Parameterization of the set of positive- definite matrices and an algorithm for its generation

Numerical analysis on set elements for positive definite symmetric matrices by parameterizatio

Algorithm for Liapunov stability analysis

Development of algorithm provides automatic computation of quadratic estimate of domain of stability for stable equilibrium states of nonlinear systems of ordinary differential equations

Cluster algebras in algebraic Lie theory

We survey some recent constructions of cluster algebra structures on coordinate rings of unipotent subgroups and unipotent cells of Kac-Moody groups. We also review a quantized version of these results.Comment: Invited survey; to appear in Transformation Group

The interstellar gas experiment

The Interstellar Gas Experiment (IGE) exposed thin metallic foils to collect neutral interstellar gas particles. These particles penetrate the solar system due to their motion relative to the sun. Thus, it is possible to entrap them in the collecting foils along with precipitating magnetospheric and perhaps some ambient atmospheric particles. For the entire duration of the Long Duration Exposure Facility (LDEF) mission, seven of these foils collected particles arriving from seven different directions as seen from the spacecraft. In the mass spectroscopic analysis of the noble gas component of these particles, we have detected the isotopes of He-3, He-4, Ne-20, and Ne-22. In the foil analyses carried out so far, we find a distribution of particle arrival directions which shows that a significant part of the trapped particles are indeed interstellar atoms. The analysis needed to subtract the competing fluxes of magnetospheric and atmospheric particles is still in progress

The Interstellar Gas Experiment: Analysis in progress

The Interstellar Gas Experiment (IGE) exposed thin metallic foils aboard the LDEF spacecraft in low Earth orbit in order to collect neutral interstellar particles which penetrate the solar system due to their motion relative to the sun. By mechanical penetration these atoms were imbedded in the collecting foils along with precipitating magnetospheric ions and, possibly, with ambient atmospheric atoms. During the entire LDEF mission, seven of these foils collected particles arriving from seven different directions as seen from the spacecraft. After the foils were returned to Earth, a mass spectrometric analysis of the noble gas component of the trapped particles was begun. The isotopes of He-3, He-4, Ne-20, and Ne-22 were detected. We have given a first account of the experiment. In order to infer the isotopic ratios in the interstellar medium from the concentrations found in the foils, several lines of investigation had to be initiated. The flux of ambient atmospheric noble gas atoms moving toward the foils due to the orbital motion of LDEF was estimated by detailed calculations. Any of these particles which evaded the baffles in the IGE collector could be entrapped in the foils as a background flux. However, the calculations have shown that this flux is negligible, which was the intent of the experiment hardware design. This conclusion is supported by the measurements. However, both the concentration of trapped helium and its impact energy indicate that the flux of magnetospheric ions which was captured was larger than had been expected. In fact, it appears that the magnetospheric particles constitute the largest fraction of the particles in the foils. Since little is known about this particle flux, their presence in the IGE foils appears fortunate. The analysis of these particles provides information about their isotropic composition and average flux

Fractional smoothness and applications in finance

This overview article concerns the notion of fractional smoothness of random variables of the form $g(X_T)$, where $X=(X_t)_{t\in [0,T]}$ is a certain diffusion process. We review the connection to the real interpolation theory, give examples and applications of this concept. The applications in stochastic finance mainly concern the analysis of discrete time hedging errors. We close the review by indicating some further developments.Comment: Chapter of AMAMEF book. 20 pages

Further development of an algorithm for the nonlinear stability analysis of the orbiting astronomical observatory paired-tracker control system Final report

Algorithm development for estimating domain of attraction of OAO paired-tracker equilibrium state with Liapunov function

Can Galactic Cosmic Rays Account for Solar 6Li Without Overproducing Gamma Rays?

Cosmic-ray interactions with interstellar gas produces both 6Li, which accumulates in the interstellar medium (ISM), and $\pi^0$ mesons, which decay to gamma-rays which propagate throughout the cosmos. Local 6Li abundances and extragalactic gamma-rays thus have a common origin which tightly links them. We exploit this connection to use gamma-ray observations to infer the contribution to 6Li nucleosynthesis by standard Galactic cosmic-ray (GCR) interactions with the ISM. Our calculation uses a carefully propagated cosmic-ray spectrum and accounts for 6Li production from both fusion reactions ($\alpha \alpha \to ^6Li$) as well as from spallation channels ({p,\alpha+CNO \to ^6Li). We find that although extreme assumptions yield a consistent picture, more realistic ones indicate that solar 6Li cannot be produced by standard GCRs alone without overproducing the hadronic gamma rays. Implications for the primordial 6Li production by decaying dark matter and cosmic rays from cosmological structure formation are discussed. Upcoming gamma-ray observations by GLAST will be crucial for determining the resolution of this problem.Comment: 4 pages, 1 figure To be published in ApJ

Isotopic Composition of Solar Wind Calcium: First in Situ Measurement by CELIAS/MTOF on Board SOHO

We present first results on the Ca isotopic abundances derived from the high resolution Mass Time-of-Flight (MTOF) spectrometer of the charge, element, and isotope analysis system (CELIAS) experiment on board the Solar and Heliospheric Observatory (SOHO). We obtain isotopic ratios 40Ca/42Ca = (128+-47) and 40Ca/44Ca = (50+-8), consistent with terrestrial values. This is the first in situ determination of the solar wind calcium isotopic composition and is important for studies of stellar modeling and solar system formation since the present-day solar Ca isotopic abundances are unchanged from their original isotopic composition in the solar nebula.Comment: 14 pages, 3 figure