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

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

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

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

Cluster structures on quantum coordinate rings

We show that the quantum coordinate ring of the unipotent subgroup N(w) of a symmetric Kac-Moody group G associated with a Weyl group element w has the structure of a quantum cluster algebra. This quantum cluster structure arises naturally from a subcategory C_w of the module category of the corresponding preprojective algebra. An important ingredient of the proof is a system of quantum determinantal identities which can be viewed as a q-analogue of a T-system. In case G is a simple algebraic group of type A, D, E, we deduce from these results that the quantum coordinate ring of an open cell of a partial flag variety attached to G also has a cluster structure.Comment: v2: minor corrections. v3: references updated, final version to appear in Selecta Mathematic

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

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

No abstract available

Intermittent release of transients in the slow solar wind: 2. In situ evidence

In paper 1, we showed that the Heliospheric Imager (HI) instruments on the pair of NASA STEREO spacecraft can be used to image the streamer belt and, in particular, the variability of the slow solar wind which originates near helmet streamers. The observation of intense intermittent transient outflow by HI implies that the corresponding in situ observations of the slow solar wind and corotating interaction regions (CIRs) should contain many signatures of transients. In the present paper, we compare the HI observations with in situ measurements from the STEREO and ACE spacecraft. Analysis of the solar wind ion, magnetic field, and suprathermal electron flux measurements from the STEREO spacecraft reveals the presence of both closed and partially disconnected interplanetary magnetic field lines permeating the slow solar wind. We predict that one of the transients embedded within the second CIR (CIR‐D in paper 1) should impact the near‐Earth ACE spacecraft. ACE measurements confirm the presence of a transient at the time of CIR passage; the transient signature includes helical magnetic fields and bidirectional suprathermal electrons. On the same day, a strahl electron dropout is observed at STEREO‐B, correlated with the passage of a high plasma beta structure. Unlike ACE, STEREO‐B observes the transient a few hours ahead of the CIR. STEREO‐A, STEREO‐B, and ACE spacecraft observe very different slow solar wind properties ahead of and during the CIR analyzed in this paper, which we associate with the intermittent release of transients

The inner source for pickup ions

Pickup ions are observed by the Solar Wind Ion Composition Spectrometer on Ulysses which appear to have been picked up close to the Sun. A transport theory for the propagation of these ions is used to constrain the spatial profiles of the ion sources. The composition is like that of the solar wind which suggests that the inner source pickup ions result from solar wind particles that are embedded in dust grains and then released. Through comparison between modeled and observed distributions, it is possible to constrain the radial and latitudinal profiles of the inner source. Inner source protons are also observed and may constitute an energetically important population in the solar wind. © 1999 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87724/2/487_1.pd