Subdiagrams of Bratteli diagrams supporting finite invariant measures

We study finite measures on Bratteli diagrams invariant with respect to the tail equivalence relation. Amongst the proved results on finiteness of measure extension, we characterize the vertices of a Bratteli diagram that support an ergodic finite invariant measure.Comment: 9 page

Invariant Measures on Stationary Bratteli Diagrams

We study dynamical systems acting on the path space of a stationary (non-simple) Bratteli diagram. For such systems we explicitly describe all ergodic probability measures invariant with respect to the tail equivalence relation (or the Vershik map). These measures are completely described by the incidence matrix of the diagram. Since such diagrams correspond to substitution dynamical systems, this description gives an algorithm for finding invariant probability measures for aperiodic non-minimal substitution systems. Several corollaries of these results are obtained. In particular, we show that the invariant measures are not mixing and give a criterion for a complex number to be an eigenvalue for the Vershik map.Comment: 40 pages. Exposition is reworke

Wordsworth and Godwin: A Study of Influence. Volume II: Appendices, Notes, and Bibliography

Abstract Not Provided

Wordsworth and Godwin: A Study of Influence, Volume I: Text

This thesis explores the relationship between William Godwin and his ideas and William Wordsworth in the context of the significant reappraisal of Godwin since 1950 (which has gained further momentum in the 1980's) and more recent questioning of the biographical status of The Prelude, so long accepted by critics. The purpose is to challenge the inadequacy of earlier over-simplistic views of Godwin's rationalism, which have led (ever since Legouis' identification of Godwin as a significant "influence" in Wordsworth's thinking) to critical acceptance of Words worth's account of Godwin's role in the poet's development, culminating in the rejection of Godwin and what he represented during the period of alleged "moral crisis"

Gas gun shock experiments with single-pulse x-ray phase contrast imaging and diffraction at the Advanced Photon Source

The highly transient nature of shock loading and pronounced microstructure effects on dynamic materials response call for {\it in situ}, temporally and spatially resolved, x-ray-based diagnostics. Third-generation synchrotron x-ray sources are advantageous for x-ray phase contrast imaging (PCI) and diffraction under dynamic loading, due to their high photon energy, high photon fluxes, high coherency, and high pulse repetition rates. The feasibility of bulk-scale gas gun shock experiments with dynamic x-ray PCI and diffraction measurements was investigated at the beamline 32ID-B of the Advanced Photon Source. The x-ray beam characteristics, experimental setup, x-ray diagnostics, and static and dynamic test results are described. We demonstrate ultrafast, multiframe, single-pulse PCI measurements with unprecedented temporal ($<$100 ps) and spatial ($\sim$2 $\mu$m) resolutions for bulk-scale shock experiments, as well as single-pulse dynamic Laue diffraction. The results not only substantiate the potential of synchrotron-based experiments for addressing a variety of shock physics problems, but also allow us to identify the technical challenges related to image detection, x-ray source, and dynamic loading

Selecting asteroids for a targeted spectroscopic survey

Asteroid spectroscopy reflects surface mineralogy. There are few thousand asteroids whose surfaces have been observed spectrally. Determining the surface properties of those objects is important for many practical and scientific applications, such as for example developing impact deflection strategies or studying history and evolution of the Solar System and planet formation. The aim of this study is to develop a pre-selection method that can be utilized in searching for asteroids of any taxonomic complex. The method could then be utilized im multiple applications such as searching for the missing V-types or looking for primitive asteroids. We used the Bayes Naive Classifier combined with observations obtained in the course of the Sloan Digital Sky Survey and the Wide-field Infrared Survey Explorer surveys as well as a database of asteroid phase curves for asteroids with known taxonomic type. Using the new classification method we have selected a number of possible V-type candidates. Some of the candidates were than spectrally observed at the Nordic Optical Telescope and South African Large Telescope. We have developed and tested the new pre-selection method. We found three asteroids in the mid/outer Main Belt that are likely of differentiated type. Near-Infrared are still required to confirm this discovery. Similarly to other studies we found that V-type candidates cluster around the Vesta family and are rare in the mid/oter Main Belt. The new method shows that even largely explored large databases combined together could still be further exploited in for example solving the missing dunite problem.Comment: accepted to A