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The aim of this study is to search for quasi-periodical structures atmoderate cosmological redshifts $z \la 0.5 $. We mainly use the SDSS DR7 dataon the luminous red galaxies (LRGs) with redshifts $0.16 \leq z \leq 0.47$. Atfirst, we analyze features (peaks) in the power spectra of radial (shell-like)distributions using separate angular sectors in the sky and calculate the powerspectra within each sector. As a result, we found some signs of a large-scaleanisotropic quasi-periodic structure detectable through 6 sectors out of atotal of 144 sectors. These sectors are distinguished by large amplitudes ofdominant peaks in their radial power spectra at wavenumbers $k$ within a narrowinterval of $0.05 < k < 0.07$~h~Mpc$^{-1}$. Then, passing from a sphericalcoordinate system to a Cartesian one, we found a special direction such thatthe total distribution of LRG projections on it contains a significant($\ga$5$\sigma$) quasi-periodical component. We assume that we are dealing witha signature of a quasi-regular structure with a characteristic scale $116 \pm10$~h$^{-1}$~Mpc. Our assumption is confirmed by a preliminary analysis of theSDSS DR12 data.

Traces of Anisotropic Quasi-Regular Structure in the SDSS Data