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

The shadow in the balance sheet: The spectre of Enron and how accountants use the past as a psychological defence against the future

Accounting frameworks play a crucial role in enabling us to make sense of business. These frameworks provide a common language for individuals, organizations and broader economic groupings to understand and make decisions about the commercial realm in which they operate. From a psychodynamic perspective, the language of accounting also plays an important role. On the one hand it offers a way to tame the uncertainty and unknowability of the future by representing it in the same comforting terms as it does the past, thus reducing anxiety. Accounting provides a ‘shorthand’, which achieves a balance between positive and negative, debit and credit, asset and liability. On the other hand, accounting can also provide an arena in which fantasies about the future can be staged. However, the use of accounting language is problematic, particularly when it comes to dealing with the future. First, accounting frameworks are inherently backward looking and second, the reassuring sense of clarity and predictability they give are bought at the price of unrealistic simplification. The shadow is never far away and is a constant source of surprises in the unfolding future of a business. Rationalizing and sanitizing the shadow through accounting language may alleviate anxiety but fails to provide an escape from its effects, and echoes from the shadow side of business are capable of shaking the world in the form of accounting scandals. Governments and businesses have reacted to scandals such as Enron and Worldcom by tightening legislation and refining accounting standards but little, if anything, has been done to bring us any closer to confronting the shadow of business where these scandals have their r

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

TiB_2 and ZrB_2 diffusion barriers in GaAs Ohmic contact technology

The transition metal diboride compounds, ZrB_2 and TiB_2, interposed between Ni/Ge/Au Ohmic contact metallization on n‐type GaAs wafers and an overlying thick Au contact layer, have been investigated to evaluate their effectiveness in stabilizing the Ohmic contact by limiting the in‐diffusion of Au. All of the metal layers were e‐beam deposited except the ZrB_2 which was rf‐diode sputtered. The barrier layer thicknesses were 50 and 100 nm for the TiB_2 and the ZrB_2, respectively. Postdeposition alloying of the contacts was performed at 400, 425, or 450 °C. Auger electron spectroscopy depth profiling of the resultant Ohmic contacts demonstrates that the barrier layers effectively preclude penetration of Au to the Ohmic contact structure. Specific contact resistivities for such contacts are in the low 10^(−7) Ω cm^2 range; although some degradation of the contact resistivity is observed after long term annealing, the values of resistivities do not exceed 1.5×10^(−6) Ω cm^2 after 92 h at 350 °C