Dual formulation of the utility maximization problem: the case of nonsmooth utility

We study the dual formulation of the utility maximization problem in incomplete markets when the utility function is finitely valued on the whole real line. We extend the existing results in this literature in two directions. First, we allow for nonsmooth utility functions, so as to include the shortfall minimization problems in our framework. Second, we allow for the presence of some given liability or a random endowment. In particular, these results provide a dual formulation of the utility indifference valuation rule

Deepest Near-IR Surface Photometry of Galaxies in the Local Sphere of Influence

We present near-IR, deep (4 mag deeper than 2MASS) imaging of 56 Local Volume galaxies. Global parameters such as total magnitudes and stellar masses have been derived and the new near-IR data combined with existing 21cm and optical B-band data. We present multiwavelength relations such as the HI mass-to-light ratio and investigate the maximum total baryonic mass a galaxy can have.Comment: 4 pages, 3 figures, To be published in the proceedings of "Galaxies in the Local Volume", ed. B. Koribalski, H. Jerje

Nuclear-spin relaxation of 207^{207}Pb in ferroelectric powders

Motivated by a recent proposal by O. P. Sushkov and co-workers to search for a P,T-violating Schiff moment of the $^{207}$Pb nucleus in a ferroelectric solid, we have carried out a high-field nuclear magnetic resonance study of the longitudinal and transverse spin relaxation of the lead nuclei from room temperature down to 10 K for powder samples of lead titanate (PT), lead zirconium titanate (PZT), and a PT monocrystal. For all powder samples and independently of temperature, transverse relaxation times were found to be $T_2\approx 1.5$ms, while the longitudinal relaxation times exhibited a temperature dependence, with $T_1$ of over an hour at the lowest temperatures, decreasing to $T_1\approx 7$s at room temperature. At high temperatures, the observed behavior is consistent with a two-phonon Raman process, while in the low temperature limit, the relaxation appears to be dominated by a single-phonon (direct) process involving magnetic impurities. This is the first study of temperature-dependent nuclear-spin relaxation in PT and PZT ferroelectrics at such low temperatures. We discuss the implications of the results for the Schiff-moment search.Comment: 6 pages, 4 figure

Quantified Morphology of HI Disks in the Universe

he upcoming new perspective of the high redshift Universe in the 21 cm line of atomic hydrogen opens possibilities to explore topics of spiral disk evolution, hitherto reserved for the optical regime. The growth of spiral gas disks over Cosmic time can be explored with the new generation of radio telescopes, notably the SKA, and its precursors, as accurately as with the Hubble Space Telescope for stellar disks. Since the atomic hydrogen gas is the building block of these disks, it should trace their formation accurately. Morphology of HI disks can now equally be quantified over Cosmic time. In studies of HST deep fields, the optical or UV morphology of high-redshift galaxy disks have been characterized using a few quantities: concentration (C), asymmetry (A), smoothness (S), second-order-moment (M20), the GINI coefficient (G), and Ellipticity (E). We have applied these parameters across wavelengths and compared them to the HI morphology over the THINGS sample. NGC 3184, an unperturbed disk, and NGC 5194, the canonical 3:1 interaction, serve as examples for quantified morphology. We find that morphology parameters determined in HI are as good or better a tracer of interaction compared to those in any other wavelength, notably in Asymmetry, Gini and M20. This opens the possibility of using them in the parameterization pipeline for SKA precursor catalogues to select interacting or harassed galaxies from their HI morphology. Asymmetry, Gini and M20 may be redefined for use on data-cubes rather than HI column density image.Comment: 6 pages, 3 figures, proceeding of the conference "Panoramic Radio Astronomy: Wide-field 1-2 GHz research on galaxy evolution", June 02 - 05 2009, Groningen, update after small edit

Bidding process in online auctions and winning strategy:rate equation approach

Online auctions have expanded rapidly over the last decade and have become a fascinating new type of business or commercial transaction in this digital era. Here we introduce a master equation for the bidding process that takes place in online auctions. We find that the number of distinct bidders who bid $k$ times, called the $k$-frequent bidder, up to the $t$-th bidding progresses as $n_k(t)\sim tk^{-2.4}$. The successfully transmitted bidding rate by the $k$-frequent bidder is obtained as $q_k(t) \sim k^{-1.4}$, independent of $t$ for large $t$. This theoretical prediction is in agreement with empirical data. These results imply that bidding at the last moment is a rational and effective strategy to win in an eBay auction.Comment: 4 pages, 6 figure

Interstellar medium disruption in the Centaurus A group

We present the results of a 21 cm neutral hydrogen (HI) line detection experiment in the direction of 18 low luminosity dwarf galaxies of the Centaurus A group, using the Australia Telescope National Facility 64m Parkes Radio Telescope and the Australia Telescope Compact Array. Five dwarfs have HI masses between M_HI=4x10^5 to M_HI=2.1x10^7 Msol and 0.04<M_HI/L_B<1.81 Msol L_{sol, B}^-1. The other 13 have upper-limits between M_HI<5x10^5 and M_HI<4x10^6 Msol (M_HI}/L_B<0.24 Msol L_{sol, B}^-1). Two of the mixed-morphology dwarfs remain undetected in HI, a situation that is in contrast to that of similar Local Group and Sculptor group objects where all contain significant amounts of neutral gas. There is a discontinuity in the HI properties of Centaurus A group low luminosity dwarfs that is unobserved amongst Sculptor group dwarfs. All objects fainter than M_B=-13 have either M_HI>10^7 Msol or M_HI<10^6 Msol. This gap may be explained by the ram pressure stripping mechanism at work in this dense environment where all galaxies with M_HI<10^7 Msol have been stripped of their gas. The required intergalactic medium density to achieve this is ~10^-3 cm^-3.Comment: 7 figures, 2 table

Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds

We present a proof of the mirror conjecture of Aganagic-Vafa [arXiv:hep-th/0012041] and Aganagic-Klemm-Vafa [arXiv:hep-th/0105045] on disk enumeration in toric Calabi-Yau 3-folds for all smooth semi-projective toric Calabi-Yau 3-folds. We consider both inner and outer branes, at arbitrary framing. In particular, we recover previous results on the conjecture for (i) an inner brane at zero framing in the total space of the canonical line bundle of the projective plane (Graber-Zaslow [arXiv:hep-th/0109075]), (ii) an outer brane at arbitrary framing in the resolved conifold (Zhou [arXiv:1001.0447]), and (iii) an outer brane at zero framing in the total space of the canonical line bundle of the projective plane (Brini [arXiv:1102.0281, Section 5.3]).Comment: 39 pages, 11 figure

One-Loop Self Energy and Renormalization of the Speed of Light for some Anisotropic Improved Quark Actions

One-loop corrections to the fermion rest mass M_1, wave function renormalization Z_2 and speed of light renormalization C_0 are presented for lattice actions that combine improved glue with clover or D234 quark actions and keep the temporal and spatial lattice spacings, a_t and a_s, distinct. We explore a range of values for the anisotropy parameter \chi = a_s/a_t and treat both massive and massless fermions.Comment: 45 LaTeX pages with 4 postscript figure

On Markovian solutions to Markov Chain BSDEs

We study (backward) stochastic differential equations with noise coming from a finite state Markov chain. We show that, for the solutions of these equations to be `Markovian', in the sense that they are deterministic functions of the state of the underlying chain, the integrand must be of a specific form. This allows us to connect these equations to coupled systems of ODEs, and hence to give fast numerical methods for the evaluation of Markov-Chain BSDEs