Dynamical Measurements of the Young Upper Scorpius Triple NTTS 155808-2219

The young, low-mass, triple system NTTS 155808-2219 (ScoPMS 20) was previously identified as a ~17-day period single-lined spectroscopic binary with a tertiary component at 0.21 arcseconds. Using high-resolution infrared spectra, acquired with NIRSPEC on Keck II, both with and without adaptive optics, we measured radial velocities of all three components. Reanalysis of the single-lined visible light observations, made from 1987 to 1993, also yielded radial velocity detections of the three stars. Combining visible light and infrared data to compute the orbital solution produces orbital parameters consistent with the single-lined solution and a mass ratio of q = 0.78 +/- 0.01 for the SB. We discuss the consistency between our results and previously published data on this system, our radial-velocity analysis with both observed and synthetic templates, and the possibility that this system is eclipsing, providing a potential method for the determination of the stars' absolute masses. Over the ~20 year baseline of our observations, we have measured the acceleration of the SB's center-of-mass in its orbit with the tertiary. Long-term, adaptive optics imaging of the tertiary will eventually yield dynamical data useful for component mass estimates.Comment: 6 Tables, 8 Figures, updated to match published tex

Strong uniqueness for stochastic evolution equations with unbounded measurable drift term

We consider stochastic evolution equations in Hilbert spaces with merely measurable and locally bounded drift term $B$ and cylindrical Wiener noise. We prove pathwise (hence strong) uniqueness in the class of global solutions. This paper extends our previous paper (Da Prato, Flandoli, Priola and M. Rockner, Annals of Prob., published online in 2012) which generalized Veretennikov's fundamental result to infinite dimensions assuming boundedness of the drift term. As in our previous paper pathwise uniqueness holds for a large class, but not for every initial condition. We also include an application of our result to prove existence of strong solutions when the drift $B$ is only measurable, locally bounded and grows more than linearly.Comment: The paper will be published in Journal of Theoretical Probability. arXiv admin note: text overlap with arXiv:1109.036

Cubature on Wiener space in infinite dimension

We prove a stochastic Taylor expansion for SPDEs and apply this result to obtain cubature methods, i. e. high order weak approximation schemes for SPDEs, in the spirit of T. Lyons and N. Victoir. We can prove a high-order weak convergence for well-defined classes of test functions if the process starts at sufficiently regular initial values. We can also derive analogous results in the presence of L\'evy processes of finite type, here the results seem to be new even in finite dimension. Several numerical examples are added.Comment: revised version, accepted for publication in Proceedings Roy. Soc.

Analysis of equilibrium states of Markov solutions to the 3D Navier-Stokes equations driven by additive noise

We prove that every Markov solution to the three dimensional Navier-Stokes equation with periodic boundary conditions driven by additive Gaussian noise is uniquely ergodic. The convergence to the (unique) invariant measure is exponentially fast. Moreover, we give a well-posedness criterion for the equations in terms of invariant measures. We also analyse the energy balance and identify the term which ensures equality in the balance.Comment: 32 page

Dimension-independent Harnack inequalities for subordinated semigroups

Dimension-independent Harnack inequalities are derived for a class of subordinate semigroups. In particular, for a diffusion satisfying the Bakry-Emery curvature condition, the subordinate semigroup with power $\alpha$ satisfies a dimension-free Harnack inequality provided $\alpha \in(1/2, 1)$, and it satisfies the log-Harnack inequality for all $\alpha \in (0,1).$ Some infinite-dimensional examples are also presented

Adjoint bi-continuous semigroups and semigroups on the space of measures

For a given bi-continuous semigroup T on a Banach space X we define its adjoint on an appropriate closed subspace X^o of the norm dual X'. Under some abstract conditions this adjoint semigroup is again bi-continuous with respect to the weak topology (X^o,X). An application is the following: For K a Polish space we consider operator semigroups on the space C(K) of bounded, continuous functions (endowed with the compact-open topology) and on the space M(K) of bounded Baire measures (endowed with the weak*-topology). We show that bi-continuous semigroups on M(K) are precisely those that are adjoints of a bi-continuous semigroups on C(K). We also prove that the class of bi-continuous semigroups on C(K) with respect to the compact-open topology coincides with the class of equicontinuous semigroups with respect to the strict topology. In general, if K is not Polish space this is not the case

The GL 569 Multiple System

We report the results of high spectral and angular resolution infrared observations of the multiple system GL 569 A and B that were intended to measure the dynamical masses of the brown dwarf binary believed to comprise GL 569 B. Our analysis did not yield this result but, instead, revealed two surprises. First, at age ~100 Myr, the system is younger than had been reported earlier. Second, our spectroscopic and photometric results provide support for earlier indications that GL 569 B is actually a hierarchical brown dwarf triple rather than a binary. Our results suggest that the three components of GL 569 B have roughly equal mass, ~0.04 Msun.Comment: 29 pages, 10 figures, accepted for publication in the Astrophysical Journal; minor corrections to Section 5.1; changed typo in 6.

Use of Perylene Diimides in Synthetic Photochemistry

Perylene diimides (PDIs) are valuable organic chromophores that stand out for their outstanding optical and redox properties. Owing to these features, PDIs have emerged as prominent dyes capable of acting as photocatalysts for numerous relevant organic transformations. This Minireview highlights the recent advances in the application of PDIs in organic photocatalysis. The various mechanistic pathways of the photo-reduction reaction of aryl halides, recently proposed in independent studies, are discussed with an eye to unsolved challenges and forward-looking opportunities regarding the use of PDIs within this field