ReadingTimeMachine/rtm-sgt-ocr-v1 · Datasets at Hugging Face

source stringlengths 1 2.05k ⌀	target stringlengths 1 11.7k
conservative assumptions, we have, therefore, obtained very robust results.	conservative assumptions, we have, therefore, obtained very robust results.
In all cases studied, the best constraints were obtained using 1.4 GHz, since the number of e and et produced by DM annihilation decreases with energy.	In all cases studied, the best constraints were obtained using 1.4 GHz, since the number of $e^-$ and $e^+$ produced by DM annihilation decreases with energy.
For higher frequencies to produce competing constraints, the observed intensity at those frequencies should be much lower than at 1.4 GHz.	For higher frequencies to produce competing constraints, the observed intensity at those frequencies should be much lower than at 1.4 GHz.
From Fig. 6,,	From Fig. \ref{Results1},
we can see that the constraints on the mx-(cAv) plane imposed from the analysis of the LMC are stronger than the ones obtained with M33 and with the Milky Way over the most of mass range considered when, excluding very low mass regions.	we can see that the constraints on the $m_{\chi}$ $\langle\sigma_Av\rangle$ plane imposed from the analysis of the LMC are stronger than the ones obtained with M33 and with the Milky Way over the most of mass range considered when, excluding very low mass regions.
In Tasitsiomietal.(2004) the estimated DM annihilation signal at different frequencies was obtained, fixing m,=50 GeV and (cav)=2x10:35 cm? s! and	In \citet{Angela} the estimated DM annihilation signal at different frequencies was obtained, fixing $m_{\chi}=50$ GeV and $\langle\sigma_Av\rangle=2 \times 10^{-26}$ $^3\,$ $^{-1}$ and
on filling the spectrum wilh a pure starburst template.	on fitting the spectrum with a pure starburst template.
For these “pure starbursts”. we have measured [, (7.7jan) from published spectra or from new extractions of unpublished archival data. and (hese measured. values are included in Table 1.	For these "pure starbursts", we have measured $_{\nu}$ $\mu$ m) from published spectra or from new extractions of unpublished archival data, and these measured values are included in Table 1.
For ULIBGs. discussed further below in section 2.3. the pL, μαι) are scaled to published luminosities for other PAII features because there may be a significant contribution to the pL, (7.7jan) from an underlving AGN continuum.	For ULIRGs, discussed further below in section 2.3, the $\nu$ $_{\nu}$ $\mu$ m) are scaled to published luminosities for other PAH features because there may be a significant contribution to the $\nu$ $_{\nu}$ $\mu$ m) from an underlying AGN continuum.
Luminosities in Table 1 range over a [actor of > 104. from log\|pL, μαι) = 41.76 for no.	Luminosities in Table 1 range over a factor of $>$ $^{4}$, from $\nu$ $_{\nu}$ $\mu$ m)] = 41.76 for no.
150. a blue compact dwarf Irom (the Bootes 10 mJy survey in Houcketal...(2007).. to log\|pL, (τιμη). = 46.10 for no.	150, a blue compact dwarf from the Bootes 10 mJy survey in \citet{hou07}, to $\nu$ $_{\nu}$ $\mu$ m)] = 46.10 for no.
197. a faint source from the FLS survey in (2007).	197, a faint source from the FLS survey in \citet{yan07}.
. All luminosities are shown compared to redshift in Figure 3.	All luminosities are shown compared to redshift in Figure 3.
The only sources included in this summary which sometime have spectroscopic imdicators ofan AGN contribution are the RAS ULIRGs. which often show the deep silicate absorption characteristic of AGN while also showing PAII features (e.g.Spoonetal.2007).	The only sources included in this summary which sometime have spectroscopic indicators of an AGN contribution are the IRAS ULIRGs, which often show the deep silicate absorption characteristic of AGN while also showing PAH features \citep[e.g. ][]{spo07} .
For such composite sources. simply taking pL, μα) would not be an appropriate measure of starburst luminosity because p L, (7.70) can be enhanced by an underlying AGN continuum.	For such composite sources, simply taking $\nu$ $_{\nu}$ $\mu$ m) would not be an appropriate measure of starburst luminosity because $\nu$ $_{\nu}$ $\mu$ m) can be enhanced by an underlying AGN continuum.
These ULIRGs are sufficiently. bright to have S/N adequate for measurement of tota fluxes in the weaker PAIL features at μη and/or 11.3j0n.. These two PAIL features are sulliciently isolated in the spectrum that they can be measured as single Gaussians on top of an underlving conünuum. so that a total flux can be determined much more precisely (han for the rjan feature.	These ULIRGs are sufficiently bright to have S/N adequate for measurement of total fluxes in the weaker PAH features at $\mu$ m and/or $\mu$ m. These two PAH features are sufficiently isolated in the spectrum that they can be measured as single Gaussians on top of an underlying continuum, so that a total flux can be determined much more precisely than for the $\mu$ m feature.
The blending of PAIT features makes especially difficult the definition of total [Iux in the 7jan feature. as discussed. for example. by Brandletal.(2006). and (2008).	The blending of PAH features makes especially difficult the definition of total flux in the $\mu$ m feature, as discussed, for example, by \citet{bra06} and \citet{pop08}.
. Furthermore. sources with deep μην silicate absorption have a continuum peak near 8jan which further complicates isolation of the 7j feature.	Furthermore, sources with deep $\mu$ m silicate absorption have a continuum peak near $\mu$ m which further complicates isolation of the $\mu$ m feature.
This peak is seen in the spectrum of Markarian 231. shown in Figure 1.	This peak is seen in the spectrum of Markarian 231, shown in Figure 1.
The effects of starburst and AGN composite spectra are illustrated in Figure 1.	The effects of starburst and AGN composite spectra are illustrated in Figure 1.
spectra are shown only between 5;jan and 144m because this is the spectral region with diagnosties that differentiate starbursts and AGN.	Rest-frame spectra are shown only between $\mu$ m and $\mu$ m because this is the spectral region with diagnostics that differentiate starbursts and AGN.
Also. these rest-frame wavelengths are all that can be observed with the IRS in sources with z 2 1.5. which are the high redshifts of particular importance to our analvsis.	Also, these rest-frame wavelengths are all that can be observed with the IRS in sources with z $\ga$ 1.5, which are the high redshifts of particular importance to our analysis.
The AGN Markarian 231 has an absorption spectrum and luminosity that is tvpical of absorbed ULIBGs (Saresvanοἱal...2008).. so this ULIBG provides an excellent representative example for an AGN contribution to the mid-infrared spectrum.	The AGN Markarian 231 has an absorption spectrum and luminosity that is typical of absorbed ULIRGs \citep{sar08}, so this ULIRG provides an excellent representative example for an AGN contribution to the mid-infrared spectrum.
For a starburst comparison to. Markarian 231. we use the IRS spectrum from	For a starburst comparison to Markarian 231, we use the IRS spectrum from
An examination of the Hubble. Deep Field. however. reveals that the host of is seen in projection near two large elliptical svstems at a redshift of z~0.56.	An examination of the Hubble Deep Field, however, reveals that the host of is seen in projection near two large elliptical systems at a redshift of $z\sim0.56$.
In this Letter. we consider the eravitational lensing influence of these galaxies on the apparent brightness of19911L.	In this Letter, we consider the gravitational lensing influence of these galaxies on the apparent brightness of.
. Examining the host galaxy of iin the LDP North reveals that it [ies in. close. proximity to several other systems: this is presented. schematically in Figure 1..	Examining the host galaxy of in the HDF North reveals that it lies in close proximity to several other systems; this is presented schematically in Figure \ref{Figure1}.
The labels for the objects depicted. are. taken from S. Gwyn's photometric catalog. of objects in the Llubble Deep Field (να Lartwiek 1996)*.	The labels for the objects depicted are taken from S. Gwyn's photometric catalog of objects in the Hubble Deep Field (Gwyn Hartwick 1996).
. Phe host of lis No.	The host of is No.
531. with a tentative spectroscopic redshift, of 2~ 1.66. while No.	531, with a tentative spectroscopic redshift of $z\sim1.66$ , while No.
512 and No.	512 and No.
524 possess spectroscopic redshifts of z=0.555 and z=0.557 respectively (Cohen et al.	524 possess spectroscopic redshifts of $z=0.555$ and $z=0.557$ respectively (Cohen et al.
1996).	1996).
System No.	System No.
510 possess a photometric redshift of z1.9 and therefore probably lies bevond the host. ofSN19071L.	510 possess a photometric redshift of $z\sim1.9$ and therefore probably lies beyond the host of.
Pwo other systems at a redshift of z~0.85 lie olf the bottom right-hand corner of the plot. but as these are at a greater projected distance than galaxy No.	Two other systems at a redshift of $z\sim0.85$ lie off the bottom right-hand corner of the plot, but as these are at a greater projected distance than galaxy No.
512. they are neglected in this analysis.	512, they are neglected in this analysis.
Given their proximity to the line-of-sight. it is prudent to consider the gravitational lensing inlluence of. galaxies No.	Given their proximity to the line-of-sight, it is prudent to consider the gravitational lensing influence of galaxies No.
512 and No.	512 and No.
524 on the observed brightness ofSN19971E.	524 on the observed brightness of.
For galactic mass objects at. cosmological distances. the tvpical scale for strong lensing is 1" and. given the separation of the galaxies and the host of.SNI9971L. a distance of 370 for No.	For galactic mass objects at cosmological distances, the typical scale for strong lensing is $\sim1\scmd$ and, given the separation of the galaxies and the host of, a distance of $3\scnd0$ for No.
512 and 574 for No.	512 and $5\scnd4$ for No.
524. there is little possibility that the supernova would. have been multiply imaged or substantially magnified.	524, there is little possibility that the supernova would have been multiply imaged or substantially magnified.
More. subtle magnifications however. will occur outside the region. of multiple imaging.	More subtle magnifications however, will occur outside the region of multiple imaging.
To examine this further we adopt the simple. pseucdo-isothermal model. of the two-dimensional gravitationa »»tential to represent cach of the foreground. galaxies (Ixochanek. Blandford. Lawrence. Naravan 1989).	To examine this further we adopt the simple pseudo-isothermal model of the two-dimensional gravitational potential to represent each of the foreground galaxies (Kochanek, Blandford, Lawrence, Narayan 1989).
These are assumed to be spherical and are centered on the optica xositions of No.	These are assumed to be spherical and are centered on the optical positions of No.
512 anc No.	512 and No.
524.	524.
Phe normalization of his potential depends upon the velocity clispersion of the ensing objects and the ratio of the lens-source and observer source angular diameter clistances.	The normalization of this potential depends upon the velocity dispersion of the lensing objects and the ratio of the lens-source and observer source angular diameter distances.
Calculating the distances in various cosmologies. including those with a substantial A erm. using the algorithms of Wavser. Helbig. Schramm (1997). it is found that the normalization is relatively insensitive to the cosmological parameters. with a <5% variation between the total magnification for reasonable cosmologies.	Calculating the distances in various cosmologies, including those with a substantial $\Lambda$ term, using the algorithms of Kayser, Helbig, Schramm (1997), it is found that the normalization is relatively insensitive to the cosmological parameters, with a $<5\%$ variation between the total magnification for reasonable cosmologies.
Lt is also assumed. that galaxies No.	It is also assumed that galaxies No.
512 and No.	512 and No.
524 have the same velocity dispersion.	524 have the same velocity dispersion.
"Three fiducial values of the velocity dispersion. are considered. LOOkm/s. 200km/s and 300km/s. the central value representing a tvpical elliptical galaxy (Whitmore. Alelzlroy. Tonry. 1985).	Three fiducial values of the velocity dispersion are considered, 100km/s, 200km/s and 300km/s, the central value representing a typical elliptical galaxy (Whitmore, McElroy, Tonry 1985).
For the lower velocity. dispersion of 00km/s. the resulting gravitational lensing magnification of due to galaxies No.	For the lower velocity dispersion of 100km/s, the resulting gravitational lensing magnification of due to galaxies No.
512 and No.	512 and No.
524 is only pp~1.08.	524 is only $\mu\sim1.08$.
Considering instead. the more typical value. of 200km/s. the eravitational lensing magnification is (/1.42. corresponding to a brightening of Q.38mags.	Considering instead the more typical value of 200km/s, the gravitational lensing magnification is $\mu\sim1.42$, corresponding to a brightening of 0.38mags.
I£ galaxics No.	If galaxies No.
512 and No.	512 and No.
524 are massive ellipticals. with velocity dispersions of 300knmi/s. the magnification is jp2.92. a brightening of 1.16mags.	524 are massive ellipticals, with velocity dispersions of 300km/s, the magnification is $\mu\sim2.92$, a brightening of 1.16mags.
The simple analysis presented in. this paper demonstrates that it is likely that the recently identifiec ugh redshift: supernova.SNLOOTI.. was milelly magnifier w the gravitational lensing influence of two galaxies ling close to the line of sight.	The simple analysis presented in this paper demonstrates that it is likely that the recently identified high redshift supernova, was mildly magnified by the gravitational lensing influence of two galaxies lying close to the line of sight.
Phe magnification is depencen upon the mass of the lensing galaxies. but if these are vpical elliptical galaxies. aappeared brighter by O.88maes.	The magnification is dependent upon the mass of the lensing galaxies, but if these are typical elliptical galaxies, appeared brighter by 0.38mags.
While this value wil depend upon the assumed form of the mass. distribution in the lensine galaxy. the estimate of the magnification http://astrowww.phys.uvic.ca/grads/gwyn/pz/hdfn/spindex.htmlpresented here will be of the right order.	While this value will depend upon the assumed form of the mass distribution in the lensing galaxy, the estimate of the magnification presented here will be of the right order.
With the value of the refractive index n» (equation 13)) we can calculate a new physical delay time as a function of the ry and the telescope diameter (D). through the formula: where OPL is given by the Formula 4...	With the value of the refractive index $n_{2}$ (Equation \ref{index7}) ) we can calculate a new physical delay time as a function of the $r_{0}$ and the telescope diameter $D$ ), through the formula: where OPL is given by the Formula \ref{opl}. .
Phen. as in Section 5.. we obtain the fluctuation due to this variation Al p(ry.D): where: we obtain: Through the Formula 15 we can estimate that a delay time [Luctuation of 10.0 ps corresponds to a refractive index variation An of 3.3197.	Then, as in Section \ref{gf}, we obtain the fluctuation due to this variation $\Delta t_{P}(r_{0},D)$ : where: we obtain: Through the Formula \ref{fis} we can estimate that a delay time fluctuation of 10.0 ps corresponds to a refractive index variation $\Delta n$ of $3.3\times 10^{-8}$.
This gives an idea of the error propagation.	This gives an idea of the error propagation.
Consequently. the total luetuation of the delay time is the sum of the geometric ancl physical component: In this sum the physical component is larger than the geometric Component of four orders of magnitude.	Consequently, the total fluctuation of the delay time is the sum of the geometric and physical component: In this sum the physical component is larger than the geometric component of four orders of magnitude.
Finally. we express this Huctuation through the extended formula: where: Substituting the constantswith these values (Roclelier. 1981)) A.—0.15. & 13= 3.5 Soy= Sande =2 we obtain the final formula used in the model: where: We note that this delay time fluctuation depends on the wavelength anc on the telescope diameter.	Finally, we express this fluctuation through the extended formula: where: Substituting the constantswith these values (Roddier, \cite{roddier}) ) $K=0.18$, $\alpha=1$, $\beta=3$, $\gamma=5$, $\eta=3$ and $\epsilon=2$ we obtain the final formula used in the model: where: We note that this delay time fluctuation depends on the wavelength and on the telescope diameter.
La particular. it also depends on the Fried radius. Figure 3. shows the trend of this Huctuation as ary function.	In particular, it also depends on the Fried radius, Figure \ref{r0} shows the trend of this fluctuation as a $r_{0}$ function.
The simulation is done for La Silla (A=0.632501. Zenith angle = 107).	The simulation is done for La Silla $\lambda=0.632\mu m$, Zenith angle $=10^{\circ}$ ).
In this Section we apply the previously. described: model to the three Chilean sites of ESO telescopes.	In this Section we apply the previously described model to the three Chilean sites of ESO telescopes.
We present the results obtained through the Formula. 17...	We present the results obtained through the Formula \ref{cava}. .
Table. 3 shows the simulation resultsforcach site. in particular	Table \ref{dia1} shows the simulation resultsforeach site, in particular
by color.	by color.
Therefore, the actual contamination level is the compromise of these two effects.	Therefore, the actual contamination level is the compromise of these two effects.
We can describe the measured alignment parameters, 7%,, as a combination of alignment from real cluster satellites and projected field galaxies.	We can describe the measured alignment parameters, $\gamma$, as a combination of alignment from real cluster satellites and projected field galaxies.
If we denote the alignment parameters from our measurements as Ym, then we can decompose it into two parts as follows:	If we denote the alignment parameters from our measurements as $\gamma_m$, then we can decompose it into two parts as follows:
In this below. we lix Monte Carlo method in Example 2. based on convergence result in1.	In this below, we fix Monte Carlo method in Example \ref{exm:EM} based on convergence result in.
. Regarding the estimation by Monte Carlo method. one mav take the simplest. choice {91=0 for the rebate pavolf as of Corollary 2.. see also [3]..	Regarding the estimation by Monte Carlo method, one may take the simplest choice $g(\beta) \equiv 0$ for the rebate payoff as of Corollary \ref{cor:mc},, see also \cite{ELTS08p}.
However. Corollary 2. can not be utilized the approximation bv PDE numerical method. since it may cause a discontinuity al the corner (2.7) of the terminial-boundary datum when /(2)4/0.	However, Corollary \ref{cor:mc} can not be utilized the approximation by PDE numerical method, since it may cause a discontinuity at the corner $(\beta, T)$ of the terminial-boundary datum when $f(\beta) \neq 0$.
For the above Monte Carlo method on(3.2).. vel another to be mentioned is a drawback in the computation by PDE numerical methods due to the possible ciscontinuity of the bouncdary-terminal data.	For the above Monte Carlo method on, yet another to be mentioned is a drawback in the computation by PDE numerical methods due to the possible discontinuity of the boundary-terminal data.
To illustrate this issue. we write Black-Scholes PDE associated to the rebate option price ViCr.1) of(3.2). Note that. PDE has a diseontinnous corner at the point (2.]T) if gio)EV4{ίM	To illustrate this issue, we write Black-Scholes PDE associated to the rebate option price $V^{\beta}(x,t)$ of, Note that, PDE has a discontinuous corner at the point $(\beta, T)$ if $g(\beta) \neq f(\beta)$.
Also recall that. the choice of ο)=f(2) mav not be possible. like in C ‘model Example 1..	Also recall that, the choice of $g(\beta) = f(\beta)$ may not be possible, like in CEV model of Example \ref{exm:cev}. .
value of à).	value of $\alpha$ ).
For comparison. we have redone the asymmetric drift correction of NGC 1023 with the method. described above for the new sample.	For comparison, we have redone the asymmetric drift correction of NGC 1023 with the method described above for the new sample.
We found Viana=270+19L2 which is in excellent agreement with the value of Paper I. We finally measured "X. as. Viana/(eg€,).	We found $V_{\rm c,flat} = 270 \pm 13$, which is in excellent agreement with the value of Paper I. We finally measured $\vpd$ as $V_{\rm c,flat}/(\len\om)$.
We used Monte Carlo to estimate the uncertainties in R by varving Vana and eg uniformly in their respective ranges. and varving ©), assuming the errors of Table S are Gaussian.	We used Monte Carlo to estimate the uncertainties in $\vpd$ by varying $V_{\rm c,flat}$ and $\len$ uniformly in their respective ranges, and varying $\om$ assuming the errors of Table \ref{tab:bar_kinematics} are Gaussian.
We report the median and the 67 per cent interval of R in ‘Table 8S..	We report the median and the 67 per cent interval of $\vpd$ in Table \ref{tab:bar_kinematics}.
The 5 SDO presented in this work. together with NCC 1023 stucied in sPaper L which we include in our saniple for this discussion. represent the largest sample of barred. galaxies. with ©, measured by means of the TW method.	The 5 SB0's presented in this work, together with NGC 1023 studied in Paper I, which we include in our sample for this discussion, represent the largest sample of barred galaxies, with $\om$ measured by means of the TW method.
For all of rem. Ris consistent with being in the range 1.0 to 1.4. =μα‘thin the errors. wwith each having a last bar.	For all of them, $\vpd$ is consistent with being in the range 1.0 to 1.4, within the errors, with each having a fast bar.
The unweightecl average for 1e sample is R=1.1.	The unweighted average for the sample is $\overline{\vpd} = 1.1$.
Phe apparent range of R spans from KS to 1.6 (0.6 to 2.1. within the 67 per cent intervals).	The apparent range of $\vpd$ spans from 0.8 to 1.6 (0.6 to 2.1, within the 67 per cent intervals).
This Esoead is not related to the properties of the galaxies in any νους wayfor the two galaxies at Vou=277\|. NGC 1028 and NGC T4440. the measured values of Rare at opposite extremes of the distribution)	This spread is not related to the properties of the galaxies in any obvious wayfor the two galaxies at $V_{\rm c, flat} = 277$, NGC 1023 and NGC 1440, the measured values of $\vpd$ are at opposite extremes of the distribution).
The fact that some of the values of R are nominally less than unity leads us to suggest that the large range of R is a result of random errors and/or scatter in the measurements.	The fact that some of the values of $\vpd$ are nominally less than unity leads us to suggest that the large range of $\vpd$ is a result of random errors and/or scatter in the measurements.
The sources of random errors are largely clue to micasurement uncertainties in all 5 quantities used to compute A. V canas etg and ,.	The sources of random errors are largely due to measurement uncertainties in all 3 quantities used to compute $\vpd$, $V_{\rm c,flat}$ , $\len$ and $\om$.
Of these. the largest is in Q,,. amounting to typical fractional uncertainties of 30 per cent. followed by ag. for which the typical fractional uncertainty is 20 per cent.	Of these, the largest is in $\om$, amounting to typical fractional uncertainties of 30 per cent, followed by $\len$, for which the typical fractional uncertainty is 20 per cent.
These uncertainties account for the typical laree (aud asvonmetric towards large values) errors on measurements of R.	These uncertainties account for the typical large (and asymmetric towards large values) errors on measurements of $\vpd$ .
A likely source of scatter is errors in.the disc PA.	A likely source of scatter is errors inthe disc PA.
= ((k ))Op = (ib - jg) ∖∖↽∐≺↵↕⋅≺↵≬⋡∶∶↸∣↗↙∕∕∕↗⋅⊳∪∣−↾∶∣⋅⋮−∣↗−↙∕∕∕↗⋅⋜↕∐≺∟−↨↥↥⊳∖↕∐≺↵∖∖↽⋜↕∖⊽≺↵⋜⋃∐↥↽≻∐⊓∐⇂≺↵⋅⊺∐≺↲↥⋜↕⊳∖↕⋜↕∐≺	= ( - ) = ( - ) where $c_s^2=\gamma p/\rho$ , $\omega_b^2=k^2b^2/\rho$ , and $A \ll 1$ is the wave amplitude.

conservative assumptions, we have, therefore, obtained very robust results.

In all cases studied, the best constraints were obtained using 1.4 GHz, since the number of e and et produced by DM annihilation decreases with energy.

In all cases studied, the best constraints were obtained using 1.4 GHz, since the number of $e^-$ and $e^+$ produced by DM annihilation decreases with energy.

For higher frequencies to produce competing constraints, the observed intensity at those frequencies should be much lower than at 1.4 GHz.

From Fig. 6,,

From Fig. \ref{Results1},

we can see that the constraints on the mx-(cAv) plane imposed from the analysis of the LMC are stronger than the ones obtained with M33 and with the Milky Way over the most of mass range considered when, excluding very low mass regions.

we can see that the constraints on the $m_{\chi}$ $\langle\sigma_Av\rangle$ plane imposed from the analysis of the LMC are stronger than the ones obtained with M33 and with the Milky Way over the most of mass range considered when, excluding very low mass regions.

In Tasitsiomietal.(2004) the estimated DM annihilation signal at different frequencies was obtained, fixing m,=50 GeV and (cav)=2x10:35 cm? s! and

In \citet{Angela} the estimated DM annihilation signal at different frequencies was obtained, fixing $m_{\chi}=50$ GeV and $\langle\sigma_Av\rangle=2 \times 10^{-26}$ $^3\,$ $^{-1}$ and

on filling the spectrum wilh a pure starburst template.

on fitting the spectrum with a pure starburst template.

For these “pure starbursts”. we have measured [, (7.7jan) from published spectra or from new extractions of unpublished archival data. and (hese measured. values are included in Table 1.

For these "pure starbursts", we have measured $_{\nu}$ $\mu$ m) from published spectra or from new extractions of unpublished archival data, and these measured values are included in Table 1.

For ULIBGs. discussed further below in section 2.3. the pL, μαι) are scaled to published luminosities for other PAII features because there may be a significant contribution to the pL, (7.7jan) from an underlving AGN continuum.

For ULIRGs, discussed further below in section 2.3, the $\nu$ $_{\nu}$ $\mu$ m) are scaled to published luminosities for other PAH features because there may be a significant contribution to the $\nu$ $_{\nu}$ $\mu$ m) from an underlying AGN continuum.

Luminosities in Table 1 range over a [actor of > 104. from log|pL, μαι) = 41.76 for no.

Luminosities in Table 1 range over a factor of $>$ $^{4}$, from $\nu$ $_{\nu}$ $\mu$ m)] = 41.76 for no.

150. a blue compact dwarf Irom (the Bootes 10 mJy survey in Houcketal...(2007).. to log|pL, (τιμη). = 46.10 for no.

150, a blue compact dwarf from the Bootes 10 mJy survey in \citet{hou07}, to $\nu$ $_{\nu}$ $\mu$ m)] = 46.10 for no.

197. a faint source from the FLS survey in (2007).

197, a faint source from the FLS survey in \citet{yan07}.

. All luminosities are shown compared to redshift in Figure 3.

All luminosities are shown compared to redshift in Figure 3.

The only sources included in this summary which sometime have spectroscopic imdicators ofan AGN contribution are the RAS ULIRGs. which often show the deep silicate absorption characteristic of AGN while also showing PAII features (e.g.Spoonetal.2007).

The only sources included in this summary which sometime have spectroscopic indicators of an AGN contribution are the IRAS ULIRGs, which often show the deep silicate absorption characteristic of AGN while also showing PAH features \citep[e.g. ][]{spo07} .

For such composite sources. simply taking pL, μα) would not be an appropriate measure of starburst luminosity because p L, (7.70) can be enhanced by an underlying AGN continuum.

For such composite sources, simply taking $\nu$ $_{\nu}$ $\mu$ m) would not be an appropriate measure of starburst luminosity because $\nu$ $_{\nu}$ $\mu$ m) can be enhanced by an underlying AGN continuum.

These ULIRGs are sufficiently. bright to have S/N adequate for measurement of tota fluxes in the weaker PAIL features at μη and/or 11.3j0n.. These two PAIL features are sulliciently isolated in the spectrum that they can be measured as single Gaussians on top of an underlving conünuum. so that a total flux can be determined much more precisely (han for the rjan feature.

These ULIRGs are sufficiently bright to have S/N adequate for measurement of total fluxes in the weaker PAH features at $\mu$ m and/or $\mu$ m. These two PAH features are sufficiently isolated in the spectrum that they can be measured as single Gaussians on top of an underlying continuum, so that a total flux can be determined much more precisely than for the $\mu$ m feature.

The blending of PAIT features makes especially difficult the definition of total [Iux in the 7jan feature. as discussed. for example. by Brandletal.(2006). and (2008).

The blending of PAH features makes especially difficult the definition of total flux in the $\mu$ m feature, as discussed, for example, by \citet{bra06} and \citet{pop08}.

. Furthermore. sources with deep μην silicate absorption have a continuum peak near 8jan which further complicates isolation of the 7j feature.

Furthermore, sources with deep $\mu$ m silicate absorption have a continuum peak near $\mu$ m which further complicates isolation of the $\mu$ m feature.

This peak is seen in the spectrum of Markarian 231. shown in Figure 1.

This peak is seen in the spectrum of Markarian 231, shown in Figure 1.

The effects of starburst and AGN composite spectra are illustrated in Figure 1.

spectra are shown only between 5;jan and 144m because this is the spectral region with diagnosties that differentiate starbursts and AGN.

Rest-frame spectra are shown only between $\mu$ m and $\mu$ m because this is the spectral region with diagnostics that differentiate starbursts and AGN.

Also. these rest-frame wavelengths are all that can be observed with the IRS in sources with z 2 1.5. which are the high redshifts of particular importance to our analvsis.

Also, these rest-frame wavelengths are all that can be observed with the IRS in sources with z $\ga$ 1.5, which are the high redshifts of particular importance to our analysis.

The AGN Markarian 231 has an absorption spectrum and luminosity that is tvpical of absorbed ULIBGs (Saresvanοἱal...2008).. so this ULIBG provides an excellent representative example for an AGN contribution to the mid-infrared spectrum.

The AGN Markarian 231 has an absorption spectrum and luminosity that is typical of absorbed ULIRGs \citep{sar08}, so this ULIRG provides an excellent representative example for an AGN contribution to the mid-infrared spectrum.

For a starburst comparison to. Markarian 231. we use the IRS spectrum from

For a starburst comparison to Markarian 231, we use the IRS spectrum from

An examination of the Hubble. Deep Field. however. reveals that the host of is seen in projection near two large elliptical svstems at a redshift of z~0.56.

An examination of the Hubble Deep Field, however, reveals that the host of is seen in projection near two large elliptical systems at a redshift of $z\sim0.56$.

In this Letter. we consider the eravitational lensing influence of these galaxies on the apparent brightness of19911L.

In this Letter, we consider the gravitational lensing influence of these galaxies on the apparent brightness of.

. Examining the host galaxy of iin the LDP North reveals that it [ies in. close. proximity to several other systems: this is presented. schematically in Figure 1..

Examining the host galaxy of in the HDF North reveals that it lies in close proximity to several other systems; this is presented schematically in Figure \ref{Figure1}.

The labels for the objects depicted. are. taken from S. Gwyn's photometric catalog. of objects in the Llubble Deep Field (να Lartwiek 1996)*.

The labels for the objects depicted are taken from S. Gwyn's photometric catalog of objects in the Hubble Deep Field (Gwyn Hartwick 1996).

. Phe host of lis No.

The host of is No.

531. with a tentative spectroscopic redshift, of 2~ 1.66. while No.

531, with a tentative spectroscopic redshift of $z\sim1.66$ , while No.

512 and No.

524 possess spectroscopic redshifts of z=0.555 and z=0.557 respectively (Cohen et al.

524 possess spectroscopic redshifts of $z=0.555$ and $z=0.557$ respectively (Cohen et al.

1996).

System No.

510 possess a photometric redshift of z1.9 and therefore probably lies bevond the host. ofSN19071L.

510 possess a photometric redshift of $z\sim1.9$ and therefore probably lies beyond the host of.

Pwo other systems at a redshift of z~0.85 lie olf the bottom right-hand corner of the plot. but as these are at a greater projected distance than galaxy No.

Two other systems at a redshift of $z\sim0.85$ lie off the bottom right-hand corner of the plot, but as these are at a greater projected distance than galaxy No.

512. they are neglected in this analysis.

512, they are neglected in this analysis.

Given their proximity to the line-of-sight. it is prudent to consider the gravitational lensing inlluence of. galaxies No.

Given their proximity to the line-of-sight, it is prudent to consider the gravitational lensing influence of galaxies No.

512 and No.

524 on the observed brightness ofSN19971E.

524 on the observed brightness of.

For galactic mass objects at. cosmological distances. the tvpical scale for strong lensing is 1" and. given the separation of the galaxies and the host of.SNI9971L. a distance of 370 for No.

For galactic mass objects at cosmological distances, the typical scale for strong lensing is $\sim1\scmd$ and, given the separation of the galaxies and the host of, a distance of $3\scnd0$ for No.

512 and 574 for No.

512 and $5\scnd4$ for No.

524. there is little possibility that the supernova would. have been multiply imaged or substantially magnified.

524, there is little possibility that the supernova would have been multiply imaged or substantially magnified.

More. subtle magnifications however. will occur outside the region. of multiple imaging.

More subtle magnifications however, will occur outside the region of multiple imaging.

To examine this further we adopt the simple. pseucdo-isothermal model. of the two-dimensional gravitationa »»tential to represent cach of the foreground. galaxies (Ixochanek. Blandford. Lawrence. Naravan 1989).

To examine this further we adopt the simple pseudo-isothermal model of the two-dimensional gravitational potential to represent each of the foreground galaxies (Kochanek, Blandford, Lawrence, Narayan 1989).

These are assumed to be spherical and are centered on the optica xositions of No.

These are assumed to be spherical and are centered on the optical positions of No.

512 anc No.

512 and No.

524.

Phe normalization of his potential depends upon the velocity clispersion of the ensing objects and the ratio of the lens-source and observer source angular diameter clistances.

The normalization of this potential depends upon the velocity dispersion of the lensing objects and the ratio of the lens-source and observer source angular diameter distances.

Calculating the distances in various cosmologies. including those with a substantial A erm. using the algorithms of Wavser. Helbig. Schramm (1997). it is found that the normalization is relatively insensitive to the cosmological parameters. with a <5% variation between the total magnification for reasonable cosmologies.

Calculating the distances in various cosmologies, including those with a substantial $\Lambda$ term, using the algorithms of Kayser, Helbig, Schramm (1997), it is found that the normalization is relatively insensitive to the cosmological parameters, with a $<5\%$ variation between the total magnification for reasonable cosmologies.

Lt is also assumed. that galaxies No.

It is also assumed that galaxies No.

512 and No.

524 have the same velocity dispersion.

"Three fiducial values of the velocity dispersion. are considered. LOOkm/s. 200km/s and 300km/s. the central value representing a tvpical elliptical galaxy (Whitmore. Alelzlroy. Tonry. 1985).

Three fiducial values of the velocity dispersion are considered, 100km/s, 200km/s and 300km/s, the central value representing a typical elliptical galaxy (Whitmore, McElroy, Tonry 1985).

For the lower velocity. dispersion of 00km/s. the resulting gravitational lensing magnification of due to galaxies No.

For the lower velocity dispersion of 100km/s, the resulting gravitational lensing magnification of due to galaxies No.

512 and No.

524 is only pp~1.08.

524 is only $\mu\sim1.08$.

Considering instead. the more typical value. of 200km/s. the eravitational lensing magnification is (/1.42. corresponding to a brightening of Q.38mags.

Considering instead the more typical value of 200km/s, the gravitational lensing magnification is $\mu\sim1.42$, corresponding to a brightening of 0.38mags.

I£ galaxics No.

If galaxies No.

512 and No.

524 are massive ellipticals. with velocity dispersions of 300knmi/s. the magnification is jp2.92. a brightening of 1.16mags.

524 are massive ellipticals, with velocity dispersions of 300km/s, the magnification is $\mu\sim2.92$, a brightening of 1.16mags.

The simple analysis presented in. this paper demonstrates that it is likely that the recently identifiec ugh redshift: supernova.SNLOOTI.. was milelly magnifier w the gravitational lensing influence of two galaxies ling close to the line of sight.

The simple analysis presented in this paper demonstrates that it is likely that the recently identified high redshift supernova, was mildly magnified by the gravitational lensing influence of two galaxies lying close to the line of sight.

Phe magnification is depencen upon the mass of the lensing galaxies. but if these are vpical elliptical galaxies. aappeared brighter by O.88maes.

The magnification is dependent upon the mass of the lensing galaxies, but if these are typical elliptical galaxies, appeared brighter by 0.38mags.

While this value wil depend upon the assumed form of the mass. distribution in the lensine galaxy. the estimate of the magnification http://astrowww.phys.uvic.ca/grads/gwyn/pz/hdfn/spindex.htmlpresented here will be of the right order.

While this value will depend upon the assumed form of the mass distribution in the lensing galaxy, the estimate of the magnification presented here will be of the right order.

With the value of the refractive index n» (equation 13)) we can calculate a new physical delay time as a function of the ry and the telescope diameter (D). through the formula: where OPL is given by the Formula 4...

With the value of the refractive index $n_{2}$ (Equation \ref{index7}) ) we can calculate a new physical delay time as a function of the $r_{0}$ and the telescope diameter $D$ ), through the formula: where OPL is given by the Formula \ref{opl}. .

Phen. as in Section 5.. we obtain the fluctuation due to this variation Al p(ry.D): where: we obtain: Through the Formula 15 we can estimate that a delay time [Luctuation of 10.0 ps corresponds to a refractive index variation An of 3.3197.

Then, as in Section \ref{gf}, we obtain the fluctuation due to this variation $\Delta t_{P}(r_{0},D)$ : where: we obtain: Through the Formula \ref{fis} we can estimate that a delay time fluctuation of 10.0 ps corresponds to a refractive index variation $\Delta n$ of $3.3\times 10^{-8}$.

This gives an idea of the error propagation.

Consequently. the total luetuation of the delay time is the sum of the geometric ancl physical component: In this sum the physical component is larger than the geometric Component of four orders of magnitude.

Consequently, the total fluctuation of the delay time is the sum of the geometric and physical component: In this sum the physical component is larger than the geometric component of four orders of magnitude.

Finally. we express this Huctuation through the extended formula: where: Substituting the constantswith these values (Roclelier. 1981)) A.—0.15. & 13= 3.5 Soy= Sande =2 we obtain the final formula used in the model: where: We note that this delay time fluctuation depends on the wavelength anc on the telescope diameter.

Finally, we express this fluctuation through the extended formula: where: Substituting the constantswith these values (Roddier, \cite{roddier}) ) $K=0.18$, $\alpha=1$, $\beta=3$, $\gamma=5$, $\eta=3$ and $\epsilon=2$ we obtain the final formula used in the model: where: We note that this delay time fluctuation depends on the wavelength and on the telescope diameter.

La particular. it also depends on the Fried radius. Figure 3. shows the trend of this Huctuation as ary function.

In particular, it also depends on the Fried radius, Figure \ref{r0} shows the trend of this fluctuation as a $r_{0}$ function.

The simulation is done for La Silla (A=0.632501. Zenith angle = 107).

The simulation is done for La Silla $\lambda=0.632\mu m$, Zenith angle $=10^{\circ}$ ).

In this Section we apply the previously. described: model to the three Chilean sites of ESO telescopes.

In this Section we apply the previously described model to the three Chilean sites of ESO telescopes.

We present the results obtained through the Formula. 17...

We present the results obtained through the Formula \ref{cava}. .

Table. 3 shows the simulation resultsforcach site. in particular

Table \ref{dia1} shows the simulation resultsforeach site, in particular

by color.

Therefore, the actual contamination level is the compromise of these two effects.

We can describe the measured alignment parameters, 7%,, as a combination of alignment from real cluster satellites and projected field galaxies.

We can describe the measured alignment parameters, $\gamma$, as a combination of alignment from real cluster satellites and projected field galaxies.

If we denote the alignment parameters from our measurements as Ym, then we can decompose it into two parts as follows:

If we denote the alignment parameters from our measurements as $\gamma_m$, then we can decompose it into two parts as follows:

In this below. we lix Monte Carlo method in Example 2. based on convergence result in1.

In this below, we fix Monte Carlo method in Example \ref{exm:EM} based on convergence result in.

. Regarding the estimation by Monte Carlo method. one mav take the simplest. choice {91=0 for the rebate pavolf as of Corollary 2.. see also [3]..

Regarding the estimation by Monte Carlo method, one may take the simplest choice $g(\beta) \equiv 0$ for the rebate payoff as of Corollary \ref{cor:mc},, see also \cite{ELTS08p}.

However. Corollary 2. can not be utilized the approximation bv PDE numerical method. since it may cause a discontinuity al the corner (2.7) of the terminial-boundary datum when /(2)4/0.

However, Corollary \ref{cor:mc} can not be utilized the approximation by PDE numerical method, since it may cause a discontinuity at the corner $(\beta, T)$ of the terminial-boundary datum when $f(\beta) \neq 0$.

For the above Monte Carlo method on(3.2).. vel another to be mentioned is a drawback in the computation by PDE numerical methods due to the possible ciscontinuity of the bouncdary-terminal data.

For the above Monte Carlo method on, yet another to be mentioned is a drawback in the computation by PDE numerical methods due to the possible discontinuity of the boundary-terminal data.

To illustrate this issue. we write Black-Scholes PDE associated to the rebate option price ViCr.1) of(3.2). Note that. PDE has a diseontinnous corner at the point (2.]T) if gio)EV4{ίM

To illustrate this issue, we write Black-Scholes PDE associated to the rebate option price $V^{\beta}(x,t)$ of, Note that, PDE has a discontinuous corner at the point $(\beta, T)$ if $g(\beta) \neq f(\beta)$.

Also recall that. the choice of ο)=f(2) mav not be possible. like in C ‘model Example 1..

Also recall that, the choice of $g(\beta) = f(\beta)$ may not be possible, like in CEV model of Example \ref{exm:cev}. .

value of à).

value of $\alpha$ ).

For comparison. we have redone the asymmetric drift correction of NGC 1023 with the method. described above for the new sample.

For comparison, we have redone the asymmetric drift correction of NGC 1023 with the method described above for the new sample.

We found Viana=270+19L2 which is in excellent agreement with the value of Paper I. We finally measured "X. as. Viana/(eg€,).

We found $V_{\rm c,flat} = 270 \pm 13$, which is in excellent agreement with the value of Paper I. We finally measured $\vpd$ as $V_{\rm c,flat}/(\len\om)$.

We used Monte Carlo to estimate the uncertainties in R by varving Vana and eg uniformly in their respective ranges. and varving ©), assuming the errors of Table S are Gaussian.

We used Monte Carlo to estimate the uncertainties in $\vpd$ by varying $V_{\rm c,flat}$ and $\len$ uniformly in their respective ranges, and varying $\om$ assuming the errors of Table \ref{tab:bar_kinematics} are Gaussian.

We report the median and the 67 per cent interval of R in ‘Table 8S..

We report the median and the 67 per cent interval of $\vpd$ in Table \ref{tab:bar_kinematics}.

The 5 SDO presented in this work. together with NCC 1023 stucied in sPaper L which we include in our saniple for this discussion. represent the largest sample of barred. galaxies. with ©, measured by means of the TW method.

The 5 SB0's presented in this work, together with NGC 1023 studied in Paper I, which we include in our sample for this discussion, represent the largest sample of barred galaxies, with $\om$ measured by means of the TW method.

For all of rem. Ris consistent with being in the range 1.0 to 1.4. =μα‘thin the errors. wwith each having a last bar.

For all of them, $\vpd$ is consistent with being in the range 1.0 to 1.4, within the errors, with each having a fast bar.

The unweightecl average for 1e sample is R=1.1.

The unweighted average for the sample is $\overline{\vpd} = 1.1$.

Phe apparent range of R spans from KS to 1.6 (0.6 to 2.1. within the 67 per cent intervals).

The apparent range of $\vpd$ spans from 0.8 to 1.6 (0.6 to 2.1, within the 67 per cent intervals).

This Esoead is not related to the properties of the galaxies in any νους wayfor the two galaxies at Vou=277|. NGC 1028 and NGC T4440. the measured values of Rare at opposite extremes of the distribution)

This spread is not related to the properties of the galaxies in any obvious wayfor the two galaxies at $V_{\rm c, flat} = 277$, NGC 1023 and NGC 1440, the measured values of $\vpd$ are at opposite extremes of the distribution).

The fact that some of the values of R are nominally less than unity leads us to suggest that the large range of R is a result of random errors and/or scatter in the measurements.

The fact that some of the values of $\vpd$ are nominally less than unity leads us to suggest that the large range of $\vpd$ is a result of random errors and/or scatter in the measurements.

The sources of random errors are largely clue to micasurement uncertainties in all 5 quantities used to compute A. V canas etg and ,.

The sources of random errors are largely due to measurement uncertainties in all 3 quantities used to compute $\vpd$, $V_{\rm c,flat}$ , $\len$ and $\om$.

Of these. the largest is in Q,,. amounting to typical fractional uncertainties of 30 per cent. followed by ag. for which the typical fractional uncertainty is 20 per cent.

Of these, the largest is in $\om$, amounting to typical fractional uncertainties of 30 per cent, followed by $\len$, for which the typical fractional uncertainty is 20 per cent.

These uncertainties account for the typical laree (aud asvonmetric towards large values) errors on measurements of R.

These uncertainties account for the typical large (and asymmetric towards large values) errors on measurements of $\vpd$ .

A likely source of scatter is errors in.the disc PA.

A likely source of scatter is errors inthe disc PA.

= ((k ))Op = (ib - jg) ∖∖↽∐≺↵↕⋅≺↵≬⋡∶∶↸∣↗↙∕∕∕↗⋅⊳∪∣−↾∶∣⋅⋮−∣↗−↙∕∕∕↗⋅⋜↕∐≺∟−↨↥↥⊳∖↕∐≺↵∖∖↽⋜↕∖⊽≺↵⋜⋃∐↥↽≻∐⊓∐⇂≺↵⋅⊺∐≺↲↥⋜↕⊳∖↕⋜↕∐≺

= ( - ) = ( - ) where $c_s^2=\gamma p/\rho$ , $\omega_b^2=k^2b^2/\rho$ , and $A \ll 1$ is the wave amplitude.