A correspondence between a class of monoids and self-similar group actions II

The first author showed in a previous paper that there is a correspondence between self-similar group actions and a class of left cancellative monoids called left Rees monoids. These monoids can be constructed either directly from the action using Zappa-Sz\'ep products, a construction that ultimately goes back to Perrot, or as left cancellative tensor monoids from the covering bimodule, utilizing a construction due to Nekrashevych, In this paper, we generalize the tensor monoid construction to arbitrary bimodules. We call the monoids that arise in this way Levi monoids and show that they are precisely the equidivisible monoids equipped with length functions. Left Rees monoids are then just the left cancellative Levi monoids. We single out the class of irreducible Levi monoids and prove that they are determined by an isomorphism between two divisors of its group of units. The irreducible Rees monoids are thereby shown to be determined by a partial automorphism of their group of units; this result turns out to be signficant since it connects irreducible Rees monoids directly with HNN extensions. In fact, the universal group of an irreducible Rees monoid is an HNN extension of the group of units by a single stable letter and every such HNN extension arises in this way.Comment: Some very minor corrections made and the dedication adde

Can the New Deal's Three R's Be Rehabilitated? A Program-by-Program, County-by-County Analysis

We examine the importance of Roosevelt's 'relief, recovery, and reform' motives to the distribution of New Deal funds across over 3,000 U.S. counties, program by program. The major relief programs most closely followed Roosevelt's three R's. Other programs were tilted more in favor of areas with higher incomes. For all programs spending for political advantage in upcoming elections was a significant factor. Roosevelt's successful reelections were based on developing specific programs for a broad range of constituents, delivering on his stated goals, but also spending more at the margin for political purposes.

Rotational predissociation of extremely weakly bound atom-molecule complexes produced by Feshbach resonance association

We study the rotational predissociation of atom - molecule complexes with very small binding energy. Such complexes can be produced by Feshbach resonance association of ultracold molecules with ultracold atoms. Numerical calculations of the predissociation lifetimes based on the computation of the energy dependence of the scattering matrix elements become inaccurate when the binding energy is smaller than the energy width of the predissociating state. We derive expressions that represent accurately the predissociation lifetimes in terms of the real and imaginary parts of the scattering length and effective range for molecules in an excited rotational state. Our results show that the predissociation lifetimes are the longest when the binding energy is positive, i.e. when the predissociating state is just above the excited state threshold.Comment: 17 pages, 5 figure

Single mode terahertz quantum cascade amplifier

A terahertz (THz) optical amplifier based on a 2.9 THz quantum cascade laser (QCL) structure has been demonstrated. By depositing an antireflective coating on the QCL facet, the laser mirror losses are enhanced to fully suppress the lasing action, creating a THz quantum cascade (QC) amplifier. Terahertz radiation amplification has been obtained, by coupling a separate multi-mode THz QCL of the same active region design to the QC amplifier. A bare cavity gain is achieved and shows excellent agreement with the lasing spectrum from the original QCL without the antireflective coating. Furthermore, a maximum optical gain of ∼30 dB with single-mode radiation output is demonstrated

Single mode terahertz quantum cascade amplifier

A terahertz (THz) optical amplifier based on a 2.9 THz quantum cascade laser (QCL) structure has been demonstrated. By depositing an antireflective coating on the QCL facet, the laser mirror losses are enhanced to fully suppress the lasing action, creating a THz quantum cascade (QC) amplifier. Terahertz radiation amplification has been obtained, by coupling a separate multi-mode THz QCL of the same active region design to the QC amplifier. A bare cavity gain is achieved and shows excellent agreement with the lasing spectrum from the original QCL without the antireflective coating. Furthermore, a maximum optical gain of ∼30 dB with single-mode radiation output is demonstrated

Mechanisms of fault mirror formation and fault healing in carbonate rocks

The development of smooth, mirror-like surfaces provides insight into the mechanical behaviour of crustal faults during the seismic cycle. To determine the thermo-chemical mechanisms of fault mirror formation, we investigated carbonate fault systems in seismically active areas of central Greece. Using multi-scale electron microscopy combined with Raman and electron energy loss spectroscopy, we show that fault mirror surfaces do not always develop from nanogranular volumes. The microstructural observations indicate that decarbonation is the transformation process that leads to the formation of smooth surface coatings in the faults studied here. Piercement structures on top of the fault surfaces indicate calcite decarbonation, producing CO2 and lime (CaO). Lime subsequently reacts to portlandite (Ca(OH)2) under hydrous conditions. Nanoscale imaging and electron diffraction reveal a thin coating of a non-crystalline material sporadically mixed with nano-clay, forming a complex-composite material that smooths the slip surface. Spectroscopic analyses reveal that the thin coating is non-crystalline carbon. We suggest that ordering (hybridisation) of amorphous carbon led to the formation of partly-hybridised amorphous carbon but did not reach full graphitisation. Calcite nanograins, 100 nm) and new nanograins formed by back-reaction (secondary nanograins, <50 nm). Hence, we suggest that the new, secondary nanograins are not the result of comminution during slip but originate from pseudomorphic replacement of calcite after portlandite. The continuous coverage of partly-hybridised amorphous carbon on all samples suggests that calcite decarbonation products may develop across the entire fault surface, controlling the formation of carbonate fault mirrors, and may facilitate slip on a decarbonation-product glide film.This study was funded by the Dutch research organisation (NWO) with the project number ALWOP.2015.082