On an action of the braid group B_{2g+2} on the free group F_{2g}

We construct an action of the braid group B_{2g+2} on the free group F_{2g} extending an action of B_4 on F_2 introduced earlier by Reutenauer and the author. Our action induces a homomorphism from B_{2g+2} into the symplectic modular group Sp_{2g}(Z). In the special case g=2 we show that the latter homomorphism is surjective and determine its kernel, thus obtaining a braid-like presentation of Sp_4(Z).Comment: 11 pages. Minor changes in v

Twisting algebras using non-commutative torsors

Non-commutative torsors (equivalently, two-cocycles) for a Hopf algebra can be used to twist comodule algebras. After surveying and extending the literature on the subject, we prove a theorem that affords a presentation by generators and relations for the algebras obtained by such twisting. We give a number of examples, including new constructions of the quantum affine spaces and the quantum tori.Comment: 27 pages. Masuoka is a new coauthor. Introduction was revised. Sections 1 and 2 were thoroughly restructured. The presentation theorem in Section 3 is now put in a more general framework and has a more general formulation. Section 4 was shortened. All examples (quantum affine spaces and tori, twisting of SL(2), twisting of the enveloping algebra of sl(2)) are left unchange

Statistical inference of one-dimensional persistent nonlinear time series and application to predictions

We introduce a method for reconstructing macroscopic models of one-dimensional stochastic processes with long-range correlations from sparsely sampled time series by combining fractional calculus and discrete-time Langevin equations. The method is illustrated for the ARFIMA(1,d,0) process and a nonlinear autoregressive toy model with multiplicative noise. We reconstruct a model for daily mean temperature data recorded at Potsdam, Germany and use it to predict the first-frost date by computing the mean first passage time of the reconstructed process and the 0 degrees C temperature line, illustrating the potential of long-memory models for predictions in the sub seasonal-to-seasonal range

Ag lime impact on yield in several tillage systems

Crop farmers in northwestern Iowa know there are benefits of applying ag lime to acidic soils. But, until recently, little data existed that told them how effective ag lime is in correcting surface soil acidity in the dominant upland soils in northwestern Iowa. Now, research in northwestern Iowa suggests that ag lime application when surface pH is low can benefit soybean yields in different tillage systems, including in no-till

Long-term microparticle flux variability indicated by comparison of Interplanetary Dust Experiment (IDE) timed impacts for LDEF's first year in orbit with impact data for the entire 5.77-year orbital lifetime

The electronic sensors of the Interplanetary Dust Experiment (IDE) recorded precise impact times and approximate directions for submicron to approximately 100 micron size particles on all six primary sides of the spacecraft for the first 346 days of the LDEF orbital mission. Previously-reported analyses of the timed impact data have established their spatio-temporal features, including the demonstration that a preponderance of the particles in this regime are orbital debris and that a large fraction of the debris particles are encountered in megameter-size clouds. Short-term fluxes within such clouds can rise several orders of magnitude above the long-term average. These unexpectedly large short-term variations in debris flux raise the question of how representative an indication of the multi-year average flux is given by the nearly one year of timed data. One of the goals of the IDE was to conduct an optical survey of impact sites on detectors that remained active during the entire LDEF mission, to obtain full-mission fluxes. We present here the comparisons and contrasts among the new IDE optical survey impact data, the IDE first-year timed impact data, and impact data from other LDEF micrometeoroid and debris experiments. The following observations are reported: (1) the 5.77 year long-term integrated microparticle impact fluxes recorded by IDE detectors matched the integrated impact fluxes measured by other LDEF investigators for the same period; (2) IDE integrated microparticle impact fluxes varied by factors from 0.5 to 8.3 for LDEF days 1-346, 347-2106 and 1-2106 (5.77 years) on rows 3 (trailing edge, or West), 6 (South side), 12 (North side), and the Earth and Space ends; and (3) IDE integrated microparticle impact fluxes varied less than 3 percent for LDEF days 1-346, 347-2106 and 1-2106 (5.77 years) on row 9 (leading edge, or East). These results give further evidence of the accuracy and internal consistency of the recorded IDE impact data. This leads to the further conclusion that the utility of long-term ratios for impacts on various sides of a stabilized satellite in low Earth orbit (LEO) is extremely limited. These observations and their consequences highlight the need for continuous, real time monitoring of the dynamic microparticle environment in LEO

Method and apparatus for determining time, direction, and composition of impacting space particles

A space particle collector for recording the time specific particles are captured, and its direction at the time of capture, utilizes an array of targets, each comprised of an MOS capacitor on a chip charged from an external source and discharged upon impact by a particle through a tab on the chip that serves as a fuse. Any impacting particle creates a crater, but only the first will cause a discharge of the capacitor. A substantial part of the metal film around the first crater is burned off by the discharge current. The time of the impulse which burns the tab, and the identification of the target, is recorded together with data from flight instruments. The metal film is partitioned into pie sections to provide a plurality of targets on each of an array of silicon wafers, thus increasing the total number of identified particles that can be collected. It is thus certain which particles were captured at what specific times

Active Spanning Trees with Bending Energy on Planar Maps and SLE-Decorated Liouville Quantum Gravity for κ> 8

We consider the Peano curve separating a spanning tree from its dual spanning tree on an embedded planar graph, where the tree and dual tree are weighted by $y$ to the number of active edges, and "active" is in the sense of the Tutte polynomial. When the graph is a portion of the square grid approximating a simply connected domain, it is known ($y=1$ and $y=1+\sqrt{2}$) or believed ($1<y<3$) that the Peano curve converges to a space-filling SLE$_{\kappa}$ loop, where $y=1-2\cos(4\pi/\kappa)$, corresponding to $4<\kappa\leq 8$. We argue that the same should hold for $0\le y<1$, which corresponds to $8<\kappa\leq 12$

Bicrossed products for finite groups

We investigate one question regarding bicrossed products of finite groups which we believe has the potential of being approachable for other classes of algebraic objects (algebras, Hopf algebras). The problem is to classify the groups that can be written as bicrossed products between groups of fixed isomorphism types. The groups obtained as bicrossed products of two finite cyclic groups, one being of prime order, are described.Comment: Final version: to appear in Algebras and Representation Theor

Long Duration Exposure Facility (LDEF) attitude measurements of the Interplanetary Dust Experiment

Analysis of the data from the Long Duration Exposure Facility (LDEF) Interplanetary Dust Experiment (IDE) sun sensors has allowed a confirmation of the attitude of LDEF during its first year in orbit. Eight observations of the yaw angle at specific times were made and are tabulated in this paper. These values range from 4.3 to 12.4 deg with maximum uncertainty of plus or minus 2.0 deg and an average of 7.9 deg. No specific measurements of pitch or roll were made but the data indicates that LDEF had an average pitch down attitude of less than 0.7 deg

IDE spatio-temporal impact fluxes and high time-resolution studies of multi-impact events and long-lived debris clouds

The purpose of the Interplanetary Dust Experiment (IDE) on the Long Duration Exposure Facility (LDEF) was to sample the cosmic dust environment and to use the spatio-temporal aspect of the experiment to distinguish between the various components of the environment: zodiacal cloud, beta meteoroids, meteor streams, interstellar dust, and orbital debris. It was found that the introduction of precise time and even rudimentary directionality as co-lateral observables in sampling the particulate environment in near-Earth space produces an enormous qualitative improvement in the information content of the impact data. The orbital debris population is extremely clumpy, being dominated by persistent clouds in which the fluxes may rise orders of magnitude above the background. The IDE data suggest a strategy to minimize the damage to sensitive spacecraft components, using the observed characteristics of cloud encounters