text:
\section{Introduction}

The galaxy luminosity function is one of the most basic and fundamentally
important quantities in observational cosmology. For example, it is
essential for the analysis of large-scale structure statistics from
redshift surveys, and knowledge of the local luminosity function is
necessary for the proper interpretation of the faint galaxy count
data and galaxy evolution at high redshift (e.g., \cite{koo92}).

Though much work has gone into determination of the local $z = 0$ optical
luminosity function (see \cite{fel77}; \cite{2:KOSII}, 1983; \cite{eep};
\cite{bin88}; and recent work by \cite{lov92}; \cite{marz94}), there is
still some uncertainty in its faint end as well as in its
normalization (e.g., \cite{coll95}). In this paper we investigate
the local luminosity function by presenting results for
a sample of 18678 Las Campanas Redshift Survey (LCRS) galaxies,
selected from CCD photometry in a ``hybrid'' red Kron-Cousins $R$-band
(see \S~\ref{lumdata} below).
This is the largest galaxy sample for which the luminosity function and mean
density have been computed. The combination of the mean survey depth
of $z = 0.1$ and the large survey volume
($1.0 \times 10^7 \ h^{-3}$~Mpc$^3$ out to $cz = 60000$ km~s$^{-1}$)
imply that our results are not biased by local inhomogeneities.
In addition, the spectra of LCRS galaxies
allow us to study the luminosity function for samples divided by
[OII] 3727 emission strength, a rough indicator of the star-formation rate
(\cite{ken92}).

We describe relevant aspects of the LCRS construction in \S~\ref{lumdata}.
We then
detail our methods for measuring the galaxy luminosity function and mean
density in \S~\ref{methods}. Our results are presented in \S~\ref{lfrholcrs},
and we compare them to those of other redshift surveys in \S~\ref{comparisons}.
Some implications of
our results for faint galaxy counts and galaxy evolution are discussed in
\S~\ref{counts}. We summarize our conclusions in \S~\ref{conclusions}.

\section{The Las Campanas Survey Data} \label{lumdata}

We begin by describing the Las Campanas survey parameters;
detailed descriptions of the LCRS may be found in Shectman et al.
(1992, 1995, 1996), Tucker (1994), and Lin (1995).
There are 23690 galaxies, with an average
redshift $z = 0.1$, which lie within the survey photometric limits
and geometric borders considered in this paper.
The survey galaxies were selected from a
CCD photometric catalog obtained from drift scans taken on the
Las Campanas 1.0~m Swope telescope with a Gunn $r$ filter (\cite{thu76}).
Follow-up spectroscopy was obtained using the
multi-object fiber-optic spectrograph on the Las Campanas 2.5~m DuPont
telescope. The survey geometry is that of six ``slices,'' $1.5\arcdeg$ in
declination by $80\arcdeg$ in right ascension, three each in the North and South
galactic caps.

The survey data may be divided into two main parts: the first 20\% of the data
was obtained using a 50-object fiber system, while the remaining 80\% of the
data was taken with a 112-object system. The survey slices were built up
by observing $1.5\arcdeg$ by $1.5\arcdeg$ spectroscopic fields, with
a maximum of 50 or 112 galaxies observed per field. The survey photometric
limits were chosen so that there would be typically more targets
per field than available fibers, and we selected targets at random among
those that met the selection criteria.
Because we generally do not re-observe any of
our fields, we keep track of the variable field-to-field sampling
fractions $f_i$ in our subsequent statistical analyses.

To be precise, though our photometry was obtained through a Gunn $r$
filter, the calibration was done relative to standard stars
(\cite{gra81}; \cite{gra82}) in the
Kron-Cousins $R$-band. Our magnitudes are thus in a ``hybrid'' Kron-Cousins
$R$ system. Nevertheless, the difference between our hybrid
Kron-Cousins $R$ system and the true one is small;
comparison of photometry of LCRS galaxies obtained in both systems
yields a zero-point difference of $< 0.1$
mag and a color term of $< 0.2$ mag per magnitude of the
color (Johnson $V -$ Kron-Cousins $R$). See Tucker (1994) and
Shectman et al.\ (1996) for more details.

Objects were selected for the survey using isophotal magnitudes $m$, applying
both faint and bright isophotal magnitude limits. The limiting isophote
is 15\% of sky, or approximately 23 mag arcsec$^{-2}$.
In addition, a central magnitude $m_c$, approximately
measuring flux that would enter through the $3.5\arcsec$-diameter aperture of
a fiber, is also computed for each object. An additional cut line in the
$m$-$m_c$ plane is then imposed in order to exclude low central surface
brightness objects, for which redshifts are more difficult to obtain.
For the 50-fiber data, the nominal isophotal magnitude
limits are $16.0 \leq m < 17.3$, and the central surface brightness cut
excludes about 20\% of objects otherwise meeting the isophotal limits.
For the 112-fiber data, the nominal isophotal limits are $15.0 \leq m < 17.7$,
with exclusion of just the lowest 4-9\% of objects by surface brightness.
We illustrate our isophotal and central magnitude selection criteria for
a sample of LCRS galaxies in Figure~\ref{figsel}.
There are small field-to-field variations from the nominal photometric limits;
these are accounted for in our analyses. We will find it convenient
to divide our data into four subsets by galactic cap, North and South,
and by fiber number, 50 and 112 fibers; we will refer to these subsets as
N50, S50, N112, and S112. Table~\ref{tabsamps} summarizes details concerning
these four samples. Also, it turn outs that our fiducial sample will be
the combined North plus South 112-fiber data set, which we will refer
to as NS112.

Throughout this paper we adopt a Hubble constant
$H_0 = 100 \ h \ {\rm km \ s}^{-1}$~Mpc$^{-1}$ and a deceleration parameter
$q_0 = 0.5$. Where the $h$ dependence is not explicitly
indicated, we have used $h = 1$.
We also assume a uniform Hubble flow so that the absolute
magnitude $M$ of a galaxy of isophotal magnitude $m$ and redshift $z$ is
given by
\begin{equation}
M = m - 25 - 5 \log d_L - k(z) \ ,
\end{equation}
where the luminosity distance $d_L$ is
\begin{equation}
d_L = \frac{c}{H_0 q_0^2}
      \left[ q_0 z + (1-q_0) (1-\sqrt{1+2 q_0 z}) \right] \ ,
\end{equation}
and where the $k$-correction $k(z)$ is taken to be
\begin{equation}
k(z) = 2.5 \log(1+z) \ ,
\end{equation}
as appropriate in the mean for an $r$-band-selected galaxy sample
(\cite{tuck94}; \cite{2:KOSSII}).
Note that galaxy peculiar velocities, of order
$\sigma_{12} / \sqrt{2} \approx 350$ km~s$^{-1}$ ($\sigma_{12}$ is the
{\em pairwise} peculiar velocity dispersion; see \cite{lin96sig}; \cite{marz95}),
and our velocity measurement errors, on average 67 km~s$^{-1}$
(\cite{lin95the}), are both quite small compared to the mean survey redshift
$cz = 30000$ km~s$^{-1}$. We therefore neglect the effect of peculiar
velocities and velocity errors in the calculation of absolute
magnitudes. Similarly, the effect of using a different value of $q_0$ is also
small: $M({q_0}') - M(q_0=0.5) \approx ({q_0}'-0.5) z$, e.g.,
$-0.04$ magnitude at our average $z = 0.1$ for the case ${q_0}' = 0.1$.

\section{Methods} \label{methods}

\subsection{Luminosity Function} \label{methods:LF}

We compute the luminosity function using two related methods which are
unbiased by density inhomogeneities in the galaxy distribution. These are
the parametric
maximum-likelihood method of Sandage, Tammann, \& Yahil (1979;
hereafter STY) and the non-parametric stepwise maximum-likelihood
(SWML) method of Efstathiou, Ellis, \& Peterson (1988; hereafter
EEP). We describe these methods below, and we will discuss some modifications
needed in the analysis of the LCRS sample in \S~\ref{methods:modifications}.

Consider a galaxy $i$ observed at redshift $z_i$ in a flux-limited redshift
survey like the LCRS. Let $m_{{\rm min},i}$ and $m_{{\rm max},i}$ denote
the apparent
magnitude limits of the field in which galaxy $i$ is located. Let $\phi(M)$
be the differential galaxy luminosity function which we want to determine.
Then the probability that
galaxy $i$ has absolute magnitude $M_i$ is given by
\begin{equation} \label{eqprob}
p_i \equiv p(M_i \vert z_i) =
    \phi(M_i) \left/ \int^{M_{\rm max}(z_i)}_{M_{\rm min}(z_i)}
                             \phi(M) dM \right. \ ,
\end{equation}
where the absolute magnitude limits at $z_i$ are
\begin{equation}
{ \left\{ \begin{array}{c}
           M_{\rm min}(z_i) \\
           M_{\rm max}(z_i)
          \end{array} \right\} } =
{ \left\{ \begin{array}{c}
           m_{{\rm min},i} \\
           m_{{\rm max},i}
          \end{array} \right\} }
- 25 - 5 \log {d_L}_i - k(z_i) \ .
\end{equation}
The luminosity distance $d_L$ and the $k$ correction $k(z)$ for
LCRS galaxies are computed as described in \S~\ref{lumdata}.
We can then form a likelihood function $\frak L$ for having a survey of $N$ galaxies,
with respective absolute magnitudes $M_i$, by multiplying the probabilities
$p_i$:
\begin{equation}
\frak L = p(M_1, \ldots , M_N \vert z_1, \ldots , z_N)
  = \prod_{i=1}^{N} p_i \ ,
\end{equation}
or
\begin{equation} \label{eqlnlike}
\ln \frak L = \sum_{i=1}^{N} \left\{
                         \ln \phi(M_i) -
                         \ln \int^{M_{\rm max}(z_i)}_{M_{\rm min}(z_i)}
                           \phi(M) dM
                       \right\} \ .
\end{equation}
In the STY method one assumes a parametric model for $\phi(M)$, and the
parameters describing $\phi(M)$ are determined by maximizing the likelihood
$\frak L$, or equivalently $\ln \frak L$,
with respect to those parameters. In our case we take as our model for
$\phi(M)$ the Schechter function (\cite{sch76})
\begin{equation} \label{eqschech}
\phi(M) = (0.4 \ln 10) \ \phi^* \ [10^{0.4(M^*-M)}]^{1+\alpha} \
                         \exp [-10^{0.4(M^*-M)}] \ ,
\end{equation}
and use the STY method to find the characteristic magnitude $M^*$ and the
faint-end slope $\alpha$.
The normalization $\phi^*$ drops out in
equation~(\ref{eqprob}) and has to be determined using a different method to be
described below in \S~\ref{methods:dens}.
Also, error ellipses in the $M^*$-$\alpha$ plane
may be drawn by finding the contour corresponding to
\begin{equation} \label{ellipse}
\ln \frak L = \ln \frak L_{\rm max} - \case{1}{2} \Delta \chi^2 \ ,
\end{equation}
where $\Delta \chi^2$ is the change in $\chi^2$ appropriate for the
desired confidence level
and a $\chi^2$ distribution with 2 degrees of freedom.

Alternatively, one does not have to assume a particular functional form
for $\phi(M)$. Rather, in the EEP stepwise maximum likelihood method (SWML),
the luminosity function is taken to be a series of $N_p$ steps, each of width
$\Delta M$ in absolute magnitude:
\begin{equation}
\phi(M) = \phi_k \ , \ \ M_k - \Delta M / 2 < M < M_k + \Delta M / 2 \ , \ \
                     k = 1, \ \ldots , \ N_p \ .
\end{equation}
In this case equation~(\ref{eqlnlike}) may be rewritten as
\begin{eqnarray}
\ln \frak L & = & \sum_{i=1}^{N} \sum_{k=1}^{N_p} W(M_i - M_k) \ \ln \phi_k
          \nonumber \\
      & - & \sum_{i=1}^{N} \ln
            \left\{ \sum_{k=1}^{N_p} \phi_k \ \Delta M \
                    H [M_k, M_{\rm min}(z_i), M_{\rm max}(z_i)]
            \right\} \ , \label{eqsteplnL}
\end{eqnarray}
where the functions $W$ and $H$ are given by
\begin{equation}
W(M_i - M_k) = \left\{ \begin{array}{ll}
                        1, & M_k - \Delta M / 2 \leq M_i
                                                \leq M_k + \Delta M / 2 \\
                        0, & {\rm otherwise}
                       \end{array}
               \right. \ ,
\end{equation}
\begin{eqnarray}
\lefteqn{ H [M_k, M_{\rm min}(z_i), M_{\rm max}(z_i)] = } \nonumber \\
& & \left\{ \begin{array}{l}
              \min [M_k + \Delta M / 2, M_{\rm max}(z_i)]
            - \max [M_k - \Delta M / 2, M_{\rm min}(z_i)] \ , \\
              \ \ \ {\rm if} \ M_k + \Delta M / 2 \geq M_{\rm min}(z_i)
                       \ {\rm and} \
                       M_k - \Delta M / 2 \leq M_{\rm max}(z_i) \\
              0, \ \ {\rm otherwise}
            \end{array}
    \right. \ .
\end{eqnarray}
We then maximize $\ln \frak L$, equation~(\ref{eqsteplnL}), with respect to
the parameters $\phi_k$, and subsequently solve for them iteratively using
\begin{eqnarray}
\phi_k \ \Delta M & = & \left. \left\{
                         \sum_{i=1}^{N} W(M_i - M_k)
                        \right\} \ \right/ \\
    & & \sum_{i=1}^{N}
         \left\{ H[M_k, M_{\rm min}(z_i), M_{\rm max}(z_i)]
                 \left/ \sum_{j=1}^{N_p} \phi_j  \Delta M \
                        H [M_j, M_{\rm min}(z_i), M_{\rm max}(z_i)]
                 \right.
         \right\} \nonumber
\end{eqnarray}
As in the STY method, the normalization of the $\phi_k$ is not determined, so
we introduce a constraint similar to that given by EEP to fix the
normalization:
\begin{equation}
g \equiv \sum_{k=1}^{N_p} \phi_k \ \Delta M \ V(M_k) / V(M_f) - 1 = 0 \ ,
\end{equation}
where $V(M)$ gives the volume (including relativistic effects) over which a
galaxy of absolute magnitude $M$ can be seen in a flux-limited survey, and
$M_f$ is a fiducial absolute magnitude, which we take to be
$-20 \approx M^*$ as appropriate for the LCRS. Also following EEP, we can
estimate the variances of the parameters $\phi_k$ from the first $N_p$
diagonal elements of the covariance matrix given by
\begin{equation}
{\rm cov}(\phi_k) = {\bf \rm I}^{-1}(\phi_k) \ ,
\end{equation}
where ${\bf \rm I}(\phi_k)$ is the information matrix
\begin{equation}
{\bf \rm I}(\phi_k) =
  - \left. \left[
           \begin{array}{cc}
             \partial^2 \ln \frak L / \partial\phi_i \partial\phi_j +
             (\partial g / \partial \phi_i)
             (\partial g / \partial \phi_j) & \partial g / \partial \phi_j \\
             \partial g / \partial \phi_i & 0
           \end{array}
  \right] \right\vert_{\phi_i, \phi_j = \phi_k} \ .
\end{equation}

We can test the goodness of fit of the STY solution by comparing it to the
SWML solution using a likelihood ratio test described by EEP. Let $\frak L_2$ be
the likelihood for the SWML solution given by equation~(\ref{eqsteplnL}),
and let $\frak L_1$ be the likelihood, again from equation~(\ref{eqsteplnL}), but
with $\phi_k$ set to $\phi_{{\rm STY},k}$, where
\begin{equation}
\phi_{{\rm STY},k} = \int^{M_k+\Delta M/2}_{M_k-\Delta M/2}
                      \phi_{\rm STY}^2(M) V(M) dM
                   \left/
                     \int^{M_k+\Delta M/2}_{M_k-\Delta M/2}
                      \phi_{\rm STY}(M) V(M) dM
                   \right. \ .
\end{equation}
As discussed in EEP, here we use this definition of $\frak L_1$ for the STY solution,
rather than equation~(\ref{eqlnlike}), in order to match the binning present
in equation~(\ref{eqsteplnL}) but absent from equation~(\ref{eqlnlike}).
EEP show that the likelihood ratio $2 \ln(\frak L_1 / \frak L_2)$
approximately follows a
$\chi^2$ distribution with $N_p-3$ degrees of freedom, giving us a means for
testing the quality of the STY solution.

Alternatively, we can also check the goodness of the STY fit by comparing
the observed absolute magnitude distribution $d N(M)$ against the distribution
$d N_{\rm STY}(M)$ expected from the STY solution and the observed redshift
distribution of the $N$ survey galaxies (\cite{yah91}):
\begin{equation}
d N_{\rm STY}(M) = \sum_{i=1}^{N} p(M \vert z_i) dM =
  \sum_{i=1}^{N} \left\{
    \phi(M) dM \left/ \int^{M_{\rm max}(z_i)}_{M_{\rm min}(z_i)}
                              \phi(M) dM \right.
                                 \right\}  \ .
\end{equation}
A $\chi^2$ test can then be used to assess how well the STY prediction matches
the observations.

\subsection{Modifications} \label{methods:modifications}

For thoroughness in the analysis of the LCRS data, we need to consider
four additional details which will modify the basic methods described
above to calculate the luminosity function.
The most important effect is that of central
surface brightness selection, while the others make fairly small changes in
$\phi(M)$.

{\it (1) Magnitude Errors.}
From repeat observations we find that our rms isophotal magnitude error
is $\sigma = 0.1$ magnitude. We make the rough approximation
that the magnitude errors are Gaussian distributed with dispersion
$\sigma$, so that
the observed luminosity function $\phi_{obs}$ is a convolution of the
true luminosity function $\phi$ with a Gaussian magnitude error
distribution (EEP). Thus
\begin{equation} \label{eqschechconv}
\phi_{obs} = \frac{1}{\sqrt{2 \pi} \sigma}
    \int^\infty_{-\infty} \phi(M') e^{-(M'-M)^2/2\sigma^2} dM' \ ,
\end{equation}
and we use $\phi_{obs}$ in place of $\phi$ in the parametric STY equations.
For simplicity, we will not make this substitution in the non-parametric
SWML equations. Accounting for this dispersion of 0.1 magnitude makes
small systematic
changes in the best-fit values of the Schechter parameters for our sample:
$\Delta M^* \approx +0.03$ and $\Delta \alpha \approx +0.03$.

{\it (2) Variable Field Sampling Fractions.}
To account for this effect we weight galaxy $i$'s entry in the likelihood
equations~(\ref{eqlnlike}) and (\ref{eqsteplnL}) by the inverse of the sampling
fraction $f_i$ of the field containing that galaxy (\cite{zuc94}):
\begin{equation}
\ln p_i \longrightarrow \frac{\ln p_i}{f_i} \ .
\end{equation}
Including this effect changes the Schechter parameters very little: both
$\vert \Delta M^* \vert$ and $\vert \Delta \alpha \vert$ are $< 0.01$.

{\it (3) Apparent Magnitude and Surface Brightness Incompletenesses.}
Our success rate in identifying spectra as galaxies and stars drops
slightly at fainter apparent magnitudes and also drops slightly close to
the limiting central surface brightness cut line (Figure~\ref{figsel}).
We define a completeness
factor $F(m, m_c-m_{c,limit})$, which is a function of isophotal
magnitude $m$ and of ``distance'' $m_c-m_{c,limit}(m)$ from the central
magnitude cut line. We take $F$ to be the fraction of spectra we identified
as galaxies
or stars in each bin on a grid of $m$ and $m_c-m_{c,limit}(m)$ values.
In Figure~\ref{figF12}, we plot the two orthogonal projections
$F_1(m)$ and $F_2(m_c-m_{c,limit})$ of the full
completeness function $F$ for each of the N50, S50, N112, and S112 samples.
From the figure we note that the completeness does not vary much with
either apparent magnitude or surface brightness; the completeness only drops
to about 0.95 at the faint isophotal magnitude limits or at the central surface
brightness limits. To account for this effect, we weight galaxy $i$'s entry
in the STY and SWML likelihood equations by the inverse of the value of $F$
appropriate for that galaxy's isophotal and central magnitudes:
\begin{equation}
\ln p_i \longrightarrow \frac{\ln p_i}{F(m_i, {m_c}_i-{m_{c,limit}}_i)} \ .
\end{equation}
The change introduced is negligible for
$M^*$, $\vert \Delta M^* \vert < 0.01$, but $\alpha$ does change systematically
by a small amount, $\Delta \alpha \approx -0.04$. (The greater
incompleteness at fainter $m$ translates to a bias against intrinsically
fainter galaxies and hence a more positive $\alpha$, if left uncorrected.)

{\it (4) Central Surface Brightness Selection.}
We empirically find in the LCRS a correlation between a galaxy's absolute
luminosity and that galaxy's distance from our central surface brightness
cut line. We demonstrate this by culling out galaxies from our N112
subset to match the more restrictive surface brightness cuts of the
N50/S50 and S112 subsets (\S~\ref{lumdata} and Table~\ref{tabsamps}).
Figure~\ref{figG(M)} shows that the effect of the
more stringent surface brightness cuts is to reduce the sampling
completeness $G(M)$ as the absolute magnitude $M$ becomes fainter, where
$G(M)$ is simply the fraction of galaxies at $M$ which remain after the
low-surface-brightness galaxies have been removed. For the N50, S50, and
S112 samples, we can
account for this bias against faint galaxies by weighting galaxy $i$'s
entry in the likelihood equations by the inverse of $G$ at
that galaxy's absolute magnitude $M_i$:
\begin{equation}
\ln p_i \longrightarrow \frac{\ln p_i}{G(M_i)} \ .
\end{equation}
We thus correct the surface brightness sampling of the
N50, S50, and S112 subsets to that of the N112 subset.
For the 50-fiber data samples, $\Delta M^* \approx -0.04$ and
$\Delta \alpha \approx -0.15$; for the S112 sample, $\Delta M^* = -0.01$
and $\Delta \alpha = -0.06$. We do not attempt to
further extrapolate and correct for the N112 sample's own central surface
brightness cut, though we expect the change to be
$\vert \Delta \alpha \vert < 0.1$ from the example of the S112 data set.

We take account of the latter three effects (2-4) together by the replacement
\begin{equation}
\ln p_i \longrightarrow W_i \ln p_i , \
    W_i \equiv \frac{1}{f_i \ F(m_i, {m_c}_i-{m_{c,limit}}_i) \ G(M_i)} \ ,
\end{equation}
that is, we weight by the inverse of the product of the three completeness
factors. However, because the weighting factors $W_i$ are greater than one,
the likelihood $\ln \frak L$ will be larger in absolute value than when no
weightings are applied. The likelihood will thus resemble that of a
larger sample, leading to systematic underestimates in the confidence
ellipses and errors
we compute (\cite{gla95c}). To remedy this, we renormalize the weights
$W_i$ so that $\sum_{i=1}^N W_i = N$, where $N$ is the number of galaxies
in the sample of interest. The original weights are multiplied by
renormalization factors of 0.4 to 0.7 depending on the data set,
in particular by 0.68 in the case of our fiducial NS112 sample.
We have verified that this procedure yields
error estimates similar to those for the case when no weights are applied.

\subsection{Mean Density} \label{methods:dens}

To calculate the mean galaxy density $\bar\rho$, one can use the
minimum-variance estimator of Davis and Huchra (1982) (also \cite{lov92}).
We can adapt it to the LCRS as follows. For galaxies $i$ within redshift
limits $z_1 < z_i < z_2$ and absolute magnitude limits $M_1 < M_i < M_2$, we
have
\begin{equation} \label{eqrho}
\bar\rho = \frac{ \sum_i w(z_i) \ W_i }
                { \int^{z_2}_{z_1} S(z) w(z) (\frac{dV}{dz}) dz } \ ,
\end{equation}
where $S(z)$ is the selection function
\begin{equation} \label{selfunc}
S(z) = \int^{\min[M_{\rm max}(z), M_2]}_{\max[M_{\rm min}(z), M_1]}
            \phi_{obs}(M) dM
     \left/
       \int^{M_2}_{M_1} \phi(M) dM
     \right. \ ,
\end{equation}
and $w(z)$ is the weight function
\begin{equation} \label{eqwt}
w(z) = \frac {1} {1 + \bar{f} \bar\rho J_3 S(z)} \ ,
\end{equation}
with
\begin{equation}
J_3 = 4 \pi \int^\infty_0 r^2 \xi(r) dr
\end{equation}
denoting the second moment of the two-point spatial correlation function
$\xi(r)$. We use $J_3 \approx 10000 \ (h^{-1}$~Mpc)$^3$ as found from a fit
to the LCRS real space correlation function (\cite{lin96sig}).
Recall $\phi_{obs}$ is the Schechter function convolved with a
Gaussian magnitude error distribution, and the weights $W_i$ account for
the sampling and completeness effects (2)-(4) of the previous subsection.
Formally we should also incorporate the completeness effects (3) and (4)
into the definition of $S(z)$ above, but since these completeness
corrections are generally not too different from unity, it is simpler
to use the weights $W_i$ instead.
Also, for simplicity, we just use the mean sampling fraction $\bar{f}$
in the denominator of $w(z)$ and ignore the field-to-field variations.

The mean density $\bar\rho$ is calculated iteratively using
equations~(\ref{eqrho})
and (\ref{eqwt}). However, we find that for the redshift and absolute
magnitude limits we are interested in, 1000 km~s$^{-1} < cz <$ 60000
km~s$^{-1}$
and $-23.0 < M < -17.5$, the minimum-variance estimator gives essentially
the same $\bar\rho$ as when we use inverse selection function
weighting,
\begin{equation}
w(z) = 1 / S(z) \ .
\end{equation}
We will thus adopt this simpler weighting. Nevertheless, we will
estimate errors $\delta \bar\rho$ in the mean density using the
minimum-variance weighting scheme
\begin{equation} \label{eqrhoerr}
\delta \bar\rho \approx
   \left[
     \frac{ \bar\rho / \bar{f} }
          { \int^{z_2}_{z_1} S(z) w(z) (\frac{dV}{dz}) dz }
   \right]^{1/2} \sim \bar\rho \left[ \frac{J_3}{V} \right]^{1/2} \ .
\end{equation}
(Here $w(z)$ is that of equation~[\ref{eqwt}]. Note also that the dependence
of $\delta \bar\rho$ on the actual value of $J_3$ used is fairly weak.)
However, this error estimate
accounts just for that part due to galaxy clustering; we add in quadrature
the uncertainty in $\bar\rho$ arising from varying $M^*$ and $\alpha$ along
their joint 1$\sigma$ error ellipse.
Finally, we can compute the normalization $\phi^*$ in the Schechter function
(\ref{eqschech}) by
\begin{equation}
\phi^* = \frac{ \bar\rho }
              { \int^{M_2}_{M_1} \phi'(M) dM } \ ,
\end{equation}
where $\phi'$ is the Schechter function with $\phi^*$ set to one. As with
$\bar \rho$, the errors in $\phi^*$ will include contributions both from
galaxy clustering and from uncertainties in $M^*$ and $\alpha$.

\section{Luminosity Function and Mean Density of LCRS Galaxies} \label{lfrholcrs}

Details of the STY fits to the luminosity functions of the N50, S50, N112,
S112, and combined NS112 samples are given in Table~\ref{tabLF}.
2$\sigma$ error ellipses, calculated using equation~(\ref{ellipse}) with
$\Delta \chi^2 = 6.17$, are plotted in Figure~\ref{figco}. The STY and SWML
solutions for the N112, S112, and NS112 samples are shown in
Figures \ref{figphi} and \ref{figphi2}. We note first that the N50 and S50
results seem discrepant with the NS112 result. We have verified that we can
recover the correct $M^*$ and $\alpha$ parameters, using the methods of
\S~\ref{methods:modifications}, for the N112 and S112 samples culled to
the 50-fiber limits. It
is thus unclear why the N50 and S50 samples are still discrepant; the
trends of the discrepancies suggest some residual zero-point offset for the
S50 sample and some remaining incompleteness in the N50 sample. Since the
50-fiber data constitute just 20\% of the whole sample, and since they
are subject to larger corrections for central surface brightness selection
(Figure~\ref{figG(M)}a), our final quoted results will use just the
112-fiber data, even though
the agreement between the N112 and S112 samples is also not quite ideal.
The N112 and S112 2$\sigma$
error ellipses just touch in Figure~\ref{figco}. The $M^*$ values {\em do}
agree well, but the S112 has an $\alpha$ more positive by 0.1 than that of
N112. This suggests an incompleteness at the faint end of the luminosity
function, but examination of Figure~\ref{figphi2} shows instead that the
difference arises from an excess of galaxies in the S112 sample at the
bright end $M \lesssim -20$. The explanation for this North/South difference
is also unclear.

We have done extensive work in eliminating residual field-to-field
photometric zero-point
offsets in our data; details of the procedures used are given in
Shectman et al. (1996). In brief, relative zero-point offsets between
our drift scans are removed by comparing data in overlapping regions
of the scans and by comparisons to additional CCD calibration frames.
Moreover, the effects of variable sky brightness and seeing on our
isophotal magnitudes are dealt with by comparing, on a field-by-field
basis, the offsets between galaxy isophotal and aperture magnitudes (using
a 12$''$-diameter aperture that should be insensitive to seeing
and sky brigtness changes). After the correction procedures, the mean
photometric zero-points from slice to slice showed no offsets greater
than $\approx 0.015$ magnitude.
It is thus unlikely that zero-point offsets internal to the
data can account for the differences seen in Figure~\ref{figco}, particularly
the suggestive offset of the S50 sample. Externally, a difference in
extinction between the North and South galactic caps comes to mind. We
have not made a previous correction for this because 96\% of our fields are at
high galactic latitudes $\vert b \vert \geq 40\arcdeg$. If we apply an
extinction law $\Delta m = -0.07 (\csc \vert b \vert - 1)$ for
$\vert b \vert < 50\arcdeg$ and $\Delta m = 0$
otherwise (\cite{san73}), the changes in
both $M^*$ and $\alpha$ are less than 0.02 for all four data sets.
An additional extinction of about 0.1 magnitude in the North relative to
the South {\em could} improve the overlap between the N112 and S112 error
ellipses, but would not help with the 50-fiber results. Another possibility
is that our errors are underestimated. However, we find that the scatter
among subsamples of the four main data sets are in fact consistent with the
estimated error ellipses for the subsamples. On the other hand, the
error estimates do not account for any {\em intrinsic} variations in
the luminosity function parameters with location in the universe.
Thus in particular the N112/S112 discrepancy in $\alpha$ may hint at
such cosmic variance, because of the large separation between the
samples, but the N50/N112 and S50/S112 differences do not, as these
last two pairs of samples are in close proximity.
Another point to note is
that the image quality for the 112-fiber photometry is appreciably
improved over that of the early 50-fiber data photometry, due to the improved
CCD's used for the 112-fiber drift scans (\cite{shec95}).
In any event, whether the sample differences are due to some residual
systematic effect(s) or not, we find that
the $M^*$ values for the N50, N112, and S112 samples are in good agreement,
and we will see below in Table~\ref{tabdens} that the galaxy number
and luminosity densities for the four main data sets are also
consistent within their estimated
2$\sigma$ errors. Nevertheless, in light of the difference in the N112
and S112 $\alpha$'s, we will revise our estimate of the error
in $\alpha$ for the NS112 sample upward from the formal value (see below).

The likelihood-ratio and $\chi^2$ test (\S~\ref{methods:LF})
probabilities $P$ listed in Table~\ref{tabLF} show that the Schechter function
generally gives only formally marginal fits ($P \geq 0.001$) to the luminosity
function of the LCRS samples.
Nonetheless, a visual inspection of Figures \ref{figphi} and \ref{figphi2}
shows that the Schechter function is still a useful approximation for the
absolute magnitude range $-23.0 \leq M \leq -17.5$. The
SWML solutions show excesses relative to the Schechter fits at the faint
end $M > -17.5$.
We adopt as the
LCRS luminosity function the result for the NS112 sample, valid for the
range $-23.0 \leq M \leq -17.5$, with 1$\sigma$ errors:
\begin{eqnarray} \label{eqlfparams}
 M^* & = & -20.29 \pm 0.02 + 5 \log h \nonumber \\
 \alpha & = & -0.70  \pm  0.05 \\
 \phi^* & = & 0.019  \pm  0.001 \ h^3 \ {\rm Mpc}^{-3} \ . \nonumber
\end{eqnarray}
Here we conservatively estimate the uncertainty in $\alpha$ to cover the
range in $\alpha$ derived from the N112 and S112 samples; the formal error
is $\pm 0.03$. Other than this enlargement of the error in $\alpha$,
we note that the errors quoted above and elsewhere in this paper are formal
values which should account for random uncertainties in the luminosity
function parameters. Systematic uncertainties arising from the
following sources should be kept in mind and were discussed previously:
completeness corrections (\S~\ref{methods:modifications}), extinction and
photometric calibrations (earlier this section), and cosmology
(\S~\ref{lumdata}).

In our subsequent analyses of the LCRS data (apart from the present paper),
we will use the luminosity function
values in (\ref{eqlfparams}) for the N50, N112, and S112 data sets, but for
the S50 data set, we use its own luminosity function parameters as given
in Table~\ref{tabLF}. In Figure~\ref{figselfunc} we plot the selection
function $S(cz)$ computed from equation~(\ref{selfunc}) using the $M^*$ and
$\alpha$ values for each of our four data sets and for the combined NS112
sample, while restricting the absolute magnitudes to $-23.0 \leq M \leq -17.5$.
Note the typical decline at high $cz$ caused by the survey's faint
apparent magnitude limits. However, there is also a decline at small $cz$,
a result of the survey's additional bright apparent magnitude limits.

The mean densities computed for the LCRS samples are given in
Table~\ref{tabdens}.
We plot in Figure~\ref{figrho}(a) the galaxy density $\rho$ as a function of
redshift $cz$, for galaxies in the NS112 sample
within absolute magnitude limits $-23.0 \leq M \leq -17.5$. We also plot
the cumulative density for galaxies lying within redshift $cz$, showing that
the density appears to have converged within the LCRS survey volume. We
stop at $cz = 60000$ km~s$^{-1}$, where the selection function
$S(cz)$ has dropped
to approximately 0.01 (Figure~\ref{figselfunc}).
We find a mean density $\bar\rho = 0.029 \pm 0.002$ galaxies
$h^3$~Mpc$^{-3}$. Galaxy
clustering contributes a 4\% fractional uncertainty to $\bar\rho$,
and uncertainties in the luminosity function parameters contribute
another fractional uncertainty of 4\%. Note from Table~\ref{tabdens} that
despite the difference in $\alpha$ values, the mean densities of the N112 and
S112 samples do in fact agree well. To compare the N112 and S112
radial density distributions in more detail,
we also plot, as a function of $cz$, the ratio of the N112 to S112
galaxy number densities (Figure~\ref{figrho}c) and
galaxy number histograms (Figure~\ref{figrho}d; account has been made of the
differences in volume and completeness).
Note that the ratios differ somewhat in
the two figures, since the density ratios
include the effect of the differing N112/S112 luminosity functions,
but the histogram ratios do not.
We find from either plot that for radial
shells of thickness 5000 km~s$^{-1}$, fluctuations in galaxy numbers
and densities of about 20\% between N112 and S112 are not uncommon.
In particular, the decline seen in the N112 sample for $cz \gtrsim
40000$~km~s$^{-1}$ is consistent with the deficit of $M \lesssim M^*$
galaxies observed in the N112 vs. S112 luminosity functions
(Figure~\ref{figphi2}). On the other hand, we also plot, as error bars
on the ratios, the expected fluctuations arising from the
combination of galaxy clustering, shot noise, and uncertainties in
$M^*$ and $\alpha$ (the last only for the density ratios). In
computing the galaxy clustering component of the fluctuations
we have accounted for the geometry
of the shells and used a fit to the LCRS power spectrum
(\cite{lin96ps}; this procedure is preferred over the approximate
error estimate of equation~[\ref{eqrhoerr}], which tends to
give an overestimate given the geometry of the
shells). We see that the observed density fluctuations between N112
and S112 appear to be consistent with the expectations,
despite the 2$\sigma$ discrepancies between the N112/S112
$M^*$-$\alpha$ error ellipses.
The N112/S112 luminosity functions thus do not differ significantly
in normalization (as described by the galaxy number densities), but
do differ in shape (specifically in $\alpha$).

We also tabulate in Table~\ref{tabdens} the
galaxy luminosity density $\rho_L$, given by
\begin{equation}
\rho_L = \int_{-23.0}^{-17.5} 10^{-0.4 M^*} \phi(M) dM \ .
\end{equation}
(Letting the integration limits go to infinity only increases $\rho_L$
by 3\%.)
The NS112 value of
$(1.4 \pm 0.1) \times 10^8 \ L_{\sun} \ h$~Mpc$^{-3}$, when increased
by 25\% as a rough isophotal-to-total light correction,
implies a critical mass-to-light ratio
$(M/L) \approx 1.6 \times 10^3 \ (M/L)_{\sun}$ to close the
universe, in agreement with previous determinations (e.g., \cite{2:KOSSII};
EEP; \cite{marz94}).
Alternatively, we obtain a cosmological density parameter
$\Omega \approx 0.2 \ [(M/L) \ / \ 300 \ h \ (M/L)_{\sun}]$,
if we set $M / L = 300 \ h \ (M/L)_{\sun}$, a
typical virial mass-to-light ratio estimated from
clusters and groups (e.g., a recent determination from the
the CNOC cluster sample gives $M / L = 295 \ h \ (M/L)_{\sun}$ in Gunn $r$;
\cite{car96}).

In addition, we have also derived $\phi^*$ for the NS112 sample by normalizing
to our galaxy number count distribution $dn(m)$. We use
\begin{equation}
\int_m^{m+\Delta m} dn(m) = \int_0^{\infty} dz (dV/dz)
                            \int_M^{M+\Delta M} \phi_{obs}(M') dM' \ ,
\end{equation}
and do a $\chi^2$-fit to find $\phi^*$, assuming Poisson errors on the counts,
and fixing $M^*$ and $\alpha$ at their maximum likelihood values.
For the counts we consider {\em all} objects in our CCD photometric catalog
with isophotal magnitudes $15.0 \leq m \leq 17.8$,
except that we make a 3\% correction
for stellar contamination, as inferred from the fraction of stars in our
spectroscopic sample. We find $\phi^* = 0.021 \ h^3$~Mpc$^{-3}$, but to
properly compare against our redshift survey value, we need to
make a 4\% reduction to account for the low surface brightness galaxies
excluded from
the redshift survey. We get $\phi^* = 0.020 \ h^3$~Mpc$^{-3}$,
in good agreement with the value
$\phi^* = 0.019 \pm 0.001 \ h^3$~Mpc$^{-3}$ derived from the redshift survey.
We show in Figure~\ref{figcounts} the $dn(m)$ distribution for the NS112
sample and the prediction based on $\phi^* = 0.021 \ h^3$~Mpc$^{-3}$,
$M^* = -20.29$, and $\alpha = -0.70$.

We have also separated the NS112 sample into two groups by [OII] 3727
emission, defining emission galaxies to be those with 3727 equivalent widths
$W_{\lambda} \geq 5$~\AA.
The emission galaxies constitute 40\% of the total sample.
The fit details are given in Table~\ref{tabLF}, the error ellipses are
plotted in Figure~\ref{figcoem5}, and the SWML and STY solutions are
shown in Figure~\ref{figphiem5}. Note that for the S112 data, we have used
separate surface brightness completeness functions $G(M)$, shown in
Figure~\ref{figG(M)}(b), for the emission and non-emission galaxies.
We see that emission and non-emission
galaxies have very different luminosity functions, with emission galaxies
dominating the faint end and non-emission galaxies prevailing in the
bright end. In particular, emission galaxies constitute about 15\% of the
total at $M = -22$, rising to about 80\% at $M = -17$.
The two populations show about equal number densities near the full-sample
$M^*$.
The emission galaxies show a much steeper faint-end slope $\alpha$
($-0.9$ vs.\ $-0.3$) and a slightly fainter $M^*$ ($-20.0$ vs.\ $-20.2$)
relative
to the non-emission galaxies. Also, note from Figure~\ref{figphiem5} that
the excesses at $M > -17.5$ relative to the Schechter fits are less
pronounced than they were for the full sample, though for consistency we
use the same fit range $-23.0 \leq M \leq -17.5$. Moreover, the probabilities
in Table~\ref{tabLF} indicate that a Schechter function is a good description
of the emission galaxy luminosity function, though again visual inspection
of Figure~\ref{figphiem5} indicates that the Schechter function provides
reasonable (though not always {\em formally} good) approximations to the
luminosity functions of both subsamples. In figure~\ref{figrho}(b), we plot
the space density of emission and non-emission galaxies.
Finally, we note that instead of our formal 1$\sigma$ errors for $\alpha$
listed in Table~\ref{tabLF}, we quote instead an error of $\pm 0.1$ for both
the emission and non-emission galaxies. We do this because of our earlier
N112/S112 difference in $\alpha$, and because of another effect to
be discussed at the end of \S~\ref{counts}.

\section{Comparisons to Other Surveys} \label{comparisons}

We next compare our luminosity function to that
from three other large, local, and optically-selected redshift surveys.
The luminosity functions from the Stromlo-APM (\cite{lov92}),
Center for Astrophysics (CfA; \cite{marz94}), and
second Southern Sky (SSRS2; \cite{daC94}) redshift surveys are detailed in
Table~\ref{tabLF} and are plotted against
that of the LCRS NS112 sample in Figure~\ref{figphicomp}. Because these
other surveys were selected in the blue, while the LCRS was selected
in the red, for the comparison we need to shift the zero-points of the various
magnitude systems. (Shifting the zero-points also roughly accounts for other
differences in the magnitude systems; e.g., the fact that LCRS
magnitudes are explicitly isophotal whereas APM magnitudes have an
isophotal-to-total magnitude correction applied.
However, applying simple constant offsets does neglect more complicated
effects, due for example to galaxy colors and morphologies.
Be aware that the specific differences we find below in the luminosity functions
will necessarily be sensitive to the exact shifts in absolute magnitudes we apply.)
For Stromlo-APM we have offset its $M_{b_J}$ magnitude scale by
1.1 magnitude to approximately match
the mean rest-frame color $\langle b_j-R \rangle_0 = 1.1$
of LCRS galaxies (\cite{tuck94}; \cite{tuck95}). We shift the SSRS2
$M_{B(0)}$ magnitude scale by the same amount, since the SSRS2 and $b_J$
zero-points agree within 0.2 magnitude (\cite{daC94}).
However, we shift the Zwicky
$M_Z$ magnitude scale for the CfA survey by another 0.7 magnitude
to match the CfA and Stromlo-APM $M^*$ values.
Note first from the figure that the
Stromlo-APM and LCRS results show consistent normalizations and are fairly
similar in overall shape, despite differences in their respective Schechter
parameters, particularly in the faint-end slope $\alpha$.
There are instead differences,
for $M_r \lesssim -21.5$ and $M_r \gtrsim -19$, which are
responsible for the shallow faint-end slope $\alpha = -0.7$ found in
the LCRS, compared to the more typical flat value $\alpha \approx -1$ seen
in the Stromlo-APM and other previous surveys.
We emphasize that even
though the LCRS is slightly biased against intrinsically faint galaxies
(because of the survey selection criteria and the correlation between
luminosity and central surface brightness), the {\it gross} features of our
luminosity function are quite similar to an $\alpha = -1$ Schechter function.
However, such a Schechter function does not provide as good a fit in {\it detail}
to the LCRS data.
As another aid in the comparison, note that for $-1 \leq \alpha \leq -0.7$,
we roughly have $(\Delta \rho_L / \rho_L) \approx
(\Delta \phi^* / \phi^*) - 0.9 \Delta M^* + \case{1}{3} (\Delta\alpha /
\alpha)$ (good to about 0.1 in $\Delta \rho_L / \rho_L$). Thus the
LCRS and Stromlo-APM surveys
have about the same luminosity density $\rho_L$ despite their different
Schechter parameters (Table~\ref{tabLF}): the 30\% difference in $\phi^*$ is
more than compensated by the 30\% difference in $M^*$ (after noting
the 1.1 magnitude zero-point shift) and one third of the 30\% difference
in $\alpha$.

We note next from Figure~\ref{figphicomp} that the CfA and SSRS2
luminosity functions show some conspicuous differences compared to the LCRS
and Stromlo-APM results. The CfA luminosity function clearly
shows a higher normalization, though its shape is
similar as it has $\alpha = -1$. On the other hand,
the SSRS2 luminosity function is quite similar to those of the LCRS
and Stromlo-APM surveys for $M_{bJ} \lesssim -19$, but for fainter
magnitudes its $\alpha = -1.2$ makes the SSRS2 result overshoot the
LCRS and Stromlo-APM luminosity functions. Though not shown in the
figure, the CfA luminosity function also has a similar excess at faint
magnitudes $M_Z \gtrsim -16$ relative to an extrapolation of the
$\alpha = -1$ fit (see Figure 9 of \cite{marz94}). It is unclear why
such a steep faint end
(see below) is not observed in the LCRS or Stromlo-APM surveys.
However, the high normalization of the CfA survey may be explained as
the result of local density inhomogeneities
(e.g., large coherent structures like the ``Great Wall''; \cite{geller89})
present in the CfA survey volume.
Both the CfA and SSRS2 surveys probe a smaller and more local volume
of space compared to either the LCRS or Stromlo-APM surveys; the mean
survey depths are about 7500 km~s$^{-1}$ for both CfA and SSRS2,
15000 km~s$^{-1}$ for Stromlo-APM, and 30000 km~s$^{-1}$ for the LCRS.
In fact Marzke et al. (1994a) and da Costa et al. (1994) both point out that
their respective surveys are not yet large enough to be ``fair''
samples of the universe. Both the LCRS and Stromlo-APM surveys should
come closer to representing fair samples, and it is remarkable that
their respective luminosity functions are quite similar in both
normalization and shape.

We do not have morphological classifications for our survey galaxies.
Nonetheless, though there is not a one-to-one correspondence between 3727
emission and morphological type, we do expect our emission galaxies to tend to
be late-type spirals and our non-emission galaxies to be early-type
ellipticals and S0's. We also tabulate in Table~\ref{tabLF} the luminosity
function for galaxies of different morphological types computed for the
Stromlo-APM and CfA (\cite{marz94b}) surveys. The sharp distinction in $\alpha$
between the early- and late-type luminosity functions in the Stromlo-APM survey
($\alpha = +0.2$ and $-0.8$ respectively) qualitatively agrees with the
emission vs.\ non-emission differences seen in the LCRS. However,
Zucca et al.\ (1994) and Marzke
et al.\ (1994b) suggest that incomplete classification of early-type galaxies
may be responsible for the difference seen in the Stromlo-APM survey. In
fact, there is no significant difference in the luminosity functions of
E-S0 and spiral (Sa-Sd) luminosity functions in the CfA survey
($\alpha = -0.8$ to $-0.9$). However, Marzke et al.\ (1994b) do find
that their faint end is dominated by Magellanic spiral and irregular galaxies,
with a very steep $\alpha = -1.87$. Moreover, da Costa et al. (1994)
attribute their steep $\alpha = -1.2$ to the dominance of blue
galaxies at the faint end. These CfA and SSRS2 results are in
qualitative agreement with the LCRS findings, as we expect
such late-type blue galaxies to be gas-rich
and to exhibit strong emission lines.

\section{Relation to Galaxy Counts and Galaxy Evolution} \label{counts}

The problem of the excess faint blue galaxy counts over the expectations
of the simplest no-evolution models has continued to be an area of intense
research (see reviews by \cite{koo92}; \cite{koo95}). The absence in
deep pencil beam redshift surveys (\cite{bro88}; \cite{col90}, 1993;
\cite{gla95a}) of high redshift $z \gtrsim 1$ galaxies, which are
predicted by simple luminosity
evolution models for the excess counts, has led to proposals of more exotic
explanations. For example, the excess blue galaxies may be star-bursting
dwarfs which have since faded
by the present day (e.g., \cite{bro88}; \cite{cow91}; \cite{bab92}),
or alternatively, extensive galaxy merging
may have occured to remove the excess galaxy population by $z = 0$
(\cite{bro92}; \cite{roc90}).

In contrast, other workers (\cite{gro95}; \cite{koo93}; \cite{met91}, 1995b)
have argued that the data may still be reasonably fit by
mild evolution models, given the uncertainties in the faint end slope
and in the normalization of the local luminosity function; note in particular
the steep $\alpha$ of the Sm-Im sample of Marzke et al.\ (1994b),
and the difference
in normalization between the Stromlo-APM and CfA surveys. In fact, even
before the CfA results, the counts in the APM galaxy catalog (\cite{mad90a})
at {\em bright} magnitudes
$b_J = 20.5$ showed a factor of 2 excess relative to no-evolution
predictions based on the counts at $b_J \approx 17$ (\cite{mad90b}).
Either significant
evolution occurred at {\em low} redshifts $z \approx 0.1$ (\cite{mad90b}),
or there are large-scale structures (voids) and/or magnitude scale errors
(\cite{met95a}) in the APM survey which are biasing the $b_J \approx 17$
counts systematically low. Choosing to normalize to the galaxy counts
at $b_J \approx 20$ corresponds to using $\phi^* = 0.03 \ h^3$~Mpc$^{-3}$,
twice the Stromlo-APM value, and using this high normalization reduces
the amount of evolution needed to reconcile with the faint count data.

There is now evidence from deep redshift surveys for evolution in the
luminosity function since redshifts $z \approx 0.5$ (\cite{eal93};
\cite{lon93}), but one which depends on galaxy type. Blue, star-forming
galaxies appear to exhibit an increased density and/or steepening faint-end
slope with increasing redshift, whereas the red galaxy population shows no
evolution with $z$ (\cite{lil95}; \cite{coll95}). There is also evidence
of an increase in star formation rate with redshift and the association of
merging activity with increased star formation (\cite{coll95};
\cite{col94e}). In particular, the number of star-forming galaxies,
defined as those with [OII] 3727 $W_{\lambda} > 20$~\AA, appears to
be 5-10 times greater at $z \gtrsim 0.5$ than at $z = 0$, for
absolute magnitudes below and including $M^*$ (\cite{coll95}).
In addition, recent galaxy number counts from the Hubble Space
Telescope (HST) Medium Deep Survey (\cite{gla95b}; Driver et al.
1995a,b) indicate that
at $B \approx 24$, the counts are dominated by galaxies with irregular and
peculiar morphologies, which show increased numbers relative to their
proportions in local surveys. However, the elliptical and spiral counts are
as expected with no evolution needed, if one adopts the Stromlo-APM
luminosity function, but with the {\em high} normalization
$\phi^* = 0.03 \ h^3$~Mpc$^{-3}$.

It is beyond the scope of this paper to undertake detailed
modelling of the evolution of galaxies, but results from the local
LCRS sample bear on two points which may be connected to understanding the
faint blue galaxies. One is the normalization of the local
luminosity function and the other is the rate of evolution for
galaxies with active star formation.
First, we note that our luminosity function normalization is consistent with
the low value from the Stromlo-APM survey, not with the high value implied
by the $b_J \approx 20$ APM galaxy counts. Thus results arguing for no or mild
evolution, e.g. the luminosity function models of Gronwall \& Koo (1995)
or the HST elliptical and spiral counts, will need to be modified if our
low normalization is not an underestimate. Because of our large survey depth, up
to $z = 0.2$, large-scale structures should not bias our results low
(cf. Figure~\ref{figrho}). The normalizations for the two completely
independent samples N112 and S112, which probe opposite directions in
the sky, agree well with each other. Also, the remaining 4\% of low central
surface brightness galaxies that are not part of the redshift survey will
not lead to such a large underestimate. We saw before that our $\phi^*$
normalization is consistent with our total number counts,
{\em including} the low surface brightness galaxies. Any potential factor
of 2 underestimate will have to come from galaxies completely missing from
our original CCD photometric catalog, because they lie below our effective
surface brightness limit. Such a bias against very low surface brightness
galaxies, as has been argued for by, e.g., McGaugh (1994) and Ferguson
\& McGaugh (1995), would be a potential problem for all bright galaxy surveys,
not just the LCRS. We have derived a firm value for the
density normalization of galaxies with central surface brightnesses
{\em above} our explicit cut line(s), examples of which are shown in
Figure~\ref{figsel}.
A final observation here is that our galaxy counts, for our hybrid
Kron-Cousins $R = 15 - 17.8$,
correspond roughly to $b_J = 16 - 19$. However, whereas the APM counts
over this range seem
too steep at face value to be consistent with no evolution, even at such
bright magnitudes (\cite{mad90b}), the Las Campanas counts shown in
Figure~\ref{figcounts} at comparable magnitudes suggest no such evidence
for evolution at low redshifts $z \approx 0.1$.

Second, we address the possibility of an increase in the number of
star-forming galxies at redshifts $z < 0.2$ explored by the LCRS, as has
been observed by redshifts $z \approx 0.3$ in deeper surveys
(\cite{coll95}), by checking whether the average equivalent width of [OII] 3727
varies with redshift. To factor out the dependence of [OII] 3727 $W_{\lambda}$
on galaxy luminosity, we plot in Figure~\ref{figeqwave} the average
$W_{\lambda}$ as a function of $z$ for seven separate absolute magnitude
bins, each one magnitude wide, from $M = -16$ to $-23$. We use only our
NS112 data. Our results indicate that the average equivalent widths generally
do not change with redshift,
although for galaxies fainter than $M = -19$, the redshift
range is not large. A similar conclusion may also be drawn by plotting the
fraction of galaxies with, say, $W_{\lambda} > 5$~\AA \ or 20~\AA.
In light of the error bars, the most significant trend seen is that for
the $-20 > M > -21$ bin, specifically a rise of about 1~\AA \
in the average $W_{\lambda}$ at $z \approx 0.1$. This may be due to
large-scale structure, as the same trend is less apparent in the N112 sample
than in the S112 sample. Alternatively, it may be an aperture effect, in
that our $3.5\arcsec$-diameter fibers cover $5 \ h^{-1}$~kpc on a galaxy
at $z = 0.1$, but only half as much at $z = 0.05$, so that there would be
a bias toward lower equivalent widths at lower redshifts if less emission
arose from the centers of galaxies compared to that from the outer regions.
An argument against the latter explanation is that we do not see any consistent
systematic trend of this kind in the other absolute magnitude bins. In any
event, the evidence for changes in $W_{\lambda}$ is not dramatic in
any of the luminosity bins.
Since 3727 equivalent width is a surrogate for the star-formation
rate (\cite{ken92}), we conclude that there is no evidence for
significant evolution in the star-forming properties of LCRS galaxies over
the redshift range we sample.
We emphasize that this conclusion is only valid over the {\em respective}
redshift ranges observable for galaxies of different luminosities, and
that galaxies fainter than $M^* + 1 \approx -19$ are not seen above
$z = 0.1$. For galaxies brighter than $M^*$, though, our no-evolution result
does extend up to $z = 0.2$. However, note that our null results say nothing
about the above-mentioned evidence
of increasing numbers of star-forming galaxies at {\em higher} redshifts
than that constrained by the LCRS, specifically
an increase for sub-$M^*$ galaxies by $z \approx 0.3$ and for $M^*$
galaxies by $z \approx 0.5$ (\cite{coll95}).

A final note is that the small increase in $W_{\lambda}$ seen for
$M^*$ galaxies does have some impact on the $\alpha$ value derived earlier
for our emission and non-emission galaxy samples.
In fact, in our earlier derivation we actually
applied redshift-dependent weights, analogous to the completeness
corrections discussed in \S~\ref{methods:modifications}, to account
for any changes in the emission (or non-emission) galaxy
fraction as a function of $z$. The weights are calculated separately
for galaxies of different absolute luminosities.
If we had not applied such
corrections, the maximum-likelihood solution for the emission galaxy
$\alpha$ would steepen by $-0.1$, while the non-emission
$\alpha$ would flatten by $+0.1$. Leaving out the additional corrections
leads primarily to a systematic increase in the emission galaxy density
with redshift (because of the steeper $\alpha$),
so that the sum of the cumulative emission and non-emission
galaxy densities overshoots that for all galaxies by about 25\% at the
$cz = 60000$ km~s$^{-1}$ limit. In light of the lack of evolution seen in the
Figure~\ref{figeqwave} results, which do {\em not} depend on the luminosity
function, we feel justified in applying the $z$-dependent corrections,
resulting in more reasonable agreement between the total galaxy density and
the sum of the emission and non-emission galaxy densities given in
Table~\ref{tabdens}.
We increase our estimated errors in the emission and non-emission $\alpha$'s
to $\pm 0.1$ in light of the above effects, as
as we alluded to before at the end of \S~\ref{lfrholcrs}.

\section{Conclusions} \label{conclusions}

We have used inhomogeneity-independent maximum-likelihood methods to
calculate the luminosity function of LCRS galaxies in the (hybrid) Kron-Cousins $R$
absolute magnitude range $-23.0 \leq M - 5 \log h \leq -17.5$, where
we find that it may be reasonably described by a Schechter function with
$M^* = -20.29 \pm 0.02 + 5 \log h$, $\alpha = -0.70 \pm 0.05$, and
$\phi^* = 0.019 \pm 0.001 \ h^3$~Mpc$^{-3}$.
There appears to be an
excess relative to the Schechter function at the faint end $M > -17.5$.
The mean galaxy density for the range $-23.0 \leq M \leq -17.5$ is
$0.029 \pm 0.002$ galaxies $h^3$~Mpc$^{-3}$ out to a redshift of
$60000$ km~s$^{-1}$,
and the run of cumulative density with redshift suggests that the density
has converged within the LCRS survey volume.
The measured (isophotal) galaxy luminosity
density is $\rho_L = (1.4~\pm~0.1) \times 10^8 \ L_{\sun} \ h$~Mpc$^{-3}$, resulting
in $\Omega \approx 0.2$, for a typical virial mass-to-light ratio of
$300 \ h \ (M/L)_{\sun}$ and a rough isophotal-to-total light correction.
We have also divided our
sample by the cut [OII] 3727 equivalent width
$W_{\lambda} \geq 5$~\AA \ , and showed
that the emission and non-emission galaxies so defined
have significantly different
luminosity functions, with emission galaxies dominating the faint end
($\alpha = -0.9 \pm 0.1$), non-emission galaxies dominating the bright end
($\alpha = -0.3 \pm 0.1$), and about equal numbers near the full-sample $M^*$.

We then compared our results to those from the optically-selected
Stromlo-APM, CfA, and SSRS2 redshift
surveys. Despite the fact that the Stromlo-APM survey has an
$\alpha \approx -1$, and the LCRS has $\alpha = -0.7$, the shapes of two
luminosity functions are remarkably similar, though they do differ in
specific details. Moreover,
our luminosity function normalization is consistent with that of Stromlo-APM;
the CfA normalization is higher but this may be biased by
density inhomogeneities in its smaller and more local survey volume.
Finally, our emission galaxy results confirm the picture
seen in these previous surveys that the faint end of the luminosity
function is dominated by late-type, blue galaxies which
are presumably also gas-rich and strong in [OII] 3727 emission.

Finally, two implications of our results may be made with
respect to the faint galaxy counts and to galaxy evolution. First,
our normalization of the luminosity function is a factor of two below the
``high'' normalization often adopted from the $b_J \approx 20$ APM galaxy
counts in calculations used to match fainter galaxy count data. If our
normalization is not an underestimate (e.g., due to
surface brightness effects), then it implies that more evolution
is required in the models, compared to using the high APM count normalization.
Second, for the redshifts sampled in the Las Campanas survey, up to about
$z = 0.2$ for galaxies brighter than $M^*$, our results do not indicate a
significant change of average [OII] 3727 equivalent width with redshift.
The star-formation rate, as measured by [OII] 3727, has apparently
not evolved rapidly over the volume sampled by the LCRS, unlike the large
increases seen in the numbers of blue star-forming galaxies in smaller,
deeper surveys at $z \gtrsim 0.3$.

In this paper we have used the Las Campanas Redshift Survey to provide an
accurate determination of the local luminosity function for the largest
galaxy sample thus analyzed. Our red $R$-band results are also complementary
to previous results in blue photometric bands.
In addition, we have begun to explore the luminosity function for
galaxy samples divided by emission properties, and in future analyses
we will examine galaxy samples defined by $b_J - R$ colors (which are
available for our Southern galaxies from APM observations),
and if possible, also by basic morphological information to be determined
from our drift-scan images. The Las Campanas Redshift Survey should
thereby provide a useful and large database of local galaxy properties,
including luminosity, emission, color, and possibly morphological information,
upon which to anchor models of faint galaxy counts and galaxy evolution
at higher redshifts.

\acknowledgments

We thank Ron Marzke for useful discussions and the anonymous referee
for helpful suggestions.
The Las Campanas Redshift Survey has been supported
by NSF grants AST 87-17207, AST 89-21326, and AST 92-20460. HL also
acknowledges support from NASA grant NGT-51093.

Note added in proof: the difference noted here between the luminosity
functions of emission and nonemission galaxies is similar
to that found in preliminary analysis of the ESP redshift
survey galaxies, e.g., Vettolani et al. (1994), IAU Symposium No.
161, 687.

redpajama_set_name: RedPajamaArXiv


By Travis Smith, CTO – Appolis Inc.
When it comes to barcodes, innovation is only scratching the surface of a powerful network of empowered workers able to make real-time decisions backed up with tailor information about what is being created during manufacturing. It is the difference between using a barcode to simply capture inventory information, and a barcode that can be scanned as part of a more intelligent manufacturing automation process. Like a network of super computers, each participant in the manufacturing operation is constantly generating signals that are potentially consumed by other players all working towards an efficient use of both labor resources and materials.
Recently a client of Appolis decided to change their process from a reactive exception process to a proactive exception process when it comes to inventory outage. In the past, a final inspection would occur to double check whether all the components on the original job where properly used. Since inventory was moving very rapidly, there was always a decent chance that real-time changes to the job were made to keep production flowing. The inspection would discover that a specific component was substituted. This signaled the production manager to manually communicate to all operators to no longer use component X which was now out of inventory, but to switch to component Y. This did not affect the job within the system, but solely relied on the mental note of an operator to make the switch in order to keep things straight!
Their newly designed process makes proactive alerts and modifications to jobs when needed. By using barcodes for more than just capturing inventory information, they can help drive efficiency and at the same time take a step towards a network of operators that are making real-time decisions about how best to deal with each unique situation. If in fact, manufacturing will be an important link to the future economy of the US, then these approaches to combining barcodes with technology should become a large part of it.


Ok so you've had your site well optimised, job done right? Wrong!
Offsite search engine optimisation is the most time consuming job of all, luckily by using us we do all the hard work on your behalf.
We need to tell the world your website exists, let the world know about your products and services, and what makes you stand out above your competition.
We do this by making sure relevant sites link back to you, because you have great content, we write press releases, join forums, become your blogger, submit and write to business directories.
This is all done manually using the correct ethical methods or as termed (white hat) poor backlinking to non-relevant website can get your website blacklisted so it's doubly important you do it right!
The disadvantage to this is that it takes time, usually months to start to see benefits, but it's always worth it in the long run, as you are not then quite as reliant on pay per clicks.
Placeyoursite generally spend around 20 to 40 hours a month on an offsite SEO project, we send you all the reports so that you can see exactly whats been done.
Then we provide a live online utility so that you can check out the sites ranking progress at anytime, and by search engine.
However our offsite SEO service still is a lot less expensive than you would think, and we can confidently beat any provider you are currently using, usually by as much as 50%.
See how much this would be for you!


Im having a problem detecting the sdcard connected to nodemcu when using sdfat.h library . Unable to initialized card..
But when just using the sd.h library it works fine.. can read and write and even detect its fat32..


text:
Hannibal : the military biography of Rome's greatest enemy, Richard A. Gabriel
The Resource Hannibal : the military biography of Rome's greatest enemy, Richard A. Gabriel
The item Hannibal : the military biography of Rome's greatest enemy, Richard A. Gabriel represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Multnomah County Library.
Gabriel, Richard A
The Romans' destruction of Carthage after the Third Punic War erased any Carthaginian historical record of Hannibal's life. What is known of him comes exclusively from Roman historians who had every interest in minimizing his success, exaggerating his failures, and disparaging his character. The charges leveled against Hannibal include greed, cruelty and atrocity, sexual indulgence, and even cannibalism. But even these sources were forced to grudgingly admit to Hannibal's military genius, if only to make their eventual victory over him appear greater. Yet there is no doubt that Hannibal was the greatest Carthaginian general of the Second Punic War. When he did not defeat them outright, he fought to a standstill the best generals Rome produced, and he sustained his army in the field for sixteen long years without mutiny or desertion. Hannibal was a first-rate tactician, only a somewhat lesser strategist, and the greatest enemy Rome ever faced. When he at last met defeat at the hands of the Roman general Scipio, it was against an experienced officer who had to strengthen and reconfigure the Roman legion and invent mobile tactics in order to succeed. Even so, Scipio's victory at Zama was against an army that was a shadow of its former self. The battle could easily have gone the other way. If it had, the history of the West would have been changed in ways that can only be imagined. In this publication, the author shows how Hannibal's genius nearly unseated the Roman Empire
Washington, D.C., Potomac Books, ©2011
A warrior's life
Hannibal's army
The origins of war
Hannibal's strategy
The invasion of Italy
Carthaginian Blitzkrieg
The Italian campaign
The end of Hannibal
Why Hannibal failed
Hannibal : the military biography of Rome's greatest enemy
the military biography of Rome's greatest enemy
Richard A. Gabriel
Carthage (Extinct city) -- History, Military
Hannibal, 247 B.C.-182 B.C. -- Military leadership
Hannibal, 247 B.C.-182 B.C
Punic War, 2nd, 218-201 B.C. -- Campaigns
Generals -- Tunisia | Carthage (Extinct city) -- Biography
Punic War, 2nd, 218-201 B.C.
Carthage (Extinct city)
Chronology -- A warrior's life -- Hannibal's army -- The origins of war -- Hannibal's strategy -- The invasion of Italy -- Carthaginian Blitzkrieg -- The Italian campaign -- The end of Hannibal -- Why Hannibal failed -- Epilogue
(hardcover : alk. paper)

 Data from Hannibal : the military biography of Rome's greatest enemy, Richard A. Gabriel - Multnomah County Library

Data Citation of the Item Hannibal : the military biography of Rome's greatest enemy, Richard A. Gabriel
http://link.multcolib.org/portal/Hannibal--the-military-biography-of-Romes/-f1XKptVlPo/
http://library.link/portal/Hannibal--the-military-biography-of-Romes/-f1XKptVlPo/

redpajama_set_name: RedPajamaCommonCrawl


text:
Del. Dance opens campaign office in Petersburg
Sep 5, 2009 at 12:01 AM Sep 10, 2014 at 12:34 PM
Top: A crowd in the front room of the campaign office of Del. Rosalyn Dance, D-63rd, listens to Jody Wagner speak. Wagner, the Democratic candidate for lieutenant governor, spoke at the opening of the campaign office Thursday, Sept. 3. The office is loca
Top: A crowd in the front room of the campaign office of Del. Rosalyn Dance, D-63rd, listens to Jody Wagner speak. Wagner, the Democratic candidate for lieutenant governor, spoke at the opening of the campaign office Thursday, Sept. 3. The office is located at 23. W. Old Street, the former Obama campaign office. The office will serve to distribute information on the Democratic gubernatorial candidates, as well. Right: Wagner addresses those attending the opening celebration.


A few months back online shopping was not a great idea for me. I tried it here and there, but never developed much linking for it. I had my reasons for it. Actually, I was more of a traditional shopper.
Then I heard people talking about these offers, discounts, coupons etc. I found that things are much cheaper online than at traditional retail.
This got me really interested!!!
Fast forward to this day, I am an online shopping addict now. And trust me, I am enjoying it. It took me a while to break away from traditional shopper's mindset. And I am happy that I did it. It has made my life a lot easier.
Now, I can explore multiple options, compare, and find the best price for anything I want to buy. Also, reading reviews and feedback from previous customers helps me arrive at a better buying decision.
Above all, there are deep discounts on almost everything!!!
The year 2018 was indeed a game-changing year for the Indian E-commerce industry.
This year Walmart acquired a 77% share in the Flipkart.
Battle of Giants- where Amazon and Walmart locked horns over the bigger slice of $20 billion E-com Both of them played to their strengths, introduced new categories, and offered deep discounts to expand their customer base. In the end, the customer won.
Govt. posing strict regulations on e-commerce business.
Ultimately all of this has uplifted Indian e-commerce by providing affordable and quality goods for customers. Also, it helped to create new skilled jobs and fresh opportunities for small suppliers, farmers, and entrepreneurs alongside. Online shoppers were in for a feast when they enjoyed biggest festive season bonanza more than once this particular year. With all these developments, E-commerce has been able to further solidify its position in the FMCG sector irrespective of authorities posing strict rules on e-commerce players.
E-commerce Growth: Also over the next 12 years, e-commerce is expected to have 8X growth from its current size.
E-commerce Contribution to FMCG: As per Nielson reports, E-commerce contribution to FMCG in 2018 is around 1.3 %. By the year 2030, it is expected to be 11 %.
The growth of Modern Trade against Traditional Trade: From the third quarter in 2016 to the third quarter of 2018, traditional trade grew at 2 percent while modern trade at 23 percent.
Festive Season Sale Spikes: In comparison to regular weeks the salary weeks witnessed 15-20 % higher sales in a given month as per the Nielsen reports. Also, the tactics adopted by modern trade retailers during festival days has favored the growth of the modern trade channel.
Rural Consumption on the Rise: Rural consumption is growing at a faster pace than urban with an index of 1.4X.
Small FMCG Manufacturers are Driving Growth: The top 50 FMCG companies contributed 60 % in terms of value, however, smaller manufacturers are driving the growth. Companies in the bracket of the top 101 to 300 contributed 11 % in terms of value. Tail-end companies beyond the top 300, the contribution was 21 %.
Although there are speculations in the market that new rules are set to spoil the e-commerce party, but experts believe that e-commerce is bound to flourish in coming years, even if regulatory bodies try to put reins on the E-com players.
The party has just begun for Indian consumers.


Ohm Srinivasan is an investment portfolio manager and co-heads the hedge fund research efforts within the Multi-Manager Investment Program (MMIP) based in Boston. With 18 years of industry experience, he is responsible for managing the MMIP hedge fund platform.
Prior to joining the firm in 2008, Ohm was vice president of investments for BattersbyCapital Management, where he was co-head of hedge fund research and a derivatives portfolio manager. His responsibilities included manager research, portfolio construction, risk management and hedge fund of funds development. He was also the portfolio manager of the systemic hedge book trading equity options and credit swaptionsto complement the portfolio of hedge funds.
Previously, Ohm was a senior trader at Cornerstone Trading for six years, where he managed multiple proprietary portfolios employing event-driven, volatility arbitrage, options market-making and quantitative equity market-neutral hedge fund strategies.
He earned a Bachelor of Science with a concentration in economics from the University of Michigan and holds the Chartered Financial Analyst designation.


FW moderates a discussion on M&A and investment in Latin America's natural resources sector between Alejandro D'Ambrosio, a partner at EY, Raúl Fernando Romero Fernández, a senior associate at Rodríguez Dávalos Asociados, and Werner Ahlers, a partner at Sullivan & Cromwell LLP.
FW: How would you characterise M&A and investment activity in the Latin American natural resources sector over the last 12-18 months? Which deals have caught your eye?
D'Ambrosio: During 2014, M&A transactions involving companies or assets which can be classified as natural resources decreased by approximately 21 percent compared to 2013. We identified approximately 110 M&A reported transactions involving natural resources in Latin America during 2014, and approximately 140 for 2013. We expect to have at least the same amount of unreported transactions every year, as small- and family-owned business are usually neither reported nor identified in the market. Though the natural resources sector suffered the impact of the strength of the US dollar, the slight deceleration of the China economy and the revolution of unconventional energy sources – namely shale oil & gas – M&A transactions in Latin America involving natural resources have remained fairly stable. Interest in these types of transactions is unlikely to decline from those levels seen in 2014. Last year in the region there were four M&A transactions with reported values higher than $1bn – two metal and mining transactions in Peru, one metal and mining deal in Chile and an oil & gas transaction in Brazil. During 2013 there were three transactions with reported values of $1bn and above; all three of those deals involved oil & gas assets in Peru, Colombia and Brazil.
Romero: The past year has seen an intense return of global M&A activity after four years of stagnant growth, and Latin America has been no exception. M&A activity in the natural resources sector of the region has been especially active in terms of volume. The past 12 months have seen interesting deals such as the one struck between an Argentinean firm and a foreign national oil company to develop the Vaca Muerta shale formation in Argentina. This deal is notable as it demonstrates a willingness to allow foreign participation in a strategic hydrocarbon area. Last year certain companies were very active in their M&A space, selling their participation in certain ventures while setting up new joint ventures to exploit new investment opportunities that will begin with the first public round of production sharing agreements in Mexico.
Ahlers: The variability in commodity prices, particularly oil prices, in the last year has clearly had an effect on dealmaking activity in the natural resources sector. Mining acquisitions have been more limited, with large international mining companies focusing more on optimising capital expenditure programs. Meanwhile, some small to midsize mining companies have stepped up deal-making by focusing on strategic acquisitions that capitalise on the low price environment. Examples of this are Lundin Mining's acquisition of gold assets in Ecuador from Kinross and its acquisition of other mining assets in Chile from Freeport. In the oil & gas sector, there does also appear to be some pull back by companies on expansion and capital expenditure programs in response to the drop in oil prices. However, while M&A activity in this sector will remain somewhat unpredictable from country to country in the region in the short-term, Repsol's recently announced acquisition of Talisman Energy proves that transformative deals are still possible. In addition, a number of key trends are likely to continue driving activity in the sector. The passage of Mexico's landmark energy reform, the discovery of unconventional gas resources throughout Latin America and a pent up backlog of investments in infrastructure in markets like Peru and Colombia are all likely to drive M&A activity. The increased interest of private equity firms and other financial investors may also drive some novel deals, such as CPPIB's acquisition of significant interests in Transportadora de Gas del Peru, Peru's largest transporter of gas and natural gas liquids in Peru. Dealmakers will also be keeping an eye out for what collateral effects the Petrobras investigations may have on deal activity in Brazil's pre-salt fields and the rest of its oil & gas industry.
FW: Are there any countries and sectors that appear to be particularly active at present? What factors are making them attractive to dealmakers?
Romero: Due to the boom of shale oil & gas in North America, and the opportunity it presents, all countries that have recognised the shale plays, such as Mexico, have the potential to attract the investment of firms and companies that have the experience and the technology required to exploit them. However, the global volatility of oil prices might affect investment decisions in the sector in the future and will help funnel them towards the natural gas industry. Due to the risks associated with venturing into new geographical locations, especially in an industry that is so extensively regulated as this one, collaboration with local strategic partners on investment schemes is vital, and so M&A activity will prove to be extremely important in the near future.
Ahlers: With the recent introduction of landmark energy reforms, there is obviously a great deal of interest in potential investment opportunities in Mexico's oil & gas sector. Although companies are still trying to understand the implementation of the new laws and regulations and accommodate to potentially shifting long-term oil price expectations, interest in the country's oil & gas – and, particularly in the short term, its related services sector – is expected to remain active as expectations for the positive long-term effects of the reforms remain high. Latin America's unconventional gas reserves and emerging role in the global liquefied natural gas (LNG) trade may also present new opportunities throughout the region. Demand for more diversified and cleaner-burning energy resources within the region is expected to fuel the development of renewables and additional regasification facilities throughout Latin America. This may, in turn, create opportunities for joint ventures and other investments in new and existing liquefaction terminals and LNG transportation infrastructure near or in Latin America, including Mexico, Peru and Colombia, and other existing and new LNG exporting countries.
D'Ambrosio: In terms of investor preferences, there were a number of attractive nations in Latin America, led by Mexico, Peru, Chile, Colombia and Brazil. The least attractive nations in the region at the moment are Venezuela and Argentina, however investor expectations may shift in the future given the presidential elections in Argentina during Q4 2015. Furthermore, the potential change in the business environment which may be brought on by the elections may well lead many foreign investors to evaluate the possibility of completing acquisitions in Argentina's natural resources sector. Investors may try to take advantage of the current low price of assets compared to other Latin American countries, before the election occurs. In terms of sectors, there are a number of differences, depending on the country in question. In Mexico, the oil & gas sector has been driven by recent changes in regulations, which have served to open the market to private investors. In the case of Peru, though there is interest in most natural resource areas, mining and the oil & gas sectors appear to be the stars. Mining for Chile and oil & gas in Colombia are the preferred sectors. With regard to Brazil, though it is still the most attractive location in the region for investors, the future evolution on transactions in the natural resources space is uncertain due to different variables. A country's economic and financial performance during 2015, the oil price and the impact of shale resources in the global market, among others, can all play a significant role. The growing interest in natural resources in Argentina has been based on undeveloped, unconventional resources in shale oil & gas in the Vaca Muerta reserves, low assets prices and small tickets compared to neighbouring countries, relatively undeveloped mining areas, and high productivity for agribusiness compared to other areas in the world.
Ahlers: Countries focused on private and foreign investment reform in Latin America, particularly those that have facilitated investment by pension fund managers, generally have been able to attract increased private equity investment. Nonetheless, the natural resources sector continues to be a sector that faces particular scrutiny from regulators and lawmakers that can pose certain obstacles or pitfalls investors should understand thoroughly. For example, in some countries we have seen unexpected changes in tax and royalty regimes, in addition to unpredictable permitting and environmental requirements, all of which have made it difficult for certain markets to strengthen – or turn around trends in underdevelopment in – the natural resource sector. On the other hand, jurisdictions that are able to address environmental and permitting regulations in a balanced, predictable way, and that are able to provide assurances of long term regulatory stability, will continue to see positive benefits from foreign investment.
D'Ambrosio: Though political and economic incentives and the regulatory environment are usually the first areas of analysis for foreign investors, in most situations those factors are balanced and analysed together with long terms expectations in these areas, the impact on expected rates of return and price for the assets, exposure to local or foreign markets, and countries' necessity to develop those sectors, which usually require incentives to invest, among other factors. Depending on aversions to risk from every type of investors, each of the these factors may have a positive impact on an investor's decision to invest, however there are limited occasions where it is difficult to find a buyer for a natural resource asset, no matter the Latin America country involved, at adequate, balanced conditions.
Romero: The stability of the global economy has certainly contributed to the growth of M&A activity not only in Latin America, but the whole world. Mexico's structural reforms, especially the energy reform, which allows private investment in a variety of activities that had been previously reserved for the state for decades, have definitely been a major factor behind current interest in the sector. As the regulatory climate becomes clearer with the issuing of regulations by newly appointed government bodies, it should serve to attract even more investment to the country.
FW: In your experience, how should foreign investors approach negotiations when identifying targets and closing deals in Latin America?
D'Ambrosio: Considering the changing and volatile economic, political and regulatory environment in Latin America, together with the volatility of commodities markets, it is critical for foreign investors to have an adequate understanding of current and expected conditions and the local culture before performing a complete risk assessment and a projection of an investment or acquisition. Obtaining different views from local advisers can be critical even for companies with a presence in Latin America, particularly if the firm's M&A or development team is based abroad. The involvement of local advisers is also critical in the second step of the investment analysis: due diligence, negotiation and closing.
Romero: Foreign investors should pay close attention to the identification of targets that can add value to their investments. It is important to identify the benefits and goals of an acquisition and to carry out the acquisition process with these factors in mind. Additionally, negotiation processes in Mexico require parties to have an open approach to the decision makers of target firms and parties should be willing to understand what their key interests are, as these can differ greatly from their own. Additionally, investors should take into account, while negotiating deals in Mexico, local practices as well as the wider legal and regulatory scheme, which may differ considerably from the applicable regimes in their countries.
Ahlers: Firms should work with sophisticated advisers that are not just deeply familiar with the target's market and jurisdiction, but with the sometimes unpredictable political and regulatory risk issues presented by investment in Latin America and the various ways of mitigating such risks that investors have successfully employed across the region. This can best be accomplished by working closely with both local and international advisers experienced in the jurisdiction, and across the region, to understand, in detail, the political and regulatory risks presented by the investment and transaction – regulatory uncertainty, foreign investment regimes, foreign exchange restrictions, and so on – and exploring thoroughly the foreign investment protections and other mechanisms to mitigate these risks. In addition, firms must conduct deep due diligence in key sensitive areas, including tax, labour, anti-corruption compliance and permitting in order to identify and allocate any lingering risks. Finally, companies should stick to their core principles in executing deals and avoid succumbing to arguments that things operate differently in the target's jurisdiction. Failure to do so may lead to the unintended assumption of risks, particularly with respect to compliance with general anti-corruption laws.
FW: Do you believe the due diligence performed by foreign acquirers is typically robust enough to properly manage and understand the key risks involved in these types of deals?
Romero: In carrying out due diligence, the proper hiring of local advisers and collaboration with those advisers certainly provides for a better and more rigorous result. In general, due diligence activities are thorough enough to deal with most risks, but it is always important to accept that the more robust the process is, the longer the acquisition will take. The timing of acquisitions can be an issue in taking advantage of key investment opportunities, such as bidding rounds, and investors must evaluate this trade-off when carrying out their M&A activities in Mexico. Moreover, investors should consider adjusting their due diligence processes in order for these to provide enough certainty in accordance to the practice and the way of doing business in Mexico, as well as to include any legal or regulatory risk that may arise from the activities performed by the companies in Mexico, whether these are affected by municipal, state or federal provisions.
Ahlers: While political risk has moderated in many countries in the region, investors should continue to monitor legal developments and ensure that they take full advantage of legal regimes for the protection of foreign investments. Understanding these risks, which can touch on core regulatory issues that could threaten a successful closing, is always the beginning of a thorough due diligence exercise. Clearly, for those investors interested in natural resources, concession regimes, permitting and environmental compliance should continue to be focal points of any diligence process. In addition, issues of labour, tax and anti-corruption compliance are always sensitive areas that should be a key focus of any transaction in the region.
D'Ambrosio: Utilising local resources for due diligence and risk assessments when carrying out a new investment or acquisition is critical. In Latin America, the changing environment, be it political, economic or regulatory, last minute updates as well as a clear understanding of the local situation is critical to having an accurate view of risks and mitigating factors which can save money and hedge future risks.
FW: How important is local knowledge when it comes to dealing with the regional challenges, policies and processes of investing in Latin America's natural resources sector? What are some of the common risks and pitfalls, and how can they be avoided?
Ahlers: For all foreign investors new to a country, or those returning to a country with a dynamic environment, the effective use of experienced international advisers familiar with techniques for addressing multijurisdictional issues and risks, and local counsel with an in depth understanding of specific jurisdictional challenges, is key to achieving deal objectives. Care should be taken to carefully select counsel for every deal to ensure the availability of the most up to date advice and deal technology. Money spent on experienced counsel can save hefty fees that may be incurred down the line to address issues that should otherwise have been identified at the outset of a deal.
D'Ambrosio: While local knowledge is critical in dealing with local and regional challenges, it is no less important to assemble a cooperative team to analyse an investment or acquisition involving resources from an investor who can clearly transmit investor strategy and culture. Teaming, ownership of the project, leadership and PMO, as well as local and technical skills, are key factors for a successful acquisition or investment in the region. Equally important is post-merger integration planning and execution and coordination between investment teams and assets management teams, which usually are different teams and sometimes have no or limited connections. Lack of understanding of local issues and culture, such as unsophisticated financial reporting systems and procedures, low quality of information, and related plans to solve or mitigate such risks, are common obstacles. Local transaction experience is key not only to identify specific risks factors but also to develop adequate solutions to eliminate or mitigate such risks, moving from identification to resolution.
Romero: Hiring adequate legal counsel and other local advisers is essential in tackling regional challenges, policies and processes. Local knowledge is necessary to carry out proper due diligence in the acquisition process, as these advisers have the experience and background to identify and evaluate the key risks involved. Projects in the natural resources sector can fail or be hindered by a lack of necessary governmental authorisations, or by failing to properly handle relations with other stakeholders involved in a project, as is the case with obtaining the necessary access rights. Local experience is also necessary to efficiently and successfully carry out investment projects in Mexico.
FW: What types of deals do you expect to see in the region's natural resources sector over the coming months? Is dealmaking set to increase, or are there barriers to progress?
D'Ambrosio: In Peru, we expect to see continued active interest from foreign investors in mining and metals and oil & gas. The current and expected short term environment should keep the country as one of the main regions for investment in natural resources, as well as infrastructure projects. Although Mexico is one of the region's best performers – not only because of the recent deregulation of its energy sector, its proximity to the US, its size compared to other Latin American countries, and its current economic and financial performance – the development of its oil & gas sector will be highly dependent on oil & gas prices in the coming years. Most of the international oil & gas players have investment plans for Mexico but break even points have been challenged by the drop in market prices. In any case, Mexico will remain one of the most attractive countries to invest in Latin America. Chile will likely continue to be attractive for investments. The challenge for investors is that assets prices are high compared to other countries. Based on Colombia's current and expected financial and economic stability, and its need for foreign investment and infrastructure development, we should expect to see continued interest there too. The challenge will be assets prices in the future, which have increased in recent months and may push down expected investor returns. Brazil will probably see a slight decrease in the number of deals in the coming months. Also, deal sizes are likely to decrease based on a number of factors, including the country's economic and financial performance in 2015. Yet the majority of transactions in Latin America will take place in Brazil. Argentina should continue to see a volatile financial, political and regulatory environment, at least until the primary presidential elections in August. After the elections, a clearer picture of the future business environment should emerge. Low assets prices will likely persist, at least through 2015, so opportunities for acquisitions and investments should remain throughout the year. We expect to see active acquisition activity based on opportunity prices to be led by investors with a risk aversion, who will probably make good returns if the political scenario changes after the October presidential elections.
Romero: The new legal framework definitely aims to promote growth in dealmaking in Mexico's oil & gas sector. Growth may come from many joint venture projects between foreign investors and local companies with experience in the sector, as well as substantial acquisitions by certain companies that are looking to diversify their activities globally. It is also possible that firms based in Mexico may carry out additional acquisitions or strategic alliances in other regions, as certain Mexican companies in the mining sector have been doing recently.
Ahlers: We expect the natural resource sector to be active in the coming months as companies begin to understand the short, medium and long-term effects of lower commodity prices. Opportunistic and strategic transactions are likely to play a key role in the sector with stronger and more resilient companies looking to consolidate their position in their corresponding markets.
FW: What final advice can you offer to foreign acquirers looking to pursue M&A and investment opportunities in this sector?
Ahlers: A company should be clear about its objectives and risk tolerance when doing a deal and resist the temptation to abandon approaches and deal technology that have proven to be successful outside of the region. Different jurisdictions often present unique challenges in the context of a deal but the most satisfied clients are those that stick to the core principles that have guided them in other transactions while focusing on creative but clean execution with experienced counsel and using proven deal practices that are informed by, and adjusted to, local conditions.
D'Ambrosio: There is a wide range of opportunities to invest in natural resources in Latin America, with a wide range of options in terms of sectors, such as mining, oil & gas, agribusiness, renewable energy, paper & forest, among others. Risks and expected returns within this developing region have the potential to increase production and trading of natural resources. The region has no conflict hypothesis, either between countries or in terms of internal disruptions. The key is to find appropriate opportunities and properly identify and measure risks and related solutions with local and foreign support.
Romero: Although the potential for high value M&A investments in Mexico's natural resources market, especially in the oil & gas sector, is undeniable, investors should take the volatility of international oil prices into account. Furthermore, they should bear in mind the inherent currency exchange risks and the reality that acquisition processes can entail transaction costs that exceed estimates. Moreover, a full understanding of the applicable tax regime and regulatory framework is required, particularly in the oil & gas industry. A thorough due diligence process is therefore essential to foresee and mitigate as many challenges as possible.
Alejandro D'Ambrosio is a partner at Ernst & Young, based in Buenos Aires, Argentina. He provides professional advice in transactions including M&A lead advice on the buy and sell side, business valuations, financial, accounting, tax and social security due diligence, and tax structuring involving assets in all Latin America countries. Mr D'Ambrosio has extensive experience in natural resources transactions, in particular related to oil & gas, mining, agriculture and different types of power generation, among other industries. He can be contacted on +54 11 4318 1549 or by email: alejandro.dambrosio@ar.ey.com.
Raúl Fernando Romero Fernández is a senior associate at Rodríguez Dávalos Asociados. He has participated in the negotiation of contracts and handling of regulated activities in several projects related to oil & gas E&P, power generation projects, distribution, storage and transportation of liquefied petroleum and natural gas, including one of the most important natural gas transportation pipeline projects in Mexico and the first private ethane transportation pipeline in Mexico. He has negotiated and executed several NAESB agreements and negotiated Mexico's first Natural Gas Operative SWAP. He can be contacted on +52 (55) 5202 04 05 or by email: rromero@rdabogados.com.mx.
Werner Ahlers is a partner in the M&A, Project Development and Finance and Corporate and Finance Groups at Sullivan & Cromwell. His experience includes a wide range of cross-border mergers and acquisitions, corporate, project and asset-backed financings and capital market transactions. Mr Ahlers is chair of the Inter-American Affairs Committee of the New York City Bar Association and a term member of the Council on Foreign Relations. He can be contacted on +1 (212) 558 4000 or by email: ahlersw@sullcrom.com.


Use a vegetable shredder to slice the cucumber into long thin pieces. Place a strip of cucumber on a clean chopping board and arrange a little of each of the shredded carrot, cucumber and cabbage. Add a few alfalfa sprouts and roll up tightly into a sushi roll. Sprinkle some sesame seeds over.
Do the same with the rest of the cucumber slices and serve with either one of the dipping sauces.