We provide a uniform bound on the partial sums of multiplicative functions under very general hypotheses. As an application, we give a nearly optimal estimate for the count of $n \le x$ for which the Alladi–Erdős function $A(n) = \sum_{p^k \parallel n} k p$ takes values in a given residue class modulo q, where q varies uniformly up to a fixed power of $\log x$. We establish a similar result for the equidistribution of the Euler totient function $\phi(n)$ among the coprime residues to the ‘correct’ moduli q that vary uniformly in a similar range and also quantify the failure of equidistribution of the values of $\phi(n)$ among the coprime residue classes to the ‘incorrect’ moduli.

The evolving global order and regional dynamics have profoundly impacted China-Southeast Asia relations. As the world grapples with the geopolitical implications of intensified US-China competition, the Association of Southeast Asian Nations countries find themselves navigating a complex interplay of opportunities and challenges. The US-led Indo-Pacific strategy has significantly reshaped the geopolitical landscape, yet Southeast Asia’s relations with China are marked by interwoven challenges and opportunities. This special issue includes six papers that cover Malaysia, Vietnam, Thailand, Indonesia, Cambodia, and the Philippines, illustrating how small and medium-sized states navigate an increasingly multipolar world. A central theme across the papers in this special issue is the critical role of domestic factors in shaping each country’s relationship with China.

The notion of Vasconcelos invariant, known in the literature as v-number, of a homogeneous ideal in a polynomial ring over a field was introduced in 2020 to study the asymptotic behavior of the minimum distance of projective Reed–Muller type codes. We initiate the study of this invariant for graded modules. Let R be a Noetherian $\mathbb {N}$-graded ring and M be a finitely generated graded R-module. The v-number $v(M)$ can be defined as the least possible degree of a homogeneous element x of M for which $(0:_Rx)$ is a prime ideal of R. For a homogeneous ideal I of R, we mainly prove that $v(I^nM)$ and $v(I^nM/I^{n+1}M)$ are eventually linear functions of n. In addition, if $(0:_M I)=0$, then $v(M/I^{n}M)$ is also eventually linear with the same leading coefficient as that of $v(I^nM/I^{n+1}M)$. These leading coefficients are described explicitly. The result on the linearity of $v(M/I^{n}M)$ considerably strengthens a recent result of Conca which was shown when R is a domain and $M=R$, and Ficarra–Sgroi where the polynomial case is treated.

A 1st-c. CE lamp from Cyprus, now in the Metropolitan Museum of Art, features a discus design of a satyr on a base before an enclosure. Formerly identified as a nude silenus, the design on this lamp and others with the same decoration in fact illustrates a motif after the Forum Marsyas statue from the Forum Romanum. The statue is typically understood as a symbol of civic libertas, and copies were erected in provincial fora and depicted on civic coinage in the 2nd and 3rd c. CE. This note argues that the lamps enhance our understanding of the Forum Marsyas in two respects. First, the lamps demonstrate that the motif was in provincial circulation ahead of the sculptural and numismatic trend. Second, it is now clear that the Forum Marsyas was used in private contexts, and potentially with a non-civic meaning, more extensively than previously understood. The lamps are therefore significant for understanding the provincial spread and legibility of this important but still enigmatic motif.

The triangle removal states that if G contains $\varepsilon n^2$ edge-disjoint triangles, then G contains $\delta (\varepsilon )n^3$ triangles. Unfortunately, there are no sensible bounds on the order of growth of $\delta (\varepsilon )$, and at any rate, it is known that $\delta (\varepsilon )$ is not polynomial in $\varepsilon $. Csaba recently obtained an asymmetric variant of the triangle removal, stating that if G contains $\varepsilon n^2$ edge-disjoint triangles, then G contains $2^{-\operatorname {\mathrm {poly}}(1/\varepsilon )}\cdot n^5$ copies of $C_5$. To this end, he devised a new variant of Szemerédi’s regularity lemma. We obtain the following results:

• • We first give a regularity-free proof of Csaba’s theorem, which improves the number of copies of $C_5$ to the optimal number $\operatorname {\mathrm {poly}}(\varepsilon )\cdot n^5$.

• • We say that H is $K_3$-abundant if every graph containing $\varepsilon n^2$ edge-disjoint triangles has $\operatorname {\mathrm {poly}}(\varepsilon )\cdot n^{\lvert V(H)\rvert }$ copies of H. It is easy to see that a $K_3$-abundant graph must be triangle-free and tripartite. Given our first result, it is natural to ask if all triangle-free tripartite graphs are $K_3$-abundant. Our second result is that assuming a well-known conjecture of Ruzsa in additive number theory, the answer to this question is negative.

Our proofs use a mix of combinatorial, number-theoretic, probabilistic and Ramsey-type arguments.

The influence of appetite and energy intake on energy compensation in response to chronic exercise remains poorly understood. This study examined the temporal impact of habitual exercise on energy intake and the homeostatic appetite regulators that influence energy compensation. Twelve-week-old male Sprague Dawley rats (n=30) fed an AIN-93M diet were randomised into 1 of 3 groups: 1) sedentary control (SED); 2) voluntary wheel exercise (EX); and 3) sedentary, weight-matched to aerobic exercise (SED-WM) for 8 weeks. Measures of energy intake, body weight, and adiposity were assessed. Appetite-regulating hormones acyl-ghrelin, active GLP-1, leptin, and insulin were measured in response to an oral glucose tolerance test. Rats with running wheels completed an average of 192kms over 8 weeks. While energy intake was initially reduced in EX, energy intake gradually increased with exercise training after week 1 (P<0.05). Body weight was lower in EX relative to SED from weeks 3-5, but did not differ at the end of the study. Fat mass and long-term satiety hormones leptin and insulin were lower in EX (P<0.05). No differences were observed in concentrations of the satiety hormone active GLP-1 or the orexigenic hormone acyl-ghrelin. Short-term homeostatic regulators of appetite do not appear to be altered with exercise training. The reduction in adiposity and associated decrease in tonic satiety hormones leptin and insulin are likely contributors to the coupling of energy expenditure with energy intake over time with voluntary exercise.

Safe and effective navigation of the world's oceans and waterways relies on maritime education and training. This involves the learning of motor, procedural and verbal components of complex skills. Motor learning theory evaluates training variables, such as instructions, feedback and scheduling, to determine best practices for long-term retention of such skills. Motor learning theory has come a long way from focusing primarily on underlying cognitive processes to now including individual and contextual characteristics in making predictions about instructional strategies and their role in performance and learning. A remaining challenge in applying recent motor learning theory to maritime education and training is a lack of empirical testing of complex vocational skills, such as simulation scenarios, with delayed retention and transfer tests. Incorporating theory-based understanding of beneficial instructional practices, through both cognitive approaches and those considering context and environment, task complexity and learner characteristics is a fruitful way forward in advancing maritime education and training.

Around the turn of the twentieth century, U.S. newspapers began to address women specifically in separate sections, hoping to gather a female audience for advertisers. Scholarship on early twentieth-century women consumers tends to emphasize possibility and self-expression. Women’s reactions to the first women’s pages, by contrast, indicate that they could feel constrained and condescended to when welcomed into the public sphere on the basis of being consumers. Readers and journalists aired their grievances about the women’s page in its first decades, and sometimes found ways to use the page to their own ends. But publishers carried on designing women’s features with advertisers in mind. By the 1920s, the women’s page had become visually seductive, didactic, domestic, and relentlessly consumerist. This article uses the women’s page to investigate the rise of ad-subsidized media in the twentieth century and to weigh up the opportunities and costs of this media system.

In a time of unprecedented displacement, hostility toward refugees is widespread. Two common strategies refugee advocates pursue to counter hostility and promote inclusion are perspective-getting exercises and providing information that corrects misperceptions. In this study, we evaluate whether these strategies are effective across four outcomes commonly used to measure outgroup inclusion: warmth toward refugees, policy preferences, behavior, and beliefs about a common misperception concerning refugees. Using three studies with nearly 15,000 Americans, we find that information and perspective-getting affect different outcomes. We show that combining both interventions produces an additive effect on all outcomes, that neither strategy enhances the other, but that bundling the strategies may prevent backfire effects. Our results underscore the promise and limits of both strategies for promoting inclusion.

This paper explores the modernisation of rural Southern Italy between 1950 and 1962, focusing on the role of the Cassa per il Mezzogiorno, a public entity created to address the socio-economic divide between the North and South of Italy. The Cassa was central to the restructuring of rural areas, promoting land reclamation, infrastructure development, and the electrification of agricultural regions. The study examines how the ‘agrarian question’ intersected with the broader ‘Southern question’, reflecting persistent economic disparities within Italy. By analysing the early stages (1950–1962) of extraordinary intervention, this article demonstrates that modernisation efforts were aimed not only at reducing regional imbalances but also at addressing structural deficiencies that hindered agricultural productivity. While significant progress was made in modernising rural Southern Italy, this paper argues that the foundational agricultural reforms, although vital, needed to be complemented by broader industrial policies to ensure long-term socio-economic convergence with the more developed North.

To be effective, central bankers must project expertise and an anti-inflation commitment. However, those attributes are usually male-coded, which may undermine female central bankers. We assess gender bias using a survey experiment fielded in Japan in September 2022, when, for the first time in decades, the Bank of Japan appeared to struggle with inflation. We exposed individuals to simplified Bank of Japan communication and randomly assigned attribution to male (Mr. Adachi) or female (Ms. Nakagawa) Policy Board members. Respondents trusted the Bank of Japan less and were more sceptical of its capacity to handle inflation when Ms. Nakagawa represented it.

The COVID-19 pandemic response made extraordinary demands on the public health workforce. In response to national studies and local observations about trauma in public health personnel, the Arizona Department of Health Services (ADHS) broadened the scope of their Health Emergency Operations Center (HEOC) Safety Officer position to include not only physical, but mental, emotional, and workplace health and safety. The new Health and Safety Officer (HSO) began in August 2022 and served through the end of the COVID-19 activation. The HSO advocated for staff, counseled HEOC leadership, and validated leadership’s prioritization of the health and wellness of HEOC staff. The impact of the HSO was felt within the HEOC and beyond, and this position should be considered a cost-effective, meaningful intervention in all jurisdictions to protect public health personnel. The HSO position is now a permanent part of the ADHS HEOC.

Identifying cryptic species and juveniles in the Ophiuroidea has always been a challenge. However, post-larval developmental studies have the potential to uncover the identity of these cryptic species and juveniles, as they offer valuable information that is not often found in adults. Although the importance of studying growth series is well-known in ophiuroids, it is difficult to obtain and identify the juvenile stages. For this reason, most studies are restricted to brooding species and information is lacking for many species, including those of the genus Ophiocoma. In this study, a growth series was developed to show the main differences during the development of two similar species of Ophiocoma: Ophiocoma echinata and Ophiocoma trindadensis. Using morphometry and scanning electron microscopy, we describe in detail the juveniles, intermediate stage, and adults of O. echinata and O. trindadensis. Differences in the shape of the ventral arm plate and dorsalmost arm spines, the number of tentacle scales, and the presence of granules ventrally were highlighted in the separation and identification of juveniles of both species.

Validated yes/no vocabulary tests that measure bilinguals’ language proficiency based on vocabulary knowledge have been widely used in psycholinguistic research. However, it is unclear what aspects of test takers’ vocabulary knowledge are employed in these tests, which makes the interpretation of their scores problematic. The present study investigated the contribution of bilinguals’ form-meaning knowledge to their item accuracy on a Malay yes/no vocabulary test. Word knowledge of Malay first- (N = 80) and second-language (N = 80) speakers were assessed using yes/no, meaning recognition, form recognition, meaning recall and form recall tests. The findings revealed that 59% of the variance in the yes/no vocabulary test score was explained by the accuracy of the meaning recognition, form recognition and meaning recall tests. Importantly, the item analysis indicated that yes/no vocabulary tests assess primarily knowledge of form recognition, supporting its use as a lexical proficiency measure to estimate bilinguals’ receptive language proficiency.