Class invariants for certain non-holomorphic modular functions

Inspired by prior work of Bruinier and Ono and Mertens and Rolen, we study class polynomials for non-holomorphic modular functions arising from modular forms of negative weight. In particular, we give general conditions for the irreducibility of class polynomials. This allows us to easily generate infintely many new class invariants

Competition and Productivity Growth in South Africa

Using three different panel data sets, we show: (i) that mark-ups are significantly higher in South African manufacturing industries than they are in corresponding industries worldwide; (ii) that competition policy (i.e a reduction of mark-ups) should have largely positive effects on productivity growth in South Africa.

Relativistic scalar fields and the quasi-static approximation in theories of modified gravity

Relativistic scalar fields are ubiquitous in modified theories of gravity. An important tool in understanding their impact on structure formation, especially in the context of N-body simulations, is the quasi-static approximation in which the time evolution of perturbations in the scalar fields is discarded. We show that this approximation must be used with some care by studying linearly perturbed scalar field cosmologies and quantifying the errors that arise from taking the quasi-static limit. We focus on f(R) and chameleon models and link the accuracy of the quasi-static approximation to the fast/slow-roll behaviour of the background and its proximity to {\Lambda}CDM. Investigating a large range of scales, from super- to sub-horizon, we find that slow-rolling ({\Lambda}CDM-like) backgrounds generically result in good quasi-static behaviour, even on (super-)horizon scales. We also discuss how the approximation might affect studying the non-linear growth of structure in numerical N-body simulations.Comment: 19 pages, 9 figure

Ultrafast Response of Photoexcited Carriers in Transition Metal Oxides under High Pressure

In this work, optical pump – near-infrared probe and near-infrared pump – mid-infrared probe spectroscopy are used for the investigation of pressure-induced insulator-tometal transitions in transition metal oxide compounds. The materials under study are a-Fe₂O₃, also known as hematite, and VO₂. Both materials undergo pressureinduced metallization. However, the physical mechanisms of this phase transition are very different for these systems and have not been fully understood up to now. Using ultrafast pump-probe spectroscopy we obtain an insight into the evolution of the band structure and electron dynamics across the insulator-to-metal transition. In the case of VO₂, our near-infrared pump – mid-infrared probe experiments reveal a non-vanishing pumping threshold for photo-induced metallization even at our highest pressures around 20 GPa. This demonstrates the existence of localized charge carriers and the corresponding persistence of a band gap. Besides the threshold behaviour for photo-induced metallization, the carrier relaxation time scale, and the linear reflectivity and transmissivity have been studied under pressure increase. An anomaly in the threshold behaviour as well as the linear reflectivity and transmissivity at a critical pressure around 7 GPa indicates band gap filling under pressure. This is further supported by results obtained under decompression, where the changes of the linear reflectivity turned out to be almost fully reversible. The observations on VO₂ are highly reproducible and can be explained in terms of a pressure-induced bandwidth-driven insulator-to-metal transition. Fe₂O₃ has been studied via optical pump – near-infrared probe spectroscopy up to pressures of 60 GPa. In the pressure range up to 40 GPa, the changes of the response can be explained by photo-induced absorption and bleaching. The pressure-dependent study of the relaxation dynamics allows to identify cooling of the electron system as origin of the picosecond relaxation process

Competition and Productivity Growth in South Africa

This article shows that mark-ups are significantly higher in South African manufacturing industries than they are in corresponding industries worldwide. We test for the consequences of this low-level of product market competition on productivity growth. The results of the paper are that high mark-ups have a large negative impact on productivity growth in South African manufacturing industry. Our results are robust to three different data sources, two alternative measures of productivity growth, and three distinct measures of the mark-up. Controlling for potential endogeneity of regressors does not eliminate the findings. The definitive version is available at www3.interscience.wiley.com.Economic

Fully decoupled current control and energy balancing of the Modular Multilevel Matrix Converter

The Modular Multilevel Matrix Converter (M3C) is a Modular Multilevel Converter topology which is suitable for high power low speed drive applications. This paper presents a fully decoupled current control which allows an independent input, output and internal balancing current control. To equalize the energy stored in the nine converter arms, an energy and balancing control is presented which includes average, horizontal, vertical and diagonal balancing control loops. Simulation results are used to verify the function of the M3C together with an induction motor drive system. Additionally, the proper function of the recently constructed arm PCB working as single phase multilevel STATCOM is presented. This PCB will be used for each arm in the laboratory prototype of the M3C in the near future