Algebraic Structures of Bernoulli Numbers and Polynomials

In a field of Laurent series, we construct a subring which has a module structure over a Weyl algebra. Identities of Bernoulli numbers and polynomials are obtained from these algebraic structures.Comment: This article was submitted to J. Number Theory on 2008. The referee(s) agreed to review the article did not write reports and not even response to the editor. The paper was rejected by J. Number Theory on 2012, since `it is impossible for us (editors) to get this paper refereed'. The author will no longer seek publication for this article in journals. Comments on the article are welcome

Intra-Household Effects on Demand for Telephone Service: Empirical Evidence

I present a game-theoretical model to estimate consumption demand, accounting for intra-household interaction among household members. Although multiple Nash equilibria of consumption decisions may exist in a household, model parameters are pointwise identified from household-level data for households with only two members. I propose a semiparametric maximum likelihood estimator and apply it to empirically analyze the subscription decision for cellular phone service in Taiwan. On average, a consumer's probability of subscribing to cellular service rises 35 percentage points when the other household member chooses to subscribe. This result suggests the existence of intra-household network effects on cellular phone consumption. The intra-household effect increases in household income, but decreases in the number of kids and the age difference in a household.consumption externality, multiple Nash equilibria, demand estimation, mobile phone service, cellular phone service, network effect

Are eBay auctions efficient? A model with buyer entries

I use a sequential-auction model to mimic the environment of Internet auction sites, such as eBay. For a sequence of auctions, new buyers may enter the auction site after some of the auctions has completed and only bid for the remaining auctions. Because an incumbent buyer may have revealed their own valuation in earlier auctions while a new entrant do not, their expectations about the future are asymmetric. As a result, a buyer with a lower valuation may win an auction while a buyer with a higher valuation may restrain from bidding higher, resulting an inefficient allocation. On the contrary, selling the multiple items in a single simultaneous auction results in an efficient outcome. The profit from selling all items together in one simultaneous auction is less than that from selling them sequentially.Internet auction, sequential auctions, affiliated private values

Bottom-up retinotopic organization supports top-down mental imagery

Finding a path between locations is a routine task in daily life. Mental navigation is often used to plan a route to a destination that is not visible from the current location. We first used functional magnetic resonance imaging (fMRI) and surface-based averaging methods to find high-level brain regions involved in imagined navigation between locations in a building very familiar to each participant. This revealed a mental navigation network that includes the precuneus, retrosplenial cortex (RSC), parahippocampal place area (PPA), occipital place area (OPA), supplementary motor area (SMA), premotor cortex, and areas along the medial and anterior intraparietal sulcus. We then visualized retinotopic maps in the entire cortex using wide-field, natural scene stimuli in a separate set of fMRI experiments. This revealed five distinct visual streams or ‘fingers’ that extend anteriorly into middle temporal, superior parietal, medial parietal, retrosplenial and ventral occipitotemporal cortex. By using spherical morphing to overlap these two data sets, we showed that the mental navigation network primarily occupies areas that also contain retinotopic maps. Specifically, scene-selective regions RSC, PPA and OPA have a common emphasis on the far periphery of the upper visual field. These results suggest that bottom-up retinotopic organization may help to efficiently encode scene and location information in an eye-centered reference frame for top-down, internally generated mental navigation. This study pushes the border of visual cortex further anterior than was initially expected

On the formation of current sheets in response to the compression or expansion of a potential magnetic field

The compression or expansion of a magnetic field that is initially potential is considered. It was recently suggested by Janse & Low [2009, ApJ, 690, 1089] that, following the volumetric deformation, the relevant lowest energy state for the magnetic field is another potential magnetic field that in general contains tangential discontinuities (current sheets). Here we examine this scenario directly using a numerical relaxation method that exactly preserves the topology of the magnetic field. It is found that of the magnetic fields discussed by Janse & Low, only those containing magnetic null points develop current singularities during an ideal relaxation, while the magnetic fields without null points relax toward smooth force-free equilibria with finite non-zero current.Comment: Accepted for publication in Ap

Unconventional superconducting pairing symmetry induced by phonons

The possibility of non-s-wave superconductivity induced by phonons is investigated using a simple model that is inspired by Sr$_2$RuO$_4$. The model assumes a two-dimensional electronic structure, a two-dimensional spin-fluctuation spectrum, and three-dimensional electron-phonon coupling. Taken separately, each interaction favors formation of spin-singlet pairs (of s symmetry for the phonon interaction and d$_{x^2-y^2}$ symmetry for the spin interaction), but in combination, a variety of more unusual singlet and triplet states are found, depending on the interaction parameters. This may have important implications for Sr$_2$RuO$_4$, providing a plausible explanation of how the observed spin fluctuations, which clearly favor d$_{x^2-y^2}$ pairing, may still be instrumental in creating a superconducting state with a different (e.g., p-wave) symmetry. It also suggests an interpretation of the large isotope effect observed in Sr$_2$RuO$_4$. These results indicate that phonons could play a key role in establishing the order-parameter symmetry in Sr$_2$RuO$_4$, and possibly in other unconventional superconductors.Comment: 6 pages, 5 figures, submitted to Phys. Rev.

Larkin-Ovchinnikov-Fulde-Ferrell state in two-color quark matter

We explore the phase structure of two-color and two-flavor QCD in the space of the quark chemical potential \mu_q and the isospin chemical potential \mu_I. Using a mean-field model we calculate the chiral and diquark condensates, \sigma and \Delta, self-consistently. In weak coupling and in the chiral limit, we confirm the interval of the isospin chemical potential, 0.71\Delta_0<\mu_I<0.75\Delta_0, in which a single plane-wave Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase is favored over isotropic superfluidity and normal quark matter. The LOFF window becomes slightly wider at high density. For stronger coupling with nonzero quark mass, which is relevant to currently available numerical simulations in lattice two-color QCD, the single plane-wave LOFF phase appears only at sufficiently high density. The prediction obtained for the LOFF region could be tested with lattice since we can prove that the present system is free from the fermion sign problem. We draw the energy landscape on which local minima corresponding to the isotropic superfluid phase and the LOFF phase and a local maximum corresponding to the gapless phase are manifest. Our results clearly illustrate the path from the the unstable gapless phase down to the LOFF phase.Comment: 10 pages, 8 figure