(Abridged) We have derived detailed R band luminosity profiles and structural parameters for a total of 430 brightest cluster galaxies (BCGs), down to a limiting surface brightness of 24.5 mag/arcsec^2. Light profiles were initially fitted with a Ser
sics R^(1/n) model, but we found that 205 (~48) BCGs require a double component model to accurately match their light profiles. The best fit for these 205 galaxies is an inner Sersic model, with indices n~1-7, plus an outer exponential component. Thus, we establish the existence of two categories of the BCGs luminosity profiles: single and double component profiles. We found that double profile BCGs are brighter ~0.2 mag than single profile BCG. In fact, the Kolmogorov-Smirnov test applied to these subsamples indicates that they have different total magnitude distributions, with mean values M_R=-23.8 +/- 0.6 mag for single profile BCGs and M_R=-24.0 +/- 0.5 mag for double profile BCGs. We find that partial luminosities for both subsamples are indistinguishable up to r = 15 kpc, while for r > 20 kpc the luminosities we obtain are on average 0.2 mag brighter for double profile BCGs. This result indicates that extra-light for double profile BCGs does not come from the inner region but from the outer regions of these galaxies. The best fit slope of the Kormendy relation for the whole sample is a = 3.13 +/- 0.04$. However, when fitted separately, single and double profile BCGs show different slopes: a_(single) = 3.29 +/- 0.06 and a_(double)= 2.79 +/- 0.08. On the other hand, we did not find differences between these two BCGs categories when we compared global cluster properties such as the BCG-projected position relative to the cluster X-ray center emission, X-ray luminosity, or BCG orientation with respect to the cluster position angle.
We define a logical framework with singleton types and one universe of small types. We give the semantics using a PER model; it is used for constructing a normalisation-by-evaluation algorithm. We prove completeness and soundness of the algorithm; an
d get as a corollary the injectivity of type constructors. Then we give the definition of a correct and complete type-checking algorithm for terms in normal form. We extend the results to proof-irrelevant propositions.
Self-dual codes over $Z_2timesZ_4$ are subgroups of $Z_2^alpha timesZ_4^beta$ that are equal to their orthogonal under an inner-product that relates to the binary Hamming scheme. Three types of self-dual codes are defined. For each type, the possible
values $alpha,beta$ such that there exist a code $Csubseteq Z_2^alpha timesZ_4^beta$ are established. Moreover, the construction of a $add$-linear code for each type and possible pair $(alpha,beta)$ is given. Finally, the standard techniques of invariant theory are applied to describe the weight enumerators for each type.
Let C be an additive subgroup of $Z_{2k}^n$ for any $kgeq 1$. We define a Gray map $Phi:Z_{2k}^n longrightarrow Z_2^{kn}$ such that $Phi(codi)$ is a binary propelinear code and, hence, a Hamming-compatible group code. Moreover, $Phi$ is the unique Gr
ay map such that $Phi(C)$ is Hamming-compatible group code. Using this Gray map we discuss about the nonexistence of 1-perfect binary mixed group code.
A key symmetry of classical $p$-branes is invariance under worldvolume diffeomorphisms. Under the assumption that the worldvolume, at fixed values of the time, is a compact, quantisable Kahler manifold, we prove that the Lie algebra of volume-preserv
ing diffeomorphisms of the worldvolume can be approximated by $su(n)$, for $ntoinfty$. We also prove, under the same assumptions regarding the worldvolume at fixed time, that classical Nambu brackets on the worldvolume are quantised by the multibrackets corresponding to cocycles in the cohomology of the Lie algebra $su(n)$.
Published galaxy power spectra from the 2dFGRS and SDSS are not in good agreement. We revisit this issue by analyzing both the 2dFGRS and SDSS DR5 catalogues using essentially identical techniques. We confirm that the 2dFGRS exhibits relatively more
large scale power than the SDSS, or, equivalently, SDSS has more small scale power. We demonstrate that this difference is due to the r-band selected SDSS catalogue being dominated by more strongly clustered red galaxies, which have a stronger scale dependent bias. The power spectra of galaxies of the same rest frame colours from the two surveys match well. If not accounted for, the difference between the SDSS and 2dFGRS power spectra causes a bias in the obtained constraints on cosmological parameters which is larger than the uncertainty with which they are determined. We also found that the correction developed by Cole et al.(2005) to model the distortion in the shape of the power spectrum due to non-linear evolution and scale dependent bias is not able to reconcile the constraints obtained from the 2dFGRS and SDSS power spectra. Intriguingly, the model is able to describe the differences between the 2dFGRS and the much more strongly clustered LRG sample, which exhibits greater nonlinearities. This shows that more work is needed to understand the relation between the galaxy power spectrum and the linear perturbation theory prediction for the power spectrum of matter fluctuations. It is therefore important to accurately model these effects to get precise estimates of cosmological parameters from these power spectra and from future galaxy surveys like Pan-STARRS, or the Dark Energy Survey, which will use selection criteria similar to the one of SDSS.
