text:
\section{Introduction}

Understanding the evolution of quasars has been a subject of great importance since their discovery over four decades ago.  In particular, there is now substantial, multifaceted, and growing evidence for a correlation between the formation and evolution of galaxies and their central supermassive black holes (\citealt{Magorrian98,Ferrarese00}; also, see the proceedings edited by \citealt{Ho04}, or the review by \citealt{Djorgovski05}, and references therein).  Studies of the evolving QSO populations are important not only for their own sake, but also for providing insights into the formation and evolution of massive galaxies in general.

While quasars represent a relatively minor contributor ($\sim10\%$) to the overall energetics of the post-recombination universe, they dominate at high energies, and their radiative and mechanical feedback may significantly affect the formation and growth of their hosts and companions \citep{Silk98,Wyithe03b}.   Quasars are a significant contributor to the metagalactic ionizing radiation field at any redshift, although their role relative to that of star-forming galaxies has likely changed over the history of the Universe.  Quasars might still be important producers of the metagalctic UV radiation at high redshifts ($z \gtrsim 4-5$) as one approaches the end of the reionization era.

Although we observe a decline in the density of quasars by a factor of $\sim 40$ between the peak of quasar activity at $z\sim 2.5$ and the end of reionization at $z\sim 6$ \citep{Fan01b}, this evolution has been traced only by the most luminous sources at redshifts beyond $z\sim 3$.   The primary observable which constrains the evolution of quasar populations and their effects on their environment is the quasar luminosity function (QLF) as a function of redshift.  At low redshifts, the QLF is well-represented by a double  power-law, $\Phi(L) = \Phi_* / L_* [(L/L_*)^\alpha + (L/L_*)^\beta]^{-1}$\citep{Boyle88,Pei95}.  The bright-end slope, $\alpha$, has typical measured values around $-3.4$ at redshifts $z<2.5$, and flattens to $\alpha \approx -2.5$ at $z\sim 4$ \citep{Fan01a}. The faint-end slope, $\beta$, is typically measured to be around $-1.7$ at low redshifts ($z \lesssim1$), although \citet{Hunt04} find a shallower value of $\beta \approx -1.2$ at $z\sim 3$.

There has been considerable progress recently in the theoretical understanding of the shape of the QLF and its evolution.  The emerging picture is a complex interplay of QSO lifetimes and luminosity histories, powered by dissipative mergers, with the bright end of the QLF dominated by short-lived phases of QSOs radiating near the peak of their luminosities and the faint end determined by the distribution of QSO fueling lifetimes and feedback \citep{Hopkins05a,Hopkins06b,Hopkins06c}.  Thus, in this model the faint end of the QLF at high redshifts represents a critical observational constraint on the early formation history of massive black holes, their contribution to the reionization, and feedback processes affecting the formation of their host galaxies.

The true shape of the QLF at $z>4$ is currently unknown, largely due to the flux limits of most large-area surveys to date.  The recent availability of deep, relatively wide-field, multicolor, optical surveys in the public domain have enabled the search for faint quasars at these high redshifts and the determination of the faint end of their QLF.  In this paper, we utilize the Deep Lens Survey \citep[DLS;][]{Wittman02} and the NOAO Deep Wide-Field Survey \citep[NDWFS;][]{Jannuzi99} which go $\sim 4$ magnitudes deeper than the Sloan Digital Sky Survey (SDSS) and other large area sky surveys, to measure the faint end of the QLF at $z\sim 4$.

The organization of the paper is as follows: in Section 2, we review the NDWFS and DLS survey data that were used for photometric candidate selection. Section 3 presents the simulations of quasar colors we have performed to obtain the QSO candidate color selection criteria. In Section 4, we describe the followup spectroscopy observations. In Section 5 we compute the QLF and analyze its shape in conjunction with published measurements at brighter magnitudes.  In Section 6 we examine the implications of our QLF by computing the contribution of quasars to the UV radiation field at $z\sim 4$.  We discuss our results in Section 7.  We use standard cosmological parameters throughout the paper: $H_0=70$ km s$^{-1}$ Mpc$^{-1}$, $\Omega_M=0.30$, and $\Omega_\Lambda=0.70$.

\section{Candidate Selection \label{sec:selection}}

We select our quasar candidates using the standard technique of looking for objects whose colors are outliers from the stellar locus.  At $z\sim 4$, our redshift of interest, $B$, $R$, and $I$ (or $z$) effectively and efficiently separate quasars from stars \citep{Kennefick95a,Kennefick95b,Richards02}.  We make use of publicly available deep imaging data from the NDWFS and the DLS, which we describe below.

\subsection{NOAO Deep Wide-Field Survey}

NDWFS is a deep imaging survey of two 9.3 deg$^2$ fields, Bo\"{o}tes and Cetus, in three optical and infrared bands ($B_W$, $R$, $I$ and $J$, $H$, $K$).  For our candidate selection, we obtained imaging data in the Bo\"{o}tes field from the Third Data Release (DR3) which is publicly available from the NOAO Science Archive\footnote{\url{http://www.archive.noao.edu/ndwfs/}}.

The custom $B_W$ filter has high transmission over most of the wavelength range commonly covered by $U$ and $B$ filters, as can be seen in Figure ~\ref{fig:nfilters}. Optical imaging for the data available in NDWFS DR3 was obtained with the  4 meter Kitt Peak National Observatory (KPNO) Mayall telescope and MOSAIC-I Wide Field Imager. The Bo\"{o}tes field is split into 27 partially overlapping subfields, each roughly 36\arcmin$\times$36\arcmin\ on the sky, with imaging products delivered on a common (tangent-projected) scale of 0\farcs258 pixel$^{-1}$. The survey design aimed for 5$\sigma$ point source detection limits of $B_W\approx 26.6$, $R \approx 26.0$ and $I \approx 26.0$ (AB mags).

We use optical ($B_W$, $R$ and $I$) imaging for five of the 27 NDWFS subfields, selected to optimize the seeing conditions and total exposure time in all three filters.  The five subfields cover a total area of 1.71 ${\mathrm{deg^{2}}}$ and their details are summarized in Table ~\ref{tabl:ndwfs_fields}.

The $B_W$, $R$, and $I$ images for a given subfield have different sizes.  We registered the images and trimmed them to their common overlapping area (listed in column 4 of Table \ref{tabl:ndwfs_fields}).  We then extracted source catalogs using SExtractor version 2.4.4 \citep{Bertin96} in dual image mode with $R$-band as the detection image and forcing the measurements in $B_W$- and $I$-bands. For detection in SExtractor, the $R$-band image was smoothed with a 3 pixel wide Gaussian filter, and the detection threshold was set to 2$\sigma$ of the sky noise.

Photometry was performed in 3\arcsec\ diameter apertures. To compensate for differences in seeing between the three bands (see Table \ref{tabl:ndwfs_fields}), this aperture magnitude was corrected to ``total'' magnitude for each band separately by subtracting an aperture correction.  To determine the aperture correction in each image, we compared the isophotal magnitude for $\mathrel{\rlap{\lower4pt\hbox{\hskip1pt$\sim$}$200 bright stellar objects to their aperture magnitude and measured the median difference.  This correction is typically $\mathrel{\rlap{\lower4pt\hbox{\hskip1pt$\sim$}$ 0.1 mag in every band.  We also correct all the magnitudes for interstellar extinction using the dust map from \citet{SFD98}. For our selection, we work with these extinction and aperture-corrected magnitudes in the $AB_{\nu}$ system, converting the published Vega-based NDWFS zeropoints to $AB_{\nu}$ magnitudes by adding 0.0, 0.26 and 0.53 mag to the $B_W$, $R$ and $I$ zeropoints, respectively.

\subsection{Deep Lens Survey}

DLS is closely related to the NDWFS in that the optical imaging has been obtained on the same 4 meter Mayall Telescope (at KPNO) and Blanco Telescope (at CTIO) using the same wide-field optical imagers Mosaic-I and Mosaic-II as the NDWFS. DLS imaging will ultimately cover a total of 28 deg$^2$ in four optical bands ($B$, $V$, $R$ and $z'$), separated on the sky into seven fields of 4 deg$^2$ (labeled F1 - F7). Each of these fields in turn is divided into 9 subfields, or ``pointings", of $35.1\arcmin \times 35.1 \arcmin$.  The final image products released by the DLS are already registered in pixel space.  Since the scale for these data is also 0\farcs258 pixel$^{-1}$, the final images have sizes $8192\times 8192$ pixels.  The DLS observational strategy was to obtain the $R$-band images on the best of the observing nights, while the $B$, $V$ and $z'$ data were taken in conditions of mixed relative quality.  In addition, the survey was designed to reach 12,000 seconds ($20\times 600$ seconds) in the $B$, $V$, and $z'$ filters and 18,000 seconds ($20\times 900$ seconds) in the $R$-band.

We used the images from the third public data release of DLS data for 6 pointings, covering a total area of 2.05 ${\mathrm{deg^{2}}}$.  The imaging data of the NDWFS and DLS differ in principle only in the filters used and fields surveyed; therefore, we applied the exact same procedure and parameters for catalog extraction as for the NDWFS data, including thresholds, apertures, and subsequent seeing and extinction corrections (see \S 2.1). The positions and several properties of the field pointings used in our survey are presented in Table \ref{tab:dls_fields}.

We extracted catalogs using SExtractor in dual image mode, with the $R$-band images as the detection image.  Photometric measurements were forced on the same pixel positions in the $B$, $V$ and $z'$ images.  The DLS data provide photometric zero-points.  The $B$, $V$, and $R$ images are calibrated to the Vega system, while the $z'$-band images are calibrated to the SDSS $AB_{\nu}$ system.  We convert from Vega magnitudes to $AB_{\nu}$ by adding $-0.09$, 0.0, and 0.2 to the $B$, $V$, and $R$ zero-points, respectively.  We also correct all the magnitudes for interstellar extinction using the dust map from \citet{SFD98}.  Although our main selection filters are $B$, $R$ and $z'$, we generated catalogs for the $V$-band data to further discriminate between our candidates and increase our efficiency, as we describe below.

\subsection{ Field-to-field Consistency}

We examined the position of the stellar locus in the $(R-z')\ vs.\ (B-R)$ and $(R-I)\ vs.\ (B_W-R)$ color-color space for the DLS and NDWFS data, respectively, to verify the consistency of the zero-points. We found discrepancies between the fields that, while small, are larger than the expected photometric errors.

To determine the zero-point shift required to bring our photometry onto a standard system we invoke a method used in the photometric quality assessment of SDSS.  Following \citet{Ivezic04}, we defined a principle axis in the aforementioned color-diagrams that follows the main sequence by iteratively fitting a line through the observed locus of well-detected stellar objects in each field.  We determined the origin of the stellar locus from the drop in density of stars along the determined track.  Figure \ref{fig:ccpos} shows the the positions of the main sequence color tracks for the five NDWFS fields on the left and the six DLS fields in our survey on the right.  The dashed lines indicate the principal axes, tracking that stellar locus, and the circles represent the origins of the locus.

Two DLS fields, F2p31 and F2p33, have bluer $(R-z')$ colors, and F2p31 is redder than the other fields in $(B-R)$.  In addition, the photometric quality of F2p31 may be slightly poorer that the other five DLS fields as the stellar locus has an rms of $\sim 6\%$ compared with $3\%$ for the remaining fields.  We apply a correction to the $z'$-band zero-points of $-0.15$ and $-0.18$ to F2p31 and F2p33, respectively.  We also apply a $z'$-band zero-point shift of $-0.05$ magnitudes to F2p31.  The NDWFS data were consistent within photometric errors; therefore no correction was applied to those fields.

\section {Color Selection Criteria Using Simulated Quasar Spectra \label{sec:specsim}}

To define color selection criteria for quasar candidates at $z \mathrel{\rlap{\lower4pt\hbox{\hskip1pt$\sim$} 4$ and determine our selection function, we simulated quasar spectra following the general procedure outlined in ~\citet{Fan99} and \citet{Richards06} and calculated their colors for the NDWFS and DLS filter combinations.  We generated a library of simulated quasar spectra, starting with a quasar template spectrum constructed from a combination of the {\it Hubble Space Telescope} ({\em HST}) radio-quiet quasar composite spectrum  from \citet{Telfer02} which covers $300-2461$\AA\ in the quasar rest frame and the SDSS quasar composite spectrum ~\citep{VandenBerk01} spanning rest-frame $800-9200$\AA.  This combined template uses the {\em HST} composite below 1275{\AA} and the SDSS composite above 2000{\AA}.  The spectra are averaged in the overlap region of $1275-2000$\AA\footnote{This combination is available at http://www.pha.jhu.edu/\~{}rt19/composite/.}.

We simulated the attenuation of each model spectrum by intervening neutral hydrogen absorbers by shifting it to a given redshift and creating random realizations of a population of discrete absorbers following the procedure outlined in ~\citet{Bershady99}.  The absorbers attenuate the template quasar spectrum with their Lyman series absorption lines and the Lyman limit break. Two separate distributions of absorbers are used, divided up according to their column density (N$_{\rm HI}$), corresponding to ``weak" absorbers and Lyman Limit Systems. We did not attempt to simulate the effect of any dust reddening or absorption by neutral hydrogen intrinsic to the quasar host galaxy.

We account for the intrinsic diversity of quasar spectral properties by varying the power-law slope of the continuum and the strength of the {Ly$\alpha$} emission line.  At UV-optical rest-frame wavelengths, the QSO continuum is best described by a broken power-law.  Shortward of {Ly$\alpha$}, we assign the spectrum a power-law index drawn from a Gaussian distribution centered on $\alpha_1 = -1.57$ with a standard deviation, $\sigma_1$, of $0.17$ \citep[$f_\nu \propto \nu^\alpha$;][]{Telfer02}.  Longward of {Ly$\alpha$} we assign the continuum a power-law index drawn from another Gaussian distribution centered on $\alpha_2=-0.5$ with $\sigma_2=0.30$ \citep{VandenBerk01,Richards03}.  We assume that the values of the two spectral slopes are uncorrelated. In addition, we vary the equivalent width, EW, of the {Ly$\alpha$} emission line assuming a Gaussian distribution of EW=$65\pm34${\AA} ~\citep{Wilkes86}, and again assume that it is uncorrelated with any of the other spectral properties.

At each $\Delta z=0.1$ in the redshift range $3.5 < z < 5.2$, we created 200 simulated quasar spectra, each with a single drawing from distributions of the two power-law continuum slopes, the Ly$\alpha$\ emission line EW, and one realization of neutral hydrogen intervening absorption systems. Convolving these spectra with the filter responses for the NDWFS and DLS filters ($B_W$, $R$, $I$ and $B$, $V$, $R$, $z'$, where the two $R$ filters are identical) we obtain simulated quasar ``color tracks'' shown by the dots in Figure \ref{fig:colortracks}.

Based on the colors of our model quasar spectra we adopt a set of color cuts for each of our datasets, NDWFS and DLS.  These are shown with dashed lines in Figure \ref{fig:colortracks}.  For the NDWFS survey, we impose the following selection criteria:
\begin{equation}
(B_W - R) \geq 2.2
\end{equation}
and
\begin{equation}
(R - I) \leq 0.25 \times (B_W - R) - 0.3.
\end{equation}
For the DLS survey, we use the following color cuts:
\begin{equation}
(B - R) \geq 2.2
\end{equation}
and
\begin{equation}
(R - z) \leq 0.45 \times (B - R) - 0.59.
\end{equation}
The DLS survey provides a fourth filter, $V$, which we use to impose an additional color criterion, based on the colors of the aforementioned simulations:
\begin{equation}
(B - V) \geq 1.0.
\end{equation}

\subsection{Morphological Criteria}

In addition to having the right colors, we required our quasar candidates to be point sources. We use the full width at half-maximum (FWHM) to discriminate between stellar and extended sources.  The left panel of Figure \ref{fig:fwhm} shows the FWHM as measured from the $R$-band image in SExtractor as a function of $R$-magnitude.  A locus of stellar sources with FWHM $\sim 1\arcsec$ is obvious.

We sought to determine a suitable morphological cut of FWHM that would eliminate galaxy contamination without sacrificing completeness.  To do this, we used the {\tt mkobjects} task in the IRAF {\tt artdata} package to insert 4200 objects with stellar profiles and $17.75 \leq R \leq 24.50$ into each field image.  We re-extract our catalogs using the same SExtractor parameters, and examine the FWHM distribution of our simulated point sources.  This distribution is shown in the right-hand panel of Figure \ref{fig:fwhm} for the same field.  The solid-line histogram shows the distribution of FWHM for simulated point sources, while the dotted line shows the FWHM distribution for sources brighter than $R=22$ and the dashed line shows the FWHM distribution for sources with $22<R<24$.  For each field, we choose as our cutoff the FWHM that retains $80\%$ of our simulated sources.  This cutoff, calculated to be 1.145\arcsec\ for NDWFS J1426+3236, is shown as horizontal dashed line in the left panel of Figure \ref{fig:fwhm} and as a vertical solid line in the right-hand panel.

\subsection{The Final Candidate List \label{sec:final_cat}}

At $z\gtrsim 4$, neutral hydrogen absorption from the {Ly$\alpha$} forest often causes $B$-band drop outs, even at the deep sensitivities of NDWFS and DLS.  Creating our catalogs in SExtractor's dual-image mode ensures that we measure a flux for each object that has an $R$-band detection, even if an object's flux drops below the $B_W$, $B$ or $V$ detection limits.  Nevertheless, the magnitude assigned to a drop-out object may be unreliable.

We define the limiting magnitude of each field based on the standard deviation per pixel for a representative region in each image.  We compute the uncertainty in  total flux in a 3\arcsec\ aperture, with area $A$, where each pixel has $1\sigma_{pix}$ counts: $f_{1\sigma} = \sigma_{pix} \sqrt{A} $.  We compute the limiting magnitude from this flux for the $B_W$ fields in NDWFS and the $B$ and $V$ field in DLS.  We assign these limits to any object whose SExtractor-determined magnitude is fainter than these limits.  We then use these limits when applying the color cuts in our candidate selection.  We note that by ignoring the fact that pixel values are correlated in these images we may be underestimating the true noise.  Furthermore, this estimate does not take into account large scale variations from the flat field and other systematic effects.  Nevertheless, this value serves as a practical lower limit on the magnitude in a band without a detection.  Since the limiting magnitudes that we compute are $B, B_W \gtrsim 27$ mags and our color criteria require that $B, B_W - R \geq 2.2$, our survey limit of $R=24$ ensures that all undetected objects meeting our color criteria will be selected.

We ran our catalogs through these selection criteria and ended up with 80 quasar candidates in the five NDWFS fields and 74 candidates in the six DLS fields, strictly based on their cataloged properties.  We then examined image cutouts of the objects and eliminated three candidates from the NDWFS sample and three candidates from the DLS sample that were image artifacts mistaken as objects by SExtractor.  We are therefore left with 77 (16 with $R \leq 23$) NDWFS candidates and 71 DLS (14 with $R \leq 23$) candidates.  We plot these objects as circles in Figure ~\ref{fig:colortracks}, indicating with a right-pointing arrow $B_W$ and $B$-band drop outs.  We list the candidates with $R<23$ in Tables \ref{tab:ndwfs_cands} and \ref{tab:dls_cands} and make the full candidate list available in electronic table format.

\section{Spectroscopy Results}

We obtained 28 spectra for the DLS and NDWFS candidates and found 23 high-redshift quasars (the remaining objects were three Lyman-break galaxies at $z\sim3.9$, one Type II AGN at $z\sim0.2$ and one featureless, unidentified spectrum).  All but two of our spectra were taken with the Low-Resolution Imaging Spectrometer \citep[LRIS;][]{Oke95} on the Keck I telescope on Mauna Kea.  Five quasars were discovered on UT 2005 November 28 and 29.  Only the red camera was used, with the 400 lines mm$^{-1}$ grating blazed at 8500 \AA.  Sixteen additional quasars were discovered during a run on UT 2006 May 20 to 22.  Again, only the red camera was used, this time with the 600 lines mm$^{-1}$ grating blazed at 7500 \AA.  The spectra were obtained one at a time using the long-slit mode at the parallactic angle.

We reduced the LRIS spectra using BOGUS, an IRAF software package developed by Stern, Bunker, \& Stanford\footnote{Available at \url{http://zwolfkinder.jpl.nasa.gov/~stern/homepage/bogus.html}} to reduce LRIS slitmask data.  We made minor modifications to the code to accommodate the single slit mode of our observations.  BOGUS reduces the two-dimensional spectra, applying a bias-correction, flat-fielding, cosmic ray removal, and sky subtraction.  Most of our spectra were observed in one exposure at a single slit position.  A handful of spectra were dithered in two positions along the slit.  For these objects, BOGUS applied a fringe correction as well.  The {\tt sham\_r} routine (part of the BOGUS package) extracts the one dimensional spectrum and performs wavelength and flux calibrations.  Since the fringing can be quite strong at the position of sky lines at red wavelengths, we interpolated over strong sky lines which appeared in our final spectra using the {\tt skyinterp} IRAF task\footnote{SKYINTERP is part of the WMKONSPEC package for reducing long-slit near-infrared spectra, where imperfect sky subtraction can often produce spectra with strong sky lines (\url{http://www2.keck.hawaii.edu/inst/nirspec/wmkonspec/index.html}). }.

Two additional spectra were taken on UT 2006 March 25 and 26 with
the Multi-Aperture Red Spectrometer \citep[MARS;][]{Barden01} on
the Mayall 4 meter telescope at Kitt Peak.  MARS is an optical spectrograph
that uses a high resistivity, p-channel Lawrence Berkeley National
Laboratory CCD with little fringing and very high throughput at
long wavelengths.  We obtained spectra of DLS~J105227.9$-$054234
and DLS~J105348.8$-$053319 using the 1\farcs7 wide long slit, OG550
order-sorting filter, and the VG8050 grism.  Across much of the
optical window this instrument configuration delivers resolution
$R \approx 1100$ spectra, as measured from sky lines filling the
slit.  The data were processed following standard optical slit
spectroscopy procedures.  The nights were not photometric, but
relative flux calibration was achieved with observations of
spectrophotometric standards from \citet{Massey90} obtained
during the same observing run.

Figures \ref{fig:spectra} and \ref{fig:spectra2} plot the 23 quasars discovered by our survey, sorted by decreasing redshift.  We mark with a vertical dotted-line expected positions of prominent ultraviolet quasar emission lines: Ly$\alpha$~1216, N~V~1240, Si~IV~1400, C~IV~1550, and C~III]~1909.

\subsection{NDWFS 1433+3408 and DLS 1053$-$0528}

These quasars, at $z=3.88$ and $z=4.02$, respectively, show prominent \ion{N}{4}] $\lambda 1486$, an extremely rare emission line.  When seen in QSOs, this line is normally accompanied by strong \ion{N}{5} $\lambda 1240$ and is a consequence of high nitrogen abundances.  Such objects are dubbed ``nitrogen-rich" and make up at most $0.2\% - 0.7\%$ of QSOs \citep{Osmer80,Baldwin03,Bentz04,Jiang08}.  The QSOs in our survey, however, do not seem to fit into this population.  Their \ion{N}{4}] $\lambda 1486$ equivalent widths (EWs) are orders of magnitude higher than nitrogen-rich QSOs, and their corresponding \ion{N}{5} $\lambda 1240$ is weak, and may even be absorbed in DLS 1053$-$0528 \citep[see][for more details on these objects]{Glikman07a}.

Strong \ion{N}{4}] $\lambda 1486$ emission has been seen in the spectrum of the Lynx arc, a gravitationally lensed \ion{H}{2} galaxy at $z=3.357$ \citep{Fosbury03}.  Here this line can be explained by a hot (80,000 K) blackbody caused by a top-heavy initial mass function (IMF) as the source of ionizing flux -- suggestive of early, metal-poor star formation, e.g., Population III stars.

\section{Computing the Luminosity Function}

The luminosity function (LF) is defined as the co-moving volume density of objects as a function of luminosity.  In the case of the quasar luminosity function (QLF) it is customary to use the absolute magnitude at 1450\AA, $M_{1450}$.  To construct the QLF for the quasars in our survey, we must first account for the incompleteness of our selection and spectroscopic followup.  We must also compute $M_{1450}$ for each of our quasars.  We describe these steps below and compute the QLF for our survey.  Table \ref{tab:qso_fsel} summarizes our results from the following sections.

\subsection{Survey Completeness \label{sec:fsel}}

To compute the quasar luminosity function, we must be able to correct our quasar counts for incompleteness in our selection technique.  To determine the completeness of our survey as a function of redshift and $R$ magnitude, we follow what is now a standard methodology of simulating the selection probability of quasars in the NDWFS and DLS fields \citep{Warren94,Kennefick95b,Richards06}.

We begin with our simulated quasar spectra, described in Section \ref{sec:specsim}, in a redshift {\it vs.} $R$-magnitude grid.  The redshift grid points are separated by 0.1 in the range $3.5 < z < 5.2$, and the magnitude grid points are separated by 0.25 magnitudes in the range $17.75 < R < 24.50$.  At each grid-point we simulate 200 spectra generated from a random drawing of distributions of the two power-law slopes, Ly$\alpha$\ emission line EW and one realization of neutral hydrogen intervening absorption systems.  The final set of simulated quasars contained 100,800 spectra that evenly samples our parameter space.  These spectra are convolved with the NDWFS and DLS filter curves to produce tables of magnitudes for all the filters in a given survey, as functions of $R$-magnitude and redshift.

The NDWFS and DLS images have $\sim 45,000$  and $\sim 60,000 - 70,000$ sources detected, respectively, in each of their fields.  We randomly distributed the 100,800 simulated quasars into twenty-four subsets of 4200 quasars, to keep the number of added sources under $10\%$ and avoid over crowding.  To properly insert the simulated quasars into our images as point sources, we determined the shape of the point spread function (PSF) by measuring several hundred well-detected, unsaturated, stars in each image using the IRAF task {\tt imexamine} and determining the $\sigma$-clipped median values of $\alpha$ and $\beta$ in the Moffat profile model,
\begin{equation}
 I = I_c (1 + (r / \alpha)^2)^{-\beta},
\end{equation}
where $I_c$ is the peak value of the intensity, $I$.  We then inserted 4200 quasars into the NDWFS and DLS images, using the IRAF {\tt mkobjects} task in the {\tt artdata} package, in all filters at the same random locations assigning them the appropriate stellar profile parameters, and magnitudes computed from the simulated spectra.  Finally, we added the camera read noise and Poisson noise to the simulated data to closely mimic real sources.

We extracted catalogs for each set of simulated quasars using the identical SExtractor parameters as the unaltered images, using the $R$-band image as the detection frame.  We then processed these objects through our selection pipeline, imposing the color and morphology cuts and assigning magnitude-limits, as described in Section \ref{sec:selection}.  We determine the recovered fraction of quasar candidates in each redshift and magnitude bin (the selection function, $f_{\rm sel}$), thereby mapping the completeness of our candidate selection.  We list the value of $f_{\rm sel}$ in column (4) of Table \ref{tab:qso_fsel}.  Figure \ref{fig:completeness} plots contours showing the completeness as a function of redshift and magnitude for the NDWFS survey on the left and the DLS survey on the right; detected quasars are marked with solid circles.

Some of our lower redshift quasars exist in areas of high incompleteness, especially in the DLS survey, due to the Ly$\alpha$\ line entering the $R$ band at $z \sim 4$.  Two of these quasars, DLS J0923$+$2952 at $z=3.84$ and DLS J1052$-$0528 at $z=3.89$, have unusually high Ly$\alpha$\ EWs.  Since our simulated quasar Ly$\alpha$\ EW distribution was chosen as a Gaussian distribution with $EW= 65\pm34${\AA}, there were no simulated spectra resembling these objects.  This may point to an underlying problem with simulating quasars using a Gaussian distribution of EWs;  on the other hand these objects may simply be unusual specimens.

\subsection{ Determining K-corrections \label{sec:kcorr} }

To determine the quasars' absolute luminosity, we need to perform a correction from an observed magnitude to a magnitude at a standard wavelength in the quasar rest-frame.  The absolute magnitude at rest-frame 1450{\AA}, $M_{1450}$, is most commonly used in expressions of QSO luminosity functions.

Using 200 simulated spectra for each $\Delta z=0.1$ interval in range $3.5 < z < 5.2$  (see Section \ref{sec:specsim}), we calculate the apparent magnitude $m_{1450}$ by convolving each spectrum with a boxcar filter equal to unity in the interval 1425{\AA}$ < \lambda < 1475${\AA} and redshifted to the observed frame. The K-correction is defined as:

\begin{equation}
 M_{1450} = m - 5\log(D_{l}/10) - K_{\rm corr},
 \label{M1450}
\end{equation}
where $D_{l}$ is the luminosity distance in parsecs, $M_{1450}$ is the absolute magnitude at rest-frame 1450\AA, and $m$ is the apparent magnitude in some fiducial filter with central wavelength $\lambda$. For a continuum-only quasar spectrum, $F_{\nu} \propto \nu^{\alpha}$, the K-correction to $M_{1450}$ would be equal to:
\begin{equation}
\label{kcorr-nu}
 K_{\rm corr}  = -2.5 (1+\alpha) \log(1+z) - 2.5 \alpha \log(1450\mathrm{\AA}/\lambda),
\end{equation}
where $\lambda$ is the effective wavelength of the filter used for the K-correction. Using simulated quasar spectra, the K-correction can be obtained as the difference between $m$ and apparent magnitude $m_{1450}$ in the observed frame as:
\begin{equation}
 K_{\rm corr}  = m - m_{1450} - 2.5\log(1+z).
\label{Kcorr}
\end{equation}

We use the simulated quasar spectra to determine the expected dispersion in the value of the $K_{\rm corr}$ with redshift. Figure ~\ref{fig:kcorr} shows the value of $K_{\rm corr}$ as well as the one sigma uncertainty interval determined from the various realizations of our simulated quasar spectra. The K-correction for $m_{R}$ (black squares) sharply rises after $z\gsim3.9$, as the {Ly$\alpha$} forest progressively moves into the $R$ band. At our probed redshift range, 1450{\AA} is observed at 6960 - 8990{\AA}.  This suggests that although our selection relies on detections in the $R$ band, our K-corrections can be based on $I$ and $z$-magnitudes for NDWFS and DLS, respectively, minimizing the effect of emission lines on $K_{\rm corr}$.  We plot the corrections to these bands with orange circles and red triangles.

The blue dashed curve in Figure \ref{fig:kcorr} shows the K-correction for the SDSS $i'$-band magnitude, determined by \citet{Richards06}.  We also convolved our simulated quasar spectra with the SDSS $i'$ filter and obtained the curve plotted with black squares in  Figure ~\ref{fig:kcorr}. The result is extremely similar to the K-correction in \citet{Richards06} below $z=4.8$, after which the inclusion of different descriptions for {Ly$\alpha$} emission and the {Ly$\alpha$} forest simulations in our spectra create a progressive offset.  The $I$ and $z$-band corrections are both consistent with the SDSS corrections out to $z=4.3$ after which they diverge slightly, but never as much as for the $R$-band.  The dispersions in the K-corrections for the SDSS $m_{i}$ and our surveys' magnitudes are equal, having a mean value of $\sigma_{\rm Kcorr}=0.08$ in both cases.

Because our quasars are at $z \sim 4$ and all our spectra cover 1450\AA\ in the quasars' rest frame, we can also measure $M_{1450}$ directly from the spectra.  To do this, we compute the magnitude from the median flux, $f_{\nu, 1450}$, between rest-frame $\lambda = 1425$\AA\ and $\lambda = 1475$\AA, $m_{1450} = -2.41-2.5\log(f_{\lambda, 1450})$ \citep[Eqn. (2) of][]{Blanton03}.  We also determine the spectrophotometric magnitude, $R_{\rm specphot}$, of each object by convolving its spectrum with the $R$-band filter profile and scaling it to the image-based $R$-band magnitude.  We determine the exact K-correction for each spectrum, independent of any modeling, where
\begin{equation}
\label{kcorr_spec}
 K_{\rm corr}  = R_{\rm specphot} - m_{1450} - 2.5\log(1+z),
\end{equation}
and apply the K-correction as shown in Equation \ref{M1450}.

This in principle should give us a more accurate measure of $M_{1450}$ over the simulated K-corrections.  However, the wavelength range of our LRIS spectra spans 5750-8300\AA, while the $R$ filter profile has $64\%$ transmission at 5750\AA\ and drops to $0\%$ below 5000\AA\ (see Figure \ref{fig:nfilters}).  We could, therefore, be underestimating the flux transmitted through the $R$-band, especially for the lower-redshift objects in our sample.

Figure \ref{fig:absmag} plots the comparison between $M_{1450}$ derived using our simulated spectra (plotted on the vertical axis) and directly from the object spectra (plotted on the horizontal axis).  The triangles are quasars from NDWFS and the asterisks are quasars from DLS.  The dotted line represents a one-to-one correlation, and while the scatter about this line can be significant (up to $\sim 0.3$ magnitude), the best fit line to these points (plotted as a solid black line) has a slope of $1.02\pm0.09$ with an intercept of $0.19\pm2.06$, suggesting an offset of $\sim 0.3$ magnitudes.  The $M_{1450}$ measured directly from the spectra tend to be fainter than $M_{1450}$ estimated from the simulations, which may (at least in part) be because of the incomplete spectroscopic coverage of the $R$-band.

Table \ref{tab:qso_fsel} lists the $M_{1450}$ magnitudes computed from applying the K-corrections from our simulated spectra and from the object spectra directly in columns (6) and (9), respectively.  In the following sections, we use both of these values to compute and analyze the QLF.

\subsection{The $z\sim 4$ Quasar Luminosity Function}

With the selection function and absolute magnitudes in hand, we are able to calculate the QLF at $z\sim 4$.  The $1/V_a$ \citep[also known as the $V/V_{\rm max}$;][]{Schmidt68} method is the most straightforward way to compute the volume density of quasars as a function of luminosity, $\Phi(M_{1450},z=4)$.  The available volume, $V_a$, is the comoving volume within which a quasar with redshift $z$ and magnitude $R$ can be found.  We determine this volume in pencil-beam units of Mpc$^3$ arcmin$^{-2}$ and multiply by the area surveyed, $A$, of the NDWFS and DLS, 1.71  deg$^2$  and 2.05 deg$^2$, respectively, correcting by our selection function and spectroscopic incompleteness (i.e., the fraction of candidates without spectra).

\subsubsection{The $R<23$ Quasars }

For candidates with  $R<23$, our spectroscopic completeness is 0.75 and 0.71 in NDWFS and DLS, respectively.  Beyond this, the completeness drops significantly to 0.33 (2/6) and 0.11 (1/8) for $23 < R \leq 23.5$ (and further, still, for $R > 23.5$ to 0.04 and 0.02) in the NDWFS and DLS, respectively.  This effectively places our survey limit at $R=23$ and we compute here the luminosity function for only these objects.  We divide our sample into one-magnitude-wide bins, which span $-27 < M_{1450} < -20$, for each survey separately, and together, as a combined sample.

While our survey sought to find quasars with $3.8< z \lesssim 5.2$ and brighter than $R=23.0$, corresponding to 4291 Mpc$^3$ arcmin$^{-2}$, this is not always the volume available to the quasars that we find.  For example, a quasar with $R=22.9$ at $z=4.1$ has $M_{1450} = -23.24$.  The limiting redshift for such a quasar would be, $z_{\rm lim}=4.18$, beyond which it would be too faint to make our magnitude limit.  Therefore, $V_a$ for this quasar is the comoving volume between $z=3.8$ to $z_{\rm lim}$, which, in this example, is 1427 Mpc$^3$ arcmin$^{-2}$.  We calculate $z_{\rm lim}$ and $V_a$ for each of our quasars separately, and list them in Table \ref{tab:qso_fsel}.

The selection function, $f_{\rm sel}$, which we described in \S \ref{sec:fsel}, is the probability that a quasar with magnitude $R$ and redshift $z$ would be selected as a candidate.  For each quasar, we scale $V_a$ by the selection function and spectroscopic completeness, $f_{\rm spec}$ (Column (7) of Table \ref{tab:qso_fsel} referring to the fraction of candidates with spectroscopic followup), in each luminosity bin.  We compute the volume density of quasars for each $M_{1450}$ bin for NDWFS and DLS separately using the following formalism:
\begin{equation}
\Phi(M_{1450},z=4) = \sum_{i}^N (f_{\rm sel}(i)\times f_{\rm spec}(i) \times V_{a}(i) \times A)^{-1}, \label{eqn:phi}
\end{equation}
where $N$ is the number of quasars in the luminosity bin.  We list the values of $\Phi$ for NDWFS and DLS as well as their average, in Table \ref{tab:lumfunc}.  Figure \ref{fig:lf1} plots $\Phi(M_{1450},z=4)$, using $M_{1450}$ from K-corrected $z$ and $I$ magnitudes on the left and directly from the quasar spectra on the right. We plot the volume densities of NDWFS (squares) and DLS (triangles) quasars as well as for the combined sample (filled circles).   We fit a single-power-law, $\Phi(M) = \Phi^* 10^{-0.4(\beta-1)M}$, to these measurements.  We find that the shape of the QLF depends strongly on how we compute $M_{1450}$.  When we compute $M_{1450}$ using the K-corrected $z$ and $I$ magnitudes, the volume density resembles a power law (with a slope of $\beta = -1.59\pm0.22$) out to the faintest bin, which suffers from the flux-limit bias of our survey (which we discuss in the next subsection).   When we compute $M_{1450}$ directly from the quasar spectra the objects populate fewer bins.  While the shape of this QLF is scattered and does not resemble a power-law, the space densities derived from the individual surveys are more consistent with each other.  Table \ref{tab:splparam} lists our fitted value for $\beta$ from both datasets.

\subsubsection{The $R>23$ Quasars }

Of the 148 candidates that we selected in \S \ref{sec:final_cat}, 117 have $R>23$, 59 in the DLS survey and 63 in the NDWFS survey.  We obtained spectra for six of these objects; two NDWFS sources were Lyman break galaxies (LBGs) at $z\sim 3.8$, three were quasars in our desired redshift range (two in the DLS and one in the NDWFS) and one NDWFS source was a Type-II AGN at $z=0.21$.  We wish to make use of the three $R>23$ quasars to enhance our measurement of the QLF.

We compute the volume density for these quasars according to Equation \ref{eqn:phi}.  However, we determine the limiting redshift, $z_{\rm lim}$, and $V_a$ assuming a survey magnitude limit of $R=23.5$ and $R=24$, when appropriate.  The largest source of uncertainty in this method arrives from spectroscopic completeness, $f_{\rm spec}$, which we use to scale our available volume $V_{a}$ and which suffers from small number statistics.  For example, in the DLS sample, we obtained one spectrum (of a quasar) out of nine candidates with $23 < R \leq 23.5$, rendering $f_{\rm spec} = \frac{1}{9} = 0.11$ and the Poisson error on this is $0.12$.

These values are listed in Table \ref{tab:qso_fsel} and we compute the QLF with these three additional quasars using both estimates of $M_{1450}$.  We plot the QLF including all of our quasars in Figure \ref{fig:lf2}.  Again, we fit a single power-law to these data and find that regardless of how we compute $M_{1450}$, the QLF resembles a power-law.  The slopes are marginally consistent, and steeper than the fit using only quasars with $R \leq 23$.  This is not surprising, as the volume densities for the faintest quasars are potentially significantly inflated because of the low spectroscopic completeness, which appears in the denominator of Equation \ref{eqn:phi}.  Nevertheless, including these data appear to remedy the divergent volume densities computed for NDWFS and DLS in the left-hand panel of Figure \ref{fig:lf1} as well as the scattered shape of the QLF in the right-hand panel of Figure \ref{fig:lf1}.

We list the volume density for our QLF including all 23 quasars for both methods of computing $M_{1450}$ in Table \ref{tab:lumfunc} and the best-fit slope in Table \ref{tab:splparam}.

\subsection{Comparison with other surveys}

We compare our binned QLF data points for $3.8 < z < 5.2$ (median $z=4.15$) with the results from other surveys at similar redshifts in Figure \ref{fig:qlf_all}.  Our results for the binned QLF using all the quasars in our survey, including those with $R>23$, are plotted with red circles.  The left-hand panel shows our QLF where $M_{1450}$ has been computed from K-corrections to the $z$ and $I$ band photometry and the right-hand panel shows the QLF where $M_{1450}$ was obtained directly from the spectra.  We plot with a dotted line the best-fit power-law for the faint end, shown in Figure \ref{fig:lf2}.

To extend our QLF into the bright end, the most suitable sample comes from the SDSS.  \citet{Richards06} determined the QLF for SDSS quasars from the Third Data Release (DR3).  We utilize their results for the $z=4.25$ bin and plot their binned LF with asterisks and their single-power-law model fit with a dash-dot-dot-dot line in Figure \ref{fig:qlf_all}.  Both the points and the curve are evolved to $z=4.15$ using the evolution model determined by  \citet{Richards06}.

\citet{Fontanot07a} present a re-analysis of the SDSS-DR3 quasars with $M_{1450} < -26$ combined with eleven quasars from the {\it Great Observatories Origins Deep Survey} (GOODS) with $M_{1450} > -23.5 $ in the range $3.5 < z < 5.2$.  We plot their QLF at $z=3.75$ and $z=4.6$ with open triangles and squares in Figure \ref{fig:qlf_all}.   We evolve both these data sets to $z=4.15$ using the same evolution model as above.  The pure density evolution (PDE) model fit from \citet{Fontanot07a}, also evolved to $z=4.15$, is plotted with a dash-dot line.

While \citet{Richards06} and \citet{Fontanot07a} rely on the same SDSS-DR3 quasars, their derived volume densities are highly discrepant.  The difference between the LFs stems from their different estimates for the completeness of the SDSS sample as a function of redshift.   \citet{Fontanot07a} estimate the completeness for the SDSS subsample used in their calculation by building a spectral library based on the quasar template spectrum from \citet{Cristiani90}.  Instead of modifying the composite using a Gaussian distribution of power-law continua \citep[as is done in this work and in][]{Richards03}, they empirically determine a distribution of continua blueward of Ly$\alpha$ from 215 high quality quasar spectra with $2.2 < z < 2.25$ in the SDSS-DR3 quasar sample. As a consequence, the distribution of power-law slopes in the \citet{Fontanot07a} library is steeper, with $\alpha_2 = -0.7 \pm 0.3$, compared with $\alpha_2 = -0.5\pm0.3$ in the \citet{Richards06} treatment.  The IGM absorption is then added in a manner similar to ours.  They use this spectral library to estimate the completeness of the SDSS color selection criteria \citep{Richards02} and find that the completeness drops to 50\% (and as low as 30\% at $z=4.4$) for $3.6 < z < 4.4$.  At $4.5<z<4.9$ the completeness rises to above 90\% and drops off again after \citep[see][Figure A.4.]{Fontanot07a}\footnote{This is discussed in detail in appendix (A.3) of \citet{Fontanot07a}.}

Using a method similar to ours to create their spectral library, \citet{Richards06} calculate a completeness of nearly $90\%$ for $z > 3.8$.  While our method more closely matches that of  \citet{Richards06}, our values seem to have better continuity with \citet{Fontanot07a}, especially for the QLF whose $M_{1450}$ was derived from K-corrected $z$ and $I$ band magnitudes (the left-hand panel of Figure \ref{fig:qlf_all}).

For comparison, we overplot in Figure \ref{fig:qlf_all} QLF model fits for several surveys at or near our survey's redshift.  The left-hand panel shows general agreement between our QLF based on $M_{1450}$ computed from simulated quasars (in all but the faintest bins) and the SDSS+GOODS analysis of \citet{Fontanot07a} as well as the VVDS survey \citep{Bongiorno07}.  The latter spectroscopically identified 130 broad-line AGN with $z=0-5$ over $\sim 1.7$ deg$^2$ in two fields.  The $z=3.0-4.0$ bin from their QLF contains 17 QSOs with a luminosity range of $-26 \lesssim M_{1450} \lesssim -22$ and is well-suited for comparison with our data.  We plot their model fit with a solid black line in Figure \ref{fig:qlf_all}.

There is a large discrepancy between our measurements and predictions for the value of the quasar density at $z\sim 4$.  The COMBO-17 survey \citep{Wolf03} covered 0.78 deg$^2$ to $R<24$ and found 11 QSOs in the redshift range $3.6 < z < 4.2$, spanning the luminosity range $-27 < M_{1450} < -24$ and 4 QSOs in the redshift range $4.3 < z < 4.8$ in the luminosity range of $-27 < M_{1450} < -26$.  While their results are in agreement with SDSS at the bright end, their QLF modeled as Pure Density Evolution (PDE, dashed line in Figure \ref{fig:qlf_all}) significantly underpredicts the number of quasars at the faint end.

\subsection{Model Fitting to the Combined QLF}

The shape of the QLF is typically parametrized by a standard double power-law form:
\begin{equation}
\Phi(M,z) = \frac{\Phi(M^*)}{10^{0.4(\alpha+1)(M-M^*)}+10^{0.4(\beta+1)(M-M^*)}}. \label{eqn:dpl}
\end{equation}
We follow the formalism of \citet{Sandage79} and \citet{Marchesini07} to determine the best fit parameter values for the QLF using the maximum likelihood (ML) method.  We combine the SDSS quasars at $z\sim 4$ with our 23 quasars to sample as broad a magnitude range as possible when fitting the double-power-law in equation \ref{eqn:dpl}.   We try different combinations of our QLF, based on the two ways of calculating $M_{1450}$, with the QLF from  \citet{Richards06} and \citet{Fontanot07a} at the bright end.  As is clear from Figure \ref{fig:qlf_all}, the bright-end QLF from \citet{Fontanot07a} has better continuity with our QLF based on $M_{1450}$ computed from simulated quasars.  There is a sharp jump between our values and  \citet{Richards06}.  We therefore do not attempt to fit these points in this case.  We do not attempt to model the evolution of the QLF, since our survey is focused on a ``snapshot" of the quasar population at a narrow redshift range.

We initially attempted to maximize the likelihood $\Lambda = \prod^N_{i=1} p_i$ with respect to all three parameters, $\alpha, \beta$ and $M^*$.  We created a gridded cube of $\alpha$, $\beta$ and $M^*$ values, spanning $\alpha,\beta = [-4,0]$ and $M^*=[-27,-20]$, and computed $\Lambda$ at each point, first using a ``coarse" grid ($\Delta\alpha,\beta = 0.1$, $\Delta M^* = 0.2$) with the intention of refining the values near the maximum.  However, due to the small number of quasars in our sample, poorly constraining the faint end, no clear maximum could be found over these reasonable ranges of $\alpha$, $\beta$ and $M^*$.

Since the ML method fails to constrain the double-power-law parameters, we fit Equation \ref{eqn:dpl} to the binned QLF using a $\chi^2$ minimization and allowing all four parameters, $\Phi^*$, $M^*$, $\alpha$, and $\beta$, to vary.   The results of our fit are listed in Table \ref{tab:dplparam} for the three combinations of data sets that we fit.  We plot with a red line in Figure \ref{fig:qlf_all} the best-fit double-power-law parameters from dataset (1) in the left-hand panel and dataset (3) on the right-hand panel.

When our QLF is combined with SDSS data on the bright end, the best-fit parameters are more strongly influenced by the choice of bright-end dataset than our method for estimating $M_{1450}$.  This is because the error bars on the bright-end bins are much smaller compared to the faint-end and strongly constrain the fit.  Furthermore, despite the different shapes of the QLF in our two derivations, the fit using the \citet{Fontanot07a} are nearly identical and largely unaffected by the four bins made up of GOODS quasars on the faint end; we excluded these bins and obtained nearly the same values for the double-power-law parameters.

 When fitting to our data combined with \citet{Richards06}, we compute, effectively, a single power law fit, with a slope $\alpha \simeq \beta = -2.3\pm0.2$.  This result is provocative, both because it preserves the slopes measured for each data set individually \citep[$\alpha \sim 2.1$ for $z=4.25$ in Figure 21 of][while we find $\beta = -2.46$ in the right-hand panel of Figure \ref{fig:lf2}]{Richards06}, and because this suggests that the number of faint AGN rises dramatically out to very faint magnitudes, and that there is no observed ``knee" to the QLF at $z\sim 4$.  This degeneracy between $\alpha$, $\beta$ and $M^*$ explains why the ML method for the double-power-law fit did not converge. Therefore, we fit a single power-law, $\Phi(M) = \Phi^* 10^{-0.4(\beta-1)M}$, to this data set using the ML method.  In this case there is one free parameter, $\beta$, which we allow to vary between $-1$ and $-4$ in steps of $\Delta\beta=0.01$.  The likelihood is maximized at $\beta = -2.67$ and the $68\%$ confidence limits are $(-2.80,-2.55)$, the $90\%$ confidence limits are $(-2.88,-2.48)$ and the $99\%$ confidence limits are $(-3.00,-2.37)$.  While this result stands in conflict with other measurements of the QLF to faint magnitudes which see a flattening of the faint end with redshift \citep[e.g.,][]{Wolf03,Hunt04}, we discuss its plausibility and possible interpretation in \S \ref{sec:discussion}.

\section{Estimating the Contribution of Quasars to the UV Radiation Field at $z\sim 4$}

We use the best-fit parameters from our $\chi^2$ minimization to all the binned data to integrate Equation \ref{eqn:dpl} and compute the emissivity of quasars at 1450\AA, $\epsilon_{1450}$.  Our computed UV radiation depends strongly on the best-fit parameters (listed in Table \ref{tab:dplparam}) for the QLF, especially the faint-end slope, $\beta$.

For dataset (1), where we combined our binned QLF using K-corrected $z$ and $I$-band photometry with the data from \citet{Fontanot07a}, we compute  $\epsilon_{1450} \cong 9 \times 10^{25}$ erg s$^{-1}$ Hz$^{-1}$ Mpc$^{-3}$.  Following \citet{Madau99}, we use our parametrized QLF together with the quasar SED of \citet{Elvis94} to compute the photoionization rate from QSOs at this redshift, $\dot{N}_{\rm QSO}  = 4 \times 10^{51}$ s$^{-1}$ (integrating $\int \Phi(L)L dL$ down to $M_{1450} = -20$).  This is almost twice the value needed to ionize the intergalactic medium (IGM) at $z = 4.15$, $\dot{N}_{\rm IGM} = 2.4 \times 10^{51}$ s$^{-1}$ and stands in contrast to previous statements on the ability of quasars to ionize the universe at higher redshifts \citep{Haiman01,Wyithe03a,Shankar07} which suggested that AGN do not produce a sufficient number of ionizing photons and starforming galaxies must play a larger role.

For dataset (3), where we combined our binned QLF using $M_{1450}$ from the object spectra with the data from \citet{Richards06} and effectively fit a single power law, we find $\epsilon_{1450}=7 \times 10^{25}$ erg s$^{-1}$ Hz$^{-1}$ Mpc$^{-3}$ and $\dot{N}_{QSO} = 3 \times 10^{51}$ photons s$^{-1}$ Mpc$^{-3}$, which also produces sufficient photons to ionize the IGM.  This value is strongly dependent on the faint limit of integration.  Because the total UV-luminosity density has to be larger from the contribution of quasars fainter than our integration limit, our computation of $\dot{N}_{QSO}$ is a lower limit of the photoionization rate.

\section{Discussion \label{sec:discussion}}

Our survey has found that the comoving volume density of quasars continues to rise as a steep power law to low luminosities, four magnitudes fainter than previous measurements.  This is true regardless of how $M_{1450}$ is computed.  This result conflicts with predictions for the evolution of the shape of the QLF with redshift, based on the observed evolution of the QLF at lower $z$.  In addition, this is surprising because objects at the faint end of a flux-limited survey, with their associated large photometric errors, tend to be undercounted.  While our results are sensitive to the fluctuations of small number statistics (our faintest bin contains between one and two objects, depending on how $M_{1450}$ is computed) it behooves us to come up with a reasonable explanation or rule out any systematics that may lead to an excess of quasars counted in error.

In this section, we consider possible explanations for overcounting our quasars at the faintest bins.  These are: (1) we are including galaxies in our sample, (2) our selection function overcorrects $\Phi(M)$ (equation \ref{eqn:phi}) leading to an overestimate of the QLF, (3) clustering of quasars in our chosen fields due to large scale structure.  We examine each of these possibilities below.

We rule out possibility (1), that we have counted galaxy interlopers as quasars, by an examination of Figure \ref{fig:spectra}.  All of the spectra except for our lowest-redshift object, NDWFS J142713.2+322842 at $z=3.74$, show strong, broad Lyman-$\alpha$ emission with the classic asymmetric profile from absorption of the blue wing of the emission line attributed to high-redshift quasars. NDWFS J142713.2+322842 is also obviously a quasar, as its \ion{C}{4} line is extremely broad, with FWHM $\simeq 11,000$ km s$^{-1}$.

To examine possibility (2), that our number counts are too high by an underestimate of the selection function, we plot the value of the selection function for each quasar versus its absolute magnitude, $M_{1450}$ in Figure \ref{fig:fselvm1450}.  As we already noted in Section \ref{sec:fsel}, $f_{\rm sel}$ is $\sim 80\%$ for most of the quasars.  At faint luminosities, $f_{\rm sel}$ drops to $\sim 0.4$, which means that $\Phi(M_{1450},z=4)$ in equation \ref{eqn:phi} is corrected for incompleteness by a factor of $\sim 2.5$.  This is insufficient to account for the steep rise in $\Phi(M)$ that we see, since a flattening of the faint-end slope of the QLF would predict fewer quasars by a factor $\gtrsim 50$.

The third possibility is that clustering due to  cosmic variance is enhancing the number of quasars that we find, which can have a significant impact in a small sample.  We examined the spatial and redshift distribution of our quasars for each field and found that of the three faintest and lowest luminosity quasars (which dominate the last two bins in our QLF)  are isolated, with the nearest quasar $\gtrsim$ 0.5 deg away.  This corresponds to a separation on the sky of $\sim$12 Mpc at $z\sim4.15$.

 DLS J105346.1$-$052859, the faintest quasar in our sample with $R=23.83$, is 4\farcm4 away from DLS J105348.8$-$053319, a much brighter quasar with $R=20.94$.  While these objects are the closest pair of quasars in our sample, their redshift difference (the faint quasar is at $z=4.02$ and the brighter quasar is at $z=4.20$, implying that their orthogonal separation is $\sim 2000$ Mpc in our stated cosmology) rules that their proximity is merely a projection effect.

There are a few quasar samples that, while small, are consistent with steeper QLF at fainter luminosities.  \citet{Cool06} found three $z> 5$ quasars in NDWFS Bo\"{o}tes using mid-infrared color selection, which is meant to be insensitive to dust reddening and avoids confusion with the stellar locus \citep{Stern05}.  None of these quasars appear in our candidate list from NDWFS.  This is because our color selection becomes highly incomplete at  $z>5$ and $R\gtrsim 23$.  In addition, the optical colors of the quasars from \citet{Cool06} fail to meet our color criteria.  Only one object, J142937.9+330416, has $B_W-R>2.2$, and none of them met the criteria set forth in eqn. (2).  While their objects are somewhat more luminous than our $z\sim 4$ quasars, with $M_{1450} = -26$ to $-24.5$, they are $1.5$ magnitudes fainter than the SDSS quasars at these redshifts.  The space density derived from the discovery of these three quasars is consistent with a luminosity function that has a steep power-law index, $\Phi(L) \propto L^{-3.2}$.  The discovery of a radio-loud, $z=6.12$ quasar in NDWFS (the probability of which is $< 1\%$) by \citet{McGreer06} also suggests that the space density of faint, high-redshift quasars may be higher than previously thought.

\section{Conclusion}

Using 23 quasars at $z\sim 4$ discovered in our survey of deep optical imaging data from the DLS and NDWFS surveys, we have measured the faint end of the QLF.  Depending on how we compute $M_{1450}$, our directly fit faint-end slope ranges between $\beta = -1.98\pm0.23$ and $\beta=-2.46\pm-0.20$, in both cases steeper than the faint-end slope measured by \citet{Fontanot07a} who find $\beta = -1.71\pm0.41$.  When we combine our QLF at the faint end with with the SDSS-based QLF at the bright end from \citet{Richards06} we conclude that the shape of the $z\sim 4$ QLF is best fit by a single power law, with a slope of $\sim -2.7\pm0.1$ (via the ML method). A QLF with this shape is able to produce enough UV photons to ionize the IGM at this redshift, which is unexpected.

This result is provocative and presents a challenge to interpretations of the shape of the QLF and its evolution \citep[e.g.][]{Hopkins06b,Shankar07} and has two immediate cosmological implications: (1) the models of the faint AGN evolution
at the epochs $\sim1$ Gyr after the end of the reionization, and possibly all the way into the reionization era, may need to be revisited; (2) AGN were a more significant contributor to the metagalactic ionizing UV flux at these epochs, affecting the evolution of the IGM.  We caution, however, that this result is currently reliant on only a few quasars at the faintest end of our survey.  Additional spectra of our $R>23$ candidates will provide a more robust measurement in this crucial luminosity regime and better constraints for theoretical models.\\ \\

\acknowledgments
We are grateful to the staff of W. M. Keck observatory for their assistance during our observing runs. This work was supported in part by the NSF grants AST-0407448 and AST-0909182, and by the Ajax foundation.  The work of DS was carried out at Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA.

This work makes use of image data from the NOAO Deep Wide-Field Survey (NDWFS) and the Deep Lens Survey (DLS) as distributed by the NOAO Science Archive. NOAO is operated by the Association of Universities for Research in Astronomy (AURA), Inc. under a cooperative agreement with the National Science Foundation.

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At an extraordinary general meeting held earlier today, shareholders of Aker Philadelphia Shipyard ASA (OSLO: AKPS) approved a proposal to change the company's name to Philly Shipyard ASA. Accordingly, Aker Philadelphia Shipyard, Inc. (APSI), the sole operating subsidiary of AKPS, will likewise change its name to Philly Shipyard, Inc. effective today.
The change of name to Philly Shipyard ASA will be registered with the Norwegian Register of Business Enterprises on December 1, 2015. In addition, Philly Shipyard ASA will change its ticker symbol on the Oslo Axess from "AKPS" to "PHLY" effective December 3, 2015. There is no change in ownership associated with this name change. Converto Capital Fund AS, an investment fund controlled by Aker ASA, remains the majority shareholder, holding 57.56% of the shares as of today.
The company's name change follows the execution in Q3 2015 of definitive documents to divest its portfolio of shipping assets, streamlining the business and marking a successful conclusion to an innovative plan to invest in eight Jones Act product tankers with an approximate contract value of USD 1 billion through the AKPS-Crowley joint venture and Philly Tankers AS.
Coinciding with the name change, the company's website (www.akerphiladelphia.com) has been updated and its web address has been changed to www.phillyshipyard.com. Company email addresses and other contact information will remain unchanged.
Philly Shipyard, Inc. is a leading U.S. commercial shipyard constructing vessels for operation in the Jones Act market. It possesses a state-of-the-art shipbuilding facility and has earned a reputation as the preferred provider of oceangoing merchant vessels with a track record of delivering quality ships. Philly Shipyard ASA is listed on the Oslo Stock Exchange and is majority-owned by Converto Capital Fund AS, which in turn is majority-owned by Aker ASA. Aker is a Norwegian industrial investment company that creates value through active ownership. Aker's investment portfolio is concentrated on key Norwegian industries that are international in scope: oil and gas, fisheries and biotechnology, and marine assets. Aker's industrial holdings comprise ownership interests in Aker Solutions, Kvaerner, Det norske oljeselskap, Aker BioMarine, Ocean Yield, Havfisk and Akastor.


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What Does DMT Feel Like? Putting Words to a DMT Experience
One of the greatest psychedelic advocates of the last century, Terence McKenna, spoke about DMT often and gave a name to the other entities that many who take DMT report interacting with, calling them "self-transforming machine elves.
"Under the influence of DMT, the world becomes an Arabian labyrinth, a palace, a more than possible Martian jewel, vast with motifs that flood the gaping mind with complex and wordless awe." – Terence McKenna
DMT God Experience
Ask someone about what their DMT experience was like, and you are likely to get a tale that defies comprehension or belief. This powerful psychedelic has had a surge of interest in recent years, thanks in part to the research of Rick Strassman and his book-turned-documentary The Spirit Molecule. DMT is known for taking people on nail-biting adventures into other realities and other dimensions, leaving those who partake in it overwhelmed with a kaleidoscope of emotions and a novel set of experiences that defy comprehension, much less description. But while language is a feeble and wholly inadequate tool for accurately describing the depth and transcendent nature of a DMT experience, there are some commonly occurring themes and general factors that many DMT experiences have in common, which can help us to better understand the incomprehensible landscapes that DMT brings us to. So what does DMT feel like, and why is it such a mystery?
The Psychedelic Inside All of Us
As one of the most fast-acting, short-lived, and potent psychedelics known to mankind, Dimethyltryptamine is made all the more mysterious by the fact that it's naturally present in humans and other mammals. As Rick Strassman writes in The Spirit Molecule, "DMT occurs in our bodies. We produce it naturally. Our brain seeks it out, pulls it in, and readily digests it. As an endogenous psychedelic, DMT may be involved in naturally occurring psychedelic states that have nothing to do with taking drugs, but whose similarities to drug-induced conditions are striking." Strassman goes on to theorize that the presence of DMT in our bodies may be related to near-death experiences, transformational spiritual experiences, or other hyper-intense moments in our lives where time seems to slow or halt, and our consciousness is fundamentally different from our normal waking state of mind.1
Strassman's theory gives some insight into what a DMT experience is actually like. Much in the same way that time "stands still" during peak or critical moments where the entirety of our attention is single-focused and all of our normal mental activity ceases, DMT is known for similarly taking people outside of time and space in a way that is highly unique and quite rare. As fantastical as that is, however, it's just the beginning. Within this novel space of altered consciousness, visual hallucinations, brightly colored shapes and patterns, profoundly meaningful associations, and curious encounters with other beings are all par for the course, all of which can range from being ecstatically blissful to absolutely terrifying.
Encounters with Other Beings
One of the greatest psychedelic advocates of the last century, Terence McKenna, spoke about DMT often and gave a name to the other entities that many who take DMT report interacting with, calling them "self-transforming machine elves." The creatures people often see during DMT experiences can range from friendly to hostile, and seem to take all kinds of shapes and sizes, but are often humanoid in appearance. While it is easy to dismiss these machine elves as figments of imagination that arise from DMT-induced hallucinations, many people report that they felt just as real as any other person they have met, having a quality that was beyond mere hallucination. Interestingly, the Amazonian psychedelic brew ayahuasca, which contains DMT as its active ingredient (but acts over a period of many hours rather than a few minutes), also produces similar encounters with seemingly sentient beings as one of its hallmark features. Whether you call them spirits, elves, inter-dimensional beings, or tricks of the mind, it's likely you will meet them under the influence of DMT.
DMT is still a great mystery, and while there are some fascinating theories about how it functions in the human body, the jury is still out on what exactly it does to our consciousness and why it occurs within us naturally. For most people who take DMT, however, their life is never quite the same afterward. After directly experiencing such a radically different reality, people often reevaluate their lives and their deeply held beliefs about the nature of existence, more often than not in a way that is both curious and positive. Nobody can experience the full depths of a DMT experience and not walk away with a profound sense of awe and some fundamental questions about what is really going on out there in the universe and inside our own minds. And who knows, they may really be one in the same.
Sourcepsychedelictimes
Ibogaine: Investigating This Alternative to Traditional Addiction Treatment
Every day another unfortunate tragedy happens as a result of our current drug epidemic. Widespread use of drugs and alcohol has reached distressing proportions, and traditional methods of treatment aren't solving the problem. The Growing Drug Problem Drug use in the U.S. has become so prevalent that the country has been...
Beyond Psychedelics 2018 in Prague will gather over 120 world scientists and researchers
Prague gets ready for Beyond Psychedelics – the Global Multidisciplinary Conference on Psychedelic Substances, Mental Health, Alternative States of Consciousness and Technologies. It is one of the largest events of this type in the world and on June 21-24, 2018, it will gather over 120 world leading psychedelic scientists and researchers to discuss potential, current challenges and future direction...
CBD Oil vs Marijuana
When people talk about marijuana or cannabis, they often think of the recreational pleasure they get after consuming it. That's the wrong...
Here's What Happens When You Touch These Pressure Points On Your Feet
Reflexology is an old technique that aims to increase blood flow to certain parts of the body to relieve pressure and pain. These points,...
5 Spiritual Benefits of Using Ayahuasca
Ayahuasca is a shamanic medicine originating from the Amazon Rainforest. Ayahuasca has a powerful effect on one's spiritual processes and can facilitate healing, awakening,...
Alex Grey Describes How His First DMT Experience Takes Him Inside...

redpajama_set_name: RedPajamaCommonCrawl


Muliplex firm PVR Ltd's shares have put up a decent show this fiscal year, appreciating by as much as 30%. A better movie content line-up, new screen additions, acquisition of SPI Cinemas, and receding worries on the threat to food and beverage revenues have brought cheer.
What's more, the December quarter results announced late last week will lend support to valuations. The last quarter was the first full quarter of consolidation with SPI Cinemas and, therefore, the consolidated numbers are not exactly comparable on a year-on-year basis.
Nonetheless, the company has done well on many parameters and surprised analysts to an extent. Consolidated revenues (including SPI Cinemas) for the December quarter increased robustly by 51% over the same period last year to ₹843 crore. Net profit grew at a much faster pace of 90% to ₹55 crore, as margins rose.
On a stand-alone basis, PVR's revenues and net profit increased by 27% and 62%, respectively. Stand-alone performance was helped by a nearly 4% increase in average ticket price and 22% higher footfalls. Advertising revenues increased at a relatively slower pace of 16%. Investors would do well to keep a tab on advertising growth in the coming quarters.
Outlook on screen additions remains encouraging. The company said that it has added 55 screens so far in this fiscal year. With the management remaining confident about adding 90-plus screens in FY19, Emkay Global Financial Services Ltd has raised its screen addition estimate to 90 from 75 screens.
However, the meaningful appreciation in the PVR stock could well mean that investors are baking in a good share of optimism in the valuations. The stock trades at 32 times estimated earnings for FY20, based on Bloomberg data.
Against this backdrop, content performance has to be extremely strong in FY20 to beat the base of 14% growth in FY19, pointed out analysts at Emkay Global. "Although predicting movie collection might not be relevant, aggressive growth assumptions, along with premium valuations, are not leaving any room for error," they said.
Essentially for investors, the buck now passes to the box- office performance.


A timeless classic moment is Mothers Day to thank them for EVERYTHING they have done for us and I would love to celebrate my special mother with a timeless classic from Uncle Jack Watches especially the black one.
I will be contacting both of you via email to discuss delivery. Thank you to everyone who entered and please stay tuned for the next competition.
Want to win one of two Uncle Jack Watches valued at $120.00 each for Mother's Day?
* Comment below on which watch you would like to win and why.
(We have the black-black and the tan-white watch available).
Would love the Tan one. It's gorgeous.
Great competition. I would love to win the Tan one for mum.
I love the Black Black Uncle Jack watch because it goes with everything! and is so stylish.
The Tan white is absolutely stunning. Would love to win it for my mum and show her my appreciation.
Love this brand in watches. Very trendy. The Tan is so stylish.
Happy Mothers Day. What a great competition. Would adore the black black for my loving mum.
Something special like a beautiful watch to spoil myself on a well deserved day. The Tan one please.
Ohhh the black one. Love it.
The Tan one is super pretty for my beautiful mum. Would be a great Mothers Day.
Mothers are precious and so are these beautiful watches. I love the Tan one.
Would love e to win this for my lovely wife for Mothers Day. She would be very happy with either as they are a fantastic brand.
The black one is so swish.
Tan is super pretty for my beautiful mother.
Mother's Day is so special and my mother in law would love the Tan one.
We would love the black black for our mum.
Oh Christine, these watches are stunning! The gorgeous black on black Uncle Jack watch would be a perfect little gift to treat myself with, as I will be celebrating my very first Mothers Day as a mother this year!
Love the black black. So funky.
Loving the line from Uncle Jack. So stylish and smart.
I'm looking for a last minute Mother's Day present for myself! Every year I get asked what do I want, just go buy it mmmmm There's no escaping my love affair with black accessories, so here I am eyeing off your classic black/black watch. The kids will love the look of surprise on my face, especially when they see it's not the usual kitchen gadget or undies and slippers!!
I'm mad about the tan watch. Christine if I won this watch I'd feel like a King, wearing a bit of bling .... KACHING!!
These watches are beautiful. I would love to spoil myself for Mothers Day.
Cool watches. The Tan is amazing and so stylish. Cool competition Christine.
Either would be a blessing for my beautiful mother. Happy Mother's Day Christine.
Cool and stylish just like mother. How beautiful for Mothers Day.
Lovely catch competition celebrating Mother's with style. Love the black black.


The Northern District of Indiana has published proposed Local Rules amendments, with the comment period open through March 31. The Local Rules Advisory Committee has recommended, and the Court has approved for public comment, amendments to Local Rules 1-1, 3-1, 5-1, 5-2 and 7-1.
Effective Dec. 1, the Southern District of Indiana adopted various Local Rules amendments, specifically to Local Rules 5-2, 5-3 and 5-7 (electronic filing); Local Rule 6-1 (extensions of time); Local Rule 81-2 (removed actions), and; Local Rule 83-5 (admission). The amendments to Local Rule 6-1(a) are significant in that they impact the process of seeking extensions of time for filing deadlines.
In reviewing the most recent edition of "Business and Commercial Litigation in Federal Courts," John Maley writes that no other book gives such practical and integrated treatment to procedural and substantive law in areas frequently encountered by federal commercial litigators.
The Southern District of Indiana Court has published for comment proposed changes to several local rules, with the full text available on the court's website. Several of the proposals address practices and procedures that arise in many cases.
In April the Supreme Court approved amendments to Rules 5, 23, 62, and 65.1 of the Federal Rules of Civil Procedure, which will take effect December 1 absent contrary action by Congress.
Local rules in the Northern and Southern district courts have changed regarding responses to motions to dismiss.
Since taking the bench in March, Magistrate Judge Doris Pryor has been immersed in the work of the court.
Intervention — Rule 24 allows a non-party to intervene in a pending action as of right in limited circumstances, either as of right or permissively.
The Southern District of Indiana made modest changes to its Uniform Case Management Plans, both the general plan and the patent litigation plan, effective Nov. 1.
A recent opinion in which Chief Judge Diane Wood issued a published order addressing jurisdictional statements on appeal is a must-read for anyone handling 7th Circuit appeals.


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Right to Life New Zealand
Upholding the sanctity of Human life and Standing Up for the Vulnerable
Letters – Abortion
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End of Life Choice Act Advertisments
Abortion Legislation Act Newspaper Ads
Abortion Legislation Act
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Abortion Statistics
Right to Life's Oral Submission on the Abortion Legislation Bill
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All Legal Decisions RTL V ASC
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Abortion Breast Cancer Link
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You are here: Home / Euthanasia / Assisted Suicide / Does David Seymour Support Assisted Suicide for "Completed Life"?
Does David Seymour Support Assisted Suicide for "Completed Life"?
Right to Life would like to correct the statement made in this media release that the proposal by the government of the Netherlands stated in the first paragraph is in fact a Private Members Bill, not a Government Bill. It is understood that parliamentarian Pia Dijkstra intends to introduce a draft bill in this regard in 2020
Media Release Monday 25th November 2019
Right to Life challenges David Seymour (pictured) who supports "choice" to tell our community whether he supports the current proposal of the The Netherlands government to provide assisted suicide to every person over the age of 75 years of age "who believes that they have completed their life".
David Seymour is the leading advocate in New Zealand for the death lobby promoting choice for assisted suicide or to receive a lethal injection. Right to Life believes that his contentious anti-life End of Life Choice Bill is but the first step in implementing the ultimate hidden agenda for disposing of the lives of those not considered worthy of living.
Our community must now watch and pay attention as this agenda unfolds in the Netherlands, because our lives and that of our children depend on it. The Dutch government recently announced its intention to introduce legislation next year to provide State funded assisted suicide for any person over the age of seventy-five who believe that their life is complete. It will not be necessary to have a terminal illness or to have even have ill health. The ultimate logical step is for the government to make it a duty to accept assisted suicide on reaching 75. This would be a considerable saving for the Dutch health services and social welfare.
Polling conducted by the Dutch government reveal that the proposal has the support of 55% of the population. Half those polled wanted no age limit, a third wanted a lower limit.
The Netherlands has endured legislation allowing doctors to assist in the suicide of their patients or to give them a lethal injection since 2002. The populace has clearly been seduced by a culture of death. It commenced with accepting the killing of the terminally ill and quickly expanded to include those with depression, Alzheimer's, dementia, the disabled and even children. Should New Zealand say yes to the referendum on the End of Life Choice Bill at the next election, there is no reason why New Zealand should not stumble blindly in the steps of the Netherlands. If we do not learn from history, the destruction of human life will be the inevitable consequence.
Euthanasia is about doctors killing their patients or assisting in their suicide. It is intrinsically evil; no referendum can legitimise that which is evil. The prohibition against taking the life of another human being is the foundation of the law and medicine. It is always wrong to kill another innocent human being. The approval of the community, even in a referendum, can never make murder acceptable. A referendum is an attempt to seduce and to implicate the whole community in the murder of the vulnerable.
Ken Orr,
Spokesperson,
Filed Under: Assisted Suicide, David Seymour, Decriminalisation, End of Life Choice Bill, Euthanasia, Media Releases Tagged With: assisted suicide, David Seymour, End of Life Choice Bill, euthanasia, euthanasia referendum
B Koning says
Hello, great article, however, I believe the use of the name 'Holland' needs to be changed. Holland is a region within The Netherlands, and is not actually the country itself.
Agree and now changed.
Rob Jonquiere says
May I – like you use misinformation – over and over again refute those? The Dutch government as such has NEVER proposed any form of legislation for 75 and older with completed life. Whatever will be brought forward is a so called MP bill that when it is published will need a Parliamentary debate, the outcome of which is not by far certain to be positive. And, importantly it will not be an addition to the existing Euthanasia Law, which is principally about MEDICAL aid in dying, contrary to the possible new initiative is principally NOT with doctors assistance. I do not need to tell you that polling results – however constructive they may be – seldom equalize parliamentary attitudes.
Last of all misunderstandings from your side: the law in the Netherlands FROM THE START has been about suffering, and not about terminal conditions, and thus principally included non-terminal and non-somatic conditions.
Dear Rob,
Thank you for your communication of 9 December I appreciate your comments and corrections. We wish to make our case with correct information and not misinformation.
We of course have to rely on the accuracy of information provided by reputable sources on the internet.We are informed that in 2016 the Dutch Minister of Health of the 2nd Rutte cabinet announced plans to draft a law to allow for assisted suicide for the elderly who believed that "their life was complete."
We note that on 2nd September 2019 the Dutch Liberal Party, D66, a member of the ruling coalition was working on a bill to be presented to Parliament in 2020 to provide for completed life.
You advise that this is to be a private member's bill and not a government bill. I have done further research and I have read on the Dutch News that parliamentarian Pia Dijkstra told the AD in an interview that she plans to introduce a draft bill early next year. I believe that this suggests that a proposed bill will indeed be a private members bill and not a government bill. I apologise for my mistake and will ensure that in future we will not repeat this error.
Ken Orr
Spokesperson ,
Pro Life App
Right to LIfe's Sarah-Jane Cleaver reads letter in support of unborn children and their mothers at Parliament Dec 2021
"There may be times when we are powerless to prevent injustice, but there must never be a time when we fail to protest."
— Elie Wiesel
Right to Life Newsletter March 2021 – Click on image below
Downright Discrimination against Downs
Click on image to contact your local MP's on their behalf at the push of a button.
Pregnant? Worried?
New Zealand's Coming Demographic Winter
Abortion Regret – Real NZ Women – Real Stories
This booklet was produced by the NZ Ministry of Health as a hard copy….It was quickly removed
The Cry of the Innocent – a Poem in Song
This is the website of Right to Life NZ Inc.


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Sue Murphy | 26th October 2020
Latest legal rankings highlight Paris Smith as 'knowledgeable, thorough and customer-focused'
Paris Smith have achieved excellent rankings in the latest Chambers and Partners Directory. Chambers and Partners is an independent research publication operating across 200 jurisdictions delivering detailed rankings and insight into the world's leading lawyers and barristers.
In this year's rankings, the Litigation team has improved by moving up a band, and Partner Mike Pavitt is the only lawyer in the South recognised for personal insolvency. All other departments have held their rankings from last year (family, banking and finance, employment, real estate, restructuring and insolvency and corporate M&A).
There are also two new leading individuals this year. Jo Spittles, a Partner in commercial property department received outstanding accolades: "She is exceedingly efficient and knowledgeable in her field. She is very proactive and has never let us down" says her profile. Similarly, a client described Partner Chris Holliss head of the debt collection and asset recovery team as "an excellent voice of reason" and commends his ability to "calm some very tense situations."
On the private client side, the firm's Family team were the only family department in Southampton and the surrounds to be listed in band 1, including 2 leading individuals Frank Prior and Huw Miles. One source commented on the team's "very helpful and skilled lawyers," adding: "We trust their advice and receive timely replies." Another interviewee says: "The lawyers are technically able and work constructively."
You can view the full rankings and firm profile on the Chambers website.


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FactoryBot.define do
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    content { Faker::Lorem.sentence }
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redpajama_set_name: RedPajamaGithub


text:
Q: Alternative triangle inequality proof I have looked everywhere for confirmation of this proof of the triangle inequality with no success.
Prove the triangle inequality:
$$\vert x + y \vert \leq \vert x \vert + \vert y \vert.$$
Proof:
Given the definition of $|x|$ to be $|x| = \max\{-x, x\}$. We know that $x \leq \vert x \vert$ and $y \leq \vert y \vert$.
So:
$$\vert x + y \vert \leq \vert \vert x \vert + \vert y \vert \vert = \vert x \vert + \vert y \vert.$$
Thus, we have proven the triangle inequality:
$$\vert x + y \vert \leq \vert x \vert + \vert y \vert.$$
What is wrong with it? If nothing is wrong with this proof, why is it not readily used as it seems to be quite concise.

A: From $x\le|x|$ and $y\le|y|$ you can deduce
$$
x+y\le |x|+|y|
$$
On the other hand, from $-x\le|x|$ and $-y\le|y|$ you can deduce
$$
-x-y\le|x|+|y|
$$
that's the same as
$$
x+y\ge-(|x|+|y|)
$$
The two inequalities say
$$
-(|x|+|y|)\le x+y\le |x|+|y|
$$
so
$$
|x+y|\le|x|+|y|
$$
You didn't use both conditions.

A: $$(1)\; |x|+|y|=\max (x,-x) +|y|\geq  x+|y|= x+\max (y,-y)\geq x+y.$$ $$(2)\;|x|+|y|= \max (x,-x) +|y|\geq -x+|y|=-x+\max (y,-y)\geq -x-y.$$ $$ \text {Therefore }\; |x|+|y|\geq \max (x+y,-x-y)= |x+y|.$$

A: Let us consider two vectors $x$ and $y$, and describe a vector $z$ on Euclidean space given by:
\begin{equation}
|z\rangle = \frac{|x\rangle}{|x|} - \frac{|y\rangle}{|y|} \label{newvec} \tag{1} .
\end{equation}
Now, we know that on Euclidean spaces, the norm of any vector, including $z$ in (\ref{newvec}) will be positive definite
$$|z|^2 = \langle z | z \rangle \geq 0$$
$$\Rightarrow \qquad \frac{\langle x | x \rangle}{|x|^2} + \frac{\langle y | y \rangle}{|y|^2} - \frac{\langle x | y \rangle + \langle y | x \rangle}{|x| |y|} = 1 + 1 - \frac{\langle x | y \rangle + \langle y | x \rangle}{|x| |y|} \geq 0$$
\begin{equation}
\therefore \qquad 2 |x| |y| \geq \langle x | y \rangle + \langle y | x \rangle \label{cond} \tag{2} .
\end{equation}
If we consider the norm of the sum of vectors $x$ and $y$, then we shall have:
\begin{equation}
\left| x + y \right|^2 = |x|^2 + |y|^2 + \langle x | y \rangle + \langle y | x \rangle \label{normsum} \tag{3} ,
\end{equation}
while the sum of the norms gives us:
\begin{equation}
\left( |x| + |y| \right)^2 = |x|^2 + |y|^2 + 2 |x| |y| \label{sumnorm}\tag{4} .
\end{equation}
Thus, comparing (\ref{normsum}) to (\ref{sumnorm}) and applying (\ref{cond}), we can see that:
$$\left( |x| + |y| \right)^2 \geq \left| x + y \right|^2$$
\begin{equation}
\Rightarrow \qquad |x| + |y| \geq \left| x + y \right| \tag{5}.
\end{equation}
Thus, proving the Triangle Inequality.

redpajama_set_name: RedPajamaStackExchange


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Minnesota amendment vote
Voter Information Portal - Office of the Minnesota
1919 - Suffrage in Minnesota and the U.S., 1919-1920 . Synopsis: In 1920, the 19th Amendment to the U.S. Constitution received approval from three-fifths of the states and the right to vote was extended to women. Minnesota was the 15th state to ratify the amendment, in 1919 (Laws 1919, First Special Session, Resolution 1). Minnesota Woman Suffrage Association | MNopedia From 1881 to 1920, the Minnesota Woman Suffrage Association (MWSA) struggled to secure women's right to vote. Its members organized marches, wrote petitions and letters, gathered signatures, gave speeches, and published pamphlets and broadsheets to force the Minnesota Legislature to recognize their right to vote. Due to their efforts, the legislature approved the Nineteenth Amendment in 1919. Minnesota Election Center - Vote.org Vote.org election center. Register to vote, check your registration status, get your absentee ballot, learn the voter ID laws, and find all the dates, deadlines and forms you need.
Coronavirus in Minnesota; an amendment would require a public vote or full approval of the entire city council along with the mayor. "We might have to take it to the people to have a vote on
1919 - Suffrage in Minnesota and the U.S., 1919-1920 Synopsis: In 1920, the 19th Amendment to the U.S. Constitution received approval from three-fifths of the states and the right to vote was extended to women. Minnesota was the 15th state to ratify the amendment, in 1919 (Laws 1919, First Special Session, Resolution 1). Our goal is to get an Equal Rights Amendment (ERA) on the Minnesota ballot for the November 3, 2020 state wide election. It passed through all 5 House Committees (see below) and a floor vote by March 7, 2019. Yay!! This will be good up until the 2020 elections. Elections & Administration: Elections Phone Numbers: Metro Area: 651-215-1440 Greater MN: 1-877-600-VOTE (8683) MN Relay Service: 711 Hours: 8 a.m. to 4:30 p.m. Public service counters at the office are currently closed. Elections & Administration: Elections Phone Numbers: Metro Area: 651-215-1440 Greater MN: 1-877-600-VOTE (8683) MN Relay Service: 711 Hours: 8 a.m. to 4:30 p.m. Public service counters at the office are currently closed.
With 70,000 voting "yes" and 33,000 voting "no" on this proposed amendment, the Minnesota Constitution was amended. Ironically, with 253,000 people voting in that election, and 150,000 not voting on the proposed amendment, it would have been well short of the votes necessary had it been held to its own standard.
Oct 31, 2016 Minnesota Constitutional Amendments This section provides a statistical overview of Minnesota's state constitutional amendment history, highlighting the number of amendments offered, ratification rates, participation rates by voters, and the frequency of multiple amendments on the ballot. 3 more rural Minnesota counties approve 'Second Amendment Feb 19, 2020 Voter Information Portal - Office of the Minnesota
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The Ballista is an extremely fast overstable driver that provides excellent control at high speeds. It is one of the fastest discs in the world and combined with it's stability is a must have in any bag. It will be overstable for beginners and slightly understable for high powered throwers.
The Opto Line plastic is very clear and super durable, ensuring a good long life.


One mark of a disciple is a praying heart. That means that when you face an impossible situation, talking with God is your initial response rather than a last resort. I have four simple and practical suggestions for developing a praying heart.
The KISS principle ("Keep It Simple Stupid") applies to intercession. Countless seminars, sermon series, and books on prayer leave us with the impression that the subject is so complicated we dare not try it until we are skilled at it.
Think about it. Do you really think God could ever be impressed by our choice of words? Is there any evidence in the Bible that God prefers long prayers over short ones? Jesus didn't think so.
Matthew 6:7 says, "And when you are praying, do not use meaningless repetition, as the Gentiles do, for they suppose that they will be heard for their many words." If God is not looking for an impressive vocabulary or a large word count in our prayers, what does He value? Simplicity and sincerity! Like children coming to their parents, so we come to God. We bring our heart cries to a loving Father.
2. Use a pen and a pad to enhance your prayer life.
Even though we might not write out the majority of our prayers completely, keeping a prayer journal of our requests is a way to encourage specificity in our prayers. Through the years I have kept a running list of my requests on one side of a legal tablet, and how God answered that request on the corresponding side. Such a record keeps me focused when I speak to God, it jogs my ever-diminishing memory about important items to talk with God about, and it provides a great reminder of God's past faithfulness.
Conversing with God should involve more than asking. Jesus' model in Matthew 6 teaches us that our prayers should include our genuine desire for God's glory, a confession of sin, and an adoration of God's name.
But the majority of the prayer includes requests for specific action by God on our behalf ("give us bread," "forgive our sins," and "deliver us from evil").
In fact, as I look at the greatest prayers in the Bible including the model prayer in Matthew 6, Jesus' priestly prayer in John 17, or Paul's prayers for the Philippian Christians in Philippians 1, each of them contain specific requests. I have not been able to find a prayer anywhere in the Bible in which the pray-er was not asking God to do something.
Paul encouraged the Philippians to "tell God your needs and don't forget to thank Him for his answers (Philippians 4:6)." Keeping a record of your requests to God is an invaluable tool for doing just that.
Here's a simple suggestion. Before you allow your feet to touch the floor in the morning, take a moment and speak to God about your plans, your concerns, and your desire for His blessing. You will be amazed at how beginning your day talking with God will increase your desire to continue the conversation throughout the day.
By spending the final moments of his day confessing his transgressions throughout the day, expressing his gratitude for God's favor, and acknowledging his dependence on God's protection through the night hours, David would be offering "sacrifices of righteousness." And he encourages us to do the same.
If you are like me, your life is filled with important meetings to attend, decisions to make, and activities to perform. But between those critical events each day are minutes of time that can be easily frittered away as we await the "next big event." I'm referring to time in the car driving an appointment, standing in line at the post office or supermarket, or waiting for the next appointment. Some people always have a book to read or a report to complete on their computer. But most of us will simply waste that time, concluding that there is not enough time to do something substantial.
Why not use that time to engage in conversation with God? Pray for those you care about. Ask God to give you favor as you await "the next big thing." Confess that you are tired and need His strength. Request God's wisdom regarding a decision you are confronting later in the day.
You don't even have to wait for a lull in the day's activities to pray. It is possible (and profitable) to converse with God even as you perform other tasks.
The more you pray . . . the more you will continue to pray. And therein is the secret to developing a praying heart.


I'm talking about my little blogging break.
Break... gap, hiatus, vacation, whatever you want to call it. I haven't been gracing this blog with my written word in nearly a week. A week is just crazy! What have I possibly been doing if I haven't made time to sit down and write?
In all honesty, I feel like everything since last Friday has been a blur. There was our late Friday night drive to the lake, where we spent the remainder of the weekend relaxing, not wearing makeup, showering if I we felt like it, and drinking homemade margaritas. And Tuesday and Wednesday have just been so swamped with getting back home again and organized and being crazy-busy at work - it makes the week go by fast at least!
I got to feeling a little guilty about not sitting down at my MacBook to bring a new post to The Samantha Life each day. I think I easily get down on myself if I don't have a new post for all 5 weekdays like I normally plan on. I mean, we invest so much time and energy (and sometimes money) into our blogs so we should make time to write a new post and do a "good job" with it on a daily basis, right?
Then on the other hand, we invest so much time and energy (and sometimes money) into our blogs so we sometimes just need to get outside, sleep, cook dinner, or start obsessing over a new show on Netflix, right? Ok, maybe that last one is just me but I just started watching Scandal and LOVE it. Capital L-O-V-E.
My little break was completely unplanned but, you know what? It felt good. I had a great weekend relaxing at the lake - thank you God, for finally giving us some nice weather! And I've actually really enjoyed getting in good workouts, cooking healthy dinners, and spending the evening watching a new show the last few days. It was an unexpected break but I think I needed it.
And now I feel even more motivated to write and am glad to be back. Sometimes a break is just what we need to get ourselves back on track.
I'd love to write more but Parker has hockey tonight so I need to go microwave my Lean Cuisine and watch as many episodes of Scandal as possible.