Independence and Alpern Multitowers

Let $T$ be any invertible, ergodic, aperiodic measure-preserving transformation of a Lebesgue probability space (X, \calB, \mu), and \P\, any finite measurable partition of $X$. We show that a (finite) Alpern multitower may always be constructed whose base is independent of \P

Bridging the Gap between the Interest Rate and Price Level Approaches in the AD-AS Model: The Role of the Loanable Funds Market

There are two generally accepted ways of plotting the aggregate demand (AD) and aggregate supply (AS) curves in the goods market. One puts the price level on the vertical axis (the P - y approach); the other plots the real interest rate on the vertical axis (the r - y approach). This paper develops the theoretical connections between these two approaches that permit one to tell a coherent dynamic story with the AD-AS model and also explores the conditions under which one approach or the other yields greater insight into the working of the model.Interest Rates; Interest; Price Level; Prices; Supply

Potentialities of proteinoids for nutritional investigation

Simultaneous synthesis of amino acids and proteinoid production for nutritional investigatio

Estimation of dynamic load demand on a ground support scheme due to a large structurally controlled violent failure – a case study

© 2015 Institute of Materials, Minerals and Mining and The AusIMM Published by Maney on behalf of the Institute and The AusIMM. In the future a larger proportion of underground mines will operate in deep, high stress environments where excavations may be exposed to very high loading demands. This case study has examined a violent structurally controlled failure occurring in a deep hardrock underground mine at a depth of 1055 metres below surface. On the basis of the damage observations the back analysis of this event concludes that the surface support system was ejected from the wall of the excavation with an initial velocity of 10.7 m s-1. Estimates of the mechanical demand imparted to the ground support scheme during failure were also calculated. These estimates carry several assumptions in order to simplify complex uncertainties concerning the loading mass of rock and transfer of kinetic energy between the rock and ground support. However, the demand may be conservatively assumed to be at least 150 kJ m-2. These results may reflect future mining conditions at great depth

Anisotropic Nonequilibrium Lattice Dynamics of Black Phosphorus

Black phosphorus has recently attracted significant attention for its highly anisotropic properties. A variety of ultrafast optical spectroscopies has been applied to probe the carrier response to photoexcitation, but the complementary lattice response has remained unaddressed. Here we employ femtosecond electron diffraction to explore how the structural anisotropy impacts the lattice dynamics after photoexcitation. We observe two timescales in the lattice response, which we attribute to electron-phonon and phonon-phonon thermalization. Pronounced differences between armchair and zigzag directions are observed, indicating a non-thermal state of the lattice lasting up to ~60 picoseconds. This non-thermal state is characterized by a modified anisotropy of the atomic vibrations compared to equilibrium. Our findings provide insights in both electron-phonon as well as phonon-phonon coupling and bear direct relevance for any application of black phosphorus in non-equilibrium conditions