Nonrational, nonsimple convex polytopes in symplectic geometry

In this research announcement we associate to each convex polytope, possibly nonrational and nonsimple, a family of compact spaces that are stratified by quasifolds, i.e. the strata are locally modelled by $\R^k$ modulo the action of a discrete, possibly infinite, group. Each stratified space is endowed with a symplectic structure and a moment mapping having the property that its image gives the original polytope back. These spaces may be viewed as a natural generalization of symplectic toric varieties to the nonrational setting. We provide here the explicit construction of these spaces, and a thorough description of the stratification.Comment: LaTeX, 7 page

Nonrational Symplectic Toric Cuts

In this article we extend cutting and blowing up to the nonrational symplectic toric setting. This entails the possibility of cutting and blowing up for symplectic toric manifolds and orbifolds in nonrational directions.Comment: 17 pages, 7 figures, minor changes in last version, to appear in Internat. J. Mat

Better capturing risks in the trading book.

The 1996 Amendment to the Basel Capital Accord, which allows, under certain conditions, the use of internal models to calculate regulatory capital requirements for market risk, has resulted in an apparently sound supervisory trading book regime for internationally active banks. Since this amendment was passed, the composition of the trading book has nevertheless changed substantially to include a more and more credit-related products such as credit derivatives and tranches of collateralised debt obligations (CDOs), as well as complex products such as hedge fund or fund of funds structured products. Furthermore, the contents of the trading book are expected to broaden due to the implementation of new international accounting and prudential standards. This development has led to an increase in credit risk in the trading book and a concomitant rise in other risks such as default risk, event risk, liquidity risk, concentration risk and correlation risk, which were not adequately captured when market risk regulations were devised. This has prompted: • banks to improve their risk assessment and control systems for trading book activities. These systems still often use Value at Risk (VaR) calculations based on a uniform 10-day holding period, which does not always appear relevant; • banking supervisors to enhance the supervision of these systems, in particular by ensuring that the measures proposed in July 2005 by the Basel Committee and the International Organisation of Securities Commissions (IOSCO), known as “Basel 2.5”, are correctly implemented. These measures aim to capture risks in the trading book in a more rigorous and comprehensive manner.

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

WATER QUALITY ISSUES FACING AGRICULTURE AND RURAL COMMUNITIES

Resource /Energy Economics and Policy,

Maximal L2L^2 regularity for Dirichlet problems in Hilbert spaces

We consider the Dirichlet problem $\lambda U - {\mathcal{L}}U= F$ in \mathcal{O}, U=0 on $\partial \mathcal{O}$. Here $F\in L^2(\mathcal{O}, \mu)$ where $\mu$ is a nondegenerate centered Gaussian measure in a Hilbert space $X$, $\mathcal{L}$ is an Ornstein-Uhlenbeck operator, and $\mathcal{O}$ is an open set in $X$ with good boundary. We address the problem whether the weak solution $U$ belongs to the Sobolev space $W^{2,2}(\mathcal{O}, \mu)$. It is well known that the question has positive answer if $\mathcal{O} = X$; if $\mathcal{O} \neq X$ we give a sufficient condition in terms of geometric properties of the boundary $\partial \mathcal{O}$. The results are quite different with respect to the finite dimensional case, for instance if \mathcal{O} is the ball centered at the origin with radius $r$ we prove that $U\in W^{2,2}(\mathcal{O}, \mu)$ only for small $r$

Separable-entangled frontier in a bipartite harmonic system

We consider a statistical mixture of two identical harmonic oscillators which is characterized by four parameters, namely, the concentrations (x and y) of diagonal and nondiagonal bipartite states, and their associated thermal-like noises (T/a and T, respectively). The fully random mixture of two spins 1/2 as well as the Einstein-Podolsky-Rosen (EPR) state are recovered as particular instances. By using the conditional nonextensive entropy as introduced by Abe and Rajagopal, we calculate the separable-entangled frontier. Although this procedure is known to provide a necessary but in general not sufficient condition for separability, it does recover, in the particular case x=T=0 (for all a), the 1/3 exact result known as Peres' criterion. This is an indication of reliability of the calculation of the frontier in the entire parameter space. The x=0 frontier remarkably resembles to the critical line associated with standard diluted ferromagnetism where the entangled region corresponds to the ordered one and the separable region to the paramagnetic one. The entangled region generically shrinks for increasing T or increasing a.Comment: 6 pages, 5 figure