We prove the convergence of moments of the number of directions of affine lattice vectors that fall into a small disc, under natural Diophantine conditions on the shift. Furthermore, we show that the pair correlation function is Poissonian for any irrational shift in dimension 3 and higher, including well-approximable vectors. Convergence in distribution was already proved in the work of Strömbergsson and the second author [The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems. Ann. of Math. (2) 172 (2010), 1949–2033], and the principal step in the extension to convergence of moments is an escape of mass estimate for averages over embedded $\operatorname {SL}(d,\mathbb {R})$-horospheres in the space of affine lattices.

In the multi-faceted trajectory of post-Kantian thought, Schelling—both the person and his philosophy—has always been a controversial figure. Popular historical accounts focus on his precocious interventions as part of the ‘Jena set’, initially building on Fichte's philosophy of the ‘I’, but quickly coming to challenge his predecessor's philosophical dominance. In the crucial period of the late 1790s, Schelling's most notable intervention was to develop a philosophy of nature alongside the Kantian and Fichtean theories of transcendental subjectivity, which caught the attention of Goethe and led to his appointment, at the age of twenty-three, as professor of philosophy at the University of Jena. But Schelling's life and philosophical work continued well beyond this well-documented period, culminating in a late system in which he developed key ideas surrounding freedom, existence, modality and the history of human consciousness that all revolved around a distinction between what he called negative and positive philosophy. This distinction, and his insistence on the need for the development of the latter mode of philosophy, came to challenge some of the core assumptions of the largely rationalist German idealist project and it remains, to this day, perhaps the most powerful alternative to the Hegelian system that rose to dominance already within Schelling's own lifetime, but also well beyond it.

The aim of this short note is to highlight a possible, hitherto unnoticed, telestich in Verg. Aen. 8.246–9, which presents the Greek word sēma (‘portent’, ‘wonder’, ‘prodigy’, ‘tomb’). To justify this identification, I will argue for its significance from its context in the poem (the battle between Hercules and Cacus), pointing out the insistence on the imagery of light and revelation, and the use of the phrase mirabile dictu, which appears in the same episode of the Aeneid, in the Latin poetic tradition.

Let $\mathcal {R}f$ be the randomization of an analytic function over the unit disk in the complex plane

$$ \begin{align*}\mathcal{R} f(z) =\sum_{n=0}^\infty a_n X_n z^n \in H({\mathbb D}), \end{align*} $$

$f(z)=\sum _{n=0}^\infty a_n z^n \in H({\mathbb D})$

$(X_n)_{n \geq 0}$

$f \in H({\mathbb D})$

${\mathcal R} f$

Open access (OA) publishing makes scholarship more accessible to readers but also presents additional hurdles for authors. This article examines determinants of OA publishing in well-respected, subscription-based journals. We find that research funding provides the strongest explanation for OA publishing, although various aspects of authorship and an author’s affiliation with a European versus a US institution also matter. We discuss the implications of our findings for publishing in scholarly journals in political science.

The Latin word lupus ‘wolf’ uniquely shares with Greek λύκος a metathesized form of Proto-Indo-European *u̯l̥kʷos, and it is unlikely that they could have arisen independently. But an early borrowing from Greek into the Italic languages can be justified, after metathesis took place, but before the changes to labiovelar consonants in each language that would exclude the possibility.

While historians have recently called attention to the racial assumptions that shaped the debates over monetary reform in either the colonial Philippines or China during the first years of the twentieth century, this article analyzes the crosscurrents between efforts to “civilize” and “develop” Filipino and Chinese monetary systems. It first examines the history of the Philippine money question (1899–1903), revealing anxieties about the apparent attachment Native Filipinos and Chinese had to silver currency. U.S. colonial officials were ambivalent toward the Native Filipinos, seeing them as possibly teachable, but so-called silver savagism was seen as too deeply engrained in the Chinese community, making the Chinese appear as a threat to monetary stability. In the last section, the article turns to China, revealing how the outcome of the Philippine money question shaped how U.S. monetary experts approached their efforts to reform China’s monetary system. Throughout this process, U.S. colonial officials and monetary experts defined the Philippines and China (“silver countries”) and Filipinos and Chinese (“silver-handling types”) as overlapping objects of development. This analysis reveals how development was simultaneously an economic, racial, and imperial language.

Can we formulate a moral theory that captures the moral significance of patterns of group behaviour we cannot affect through our own action while at the same time avoiding the so-called ‘Ideal Worlds’ objection? In a recent article, Caleb Perl has argued that we can. Specifically, Perl claims that one view that does so is his Patterned View: roughly, you ought to act only in accordance with that set of sufficiently general rules that has optimal moral value (Perl 2021: 98). The Patterned View undoubtedly constitutes a welcome contribution to our existing set of moral theories. However, does it avoid the Ideal Worlds objection? In this article, I argue ‘no’.

Multiple epidemiological studies have shown an increased prevalence of adverse mental health outcomes in refugee populations and have highlighted children and adolescents to be particularly at risk. This commentary considers a Cochrane Review examining the efficacy of community-based interventions at improving the mental health of refugee children and adolescents in high-income countries. The review concludes that community-based interventions are ineffective at improving mental health in such populations. Notably, the data are limited by significant risk of bias and a small sample size. This article aims to critically appraise this systematic review, extrapolate implications for current practice and identify avenues for further research.

We give a sharp estimate for the first eigenvalue of the Schrödinger operator $L:=-\Delta -\sigma $ which is defined on the closed minimal submanifold $M^{n}$ in the unit sphere $\mathbb {S}^{n+m}$, where $\sigma $ is the square norm of the second fundamental form.

Kvačekite is a new mineral species discovered in a sample collected from the now abandoned Bukov uranium mine, western Moravia, Czech Republic. It occurs as rare anhedral grains, up to 15 μm in size, associated with nickeltyrrellite, tyrrellite, berzelianite, hakite-(Zn), hakite-(Cd), eucairite, clausthalite, and gold in calcite gangue. In reflected light, kvačekite is white with a faint yellowish shade; bireflectance, pleochroism and anisotropy are absent. Internal reflections were not observed. Reflectance values for the four COM wavelengths for kvačekite in air [R (%) (λ in nm)] are: 54.9 (470); 53.5 (546); 52.6 (589); and 52.2 (650). The empirical formula, based on electron-microprobe analyses (EPMA), is (Ni0.95Cu0.04Co0.03)Σ1.02Sb1.00(Se0.97S0.01)Σ0.98. The ideal formula is NiSbSe, which requires (in wt.%) Ni 22.63, Sb 46.93, Se 30.44, total 100.00. Kvačekite is cubic, P213, with unit-cell parameters a = 6.09013(13) Å, V = 225.881(15) Å3 and Z = 4. The strongest reflections in the X-ray powder diffraction pattern of synthetic kvačekite [d, Å (I) hkl] are: 3.0458 (11) 200; 2.7242 (100) 201, 210; 2.4867 (71) 211; 1.8632(39) 311; 1.6277(29) 321, 312; and 1.3290 (13) 421. Given the similarity with ullmannite, NiSbS, the crystal structure was refined from the powder X-ray diffraction data starting from those atomic coordinates using the synthetic analogue of kvačekite. Its crystal structure is formed by corner-sharing [NiSb3Se3] octahedra which form a three-dimensional network. The identity of the natural kvačekite and synthetic cubic NiSbSe were confirmed by a study of their chemical composition, reflectance measurements, Raman spectroscopy and electron back-scattered diffraction (EBSD) measurements on the mineral. Kvačekite is named after Milan Kvaček (1930–1993), a prominent Czech mineralogist. The mineral and its name have been approved by the Commission on New Minerals, Nomenclature and Classification of the International Mineralogical Association (IMA2023-095).