We give a new proof of the singular continuity of Minkowski’s $?$-function. Our proof follows by showing that the maximal Lyapunov exponent of a specific pair of $3\times 3$ nonnegative integer matrices related to Stern’s diatomic sequence is strictly greater than $\log 2$.

Silvennoinen (2025) analyzes the stored sequence going forward as an adverb that inherits adverb-class morphosyntax. This reply challenges that categorization on empirical grounds. The construction fails the key distributional test for adverbs: it cannot occur in integrated-medial position between subject and verb (*We going forward will prioritize replication), the diagnostic slot for core adverbs (We certainly will prioritize replication). Analysis of Silvennoinen’s corpus (n = 1,517) confirms this restriction – apparent ‘medial’ tokens prove either to be NP-internal modifiers or parenthetical supplements, never integrated clausal constituents. Instead, going forward patterns with PP adjuncts, occurring clause-initially, clause-finally, or as supplements. Internally, deverbal going heads the construction and licenses a directional complement forward(s), parallel to established deverbal prepositions like according [to …] and depending [on …]. The construction thus projects PP, not AdvP, aligning with The Cambridge Grammar of the English Language’s flexible-complement analysis of prepositions. This case demonstrates that storage and semantic specialization do not force categorical reanalysis.

El comercio transpacífico entre América Latina y Asia Oriental durante el período previo a la Segunda Guerra Mundial ha sido escasamente estudiado. En este artículo, analizamos la construcción desde Argentina del vínculo mercantil con Japón entre 1934 y 1940. Al hacerlo, ponderamos las oportunidades y las limitaciones que surgieron en un contexto de des-globalización económica, y arrojamos luz sobre las posibilidades de diversificación geográfica del comercio exterior argentino. Abordando diversas fuentes de los sectores público y privado, el estudio revela que las iniciativas gubernamentales por profundizar los lazos con el socio oriental, apoyadas por los agroexportadores, enfrentó críticas de los empresarios textiles, quienes acusaron a Japón de ejercer dumping financiero y social.

Resource restrictions and changes to the ways in which psychiatrists are managed threaten professional autonomy and motivation. With examples from English National Health Service practice, maintaining knowledge and expertise, involvement in education and training, supporting research delivery and developing active followership skills represent transferable and realistic strategies that can improve psychiatrists’ autonomy wherever they work.

The Harnischia complex of the tribe Chironomini (Diptera: Chironomidae) comprises 20 genera. In the present study, we contribute to the taxonomic understanding of the genera Beckidia Sæther, Cryptochironomus Kieffer, and Cryptotendipes Beck and Beck of this complex in India. Our study employed an integrative taxonomic approach, incorporating morphological characteristics and molecular tools, to describe a new Cryptotendipes species. The genus Cryptotendipes, which comprises 26 species globally, is represented by five species in India, including the species that is newly described in the present study. In addition, we report new faunistic records for Beckidia hirsti (Freeman, 1957) and Cryptochironomus tamaichimori Sasa in Sasa and Kawai, 1987 for the first time from India.

Let $\gamma _{n}= O (\log ^{-c}n)$ and let $\nu $ be the infinite product measure whose nth marginal is Bernoulli $(1/2+\gamma _{n})$. We show that $c=1/2$ is the threshold, above which $\nu $-almost every point is simply Poisson generic in the sense of Peres and Weiss, and below which this can fail. This provides a range in which $\nu $ is singular with respect to the uniform product measure, but $\nu $-almost every point is simply Poisson generic.

Considerable evidence survives of the cooking and eating of kebabs as a major form of meat consumption in early China. Not only are there numerous artistic depictions in both painting and low-relief stone sculpture of this practice, but there are also some very early excavated skewers, grills, and indeed preserved meat kebabs, not to mention references in contemporary literature, and this evidence significantly predates any documentation of kebabs in the Middle East. However, in spite of this wealth of documentation, this tradition has gone largely unexplored, partly due to scholars failing to understand the relevant terminology and partly due to an unjustified belief that all kebab cooking must derive from the Middle East. This article explores the indigenous ancient Chinese tradition of kebab cooking, focused on grilling and roasting of smaller (luan) or larger (zi) pieces of meat seasoned with soybean pastes and sauces, which developed independently of other similar culinary practices elsewhere. This analysis is focused on literary evidence of the Chinese kebab, with particular reference to the contents of a recently discovered very early cookbook, dating to the Han Dynasty, excavated from the tomb of Wu Yang, first marquis of Yuanling, who died in 162 BCE.

Cette étude porte sur le changement linguistique en lien avec la référence temporelle au futur en français québécois du 21e siècle dans les données du Corpus de français parlé au Québec (CFPQ), qui couvrent la période 2006–2019. Trois variantes sont analysées: le présent du futur (PDF), le futur fléchi (FF) et le futur périphrastique (FP). Bien que plusieurs contraintes identifiées précédemment jouent un rôle semblable dans la variation (p. ex. la polarité, la présence de locutions adverbiales temporelles), la présente étude montre les taux les plus élevés de PDF en français québécois parmi les études antérieures consultées. Selon une interprétation en temps apparent, il y a une augmentation du PDF en contexte affirmatif et négatif qui n’est pas attribuable à un effet lexical. Ce résultat suggère que le PDF jouerait un rôle important dans le changement en cours par rapport à la référence temporelle au futur en français québécois.

Given $\beta>1$, let $T_\beta $ be the $\beta $-transformation on the unit circle $[0,1)$, defined by $T_\beta (x)=\beta x-\lfloor \beta x\rfloor $. For each $t\in [0,1)$, let $K_\beta (t)$ be the survivor set consisting of all $x\in [0,1)$ whose orbit $\{T^n_\beta (x): n\ge 0\}$ never enters the interval $[0,t)$. Kalle et al [Ergod. Th. & Dynam. Sys. 40(9) (2020), 2482–2514] considered the case $\beta \in (1,2]$. They studied the set-valued bifurcation set $\mathscr {E}_\beta :=\{t\in [0,1): K_\beta (t')\ne K_\beta (t)~\text { for all } t'>t\}$ and proved that the Hausdorff dimension function $t\mapsto \dim _H K_\beta (t)$ is a non-increasing Devil’s staircase. In a previous paper [Ergod. Th. & Dynam. Sys. 43(6) (2023), 1785–1828], we determined, for all $\beta \in (1,2]$, the critical value $\tau (\beta ):=\min \{t>0: \eta _\beta (t)=0\}$. The purpose of the present article is to extend these results to all $\beta>1$. In addition to calculating $\tau (\beta )$, we show that: (i) the function $\tau : \beta \mapsto \tau (\beta )$ is left-continuous on $(1,\infty )$ with right-hand limits everywhere, but has countably infinitely many discontinuities; (ii) $\tau $ has no downward jumps; and (iii) there exists an open set $O\subset (1,\infty )$, whose complement $(1,\infty )\setminus O$ has zero Hausdorff dimension, such that $\tau $ is real-analytic, strictly convex, and strictly decreasing on each connected component of O. We also prove several topological properties of the bifurcation set $\mathscr {E}_\beta $. The key to extending the results from $\beta \in (1,2]$ to all $\beta>1$ is an appropriate generalization of the Farey words that are used to parameterize the connected components of the set O. Some of the original proofs from the above-mentioned papers are simplified.

Recent work showing the existence of conflict-free almost-perfect hypergraph matchings has found many applications. We show that, assuming certain simple degree and codegree conditions on the hypergraph $ \mathcal{H}$ and the conflicts to be avoided, a conflict-free almost-perfect matching can be extended to one covering all vertices in a particular subset of $ V(\mathcal{H})$, by using an additional set of edges; in particular, we ensure that our matching avoids all additional conflicts, which may consist of both old and new edges. This setup is useful for various applications in design theory and Ramsey theory. For example, our main result provides a crucial tool in the recent proof of the high-girth existence conjecture due to Delcourt and Postle. It also provides a black box which encapsulates many long and tedious calculations, greatly simplifying the proofs of results in generalised Ramsey theory.

Through the concept of the global sound archive, we propose a holistic perspective to study the sound universe accessible through the Internet. This concept refers to a reservoir of extremely heterogeneous, expansive, and unstable sound fixations that include musical expressions, soundscapes, corporeal sounds, voice messages generated through instant messaging apps, podcasts, and many other sonic phenomena. In the development of the article, we describe how agents contribute to this archive, where the sound fixations it contains are hosted, and what its central attributes are. This investigation is informed by concepts of diversity, expansiveness, instability, modularity, and intermediality.1

Excavations at the Agora of Amathous, Cyprus, were carried out between 1977 and 2003, initially under the auspices of the Department of Antiquities and the direction of Michael Loulloupis, and subsequently by the French School at Athens, under the direction of Jean-Paul Prête. While the plans and chronological phases of the Agora’s buildings have been successfully reconstructed, the rich assemblage of architectural decorations – exceptionally well preserved – has yet to be thoroughly studied. The remarkable state of preservation and completeness was the primary motivation for undertaking the current research, which aims to identify the fragments of architectural decoration with their respective stoas. The reconstructed decorative program significantly enhances our understanding of historical Cypriot architecture, illuminating the influence of Alexandria and other Mediterranean centers on architectural trends. It highlights how agoras were framed with colonnaded stoas that combined traditional elements with innovative designs, revitalizing the architectural landscape of Cyprus in the Hellenistic and Roman periods.