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Here we want to examine the scan fitting procediye by the Monte Carlo method. ocusiug our interest. by conrast. on the sinall fraction of he data near the planets. which ροήτς optimizations in he design of our pipeline suied to that task. | Here we want to examine the beam fitting procedure by the Monte Carlo method, focusing our interest, by contrast, on the small fraction of the data near the planets, which permits optimizations in the design of our pipeline suited to that task. |
Ou a laptop. our pipeline cau sinulate a panet crossie and subsequeu )oann reconstruction m a few seconds. fast enough that. ou a cluster. we can rapidly generate thousands of siuulations. | On a laptop, our pipeline can simulate a planet crossing and subsequent beam reconstruction in a few seconds, fast enough that, on a cluster, we can rapidly generate thousands of simulations. |
The modeling inclides simulated potting. realistic beans. λαοί». L/f and white noise. the CAB. ando several tinue-donuadu filters. | The modeling includes simulated pointing, realistic beams, planets, $1/f$ and white noise, the CMB, and several time-domain filters. |
We test our beam fitting methods using these simulated observations. characterizing ιο beam errors bv the Moute Carlo uethod. | We test our beam fitting methods using these simulated observations, characterizing the beam errors by the Monte Carlo method. |
The pointing is generated on rings aud imceludes a randomized re-poiutiung eror between ries. | The pointing is generated on rings and includes a randomized re-pointing error between rings. |
We model mitation of the satellite spin axis as a cross-scan oscillation at a fixed freqchev. | We model nutation of the satellite spin axis as a cross-scan oscillation at a fixed frequency. |
We translate the poiutiug iuto the rene where the plauet is fixed. accounting for linear notions of the planet ou the sky. appropriate for the jour time scales here. | We translate the pointing into the frame where the planet is fixed, accounting for linear motions of the planet on the sky, appropriate for the few-hour time scales here. |
7Oosunnarnzes the optical properties of the nuuissionus telescope. | summarizes the optical properties of the mission's telescope. |
For the beam. we use the detailed calculations produced by the collaboration based on models of the telescope opticsC2???). | For the beam, we use the detailed calculations produced by the collaboration based on models of the telescope optics. |
, Bean values we provked ou a tabulated erid. which we evaluate at uon-erid points bv interpolation. | Beam values are provided on a tabulated grid, which we evaluate at non-grid points by interpolation. |
We fit a Cassian to capture the bemus largest scales. then use 2-d cubic spline interpolation to reproduce the residuals to this fit. | We fit a Gaussian to capture the beam's largest scales, then use 2-d cubic spline interpolation to reproduce the residuals to this fit. |
The interpolated beam is the sum of the Caussian aud the spline interpolation and reproduces the exidded beam exactly on pixel centers. | The interpolated beam is the sum of the Gaussian and the spline interpolation and reproduces the gridded beam exactly on pixel centers. |
We model the planet as a poiut source. sothat after convolution with the beam. the plauct signal reseiibles the beam shape. with peak temperature eiven by Table 1.. | We model the planet as a point source, so that after convolution with the beam, the planet signal resembles the beam shape, with peak temperature given by Table \ref{tab:planet_brightness}. |
To include the impact of the CAIB on the planet fits. we simulate small scale CMD modes. | To include the impact of the CMB on the planet fits, we simulate small scale CMB modes. |
These are computed by FFT ina dat skv approximation on a plane surrounding the planet scan. expanded to avoid edge effects im the bea data. | These are computed by FFT in a flat sky approximation on a plane surrounding the planet scan, expanded to avoid edge effects in the beam data. |
Because of the high planet signal. we fiud that the CMD does not have a material effect on the beam TOCOVOIV. | Because of the high planet signal, we find that the CMB does not have a material effect on the beam recovery. |
Our simulated detectors are primarily characterized by their noise attributes. which we set to mumic the actual ddetectors2). | Our simulated detectors are primarily characterized by their noise attributes, which we set to mimic the actual detectors. |
Optionally. for the IFT detectors. we include a time-coustant and/or nonlinear response iu our simulations. | Optionally, for the HFI detectors, we include a time-constant and/or nonlinear response in our simulations. |
To capture low-frequeney drifts im the clectrouic auplificrs and bolometer temperatures. wo use a nolse power spectrum of the form. where the low frequency index àL.7 for ΤΕΙ aud ac2.0 for ΠΕΙ. | To capture low-frequency drifts in the electronic amplifiers and bolometer temperatures, we use a noise power spectrum of the form where the low frequency index $\alpha \approx 1.7$ for LFI and $\alpha \approx 2.0$ for HFI. |
We consider this noise as a sun of correlated aud white parts. gencrated in separate steps. | We consider this noise as a sum of correlated and white parts, generated in separate steps. |
The correlated low frequency part is generated via an | The correlated low frequency part is generated via an |
region, except lor (he J=9 transition. which shows weak maser action. | region, except for the $J=9$ transition, which shows weak maser action. |
The observed line velocities agree well with those observed in vibrationally excited HCSN by Wyrowski et . ( | The observed line velocities agree well with those observed in vibrationally excited $_3$ N by Wyrowski et al. ( |
2002). who used their extensive data to model the physical parameters of the hot. dense emission region. | 2002), who used their extensive data to model the physical parameters of the hot, dense emission region. |
VLA observations of the J=13 line reveal the emission region is compact and covers only the western part of the embedded region. similarly to zunmonia. | VLA observations of the $J=13$ line reveal the emission region is compact and covers only the western part of the embedded region, similarly to ammonia. |
Since in addition to CRL 618 we detected (-tvpe LCN lines toward hot molecular cores in regions of hieh-mass star Formation. they also represent an interesting new Cool to study the immediate raljcinitv of voung (proto-)stellar objects. | Since in addition to CRL 618 we detected $\ell$ -type HCN lines toward hot molecular cores in regions of high-mass star formation, they also represent an interesting new tool to study the immediate vicinity of young (proto-)stellar objects. |
Triggered by (he raclioastronomical observations presented here. a laboratory investigation of direct. (-tvpe transitions of ICN (vs= 1) has been carried out in the Cologne laboratory covering rotational quantum numbers up to 7=35 at GGlIlIz (Thorwirth et al.. | Triggered by the radioastronomical observations presented here, a laboratory investigation of direct $\ell$ -type transitions of HCN $v_2=1$ ) has been carried out in the Cologne laboratory covering rotational quantum numbers up to $J=35$ at GHz (Thorwirth et al., |
in preparation) The complete analvsis will be presented in a following paper. | in preparation) The complete analysis will be presented in a following paper. |
The present study was supported by the Deutsche Forschuneseemeinschalt (DEG) via Grant 4494 aud by special finding from the Ministry of Science of the Land | The present study was supported by the Deutsche Forschungsgemeinschaft (DFG) via Grant 494 and by special funding from the Ministry of Science of the Land Nordrhein-Westfalen. |
FW is supported by the National Science Foundation under Grant NSF | FW is supported by the National Science Foundation under Grant NSF AST-9981289. |
We would also like to thank an anonvinous referee for valuable suggestions on the niaser Interpretation. | We would also like to thank an anonymous referee for valuable suggestions on the maser interpretation. |
relativistic hydrodsnamic equations have been formulated as a first-orcer. Hux-conservative hyperbolic system. and solved. using a suitable Ciodunov-ty scheme. | relativistic hydrodynamic equations have been formulated as a first-order, flux-conservative hyperbolic system and solved using a suitable Godunov-type scheme. |
Among the simplifying conditions we have assumedpe a constant angular momentum cisc around a Schwarzschilel (nonrotating) black hole. | Among the simplifying conditions we have assumed a constant angular momentum disc around a Schwarzschild (nonrotating) black hole. |
The self-eravity of the disc has been neglected. and the evolution of the central black hole has been assumed to be that of a sequence of exact Schwarzschilel black holes of varving mass. | The self-gravity of the disc has been neglected and the evolution of the central black hole has been assumed to be that of a sequence of exact Schwarzschild black holes of varying mass. |
We have found that by allowing the mass of the black hole to grow the runaway instability appears a dynamical timescale. | We have found that by allowing the mass of the black hole to grow the runaway instability appears on a dynamical timescale. |
Ehe mass Uux diverges and the ondisc entirely falls into the hole in a few orbital periods (1 + 100). | The mass flux diverges and the disc entirely falls into the hole in a few orbital periods (1 $\to$ 100). |
Therefore. the appearance of the runaway instability in constant angular momentum cdises found in our simulations is in complete agreement with previous estimates [rom stationary models (22).. | Therefore, the appearance of the runaway instability in constant angular momentum discs found in our simulations is in complete agreement with previous estimates from stationary models \citep{abramowicz:83,nishida:96a}. |
Our simulations provide the first estimation of the timescale associated with the runaway instability. | Our simulations provide the first estimation of the timescale associated with the runaway instability. |
For a black hole of 2.5M. and disc-to-hole mass ratios between 1 and 0.05 this timescale never exceeds 1s [or a large range of mass fluxes and it is typically about 50ms. | For a black hole of $2.5\ \mathrm{M_{\odot}}$ and disc-to-hole mass ratios between 1 and 0.05 this timescale never exceeds $1\ \mathrm{s}$ for a large range of mass fluxes and it is typically about $50\ \mathrm{ms}$. |
We have found that the dependence of the timescale on the disc-to-hole mass ratio is weak and that the runaway instability occurs faster the larger it is the initial mass Lux (stationary regime) from the cise to the black hole. | We have found that the dependence of the timescale on the disc-to-hole mass ratio is weak and that the runaway instability occurs faster the larger it is the initial mass flux (stationary regime) from the disc to the black hole. |
We note that our study has been restricted: to a polvtropic eas. with a particular choice of # and + corresponding to a gas of degenerate relativistic electrons. | We note that our study has been restricted to a polytropic gas, with a particular choice of $\kappa$ and $\gamma$ corresponding to a gas of degenerate relativistic electrons. |
We are aware of the over-simplification of such an Los. Llowever. the work of ? has shown that the conclusion of | We are aware of the over-simplification of such an EoS. However, the work of \citet{nishida:96b} has shown that the conclusion of |
The nuderstanding of the flow dynamics within stellar radiative zones constitutes a major challenec or the curent hneorv of sellar evolution. | The understanding of the flow dynamics within stellar radiative zones constitutes a major challenge for the current theory of stellar evolution. |
These notious transport chenucal elenents and it turus out hat their coutribution might reconcile the existing uodels of stellar sructure with the observations of the surface abundances (Pinsouneaul 1998) ). | These motions transport chemical elements and it turns out that their contribution might reconcile the existing models of stellar structure with the observations of the surface abundances (Pinsonneault \cite{pin}) ). |
By transporting aneular momenta. such flows also play au important role in the evolution of sars rotation. | By transporting angular momentum, such flows also play an important role in the evolution of star's rotation. |
Iu particular. they could explain the nearly xMid body rotaion of the solar rachative zoue Which has been revealed by helioseisiiologv. (Cough et al. 1996)). | In particular, they could explain the nearly solid body rotation of the solar radiative zone which has been revealed by helioseismology (Gough et al. \cite{gough}) ). |
Wo consier here the effects of the very. high thermal diffusivity of stear muteriors on the dynamics of these motions. | We consider here the effects of the very high thermal diffusivity of stellar interiors on the dynamics of these motions. |
Iu most cases, radiation dominates the thermal exchanges within radiative zones. | In most cases, radiation dominates the thermal exchanges within radiative zones. |
This heat transport is so efficient that jc thermal diffusivities associated with the radiative fux are larger by several orders of magnitude than the thermal diffusivities encountered ii colder media like planetary auospheres. | This heat transport is so efficient that the thermal diffusivities associated with the radiative flux are larger by several orders of magnitude than the thermal diffusivities encountered in colder media like planetary atmospheres. |
For example. the thermal diffisivity varies between 10? and |O°ci?s! inside the DII whereas it is equal to 0.15enis1 in the standard conditions of the terrestrial atmosphere. | For example, the thermal diffusivity varies between $10^5$ and $10^7 \;{\rm cm}^2
{\rm s}^{-1}$ inside the sun whereas it is equal to $0.18\;{\rm cm}^2
{\rm s}^{-1}$ in the standard conditions of the terrestrial atmosphere. |
This proertv of the stellar fluid is expected to strongly affect the How dynamics especialv inside the stably stratified radiative zone where the time scale of thermal ditmsSjon appears to be shorter than the dynamical time scale characterizing radial iioions. | This property of the stellar fluid is expected to strongly affect the flow dynamics especially inside the stably stratified radiative zone where the time scale of thermal diffusion appears to be shorter than the dynamical time scale characterizing radial motions. |
Uelioscisinology data show hat the thermal strucure of this region is very close to the one predicted by lydrostatic models. indicating that existing fluid motions are not fast enough to imodifv significantly the thermal structure built up by the radiative flux (Cauuto Christenscu-Dalseaard L998)}). | Helioseismology data show that the thermal structure of this region is very close to the one predicted by hydrostatic models, indicating that existing fluid motions are not fast enough to modify significantly the thermal structure built up by the radiative flux (Canuto Christensen-Dalsgaard \cite{can}) ). |
Qualitatively. the damping of temperaure fluctuations bv thermal diffusion is expected to have two main effects on the dynamics. | Qualitatively, the damping of temperature fluctuations by thermal diffusion is expected to have two main effects on the dynamics. |
The first oue is to reduce the auplitude of the buovaucy force. | The first one is to reduce the amplitude of the buoyancy force. |
This restoriug force acts on fui parcels ¢isplaced from treir equilibria level and ids proportional to the density differcuce between the parcel aud its environment. | This restoring force acts on fluid parcels displaced from their equilibrium level and is proportional to the density difference between the parcel and its environment. |
Since deusity fluctuations are proportional to temperature fluctuations for incompressible motions. fast thermal exchanges reduce the force amplitude. | Since density fluctuations are proportional to temperature fluctuations for incompressible motions, fast thermal exchanges reduce the force amplitude. |
Au important consequence of this effect is to favour the onset of shear laver instabilities in stably stratified lavers (Duclis 197LL. Zalu 197 1)). | An important consequence of this effect is to favour the onset of shear layer instabilities in stably stratified layers (Dudis \cite{dudis}, Zahn \cite{zan}) ). |
The second main effect of the thermal diffusion is to increase the dissipation of kinetic energv. | The second main effect of the thermal diffusion is to increase the dissipation of kinetic energy. |
Any vertica notion in a quiescent atinosphere induces a work of the movancy force so that a fraction of the injected. kinetic energv is necessarily transformed iuto potential energy. | Any vertical motion in a quiescent atmosphere induces a work of the buoyancy force so that a fraction of the injected kinetic energy is necessarily transformed into potential energy. |
If he fluid parcels could “fall” adiabatically towards their equilibrium position. all the stored potential enerev couk return back to kinetic cucrey. | If the fluid parcels could "fall" adiabatically towards their equilibrium position, all the stored potential energy could return back to kinetic energy. |
However. the damping of cluperature fluctuatious provokes an irreversible loss of sinetic energv. | However, the damping of temperature fluctuations provokes an irreversible loss of kinetic energy. |
A simple example of this process is the damping of eravity waves. | A simple example of this process is the damping of gravity waves. |
Both effects of the thermal diffusivity. are thus opposed. | Both effects of the thermal diffusivity are thus opposed. |
While a decrease of the buovancy force aiuitude reduces the associated. work aud thus the αλλο of kinetic enerev extracted. the second effect increases the fraction of the kinetic euergv which is | While a decrease of the buoyancy force amplitude reduces the associated work and thus the amount of kinetic energy extracted, the second effect increases the fraction of the kinetic energy which is |
In the currently accepted ACDAL. paradigm.. for. cosmic. structure formation... small dark matter haloes form⋅ [irs⋅ while more massive haloes form later through accretion of diffuse matter and mergers between smaller systems. | In the currently accepted $\Lambda$ CDM paradigm for cosmic structure formation, small dark matter haloes form first while more massive haloes form later through accretion of diffuse matter and mergers between smaller systems. |
During the last decades. we have witnessed a rapid development of numerical algorithms and a significant increase in numerica resolution. that have allowed us to improve our knowledge of the formation and evolution of dark matter structures. | During the last decades, we have witnessed a rapid development of numerical algorithms and a significant increase in numerical resolution, that have allowed us to improve our knowledge of the formation and evolution of dark matter structures. |
In particular. the increase in numerical resolution has allow uss to overcome"Ore: the κοso-called:ρώταproblem. ic.τς tx: rapid disruption of galaxv-size substructures in groups anc clusterstherein). | In particular, the increase in numerical resolution has allowed us to overcome the so-called, i.e. the rapid disruption of galaxy-size substructures in groups and clusters. |
. I£ any. we are now facing he opposite problem. at least on galaxy scales. where many more substructures than visible chvarl galaxies are founcherein). | If any, we are now facing the opposite problem, at least on galaxy scales, where many more substructures than visible dwarf galaxies are found. |
. According to the two stage theory proposed by2.. the ohvsical properties of galaxies are determined by cooling an condensation of gas within the potential wells of dark matter aloes. | According to the two stage theory proposed by, the physical properties of galaxies are determined by cooling and condensation of gas within the potential wells of dark matter haloes. |
“Pherclore. substructures represent the birth-sites o uminous galaxies. ancl the analysis of their mass and spatia distribution. as well as of their merger and mass accretion ustories provide important information about the expectec wopertiesI of ggalaxies in the frameworkof hierarchical ggalaxy ormation models. | Therefore, substructures represent the birth-sites of luminous galaxies, and the analysis of their mass and spatial distribution, as well as of their merger and mass accretion histories provide important information about the expected properties of galaxies in the framework of hierarchical galaxy formation models. |
Nowadavs. a wealth of substructures are routinely identifiecl in dissipationless simulations. and their statistical »operties and evolution have been studied in detail in the vast vears. | Nowadays, a wealth of substructures are routinely identified in dissipationless simulations, and their statistical properties and evolution have been studied in detail in the past years. |
The identification of dark matter substructures. | The identification of dark matter substructures, |
CRISP data are obtained while continuously cyeling through a 4-state liquid-crystal (LC) scheme. which converts combinations of the incoming polarization states Q. U. and V to linear polarization that can be analyzed with the polarizing beam splitter close to the final focal plane. | CRISP data are obtained while continuously cycling through a 4-state liquid-crystal (LC) scheme, which converts combinations of the incoming polarization states Q, U, and V to linear polarization that can be analyzed with the polarizing beam splitter close to the final focal plane. |
Data are simultaneously recorded using two narrow-band cameras (called transmitted and reflected camera) in a dual-beam setup and a wide-band camera (receiving of the light passing the prefilter via a beam-splitter) placed before the liquid-crystal variable retarders. | Data are simultaneously recorded using two narrow-band cameras (called transmitted and reflected camera) in a dual-beam setup and a wide-band camera (receiving of the light passing the prefilter via a beam-splitter) placed before the liquid-crystal variable retarders. |
The frame rate of ~36 Hz is set by the rotating chopper. which has a duty cycle setting the exposure time at 16 ms. | The frame rate of $\sim$ 36 Hz is set by the rotating chopper, which has a duty cycle setting the exposure time at 16 ms. |
CCD readout is performed during the dark part of the cyele. | CCD readout is performed during the dark part of the cycle. |
For the data shown in this paper. 4 full were completed before tuning to the next of a total of 12 wavelengths. | For the data shown in this paper, 4 full LC-cycles were completed before tuning to the next of a total of 12 wavelengths. |
The complete linescan of4 LC-states x 4 repeats x 13 wavelengths = 202 frames covers ~6 seconds. | The complete linescan of 4 LC-states $\times$ 4 repeats $\times$ 12 wavelengths = 202 frames covers $\sim 6$ seconds. |
The data required for calibrating the science data from CRISP are obtained in the following way. | The data required for calibrating the science data from CRISP are obtained in the following way. |
The dark images are recorded in a similar way as the science data. but with the light path blocked after the exit window of the vacuum tube. | The dark images are recorded in a similar way as the science data, but with the light path blocked after the exit window of the vacuum tube. |
The final dark is the average of a large number of darks (typically 100-1000). | The final dark is the average of a large number of darks (typically 100–1000). |
Flatfields are obtained by summing many (~ 1000) images of the Sun taken with the telescope pointing moving across the solar disk. | Flatfields are obtained by summing many $\sim$ 1000) images of the Sun taken with the telescope pointing moving across the solar disk. |
As such. the flatfields include both transmission variations over the FOV as actual CCD gain variations. as do the gains that are derived from these flatfields. | As such, the flatfields include both transmission variations over the FOV as actual CCD gain variations, as do the gains that are derived from these flatfields. |
Therefore. in this paper. "flatfielding" and “gain correction" imply the same correction. | Therefore, in this paper, “flatfielding“ and “gain correction“ imply the same correction. |
The polarization calibration data is obtained. by producing light with known polarization states using a linear polarizer and a quarter-wave plate placed below the exit window of the vacuum tube in the tower. | The polarization calibration data is obtained by producing light with known polarization states using a linear polarizer and a quarter-wave plate placed below the exit window of the vacuum tube in the tower. |
The modulation scheme 1s then calibrated using the method described in Appendix AppendixA:.. | The modulation scheme is then calibrated using the method described in Appendix \ref{appa}. |
The (time-dependent) telescope Mueller matrix has been measured by ? and is assumed to be known here. | The (time-dependent) telescope Mueller matrix has been measured by \citet{jakob:2006} and is assumed to be known here. |
Por ground-based. high-resolution imaging. image restoration is a vital tool. | For ground-based, high-resolution imaging, image restoration is a vital tool. |
However. 1t is especially important for multi-wavelength and polarimetric observations. because it will reduce differential image shifts and blurring between images recorded at different wavelengths and polarization states. | However, it is especially important for multi-wavelength and polarimetric observations, because it will reduce differential image shifts and blurring between images recorded at different wavelengths and polarization states. |
For polarimetric data. this implies that the image restoration has to be done demodulating the data (to convert the LC-states to Stokes parameters ΤΟ.ΝΟ, because the images of the different LC-states are each associated with a particular seeing disturbance that must be compensated for individually. to reduce artificial. seeing-induced signals. | For polarimetric data, this implies that the image restoration has to be done demodulating the data (to convert the LC-states to Stokes parameters I,Q,U,V), because the images of the different LC-states are each associated with a particular seeing disturbance that must be compensated for individually, to reduce artificial, seeing-induced signals. |
In our analysis we focused on image restoration using MOMFBD (?).. but some of the complications discussed below are equally relevant for Speckle restorations. | In our analysis we focused on image restoration using MOMFBD \citep{vannoort:2005}, but some of the complications discussed below are equally relevant for Speckle restorations. |
MOMFBD has several properties that can complicate calibrations. | MOMFBD has several properties that can complicate calibrations. |
The loss of the direct relation between input data pixels and restored data pixels means that all calibrations that cannot be done image restoration. and hence before demodulating. cannot be done on a pixel-by-pixel basis. but involve the point-spread-functions (PSFs. which result from seeing and the finite pupil size) of the input Images. | The loss of the direct relation between input data pixels and restored data pixels means that all calibrations that cannot be done image restoration, and hence before demodulating, cannot be done on a pixel-by-pixel basis, but involve the point-spread-functions (PSFs, which result from seeing and the finite pupil size) of the input images. |
Similarly. artificial features in the input images should be removed as much as possible before image restoration. because they will interfere with the wavefront sensing and can be strongly amplified by the deconvolution. | Similarly, artificial features in the input images should be removed as much as possible before image restoration, because they will interfere with the wavefront sensing and can be strongly amplified by the deconvolution. |
Input images that are not monochromatic over the FOV are rather hard to deal with. because this cannot be properly corrected without knowing the entire line profile. | Input images that are not monochromatic over the FOV are rather hard to deal with, because this cannot be properly corrected without knowing the entire line profile. |
Both the wavelength changes over the FOV and the assumption of noise with à Gaussian distribution of à constant width are limiting factors for the maximum (polarimetric) accuracy that can be obtained when using image restoration. | Both the wavelength changes over the FOV and the assumption of noise with a Gaussian distribution of a constant width are limiting factors for the maximum (polarimetric) accuracy that can be obtained when using image restoration. |
To avoid interference from artifacts in the narrow band cameras on the wavefront sensing. one can only use images from the | To avoid interference from artifacts in the narrow band cameras on the wavefront sensing, one can only use images from the |
literature data for the electron temperature. electron density ane also for the abundances show a large spread. indicating that the use of line diagnostics is not reliable. | literature data for the electron temperature, electron density and also for the abundances show a large spread, indicating that the use of line diagnostics is not reliable. |
Comparison of the various abundance determinations indicates that the uncertainty in the electron. temperature is the main source of uncertainty in the abundance determination. | Comparison of the various abundance determinations indicates that the uncertainty in the electron temperature is the main source of uncertainty in the abundance determination. |
The Large spread in the literature data makes a comparison with our results meaningless. | The large spread in the literature data makes a comparison with our results meaningless. |
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