Let Γ be a finite graph and let $A(\Gamma)$ be the corresponding right-angled Artin group. From an arbitrary basis $\mathcal B$ of $H^1(A(\Gamma),\mathbb F)$ over an arbitrary field, we construct a natural graph $\Gamma_{\mathcal B}$ from the cup product, called the cohomology basis graph. We show that $\Gamma_{\mathcal B}$ always contains Γ as a subgraph. This provides an effective way to reconstruct the defining graph Γ from the cohomology of $A(\Gamma)$, to characterize the planarity of the defining graph from the algebra of $A(\Gamma)$ and to recover many other natural graph-theoretic invariants. We also investigate the behaviour of the cohomology basis graph under passage to elementary subminors and show that it is not well-behaved under edge contraction.

How closely related are modern anti-democratic beliefs among white Americans, and to what extent are these beliefs shaped by exclusionary racial attitudes? Using data from the Political Unrest Study, the Collaborative Multiracial Post-Election Survey (CMPS), Democracy Fund + UCLA Nationscape, and the Survey of the Performance of American Elections (SPAE), we find that support for voting restrictions, opposition to voting expansions, belief in widespread voter fraud, and support for overturning democratic election results load onto a single underlying dimension. While the prevalence of anti-democratic beliefs among white Americans has remained stable over the past decade, these beliefs have become increasingly interconnected. Furthermore, racial attitudes towards out-groups—including racial resentment, anti-immigrant sentiment, and white racial grievance—strongly correlate with anti-democratic beliefs, whereas in-group racial attitudes do not. Analysis of multiple waves of the American National Election Studies (ANES) reveals that racial resentment and white grievance now explain twice as much variation in anti-democratic beliefs as they did in 2012. Experimental evidence also demonstrates that white Americans react negatively to voting expansions when the racial implications of these reforms are made explicit. These findings underscore the growing alignment between anti-democratic beliefs and racial attitudes in contemporary U.S. politics.

Five discrete bismuth telluride compositions, characterised by high and variable degrees of Pb and Se substitutions, were observed at the Stall Lake VMS deposit in the Snow Lake area, Canada. The major cation substitutions are Pb (3.0 to 11.0 wt.%), Fe (0.2 to 1.4 wt.%), Cu (up to 0.9 wt.%) and Ag (up to 3.2 wt.%). The main anion substitution is Se (0.3 to 7.9 wt.%); S never exceeds 0.3 wt.%. These results were compared to a literature data compilation of all publicly available data for the pure bismuth tellurides tsumoite and tellurobismuthite, and the Pb-bearing rucklidgeite and kochkarite. On the basis of these new data and the literature compilation, a few generalisations about the substitutions in bismuth tellurides can be made. The major conclusion is that bismuth tellurides always contain at least some substitutional cations (Pb, Ag, Fe, Cu, Sb and Au), typically combining to ∼2 wt.% if Pb is excluded, and anions (mostly Se and some S, typically <1 wt.% combined). Another conclusion is that bismuth tellurides have highly variable compositions, which can be quite far from their theoretical ones, to the point of defining specific mineral varieties such as high-Pb tsumoite, low-Pb kochkarite, and high-Se rucklidgeite. Two high-Se bismuth telluride compositions were observed at Stall Lake (average Se ≈ 4.9 and ≈ 7.2 wt.%), which had never been documented before. This observation, in conjunction with the bismuth tellurides literature data, emphasises the high potential for both cation and anion substitutions in these minerals.

We compute primes $p \equiv 5 \bmod 8$ up to $10^{11}$ for which the Pellian equation $x^2-py^2=-4$ has no solutions in odd integers; these are the members of sequence A130229 in the Online Encyclopedia of Integer Sequences. We find that the number of such primes $p\leqslant x$ is well approximated by

$$ \begin{align*}\frac{1}{12}\pi(x) - 0.037\int_2^x \frac{dt}{t^{1/6}\log t},\end{align*} $$

where $\pi (x)$ is the usual prime counting function. The second term shows a surprising bias away from membership of this sequence.

We consider interacting urns on a finite directed network, where both sampling and reinforcement processes depend on the nodes of the network. This extends previous research by incorporating node-dependent sampling and reinforcement. We classify the sampling and reinforcement schemes, as well as the networks on which the proportion of balls of either colour in each urn converges almost surely to a deterministic limit. We also investigate conditions for achieving synchronisation of the colour proportions across the urns and analyse fluctuations under specific conditions on the reinforcement scheme and network structure.

We prove structural results for measure-preserving systems, called Furstenberg systems, naturally associated with bounded multiplicative functions. We show that for all pretentious multiplicative functions, these systems always have rational discrete spectrum and, as a consequence, zero entropy. We obtain several other refined structural and spectral results, one consequence of which is that the Archimedean characters are the only pretentious multiplicative functions that have Furstenberg systems with trivial rational spectrum, another is that a pretentious multiplicative function has ergodic Furstenberg systems if and only if it pretends to be a Dirichlet character, and a last one is that for any fixed pretentious multiplicative function, all its Furstenberg systems are isomorphic. We also study structural properties of Furstenberg systems of a class of multiplicative functions, introduced by Matomäki, Radziwiłł, and Tao, which lie in the intermediate zone between pretentiousness and strong aperiodicity. In a work of the last two authors and Gomilko, several examples of this class with exotic ergodic behavior were identified, and here we complement this study and discover some new unexpected phenomena. Lastly, we prove that Furstenberg systems of general bounded multiplicative functions have divisible spectrum. When these systems are obtained using logarithmic averages, we show that a trivial rational spectrum implies a strong dilation invariance property, called strong stationarity, but, quite surprisingly, this property fails when the systems are obtained using Cesàro averages.

This article offers the first detailed study of a manuscript preserving notes from the Modern Greek course held in 1801-2 by Jean-Baptiste-Gaspard d'Ansse de Villoison in Paris. The notebook was kept by Karl Benedikt Hase, later Professor of Modern Greek at the French École de langues orientales vivantes, during his attendance of Villoison's course as a student. The article sketches first the historical context of the notebook, before an analysis of its contents, and finally a comparison with Hase's later published work on the primary text at its core, Amiras’ Greek translation of Costin's History of Moldavia.

Mango is a delicious tropical fruit with high economic value worldwide. The Forest-Savanna Transition zone of Ghana contributes significantly to the production of mangoes for both local and international markets. The zone is plagued with the fruit fly ‘menace’ like all mango-producing areas in Ghana. Not much has been done in terms of species monitoring. A 24- month fruit fly monitoring survey was conducted in eight mango orchards, to assess the composition of fruit flies associated with Mango and their damage levels. Four para-pheromone attractants (Methyl Eugenol, Terpinyl Acetate, Trimedlure, and Cuelure) were used to monitor fruit flies. Eight improvised water bottle traps (two per lure) were purposefully deployed in each orchard. A total of 18 tephritid species belonging to five genera were recorded. Bactrocera (one species), Ceratitis (six species), Dacus (eight species), Zeugodacus (one species) and Xanthaciura (two species). Bactrocera dorsalis was the most abundant species (90% of the collected samples), while the native mango fly, C. cosyra constituted 0.5%. Dacus fuscovittatus and Dacus pleuralis were for the first time captured and identified in Ghana. Dacus langi, Dacus carnesi, Dacus (diastatus?), Ceratitis silvestrii and C. quinaria were recorded for the first time in the zone. The zone recorded a diversity index of 0.41. Damage levels ranged from 41–91%. Ten out of the 18 species, are of economic importance on mango and must be watched. Periodic updates on seasonal fluctuations, species composition and new arrivals are key to the successful implementation of any management strategy.

The aim of this paper is to give a full exposition of Leibniz’s mereological system. My starting point will be his papers on Real Addition, and the distinction between the containment and the part-whole relation. In the first part (§2), I expound the Real Addition calculus; in the second part (§3), I introduce the mereological calculus by restricting the containment relation via the notion of homogeneity which results in the parthood relation (this corresponds to an extension of the Real Addition calculus via what I call the Homogeneity axiom). I analyze in detail such a notion, and argue that it implies a gunk conception of (proper) part. Finally, in the third part (§4), I scrutinize some of the applications of the containment-parthood distinction showing that a number of famous Leibnizian doctrines depend on it.