Carlsen [‘$\ast $-isomorphism of Leavitt path algebras over $\Bbb Z$’, Adv. Math. 324 (2018), 326–335] showed that any $\ast $-homomorphism between Leavitt path algebras over $\mathbb Z$ is automatically diagonal preserving and hence induces an isomorphism of boundary path groupoids. His result works over conjugation-closed subrings of $\mathbb C$ enjoying certain properties. In this paper, we characterise the rings considered by Carlsen as precisely those rings for which every $\ast $-homomorphism of algebras of Hausdorff ample groupoids is automatically diagonal preserving. Moreover, the more general groupoid result has a simpler proof.

In this note, we start on the study of the sufficient conditions for the boundedness of Hausdorff operators

$$ \begin{align*}(\mathcal{H}_{K,\mu}f)(z):=\int_{\mathbb{D}}K(w)f(\sigma_w(z))d\mu(w)\end{align*} $$

$\mu $

$\mu $

$\mathbb {D}$

$\sigma _w(z)$

$\mathbb {D}$

This paper examines how unionization affects economic growth through its impact on industry concentration in a two-country model of international trade and endogenous productivity growth. Knowledge spillovers link firm-level productivity in innovation with geographic patterns of industry ensuring a faster rate of output growth when industry is relatively concentrated in the country with the greater labor supply. We show that stronger bargaining power in the relatively large country increases the rate of output growth when labor unions are employment-oriented but decreases the rate of growth when unions are wage-oriented. We then calibrate the model using labor market data for the United Kingdom and France and study the effects of union bargaining power on industry location patterns, output growth, and national welfare.

Although federal judges are the ultimate arbiters of insider trading enforcement, the role of their political ideology in insider trading is unclear. Using the partisanship of judges’ nominating presidents to measure judge ideology, we first document that liberal judges are associated with heavier penalties in insider trading lawsuits than conservative judges. Next, we find that firms located in circuits with more liberal judges have fewer opportunistic insider sales. Cross-sectional analyses show that this deterrent effect is stronger when managers face a higher risk of insider trading lawsuits. Finally, we find that the Securities and Exchange Commission considers judges’ ideology when selecting litigation forums.

This paper initiates the reverse mathematics of social choice theory, studying Arrow’s impossibility theorem and related results including Fishburn’s possibility theorem and the Kirman–Sondermann theorem within the framework of reverse mathematics. We formalise fundamental notions of social choice theory in second-order arithmetic, yielding a definition of countable society which is tractable in ${\mathsf {RCA}}_0$. We then show that the Kirman–Sondermann analysis of social welfare functions can be carried out in ${\mathsf {RCA}}_0$. This approach yields a proof of Arrow’s theorem in ${\mathsf {RCA}}_0$, and thus in $\mathrm {PRA}$, since Arrow’s theorem can be formalised as a $\Pi ^0_1$ sentence. Finally we show that Fishburn’s possibility theorem for countable societies is equivalent to ${\mathsf {ACA}}_0$ over ${\mathsf {RCA}}_0$.

The majority of studies on ‘faith’ (fides) in the thought of Thomas Aquinas consider it in a religious or theological context: fides as the theological virtue by which one assents to the truths of divine revelation. The focus on theological faith is appropriate, given its central importance as a theological virtue, but this is not the only sense of fides that Thomas identifies. The present study investigates two non-theological senses formulated in his commentary on the De Trinitate of Boethius: first, fides as the proximate cause of assenting to principles within a given science (‘epistemic faith’) and, second, fides as an indispensable element of society (‘societal faith’). These senses have been largely overlooked in secondary literature but, I argue, might help to dispel mischaracterizations of faith as fundamentally unreasonable.

Tertiary weathered sediments located immediately to the west of the harbor at Newhaven, Sussex, UK, were investigated by examination of major and trace elements by scanning electron microscope (SEM), microprobe, and inductively coupled plasma mass spectrometer (ICP-MS), and the mineralogy was studied by optical petrography, X-ray diffraction (XRD), transmission electron microscope (TEM), selective leaching, and thermodynamic modeling. Studied outcrops experienced acid leaching by sulfuric acid percolating downward through Tertiary sediments overlying Cretaceous chalk. The progressive neutralization of the percolating acid fluids resulted in “sequentially” layered neoformation of minerals: jarosite, iron oxides, aluminous minerals (sulfates, oxyhydroxides), gypsum, and Fe-Mn oxides. Substantial agreement was found between field observations and mineral assemblages obtained by modeling with the program CHILLER. These results suggest that the initial assumptions on the weathering process and mechanisms are correct. The relevance and implications of this study in the modeling of future denudation and weathering processes of radioactive waste-disposal sites (both deeply buried sites for high-leveI waste and surface sites for low-level waste) are discussed. Neoformed phases, such as jarosite, aluminous minerals, and silico-aluminous gels may play a significant role in the efficient trapping of mobilized pollutant radionuclides.

Selected Brazilian Oxisols were sampled and submitted to high-gradient magnetic separation (HGMS) to study the iron oxide-clay mineral associations. The soils, derived from four different parent materials, have mineralogy dominated mostly by hematite, goethite, and kaolinite. Gibbsite appears in most soil samples. The high-gradient magnetic separation showed good separation for some soils, as indicated by color differentiation and iron oxide segregation between magnetic and nonmagnetic fractions. Soils that showed a somewhat low surface area for the iron oxides associated with high phosphate adsorption were poorly separated by HGMS. This suggests a strong interaction between kaolinite and iron oxides, which would indicate a low estimation of their surface areas obtained by the difference method using BET-N2 data. A relative concentration of anatase and rutile in the magnetic portion of some of the samples was attributed to the presence of Fe, either as coatings on the crystals or within the structure of these two minerals.

The importance of precipitation rate as an effective control on illite and kaolanite formation during diagenesis has been examined by measuring precipitation rates, from Al fluid concentration, in a Dickson fluid-sampling vessel at 160°-250° and 500 bars (50 MPa). These experiments are considered to be analogues of the precipitation of clays in sandstones from porewaters containing dissolved carboxylic acids, which have a transient stability and may influence aluminosilicate solubility. Precipitated illite had a lath-shaped morphology and its composition was consistent with authigenic illite in sandstones. Kaolinite formed tabular rather than vermicular shaped crystals. Kaolinite precipitation rate was two orders of magnitude faster than illite precipitation and was rate-limited by the decomposition of oxalate; kaolinite formation should be equilibrium-controlled at virtually all stages of burial. Extrapolation of illite precipitation rate to burial temperatures indicates that the first appearance of illite in a burial sequence may be kinetically controlled. A model of illite precipitation based on these experimental results has been used to predict the time required to precipitate illite during burial of a sandstone, taking into account temperature changes during burial. For northern North Sea examples, a predicted illitization threshold of -60°C occurring at 60–80 Ma corresponds to the observed initiation of authigenic illite precipitation. Times of around 2–5 Ma would be required to reach a 98% approach to equilibrium at this threshold. The main phase of illite precipitation in the northern North Sea basin is a later, hydrologically controlled event (30-50 Ma). Equilibrium would be approached in around 0.1 Ma during this phase, which is consistent with the narrow illite K/Ar age range (1-5 Ma) recorded for some sequences.

The fine silt (2–5 μm) coarse clay (0.1–2 μm) and fine clay (<0.1 μm) fractions of a Vertisol from South Italy were studied with X-ray diffraction. The most reactive fine clay (<0.1 μm) fraction was investigated in detail using a curve decomposition method analysis of X-ray diffraction diagrams, FTIR spectroscopy and chemical analysis. In the soil parent material, the fine clay fraction was dominated by low-charge smectites (beidellite and montmorillonite) whereas, high-charge beidellite was the dominant clay mineral in the fine clay from the upper soil horizons. This suggested that high-charge beidellite was produced through alteration of the preexisting low-charge smectites and was the stable clay phase in this soil environment, characterized by high pH (>8.0). After K-saturation and 25 wetting and drying cycles, the high-charge beidellite from the soil horizons lost expandability far more than the original low-charge smectites.

The dissolution of two Ca2+-exchanged nontronite samples has been studied in 10% HCl. Early acid-dissolution studies (Osthaus, 1954) have indicated that after two hours of dissolution most of the octahedral Fe3+ (VIFe3+) would be removed leaving mainly tetrahedral Fe3+ (IVFe3+) in the nontronite structure. In the present study, 57Fe Mössbauer spectra of acid-treated samples were recorded and fitted with two octahedral Fe3+ (2 × VIFe3+) and two octahedral and one tetrahedral (2 × VIFe3+, 1 × IVFe3+) doublet models. The Mössbauer spectra of acid-treated Garfield nontronite samples could be adequately fitted with two-doublet models but acid-treated Hohen Hagen nontronite samples could not. Isomer shift and quadrupole splitting values obtained from the two-doublet models corresponded to VIFe3+ and not IVFe3+, as was suggested by the Osthaus (1954) experiment. When an IVFe3+ doublet was included in the model used to fit the Mössbauer spectra of acid-treated Garfield nontronite samples, a slight increase in the intensity of the IVFe3+ doublet occurred with increasing dissolution, but this was much lower than indicated by Osthaus (1954). No trend in the intensity of the IVFe3+ doublet was observed for acid-treated Hohen Hagen nontronite. Therefore, acid treatment appears to remove VIFe3+ and IVFe3+ from the nontronite structure at about the same rate. Mössbauer spectroscopy, infrared spectroscopy and X-ray powder diffraction data indicate that the nontronite that remains undissolved following acid treatment is structurally similar to the untreated nontronite.