We present the mid-infrared (MIR) luminosity function (LF) of local (z < 0.3) star-forming (SF) galaxies in the North Ecliptic Pole (NEP) field. This work is based on the NEP-Wide point source catalogue and the spectroscopic redshift (z) data for  1700 galaxies obtained by the optical follow-up survey with MMT/Hectospec and WIYN/Hydra. The AKARI's continuous 2 - 24 μm coverage and the spectroscopic redshifts enable us to determine the spectral energy distribution (SED) in the mid-infrared and derive the luminosity functions of galaxies. Our 8 μm LF finds good agreements with the results from SWIRE field over the wide luminosity range, while showing signicant difference from the NOAO deep data in the faint end. The comparison with higher-z sample shows significant luminosity evolution from z > 0.3 to local universe. 12 μm LF also shows a clear indication of luminosity evolution.

Quasars are among the farthest and brightest objects known in the universe. Because quasars are mostly observed in the redshift range between 1 and 3, they can be used to study large scale structure in the universe, and its evolution over the past billion years. An important issue is the evolution of the quasar luminosity function, which has been investigated for relative small samples of the 2QZ catalog. Here we extend the study to 3 quasar samples, the most recent data of the Milliquas, Master and 2QZ quasar catalogs to determine the luminosity function of quasars and its evolution, using the Standard cosmological ΛCDM model with ΩΛ = 0.73, ΩM = 0.27, and H0 = 70kms-1Mpc-1. For the purpose of this analysis we initially used 0.25-mag bins and approximately 0.180-redshift bins, then calculated the comoving distance and comoving volume for each bin of redshift and calculated the number of objects in each bin per unit volume, in order to find the number density per absolute magnitude bin. Our analysis on the basis of these new and much more complete datasets is largely in agreement with earlier studies of the luminosity evolution of quasars.

We present the 18μm luminosity function (LF) of galaxies at 0.006 < z < 0.8 (the average redshift is ~ 0.04) using the AKARI mid-infrared All-Sky Survey catalogue. We have selected 243 galaxies at 18μm from the Sloan Digital Sky Survey (SDSS) spectroscopic region. These galaxies then have been classified into five types; Seyfert 1 galaxies (Sy1, including quasars), Seyfert 2 galaxies (Sy2), low ionization narrow emission line galaxies (LINER), galaxies that are likely to contain both star formation and Active Galactic Nuclei (AGN) activities (composites), and star forming galaxies (SF) using optical emission lines such as the line width of H α or the emission line ratios of [OIII]/ Hβ and [NII]/ Hα . As a result of constructing the LF of Sy1 and Sy2, we found the following results; (i) the number density ratio of Sy2 to Sy1 is 1.64±0.37 , larger than the results obtained from optical LF and (ii) the fraction of Sy2 in the entire AGN population may decrease with 18μm luminosity. These results suggest that most of the AGNs in the local universe are obscured by dust and the torus structure probably depends on the mid-infrared luminosity.

The luminosity function (LF) and present day mass function(PDMF) for main sequence (MS) stars in the Praesepe and Hyades clusters are derived, showing the Wielen Dip which occurs at Mv = 9m in the LF. This dip is about 2 mag fainter than the case for the Pleiades cluster whose Wielen Dip position is consistent with that for the solar neighborhood field stars. The Wielen Dips of these clusters are reproduced by using a bimodal initial mass function (IMF).

The bright part of the halo luminosity function is derived from a sample of the 233 NLTT propermotion stars, which are selected by the 220 km/ see of cutoff velocity in transverse to rid the contamination by the disk stars and corrected for the stars omitted in the sample by the selection criterion. It is limited to the absolute magnitude range of Mv=4-8, but is based on the largest sample of halo stars up to now. This luminosity function provides a number density of 2.3 · 10-5pc-3 and a mass density of 2.3 · 10-5pc-3 for 4 < Mv < 8 in the solar neighborhood. These are not sufficient for disk stability. The kinematics of the sample stars are < U > = - 7 km/sec, < V > = - 228 km/sec, and < W > = -8 km/sec with (σu,σv,σw) = (192, 84, 94) km/sec. The average metallicity of them is [Fe/H] = - 1.7±0.8. These are typical values for halo stars which are selected by the high cutoff velocity. We reanalyze the luminosity function for a sample of 57 LHS proper-motion stars. The newly derived luminosity function is consistent with the one derived from the NLTT halo stars, but gives a somewhat smaller number density for the absolute magnitude range covered by the LF from NLTT stars. The luminosity function based on the LHS stars seems to have a dip in the magnitude range corresponding to the Wielen Dip, but it also seems to have some fluctuations due to a small number of sample stars.

In the best observed Pleiades cluster, the luminosity function(LF) and mass function(MF) for main sequence(MS) stars extended to Mv ≈ 15.5(V≈21) are very similar to the initial luminosity function(ILF) and initial mass function(IMF) for field stars in the solar neighborhood showing a bump at log m≃-0.05 and a dip at log m ≃ -0.12. This dip is equivalent to the Wielen dip appearing in the LF for the field stars. The occurence of these bump and dip is independent of adopted mass-luminosity relation(MLR) . and their characteristics could be explained by a time-dependent bimodal IMF. The model with this IMF gives a total cluster mass of ~700M⊙, ~25 brown dwarfs and ~3 white dwarfs if the upper mass limit of progenitor of white dwarf is greater than 4.5M⊙. The cluster age on the basis of LF for brightest stars is given by ~ 8×107yr and all stars in the cluster lie along the single age sequence in the C-M diagram without showing a large dispersion from the sequence.

Disk stellar luminosity function has been derived with stars in the Lowell Proper Motion Survey which contains about 9000 stars with μ ≥ 0 " .27 of arc/yr, $8\;<\;m_{pg}\;<\;17$ and with bright stars in the Smithsonian Astrophysical Observatory (SAO) Star Catalogue, Luminosity function has been obtained with stars within 20 pc by Luyten's mean absolute magnitudes method using Reduced Proper Motion Diagram to select disk stars. Magnitudes and colors, in the SAO Star Catalogue as well as in the Lowell Proper Motion Survey have been transformed to the UBV system from the published UBV data. It has been found that stars which have higher proper motion than the original limit of the proper motion survey are missed, when the relation between the absolute magnitude and reduced proper motion is applied to sample stars without considering the dispersion in magnitude. Correction factors for missing stars have been estimated according to their limits of proper motion which are dependent on the absolute magnitude. Resulting luminosity function shows Wielen's dip at M B ∼ 10 , and systematic enhancement of stars on the average of about Δ log Φ ( M B ) ∼ 0.2 compared with Luyten's luminosity function.

We have derived the luminosity function for subdwarfs on the basis of the proper motion data in LHS Catalogue, utilizing the reduced proper motion diagram for the selection of sub dwarfs and the hybrid method combining the mean absolute magnitude method and V/ V m method to estimate the distance and density of subdwarfs. The luminosity function found here is almost flat, showing a very slow increase up to M V = 9 or M B = 10 , and the overall halo density is larger than those derived by Schmidt (1975), Chiu (1980), Reid (1984), Lee (1985), and Dawson (1986), but smaller than that by Eggen (1983). Comparison with 1/100 of disk stellar luminosity function implies that no conclusive dip in the halo luminosity function is found.