Laplacian Solitons and Symmetry in G_2-geometry

In this paper, it is shown that (with no additional assumptions) on a compact 7-dimensional manifold which admits a $G_2$-structure soliton solutions to the Laplacian flow of R. Bryant can only be shrinking or steady. We also show that the space of symmetries (vector fields that annihilate via the Lie derivative) of a torsion-free $G_2$-structure on a compact 7-manifold is canonically isomorphic to $H^1(M,\mathbb{R})$. Some comparisons with Ricci solitons are also discussed, along with some future directions of exploration

First-order intertwining operators and position-dependent mass Schrodinger equations in d dimensions

The problem of d-dimensional Schrodinger equations with a position-dependent mass is analyzed in the framework of first-order intertwining operators. With the pair (H, H_1) of intertwined Hamiltonians one can associate another pair of second-order partial differential operators (R, R_1), related to the same intertwining operator and such that H (resp. H_1) commutes with R (resp. R_1). This property is interpreted in superalgebraic terms in the context of supersymmetric quantum mechanics (SUSYQM). In the two-dimensional case, a solution to the resulting system of partial differential equations is obtained and used to build a physically-relevant model depicting a particle moving in a semi-infinite layer. Such a model is solved by employing either the commutativity of H with some second-order partial differential operator L and the resulting separability of the Schrodinger equation or that of H and R together with SUSYQM and shape-invariance techniques. The relation between both approaches is also studied.Comment: 25 pages, no figure, 1 paragraph added in section 4, 1 additional referenc

The role of rr-mode damping in the thermal evolution of neutron stars

The thermal evolution of neutron stars (NSs) is investigated by coupling with the evolution of $\textit{r}$-mode instability that is described by a second order model.The heating effect due to shear viscous damping of the $\textit{r}$-modes enables us to understand the high temperature of two young pulsars (i.e., PSR B0531+21 and RX J0822-4300) in the framework of the simple $npe$ NS model, without superfluidity or exotic particles.Moreover, the light curves predicted by the model within an acceptable parameter regime may probably cover all of the young and middle-aged pulsars in the $\lg T_s^{\infty}-\lg t$ panel, and an artificially strong $p$ superfluidity invoked in some early works is not needed here. Additionally, by considering the radiative viscous damping of the $\textit{r}$-modes, a surprising extra cooling effect is found, which can even exceed the heating effect sometimes although plays an ignorable role in the thermal history.Comment: 12 pages, 3 figure

A young binary Brown Dwarf in the R-CrA star formation region

We present imaging and spectroscopic observations with HST (WFPC2, ACS/HRC and STIS), VLT (FORS2) and Keck (HIRES) of the dM8 ultra-cool dwarf DENIS-P J185950.9-370632, located in the R-CrA region. The presence of lithium absorption at 670.8 nm and the strong Halpha emission indicate a young age and a sub-stellar mass. Our diffraction-limited images resolve a companion at the separation limit of HST/ACS (~0.06"). The 2.1 mJy flux in the LW2 filter (5.0-8.5 microns) of the Infrared Space Observatory (see 1999A&A...350..883) likely corresponds to an infrared excess, suggesting the presence of circumstellar material. Proper motion and photometric measurements, as well as the Halpha activity, confirm membership in the R-CrA star forming region. If confirmed by further observations, DENIS-P J185950.9-370632 would be the first accreting sub-stellar multiple system observed to date.Comment: 18 pages, 11 figures, 3 tables Version with full resolution figures available on: ftp://ftp.mpe.mpg.de/people/hbouy/publications/DENIS1859.ps.g

Comments on "A reconsideration of tax shield valuation" by Enrique R. Arzac and Lawrence R. Glosten

While Arzac and Glosten (2005) affirm that "the value of tax shields depends upon the nature of the equity stochastic process, which, in turn, depends upon the free cash flow process," I prove that the value of tax shields depends only upon the nature of the stochastic process of the net increase of debt. Arzac and Glosten (2005) formulate the constant leverage ratio assumption as Dt = L•Et. The assumption of Fernández (2004) is E{Dt}= L•E{Et}, where E{•} is the expected value operator, D the value of debt, E the equity value, and L a constant. The Arzac and Glosten (2005) assumption requires continuous debt rebalancing, while mine does not. Under both financial policies, the expected leverage ratio is constant, but the Arzac and Glosten (2005) assumption is too extreme.Value of tax shields; required return to equity; cost of capital; net increase of debt;

Improved Lower Bounds on the Compatibility of Multi-State Characters

We study a long standing conjecture on the necessary and sufficient conditions for the compatibility of multi-state characters: There exists a function $f(r)$ such that, for any set $C$ of $r$-state characters, $C$ is compatible if and only if every subset of $f(r)$ characters of $C$ is compatible. We show that for every $r \ge 2$, there exists an incompatible set $C$ of $\lfloor\frac{r}{2}\rfloor\cdot\lceil\frac{r}{2}\rceil + 1$ $r$-state characters such that every proper subset of $C$ is compatible. Thus, $f(r) \ge \lfloor\frac{r}{2}\rfloor\cdot\lceil\frac{r}{2}\rceil + 1$ for every $r \ge 2$. This improves the previous lower bound of $f(r) \ge r$ given by Meacham (1983), and generalizes the construction showing that $f(4) \ge 5$ given by Habib and To (2011). We prove our result via a result on quartet compatibility that may be of independent interest: For every integer $n \ge 4$, there exists an incompatible set $Q$ of $\lfloor\frac{n-2}{2}\rfloor\cdot\lceil\frac{n-2}{2}\rceil + 1$ quartets over $n$ labels such that every proper subset of $Q$ is compatible. We contrast this with a result on the compatibility of triplets: For every $n \ge 3$, if $R$ is an incompatible set of more than $n-1$ triplets over $n$ labels, then some proper subset of $R$ is incompatible. We show this upper bound is tight by exhibiting, for every $n \ge 3$, a set of $n-1$ triplets over $n$ taxa such that $R$ is incompatible, but every proper subset of $R$ is compatible

Ensemble Properties of Comets in the Sloan Digital Sky Survey

We present the ensemble properties of 31 comets (27 resolved and 4 unresolved) observed by the Sloan Digital Sky Survey (SDSS). This sample of comets represents about 1 comet per 10 million SDSS photometric objects. Five-band (u,g,r,i,z) photometry is used to determine the comets' colors, sizes, surface brightness profiles, and rates of dust production in terms of the Af{\rho} formalism. We find that the cumulative luminosity function for the Jupiter Family Comets in our sample is well fit by a power law of the form N(< H) \propto 10(0.49\pm0.05)H for H < 18, with evidence of a much shallower fit N(< H) \propto 10(0.19\pm0.03)H for the faint (14.5 < H < 18) comets. The resolved comets show an extremely narrow distribution of colors (0.57 \pm 0.05 in g - r for example), which are statistically indistinguishable from that of the Jupiter Trojans. Further, there is no evidence of correlation between color and physical, dynamical, or observational parameters for the observed comets.Comment: 19 pages, 8 tables, 11 figures, to appear in Icaru