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Structure is seen on the largest measurable scales (e.g. de Lapparent. Cellar IIuchra 1986).	Structure is seen on the largest measurable scales (e.g. de Lapparent, Gellar Huchra 1986).
To determine whether the effects. of clustering are significant we constructed a radial density profile. as shown in Fig.	To determine whether the effects of clustering are significant we constructed a radial density profile, as shown in Fig.
9.	9.
This was derived from those bins for which more than 100 galaxies are seen over the whole range from 0.015<z«0.12 (Le. 19.75«Al«18.75 and 21.1«pi.< 22.6).	This was derived from those bins for which more than 100 galaxies are seen over the whole range from $0.015<z<0.12$ (i.e. $-19.75 < M < -18.75$ and $21.1 < \mu_e < 22.6$ ).
Those galaxies which are brighter cannot be seen at 2<0.015 due to the bright magnitude eut atom=14.00 and would therefore bias the number density towards the bright. end.	Those galaxies which are brighter cannot be seen at $z < 0.015$ due to the bright magnitude cut at $m = 14.00$ and would therefore bias the number density towards the bright end.
For these hieh-visibility galaxies we calculated their number-density (0) in equal volume intervals of 5.010* Alpe?. from +=0.0185 loz— 02.	For these high-visibility galaxies we calculated their number-density $\phi$ ) in equal volume intervals of $5.0\,\times 10^{3}$ $^{3}$, from $z=0.0185$ to $z=0.12$ .
Eο.	Fig.
9 shows that clustering is severe with what appears to be a large local void around +=0.04 and walls ab 2=0.06 and z=0.11.	9 shows that clustering is severe with what appears to be a large local void around $z=0.04$ and walls at $z=0.06$ and $z=0.11$.
The ESO Slice Project. (1991) survey (Zucca et al.	The ESO Slice Project (ESP) survey (Zucca et al.
LOOT) whose line-ol-sight. (RA ~ 00h. 09 40) is just outside the 2dE SGP region. measures an under-density at 140A *\Ipe (27 0.045) and an over-density at z&Ol.	1997) whose line-of-sight (RA $\sim 00$ h, $\delta \sim -40$ ) is just outside the 2dF SGP region, measures an under-density at $\leq 140h^{-1}$ Mpc $z \approx 0.045$ ) and an over-density at $z \approx 0.1$.
The structure that they see. closely resembles the structure that we see.	The structure that they see closely resembles the structure that we see.
Ao reliable measure of the BBD needs to correct for this clustering-bias.	A reliable measure of the BBD needs to correct for this clustering-bias.
Here we adopt a strategy which implicitly assumes. firstly. that clustering is independent of either. AL or yr. ancl secondly. that evolutionary processes to z — 0.12 are negligible.	Here we adopt a strategy which implicitly assumes, firstly, that clustering is independent of either $M$ or $\mu$, and secondly, that evolutionary processes to z = 0.12 are negligible.
On the basis of these caveats we constructed a weighting matrix. WAL).	On the basis of these caveats we constructed a weighting matrix, $W(M,\mu)$.
This was determined. from the hieh-visibility galaxies by taking the ratio of the number-cdensity of high-visibility galaxies over the full redshift range divided bv the number-densitv of high-visibilitv galaxies over the redshift range of cach bin. Le: This weighting matrix is shown in Fig.	This was determined from the high-visibility galaxies by taking the ratio of the number-density of high-visibility galaxies over the full redshift range divided by the number-density of high-visibility galaxies over the redshift range of each bin, i.e.: This weighting matrix is shown in Fig.
10.	10.
Theimplication is that the number-cdensity of low-Iuminosity systems will be amplified by almost a factor of 1.5. to correct	Theimplication is that the number-density of low-luminosity systems will be amplified by almost a factor of 1.5, to correct
to this equilibrium are (Frieman&Rotenbere1960:Chanmueam1979): SÉ ciptve Fu£n-o(4) Where F((£)) = £c grad))P) + Phi, ++ ++ — V)£)).	to this equilibrium are \citep{RevModPhys.32.898,1979MNRAS.187..769C}: ^2 + 2 i - ) = 0, Where ) = + )P) + _g + + - ).
The perturbation of (he magnetic field is b=Vx(€xDo).	The perturbation of the magnetic field is $\bb = \curl(\xxi \times \BO) $.
For incompressible (V.£=0) perturbations. eq. (9)	For incompressible $\diver\xxi = 0$ ) perturbations, eq. )
) can be written as (wo scalar equations: (Pum 1 - va	can be written as two scalar equations: ^2 - ^2) _T = _T ^2 - (r _r) = - 2 ) _r + ( _T
PDAL is supported by a graut from the French. Agence Nationale de la Recherche (ANR).	PDM is supported by a grant from the French Agence Nationale de la Recherche (ANR).
These simulatious are available as part of the CGalMer simulation data base ).	These simulations are available as part of the GalMer simulation data base ).
The authors wish to thank the referee for their constructive aud helpful comments aud A. Pipiuo for a critical reading of an early version of this manuscript aud helpful suggestions.	The authors wish to thank the referee for their constructive and helpful comments and A. Pipino for a critical reading of an early version of this manuscript and helpful suggestions.
The authors wish to thank the referee for their constructive aud helpful comments aud A. Pipiuo for a critical reading of an early version of this manuscript aud helpful suggestions.O	The authors wish to thank the referee for their constructive and helpful comments and A. Pipino for a critical reading of an early version of this manuscript and helpful suggestions.
The authors wish to thank the referee for their constructive aud helpful comments aud A. Pipiuo for a critical reading of an early version of this manuscript aud helpful suggestions.OO	The authors wish to thank the referee for their constructive and helpful comments and A. Pipino for a critical reading of an early version of this manuscript and helpful suggestions.
where Ay and D, is (he power spectrum of signal @ and 5 respectively.	where $A_k$ and $B_k$ is the power spectrum of signal $a$ and $b$ respectively.
The decreasing; of the uncorrelated signal is inversely proportional to the square root of the number of random walk. and it can be further decreased by 1/V/L.N. with binning L=.N multipole numbers and averaging from NV sets of NPS.	The decreasing of the uncorrelated signal is inversely proportional to the square root of the number of random walk, and it can be further decreased by $1/\sqrt{LN}$ with binning $L\equiv \Delta \l$ multipole numbers and averaging from $N$ sets of XPS.
Therefore XPS is useful in reducing uncorrelated signals while preserving the correlated one. which is employed by WMADP to extract CMD spectrum bv crossing the foreground-eleaned maps from Dillerencing Assemblies (DA) 2003.2007;Nortaοἱal.2009;Larsonet 2011)..	Therefore XPS is useful in reducing uncorrelated signals while preserving the correlated one, which is employed by WMAP to extract CMB spectrum by crossing the foreground-cleaned maps from Differencing Assemblies (DA) \citep{wmap1yrpower,wmap3yrtem,wmap5yrpower,wmap7yrpower}.
For patches on V and W band map with low variances. hence satisfied Eq.(5)). we can write n=αχ+nm and ap=UR-+nm. where ας is the Fourier mode of CAIB. hy. and 9i are that of V and. Wo band beam. ancl ny and n, that of V and W band noise. respectively,	For patches on V and W band map with low variances, hence satisfied \ref{cl}) ), we can write $a_{\bi k}^{\rm V}=a_{\bi k}^{\rm c}b_{\bi k}^{\rm v}+ n^{\rm v}_{\bi k}$ and $a_{\bi k}^{\rm W}=a_{\bi k}^{\rm c}b_{\bi k}^{\rm w}+ n^{\rm w}_{\bi k}$, where $a_{\bi k}^{\rm c}$ is the Fourier mode of CMB, $b_{\bi k}^{\rm v}$ and $ b_{\bi k}^{\rm w}$ are that of V and W band beam, and $n^{\rm v}_{\bi k}$ and $n^{\rm w}_{\bi k}$ that of V and W band noise, respectively.
In APS the correlated. signal (erg,Pohr) is What we look lor whereas those uncorrelated terms between CAIB ancl noises Ay. A, and between noises X," shall be decreased according to Eq.(7)).	In XPS the correlated signal $\langle\|a^{\rm c}_{\bi k}\|^2 b_{\bi k}^{\rm v} b_{\bi k}^{\rm w} \rangle$ is what we look for whereas those uncorrelated terms between CMB and noises $\xk^{\rm cw}$, $\xk^{\rm cv}$ and between noises $\xk^{\rm vw}$ shall be decreased according to \ref{xpsuncorr}) ).
The window functions of the WAIAP DA maps are directly measured [rom Jupiter (Pageοἱal.2003:Lllet2009) and are available at the official website?.	The window functions of the WMAP DA maps are directly measured from Jupiter \citep{wmap1yrbeam,wmap5yrbeam} and are available at the official website.
. The frequency band maps. however. are combined from the DA maps. so the corresponding window functions do not exist.	The frequency band maps, however, are combined from the DA maps, so the corresponding window functions do not exist.
Note that the window functions of the DA maps even at the same [requency band have different profiles. particularly for the W [requeney. bod.	Note that the window functions of the DA maps even at the same frequency band have different profiles, particularly for the W frequency band.
It is (hen demonstrated in Chiang&Chen(2011) that the window functions of the frequency band maps can be estimated [rom bright point sources ancl itis shown that the window function of the W band map takes the form of that of WI DA. whereas that of V band takes that of VI or V2 DÀ.	It is then demonstrated in \citet{xps} that the window functions of the frequency band maps can be estimated from bright point sources and it is shown that the window function of the W band map takes the form of that of W1 DA, whereas that of V band takes that of V1 or V2 DA.
The simplest inflation theory predicts the CAIB anisotropies. amplified from. quantum fluctuations. constitute a Gaussian random field (GRE)	The simplest inflation theory predicts the CMB anisotropies, amplified from quantum fluctuations, constitute a Gaussian random field (GRF)
Most of the following speculations are based on the results reported in section 7 where the accretion rate of BLRG and Sevlerts are compared.	Most of the following speculations are based on the results reported in section \ref{sec:mass} where the accretion rate of BLRG and Seyferts are compared.
We are aware that our sample is small and far [rom to be complete.	We are aware that our sample is small and far from to be complete.
ILowever. we note that (he average accretion rate obtained in this work for BLRG is consistent with what obtained by Marchesiniοἱal.(2004)... using a larger sample.	However, we note that the average accretion rate obtained in this work for BLRG is consistent with what obtained by \citet{mar04}, using a larger sample.
We also computed. as a further check. the average accretion rate of 17 Sevlert 1 galaxies reported in the AGN compilation by Woo&Urry(2002).. for which it was possible to obtain the masses via reverberation mapping method.	We also computed, as a further check, the average accretion rate of 17 Seyfert 1 galaxies reported in the AGN compilation by \citet{woo02}, for which it was possible to obtain the masses via reverberation mapping method.