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

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

Solar wind observations with the ion composition instrument aboard the ISEE-3 ICE spacecraft

The principal observations obtained by the Ion Composition Instrument (ICI) flown on the ISEE-3/ICE spacecraft, which was in the solar wind from September 1978 to the end of 1982, before being directed to the far magnetotail of the Earth are discussed. Almost continuous observations were made of the abundances of 3He++, 4He++, O6+, O7+, Ne, Si and Fe in various charge states, and of their bulk speeds and temperatures. The results show that there is a strong tendency in the collisionless solar wind for the ionic temperatures to be proportional to the masses. For heavier ions these temperatures exceed typical coronal electron temperatures. 4He++, especially in high speed streams, moves faster than H+, and travels at the same speed as heavier ions. The mechanism leading to this heating and rapid streaming is still not entirely clear

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

Heating of Pickup and Solar Wind Ions at Jupiter’s Bow Shock

Interstellar pickup ions are dynamically important in the outer heliosphere where they mass‐load and heat the solar wind. Some of these pickup ions are transformed into energetic neutral atoms (ENAs) by charge exchange with the residual cold interstellar gas that is the primary constituent of the outer heliosphere. The most detailed measurements of interstellar pickup ions in the heliosphere are currently available only between ∼1 and ∼5 AU. Among the most interesting and least expected observations are those of ubiquitous suprathermal tails on the distribution of pickup and solar wind protons and all heavier ions that can be measured. Here we report new measurements of solar wind proton and alpha particle distributions and of pickup He+ spectra upstream and downstream of Jupiter’s bow shock. We find that in the magnetosheath, 27% of the total pickup H+ density is in the tail portion of the distribution, compared to only 0.4% in the upstream spectrum. For He+ the entire core distribution is apparently heated in crossing the shock. These results have important implications for particle acceleration at the heliospheric termination shock, and for predicting the fluxes of energetic neutral atoms in the inner heliosphere produced from solar wind and pickup ions heated and accelerated at the termination shock. © 2004 American Institute of PhysicsPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87300/2/201_1.pd

Grasping the Links in the Chain: Understanding the Unintended Consequences of International Counter-Narcotics Measures for the EU

No abstract available

Grass fires—an unlikely process to explain the magnetic properties of prairie soils

It has been proposed that grass fires affect the magnetic properties of soils by combining generally reducing soil conditions with elevated temperatures. To explore this supposition, we analysed surface and subsurface samples from loessic soils and compared their differences in magnetic properties as a function of fire intensity. Fire intensity was established based on types of burnt vegetation, which ranged from low-intensity fires in short-grass areas to high-intensity fires in tall-grass and forested areas. We measured low-field magnetic susceptibility (χ), a common proxy for the abundance of magnetic minerals, frequency-dependent susceptibility (χFD), a proxy for the presence of ultrafine-grained superparamagnetic minerals, and susceptibility of anhysteretic remanent magnetization (χARM), a magnetic parameter highly dependent on the presence of fine, single-domain magnetic particles. Although intense fires led to an increase in frequency-dependent susceptibility and low-field magnetic susceptibility, moderately intense fires did not produce significant changes in magnetic properties. Observed magnetic changes are limited to sites that were very heavily burnt in forest areas. Grass fires are therefore an unlikely mechanism to explain a measurable component of the magnetic enhancement in prairie soils

Big Bang Nucleosynthesis with Long Lived Charged Massive Particles

We consider Big Bang Nucleosynthesis (BBN) with long lived charged massive particles. Before decaying, the long lived charged particle recombines with a light element to form a bound state like a hydrogen atom. This effect modifies the nuclear reaction rates during the BBN epoch through the modifications of the Coulomb field and the kinematics of the captured light elements, which can change the light element abundances. It is possible that the heavier nuclei abundances such as $^7$Li and $^7$Be decrease sizably, while the ratios $Y_p$, D/H, and $^3$He/H remain unchanged. This may solve the current discrepancy between the BBN prediction and the observed abundance of $^7$Li. If future collider experiments found signals of a long-lived charged particle inside the detector, the information of its lifetime and decay properties could provide insights to understand not only the particle physics models but also the phenomena in the early universe in turn.Comment: 20 pages, 6 figures, published version in Physical Review

Weak pitch angle scattering of few MV rigidity ions from measurements of anisotropies in the distribution function of interstellar pickup H +

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95477/1/grl8632.pd