Invariant subspaces with no generator and a problem of H. Helson

In the almost periodic context, any $H_0^2-$space cannot be generated by one of its elements. Together with cocycle argument, this derives that there exist all kinds of invariant subspaces without single generator, from which we can answer some questions on invariant subspace theory.Comment: 19 page

Cosmic Star Formation Activity at z=2.2 Probed by H-alpha Emission Line Galaxies

We present a pilot narrow-band survey of H-alpha emitters at z=2.2 in the Great Observatories Origins Deep Survey North (GOODS-N) field with MOIRCS instrument on the Subaru telescope. The survey reached a 3 sigma limiting magnitude of 23.6 (NB209) which corresponds to a 3 sigma limiting line flux of 2.5 x 10^-17 erg s^-1 cm^-2 over a 56 arcmnin^2 contiguous area (excluding a shallower area). From this survey, we have identified 11 H-alpha emitters and one AGN at z=2.2 on the basis of narrow-band excesses and photometric redshifts. We obtained spectra for seven new objects among them, including one AGN, and an emission line above 3 sigma is detected from all of them. We have estimated star formation rates (SFR) and stellar masses (M_star) for individual galaxies. The average SFR and M_star is 27.8M_solar yr^-1 and 4.0 x 10^10M_solar, respectivly. Their specific star formation rates are inversely correlated with their stellar masses. Fitting to a Schechter function yields the H-alpha luminosity function with log L = 42.82, log phi = -2.78 and alpha = -1.37. The average star formation rate density in the survey volume is estimated to be 0.31M_solar yr^-1Mpc^-3 according to the Kennicutt relation between H-alpha luminosity and star formation rate. We compare our H-alpha emitters at z=2.2 in GOODS-N with narrow-band line emitters in other field and clusters to see their time evolution and environmental dependence. We find that the star formation activity is reduced rapidly from z=2.5 to z=0.8 in the cluster environment, while it is only moderately changed in the field environment. This result suggests that the timescale of galaxy formation is different among different environments, and the star forming activities in high density regions eventually overtake those in lower density regions as a consequence of "galaxy formation bias" at high redshifts.Comment: Accepted for publication in PASJ Subaru Special Issue, 11 pages, 10 figure

A massive disk galaxy at z>3 along the sightline of QSO 1508+5714

We have obtained deep images in the BVRIJHKs bands of the field centered on QSO 1508+5714 (z_{em} =4.28) with the Suprime camera, FOCAS and MOIRCS cameras on Subaru telescope. We report here the detection of a B-dropout galaxy, which is 3\secpoint 5 north-west of the QSO sightline. A photometric redshift analysis is presented to complement the color selection. Given the photometric properties of this object ($M = -22.2$, making $L\approx 3 L^{\ast}$, if placed at its photometric redshift $z\sim 3.5$), as well as the S$\acute{e}$rsic index ($n \sim 1$) derived from a 2-D imaging decomposition of the HST WFPC2 image taken in the $I_{F814}$ filter, the identified system is consistent with a massive disk galaxy at z>3. If confirmed, it would be one of the most distant massive disk galaxies known so far.Comment: 12 pages, 6 figures, accepted by PASJ, Vol.61/No.5, 200

Private Provision of Public Goods between Families

We consider a two-stage voluntary provision model where individuals in a family contribute to a pure public good and/or a household public good, and, at the same time, the parent makes private transfers to her child within the same family. We show not only that Warr’s neutrality holds regardless of the different timings of parent-to-child transfers, but also that there is a continuum of Nash equilibria in the sense that individuals’ contributions and parental transfers are indeterminate, although the allocation of each’s private consumption and total public good provision is uniquely determined. We further show that, even in the presence of impure altruism or productivity difference in supplying public goods, neutrality and uniqueness of the equilibrium allocation may persist.