set), which is f(A). f(A) is always a subset of B, it may not be all of B itself.

for example, if we have:

$$f:\mathbb{R} \to \mathbb{R}, f(x) = x^2$$

then we are saying f (the "squaring function") is defined for every real number x, and that x2 is also a real number. as it turns out, x2 is always non-negative, so in this case, the range of f is considerably smaller than the co-domain.

in general, you can always make the domain (the set A) smaller (this is called a restriction), and the co-domain bigger. in calculus, it is common to choose the entire real numbers as the co-domain, rather than trying to figure out ahead of time what the actual range is. often, we are only concerned with the behavior of f on a particular kind of subset of R, an interval (usally denoted I, or [a,b] or (a,b) if we wish to specify whether the interval includes the boundary points).

often, A is called "the source (or start) set", and B the "target set" (and the arrow is suggestive of some kind of motion, or action, or transformation).

6. Jan 5, 2012

### JHamm

Re: Can someone explain to me what a "function arrow" is?

Exactly, the bit with the arrow doesn't tell you what the function really does, it just tells you the set of its domain and the set of its range.


text:
# American Institute of Mathematical Sciences

August  2019, 24(8): 4513-4545. doi: 10.3934/dcdsb.2019154

## Mean-square approximations of Lévy noise driven SDEs with super-linearly growing diffusion and jump coefficients

 School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, China

* Corresponding author: x.j.wang7@csu.edu.cn; x.j.wang7@gmail.com(Xiaojie Wang)

Received  November 2017 Revised  March 2019 Published  June 2019

Fund Project: This work was supported by NSF of China (11571373, 11671405, 91630312), NSF of Hunan Province (2016JJ3137), Innovation-Driven Project of CSU (2017CX017), Shenghua Yuying Program of CSU and Hunan Provincial Innovation Foundation For Postgraduate (CX2018B051)

This paper first establishes a fundamental mean-square convergence theorem for general one-step numerical approximations of Lévy noise driven stochastic differential equations with non-globally Lipschitz coefficients. Then two novel explicit schemes are designed and their convergence rates are exactly identified via the fundamental theorem. Different from existing works, we do not impose a globally Lipschitz condition on the jump coefficient but formulate appropriate assumptions to allow for its super-linear growth. However, we require that the Lévy measure is finite. New arguments are developed to handle essential difficulties in the convergence analysis, caused by the super-linear growth of the jump coefficient and the fact that higher moment bounds of the Poisson increments $\int_t^{t+h} \int_Z \,\bar{N}(\mbox{d}s,\mbox{d}z), t \geq 0, h >0$ contribute to magnitude not more than $O(h)$. Numerical results are finally reported to confirm the theoretical findings.

Citation: Ziheng Chen, Siqing Gan, Xiaojie Wang. Mean-square approximations of Lévy noise driven SDEs with super-linearly growing diffusion and jump coefficients. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 4513-4545. doi: 10.3934/dcdsb.2019154
##### References:
 [1] A. Andersson and R. Kruse, Mean-square convergence of the BDF2-Maruyama and backward Euler schemes for SDE satisfying a global monotonicity condition, BIT Numer. Math., 57 (2017), 21-53. doi: 10.1007/s10543-016-0624-y. Google Scholar [2] D. Applebaum, Lévy Processes and Stochastic Calculus, Cambridge University Press, 2009. doi: 10.1017/CBO9780511809781. Google Scholar [3] W.-J. Beyn, E. Isaak and R. Kruse, Stochastic C-stability and B-consistency of explicit and implicit Euler-type schemes, J. Sci. Comput., 67 (2016), 955-987. doi: 10.1007/s10915-015-0114-4. Google Scholar [4] W.-J. Beyn, E. Isaak and R. Kruse, Stochastic C-stability and B-consistency of explicit and implicit Milstein-type schemes, J. Sci. Comput., 70 (2017), 1042-1077. doi: 10.1007/s10915-016-0290-x. Google Scholar [5] N. Bruti-Liberati and E. Platen, Strong approximations of stochastic differential equations with jumps, J. Comput. Appl. Math., 205 (2007), 982-1001. doi: 10.1016/j.cam.2006.03.040. Google Scholar [6] K. Dareiotis, C. Kumar and S. Sabanis, On tamed Euler approximations of SDEs driven by Lévy noise with applications to delay equations, SIAM J. Numer. Anal., 54 (2016), 1840-1872. doi: 10.1137/151004872. Google Scholar [7] S. Deng, W. Fei, W. Liu and X. Mao, The truncated EM method for stochastic differential equations with Poisson jumps, J. Comput. Appl. Math., 355 (2019), 232-257. doi: 10.1016/j.cam.2019.01.020. Google Scholar [8] W. Fang and M. B. Giles, Adaptive Euler-Maruyama method for SDEs with non-globally Lipschitz drift: Part Ⅰ, finite time interval, preprint, arXiv: 1609.08101.Google Scholar [9] A. Gardoń, The order of approximation for solutions of Itô-type stochastic differential equations with jumps, Stoch. Anal. Appl., 22 (2004), 679-699. doi: 10.1081/SAP-120030451. Google Scholar [10] I. Gyöngy and N. V. Krylov, On stochastic equations with respect to semimartingales Ⅰ, Stoch., 4 (1980), 1-21. doi: 10.1080/03610918008833154. Google Scholar [11] D. J. Higham and P. E. Kloeden, Numerical methods for nonlinear stochastic differential equations with jumps, Numer. Math., 101 (2005), 101-119. doi: 10.1007/s00211-005-0611-8. Google Scholar [12] D. J. Higham, X. Mao and A. M. Stuart, Strong convergence of Euler-type methods for nonlinear stochastic differential equations, SIAM J. Numer. Anal., 40 (2002), 1041-1063. doi: 10.1137/S0036142901389530. Google Scholar [13] D. J. Higham and P. E. Kloeden, Strong convergence rates for backward Euler on a class of nonlinear jump-diffusion problems, J. Comput. Appl. Math., 205 (2007), 949-956. doi: 10.1016/j.cam.2006.03.039. Google Scholar [14] L. Hu and S. Gan, Convergence and stability of the balanced methods for stochastic differential equations with jumps, Int. J. Comput. Math., 88 (2011), 2089-2108. doi: 10.1080/00207160.2010.521548. Google Scholar [15] M. Hutzenthaler and A. Jentzen, Convergence of the stochastic Euler scheme for locally Lipschitz coefficients, Found. Comput. Math., 11 (2011), 657-706. doi: 10.1007/s10208-011-9101-9. Google Scholar [16] M. Hutzenthaler and A. Jentzen, Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients, American Mathematical Society, 2015. doi: 10.1090/memo/1112. Google Scholar [17] M. Hutzenthaler, A. Jentzen and P. E. Kloeden, Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients, Proc. R. Soc. A, 467 (2011), 1563-1576. doi: 10.1098/rspa.2010.0348. Google Scholar [18] M. Hutzenthaler, A. Jentzen and P. E. Kloeden, Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz coefficients, Ann. Appl. Probab., 22 (2012), 1611-1641. doi: 10.1214/11-AAP803. Google Scholar [19] M. Hutzenthaler and A. 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Li, Weak approximations and extrapolations of stochastic differential equations with jumps, SIAM J. Numer. Anal, 37 (2000), 1747-1767. doi: 10.1137/S0036142998344512. Google Scholar [29] Y. Maghsoodi, Mean-square efficient numerical solution of jump-diffusion stochastic differential equations, Sankhy$\bar{a}$ Ser. A., 58 (1996), 25–47. Available from: https://www.jstor.org/stable/25051081. Google Scholar [30] X. Mao and L. Szpruch, Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients, J. Comput. Appl. Math., 238 (2013), 14-28. doi: 10.1016/j.cam.2012.08.015. Google Scholar [31] X. Mao and L. Szpruch, Strong convergence rates for backward Euler-Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients, Stoch., 85 (2013), 144-171. doi: 10.1080/17442508.2011.651213. Google Scholar [32] X. 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##### References:
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Math., 11 (2011), 657-706. doi: 10.1007/s10208-011-9101-9. Google Scholar [16] M. Hutzenthaler and A. Jentzen, Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients, American Mathematical Society, 2015. doi: 10.1090/memo/1112. Google Scholar [17] M. Hutzenthaler, A. Jentzen and P. E. Kloeden, Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients, Proc. R. Soc. A, 467 (2011), 1563-1576. doi: 10.1098/rspa.2010.0348. Google Scholar [18] M. Hutzenthaler, A. Jentzen and P. E. Kloeden, Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz coefficients, Ann. Appl. Probab., 22 (2012), 1611-1641. doi: 10.1214/11-AAP803. Google Scholar [19] M. Hutzenthaler and A. 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Platen, Numerical Solution of Stochastic Differential Equations, Springer, Berlin, 1992. doi: 10.1007/978-3-662-12616-5. Google Scholar [24] A. Kohatsu-Higa and P. Tankov, Jump-adapted discretization schemes for Lévy-driven SDEs, Stoch. Proc. Appl., 120 (2010), 2258-2285. doi: 10.1016/j.spa.2010.07.001. Google Scholar [25] C. Kumar and S. Sabanis, On explicit approximations for Lévy driven SDEs with super-linear diffusion coefficients, Electron. J. Probab., 22 (2017), No. 73, 1–19. doi: 10.1214/17-EJP89. Google Scholar [26] C. Kumar and S. Sabanis, On tamed Milstein schemes of SDEs driven by Lévy noise, Discrete Contin. Dyn. Syst. Ser. B, 22 (2017), 421-463. doi: 10.3934/dcdsb.2017020. Google Scholar [27] W. Liu and X. Mao, Strong convergence of the stopped Euler-Maruyama method for nonlinear stochastic differential equations, Appl. Math. Comput., 223 (2013), 389-400. doi: 10.1016/j.amc.2013.08.023. Google Scholar [28] X. Q. Liu and C. W. Li, Weak approximations and extrapolations of stochastic differential equations with jumps, SIAM J. Numer. Anal, 37 (2000), 1747-1767. doi: 10.1137/S0036142998344512. Google Scholar [29] Y. Maghsoodi, Mean-square efficient numerical solution of jump-diffusion stochastic differential equations, Sankhy$\bar{a}$ Ser. A., 58 (1996), 25–47. Available from: https://www.jstor.org/stable/25051081. Google Scholar [30] X. Mao and L. Szpruch, Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients, J. Comput. Appl. Math., 238 (2013), 14-28. doi: 10.1016/j.cam.2012.08.015. Google Scholar [31] X. Mao and L. Szpruch, Strong convergence rates for backward Euler-Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients, Stoch., 85 (2013), 144-171. doi: 10.1080/17442508.2011.651213. Google Scholar [32] X. Mao, The truncated Euler-Maruyama method for stochastic differential equations, J. Comput. Appl. Math., 290 (2015), 370-384. doi: 10.1016/j.cam.2015.06.002. Google Scholar [33] X. Mao, Convergence rates of the truncated Euler-Maruyama method for stochastic differential equations, J. Comput. Appl. Math., 296 (2016), 362-375. doi: 10.1016/j.cam.2015.09.035. Google Scholar [34] R. Mikulevicius and H. Pragarauskas, On ${L}_{p}$-estimates of some singular integrals related to jump processes, SIAM J. Math. Anal., 44 (2012), 2305-2328. doi: 10.1137/110844854. Google Scholar [35] G. N. Milstein, A theorem on the order of convergence of mean-square approximations of solutions of systems of stochastic differential equations, Tero. Prob. Appl., 32 (1987), 809-811. doi: 10.1137/1132113. Google Scholar [36] G. N. Milstein and M. V. Tretyakov, Stochastic Numerics for Mathematical Physics, Springer, Berlin, 2004. doi: 10.1007/978-3-662-10063-9. Google Scholar [37] G. N. Milstein and M. V. Tretyakov, Numerical integration of stochastic differential equations with nonglobally Lipschitz coefficients, SIAM J. Numer. Anal., 43 (2005), 1139-1154. doi: 10.1137/040612026. Google Scholar [38] E. Platen and N. Bruti-Liberati, Numerical Solution of Stochastic Differential Equations with Jumps in Finance, Springer, Berlin, 2010. doi: 10.1007/978-3-642-13694-8. Google Scholar [39] P. Protter, Stochastic Integration and Differential Equations: A New Approach, Springer, Berlin, 1990. doi: 10.1007/978-3-662-02619-9. Google Scholar [40] S. Sabanis, Euler approximations with varying coefficients: the case of super-linearly growing diffusion coefficients, Ann. Appl. Probab., 26 (2016), 2083-2105. doi: 10.1214/15-AAP1140. Google Scholar [41] S. Sabanis, A note on tamed Euler approximations, Electron. Commun. Probab, 18 (2013), 1-10. doi: 10.1214/ECP.v18-2824. Google Scholar [42] S. Sabanis and Y. Zhang, On explicit order 1.5 approximations with varying coefficients: the case of super-linear diffusion coefficients, J. Complexity, 50 (2019), 84-115. doi: 10.1016/j.jco.2018.09.004. Google Scholar [43] Ł Szpruch and X. Zhāng, $V$-integrability, asymptotic stability and comparison property of explicit numerical schemes for non-linear SDEs, Math. Comp., 87 (2018), 755-783. doi: 10.1090/mcom/3219. Google Scholar [44] A. Tambue and J. D. Mukam, Strong convergence of the tamed and the semi-tamed Euler schemes for stochastic differential equations with jumps under non-global Lipschitz condition, preprint, arXiv: 1510.04729.Google Scholar [45] M. V. Tretyakov and Z. Zhang, A fundamental mean-square convergence theorem for SDEs with locally Lipschitz coefficients and its applications, SIAM J. Numer. Anal., 51 (2013), 3135-3162. doi: 10.1137/120902318. Google Scholar [46] X. Wang and S. Gan, Compensated stochastic theta methods for stochastic differential equations with jumps, Appl. Numer. Math., 60 (2010), 877-887. doi: 10.1016/j.apnum.2010.04.012. Google Scholar [47] X. Wang and S. Gan, The tamed milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients, J. Differ. Equ. Appl., 19 (2013), 466-490. doi: 10.1080/10236198.2012.656617. Google Scholar [48] X. Yang and X. Wang, A transformed jump-adapted backward Euler method for jump-extended CIR and CEV models, Numer. Algor., 74 (2017), 39-57. doi: 10.1007/s11075-016-0137-4. Google Scholar [49] Z. Zhang and H. Ma, Order-preserving strong schemes for SDEs with locally Lipschitz coefficients, Appl. Numer. Math., 112 (2017), 1-16. doi: 10.1016/j.apnum.2016.09.013. Google Scholar [50] Z. Zhang, New explicit balanced schemes for SDEs with locally Lipschitz coefficients, preprint, arXiv: 1402.3708.Google Scholar [51] X. Zong, F. Wu and C. Huang, Convergence and stability of the semi-tamed Euler scheme for stochastic differential equations with non-Lipschitz continuous coefficients, Appl. Math. Comput., 228 (2014), 240-250. doi: 10.1016/j.amc.2013.11.100. Google Scholar
Mean-square convergence rates for (87) (left) and (88) (right)
CPU time of the tamed and sine methods with different stepsizes
 $h$ CPU time (second) non-additive case additive case tamed method sine method tamed method sine method $2^{-8}$ 0.869440 0.744448 0.794577 0.632519 $2^{-9}$ 1.203300 0.932720 1.031226 0.776562 $2^{-10}$ 1.625105 1.100245 1.276387 0.906966 $2^{-11}$ 2.951017 1.887072 2.355608 1.433305 $2^{-12}$ 5.789335 3.588197 4.325145 2.473830
 $h$ CPU time (second) non-additive case additive case tamed method sine method tamed method sine method $2^{-8}$ 0.869440 0.744448 0.794577 0.632519 $2^{-9}$ 1.203300 0.932720 1.031226 0.776562 $2^{-10}$ 1.625105 1.100245 1.276387 0.906966 $2^{-11}$ 2.951017 1.887072 2.355608 1.433305 $2^{-12}$ 5.789335 3.588197 4.325145 2.473830
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# No increment of a variable in a Sweave code chunk which is wrapped by a \whiledo loop

I already searched in different forums but until now I couldn’t find a solution. So I hope that you can help me…

Like mentioned in the title there is no increment of my variable x in the code chunk which is wrapped by a \whiledo loop. Let’s have a look at my code:

    \documentclass[10pt, a4paper]{article}
\usepackage{ifthen}
\usepackage{pifont}

\begin{document}
\SweaveOpts{concordance=TRUE}

\newcounter{ctra}
\setcounter{ctra}{1}
\whiledo {\value{ctra} < 7}
{

<<echo=FALSE, results=hide>>=

if(!exists("x")){x=numeric()}

if(length(x)==0)
{
x=2
}else{
x=x+1
}
@

\Sexpr{x} \\
\stepcounter{ctra}
}
\end{document}

When I now compile the script in RStudio I get a pdf with a bunch of 2 but I expected a numerical series like 2, 3, 4, 5, 6 and 7.

Can anybody give me a hint to solve that problem? And please explain the background if necessary, because I’m not very experienced in Sweave.

Here I edit my question for the first time…

This numerical series I need to get the right data into my table. The code of two table rows will be something like that

    \setlength{\arrayrulewidth}{1pt}
\begin{tabular}{|p{3.5cm}*{5}{p{1.75cm}}|}
\hline
\textbf{Stab} & \textbf{\ctab Spr \Sexpr{vers[1]}} & \textbf{\ctab Spr \Sexpr{vers[2]}} & \textbf{\ctab Spr \Sexpr{vers[3]}} & \textbf{\ctab Spr \Sexpr{vers[4]}} & \textbf{\ctab Spr \Sexpr{vers[5]}} \\
\hline
\rowcolor[gray]{0.7}
\hspace{0.5cm}Dampf [-] & \ctab \Sexpr{Drsp[[1]][vers[1]]} & \ctab \Sexpr{Drsp[[1]][vers[2]]} & \ctab \Sexpr{Drsp[[1]][vers[3]]} & \ctab \Sexpr{Drsp[[1]][vers[4]]} & \ctab    \Sexpr{Drsp[[1]][vers[5]]} \\
\hspace{0.5cm}MaUbschw [bar] & \ctab \Sexpr{Drsp[[2]][ vers[1]]} & \ctab \Sexpr{Drsp[[2]][vers[2]]} & \ctab \Sexpr{Drsp[[2]][vers[3]]} & \ctab \Sexpr{Drsp[[2]][vers[4]]} & \ctab \Sexpr{Drsp[[2]][vers[5]]} \\
% and so on...
\hline
\end{tabular}

But my above loaded data – in the script - has a high quantity of rows – up to 200 rows. The data file is comparable with an R data.frame.

One row in my data will be one column in my table.

This is too much to put it just in one table. My solution is to put a loop over the table and create a table with only 5 columns. In the pdf I will have some tables one below the other.

Therefore I make a vector with the quantity of rows.

    vers=c(1:nrow(Drsp)) # R-code

In the first loop the first elements of the vector will be taken to fill the table with 5 columns. Because I have 5 columns I can “shorten” the vector before we will go in the second loop.

    vers=vers[-c(1:5)] # R-code

For the second table I have the right data in the first 5 elements of the vector.

I think now it’s time to have a look at my compound code:

    \documentclass[10pt, a4paper]{article}
\usepackage{ifthen}
\usepackage{pifont}

% Centering in the table
\newcommand{\ctab}{\centering\arraybackslash}

\begin{document}
\SweaveOpts{concordance=TRUE}

<<echo=FALSE, results=hide>>=

# Create the vector
vers=c(1:nrow(Drsp))
@

\newcounter{ctra}
\setcounter{ctra}{1}
\whiledo {\value{ctra} < \Sexpr{nrow(Drsp)}}
{

<<echo=FALSE, results=hide>>=

if(!exists("x")){x=numeric()}

if(x>=1){vers=vers[-c(1:5)]} # shorten my vector in every loop

if(length(x)==0)
{
x=1
}else{
x=x+1
}
@

% table with the right data, because every loop the vector will be shorten
\setlength{\arrayrulewidth}{1pt}
\begin{tabular}{|p{3.5cm}*{5}{p{1.75cm}}|}
\hline
\textbf{Stab} & \textbf{\ctab Spr \Sexpr{vers[1]}} & \textbf{\ctab Spr \Sexpr{vers[2]}} & \textbf{\ctab Spr \Sexpr{vers[3]}} & \textbf{\ctab Spr \Sexpr{vers[4]}} & \textbf{\ctab Spr \Sexpr{vers[5]}} \\
\hline
\rowcolor[gray]{0.7}
\hspace{0.5cm}Dampf [-] & \ctab \Sexpr{Drsp[[1]][vers[1]]} & \ctab \Sexpr{Drsp[[1]][ vers[2]]} & \ctab \Sexpr{Drsp[[1]][ vers[3]]} & \ctab \Sexpr{Drsp[[1]][ vers[4]]} & \ctab    \Sexpr{Drsp[[1]][ vers[5]]} \\
\hspace{0.5cm}MaUbschw [bar] & \ctab \Sexpr{Drsp[[2]][ vers[1]]} & \ctab \Sexpr{Drsp[[2]][ vers[2]]} & \ctab \Sexpr{Drsp[[2]][ vers[3]]} & \ctab \Sexpr{Drsp[[2]][ vers[4]]} & \ctab \Sexpr{Drsp[[2]][ vers[5]]} \\
% and so on...
\hline
\end{tabular}

\addtocounter{ctra}{5}  % because of the 5 table columns

}  % End whiledo loop
\end{document}

Okay, I hope I have done everything right…

If there is a easier way to reach my goal please let me know;-)

Sweave processes the source file by ignoring all LaTeX code and executing the R code. This means that code in a LaTeX loop will be executed only once by R. In the generated .tex code any \Sexpr variables are substituted by the value after the single run, in this case \Sexpr{x} is replaced by the string 2. When running LaTeX afterwards, the loop is executed and the string 2 is printed several times.

As an alternative you can put the loop in R and write the desired LaTeX code from there. MWE (save as .Snw, run from within R Sweave("yourfile.Snw"), then compile the generated yourfile.tex):

Edit: new Snw file, same idea, a bit more complex code

Adjust to taste. Convert \ into \\ and put a \n where you want a newline.

\documentclass{article}
\begin{document}
<<results=tex,echo=FALSE>>=

lines_per_table <- 5
cols_per_table <- 4

Drsp <- matrix(rexp(100, rate=.1), ncol=20)
vers <- c(1:ncol(Drsp))

for(x in seq(0,ncol(Drsp),lines_per_table)){
cat("\\begin{tabular}{l|ccccc|}\n")
cat("\\hline\n")
cat("\\textbf{Stab} ")
for(y in seq(cols_per_table)){
cat("& Spr",vers[y])
}
cat("\\\\\n")
cat("\\hline\n")
for(y in seq(lines_per_table)){
cat("line",y)
for(z in seq(cols_per_table)){
cat("&",Drsp[y,vers[z]])
}
cat("\\\\\n")
}
cat("\\hline\n")
cat("\\end{tabular}\n\n")
vers <- vers[-c(1:cols_per_table)]
}
@
\end{document}

Result:

etc.

End edit

yourfile.Snw

\documentclass{article}
\begin{document}
\noindent
<<results=tex,echo=FALSE>>=
for(x in seq(7)){
cat("x is \\textbf{",x,"}\\\\",sep="")
}
@
\end{document}

Mind the results=tex option.

Auto-generated yourfile.tex

\documentclass{article}
\usepackage{Sweave}
\begin{document}
\noindent
x is \textbf{1}\\x is \textbf{2}\\x is \textbf{3}\\x is \textbf{4}\\x is \textbf{5}\\x is \textbf{6}\\x is \textbf{7}\\\end{document}

Result:

x is 1

x is 2

x is 3

x is 4

x is 5

x is 6

x is 7

• Thanks a lot for your answer! I think I have to explain may purpose a little more.. – tueftla Jun 14 '16 at 12:35
• That looks and works perfect! Thanks a lot! I had to play a little to get my desired format and get my data in the tables… – tueftla Jun 15 '16 at 8:32