We develop a representation-theoretic refinement of the Iwasawa theory of finite Cayley graphs. Building on analogies between graph zeta functions and number-theoretic L-functions, we study $\mathbb {Z}_\ell $-towers of Cayley graphs and the asymptotic growth of their Jacobians. The main result establishes that the Iwasawa polynomial associated to such a tower admits a canonical factorisation indexed by the irreducible representations of the underlying group. This leads to the definition of representation-theoretic Iwasawa polynomials, whose properties are studied.

We study a pair of finite multisets of nonnegative integers which have coinciding representation functions. We show that there is a close connection to factorisation of polynomials into cyclotomic polynomials. As an application, we give a complete characterisation of pairs of such sets whose union is the interval $[0,m]$ with two elements removed.

This article contends that meteorology endured a severe crisis in the USSR in 1972. During a devastating drought this year, meteorology lost its reliability as a science able to forecast the weather many weeks and months in advance. Many professional users turned to an alternative weather forecaster, Anatolii D′iakov, who predicted the weather for the next season by observing the sun. The argument made here is threefold. First, the fundamental reason for the crisis in long-range weather forecasting lies in the disruption of a bond of trust between meteorologists and the government, built on unfulfilled prospects of rapid and sudden, but unrealistic, progress in long-range forecasting to help agriculturalists of the steppe regions. Meteorologists could not fulfil the high expectations put in them. Second, journalists covering rural matters were instrumental in extolling D′iakov’s alternative forecasts and in lambasting ‘official’ meteorology; however, they did not succeed in convincing the leadership to purge forecasters and reorganize meteorology. The meteorologists preserved their autonomy to deal with D′iakov. Third, the article reflects on the consequences of the failure of long-term forecasting for the status of science within Soviet governance and ideology.

The agricultural extension system in Alberta, Canada, has undergone significant shifts in recent decades due to a reduction of provincial government oversight. This change highlights the need to assess the effectiveness of currently available extension tools and to explore opportunities for collaboration and growth across the system. The present study employs a scientific survey targeting professionals involved in agricultural entomology extension to identify key challenges and areas for improvement. In addition, we develop a visual map of online entomology resources in Alberta to facilitate user access to information. Although traditional communication methods remain valuable, there is potential to expand the use of digital tools for entomological extension activities. Survey respondents report cost and the loss of chemical control options as the primary pest management challenges, as well as funding, access, and coordination of efforts as significant barriers to extension. Physical or cultural barriers to access extension information and limited public knowledge about insects pose additional hurdles to effective extension. The survey findings offer valuable insights into opportunities to enhance agricultural extension in Alberta, such as the adoption of standardised evaluation methods and the establishment of a centralised information hub. We provide a freely available online hub that consolidates online extension entomology resources in Alberta.

After years of focussing on infectious and degenerative illnesses, U.S. public health turned to the problem of accidents. Over the course of the twentieth century, safety practitioners repurposed the models of infectious disease control, risk-factor medicine, and biomechanics to improve the precision of injury data and to guide its applications. The resulting set of frameworks, methods, and practices, collectively referred to as ‘the epidemiology of accidents’, changed how health professionals analysed injuries but never produced a lasting consensus on appropriate safety interventions. This article uses the understudied history of home accident prevention to explain why mid-twentieth-century public health failed to prioritise injury control and what made home accidents especially intractable. During the 1940s, the American Public Health Association and U.S. Public Health Service collected statistics from communities across the country to determine the causes of home accidents and to inform local safety campaigns. These investigations were comprehensive but nonspecific, seeking to educate families about all the dangers of domestic space. After John Gordon published his influential study on accidents in 1949, this approach shifted from counting cases associated with risky behaviours and conditions to quantifying the extent to which isolable risk factors contributed to injuries. From the 1960s to 1970s, William Haddon changed accident prevention again, defining injuries as ‘abnormal energy exchanges’ and finding ways to minimise harm when accidents happened. Across these iterations, the epidemiology of accidents tried to identify, classify, quantify, and control the causes of home injuries but fell short of translating research into policy.

We study the congruence classes attained by positive integers D with a prescribed period for the continued fraction of $\sqrt D$. As an application, we refine the results on large ranks of universal quadratic forms over real quadratic fields by imposing congruence conditions on their discriminants.

This article examines the Iranian mosque in Mumbai, known as Mughal Masjid, built in the 1860s by a Shirazi master mason for the Shirazi diaspora community, as a lens through which to reconsider the stereotype of the Iranian mosque. Conceived as a garden mosque, it combines the architectural traditions of mosques in the southern Zagros region with the spatial ambience of a Shirazi garden. With a survey of mosques across the southern Zagros, the article shows that historical mosques in this region are typically domeless, hypostyle structures, challenging the stereotype of the Iranian mosque defined by domes and monumental minarets. The article also critiques the stylistics of Mohammad-Karim Pirnia, arguing that nationalist historiography and colonial scholarship advance different narratives yet share a meta-narrative and epistemology that obscure regional diversity and marginalize Qajar architectural significance.

To understand the international nature of the macroprudential policy and the potential cross-border regulatory leakages these imply, we develop a three-country center-periphery framework with financial frictions and limited financial intermediation in emerging economies. Each country has a macroprudential instrument to smooth credit spread distortions; however, the banking regulations can leak to other economies and be subject to costs. Our results show the presence of cross-border regulation spillovers that increase with the extent of financial frictions, which are driven by the capacity of the regulation to limit aggregate intermediation, and that can be magnified if policymakers are forward-looking. We discuss the policy implications of the resulting macroprudential interdependence and the potential scope for policy design that improves the management of the trade-off between mitigating the financial frictions and curtailing intermediation.

Consider a sequence $P_n$ of positive recurrent transition matrices or kernels that approximate a limiting infinite state matrix or kernel $P_{\infty}$. Such approximations arise naturally when an infinite state Markov chain is truncated and replaced with a finite-state approximation. Another situation of such approximations is when $P_{\infty}$ is a simplified limiting approximation to $P_n$ when n is large. In both settings, it is often verified that the approximation $P_n$ has the characteristic that its stationary distribution $\pi_n$ converges to the stationary distribution $\pi_{\infty}$ associated with the limit. We show that when the state space is countably infinite, this stationary distribution convergence implies that $P_n^m$ can be approximated uniformly in m by $P_{\infty}^m$ when n is large. We show that this ability to approximate the marginal distributions at all time scales m fails in continuous state space, but is valid when the convergence is in total variation or when we have weak convergence and the kernels are suitably Lipschitz. When the state space is discrete (as in the truncation setting), we further show that stationary distribution convergence also implies that all the expectations that are computable via first transition analysis (e.g. mean hitting times, expected infinite horizon discounted rewards) converge to those associated with the limit $P_{\infty}$. Simply put, we show that once we have established stationary distribution convergence, we can immediately infer convergence for a large range of other expectations.

The Benedictine Abbey in Tyniec is the oldest existing monastery in Poland (11th cent. AD). The historic walls of the Monastery have survived to this day and crown the limestone hill on the Vistula River. The geological structure of the surrounding area is reflected in the composition of the mortars.

In vicinity of Tyniec one may observe outcrops of Upper Jurassic limestones represented by two facies: bedded limestones with cherts and massive limestones. Recently, it was discovered that the monks not only fortified the Tyniec hill but also partly built it up with loess. Additionally, a massive “stepped” stone platform was later built to strengthen the edge of the hill. The mortars radiocarbon dating provides the first attempt to obtain the wide chronology of the extension of Tyniec. For this purpose, the chronologically oldest layers were analyzed.

Sequential dissolution of mortars was applied to separate the carbonates of different origin. The obtained results illustrated the huge influence of mortar components and the local geological structure on the 14C measurements. In addition to the mortar, 14C measurements were also made for charcoal from Tyniec Abbey. Radiocarbon dating was performed on the selected fractions using accelerator mass spectrometry (AMS). Radiocarbon dating results of samples from the oldest part of the stone platform make it possible to associate its construction with the earliest monastery buildings.

Labour contractors (enganchadores) were key figures in capitalist modernisation in northern Peru after 1880. Via overlapping networks of monetary, moral and coercive mechanisms, they shaped circuits of accumulation by linking highland labour to coastal sugar plantations. The reliance of coastal sugar planters on highland enganchadores for guaranteeing labour supply highlights the failure of an independent national state to consolidate in this period beyond local and regional hegemonies. Therefore, an examination of enganchadores and the hybrid markets they embodied challenges both linear narratives about the rise of modern economies and conceptual binaries between market and non-market, state and non-state and centre and periphery in Peru and globally.

Vertical take-off and landing (VTOL) vehicles are gaining traction in both the delivery drone market and passenger transportation, driving the development of urban air mobility (UAM) systems. UAM seeks to alleviate road congestion in dense urban areas by leveraging urban airspace. To handle UAM traffic, vertiport terminals (vertiminals) play a critical role in supporting VTOL vehicle operations such as take-offs, landings, taxiing, passenger boarding, refuelling or charging and maintenance. Efficient scheduling algorithms are essential to manage these operations and optimise vertiminal throughput while ensuring safety protocols. Unlike fixed-wing aircraft, which rely on runways for take-off and climbing in fixed directions, VTOL vehicles can utilise multiple surface directions for climbing and approach. This flexibility necessitates specialised scheduling methods. We propose a mixed integer linear programme (MILP) formulation to holistically optimise vertiminal operations, including taxiing, climbing (or approach) using multiple directions and turnaround at gates. The proposed MILP reduces delays by up to 50%. Additionally, we derive equations to compute upper bounds of the throughput capacity of vertiminals, considering its core elements: the touchdown and lift-off (TLOF) pad system, taxiway system and gate system. Our results demonstrate that the MILP achieves throughput levels consistent with the theoretical maximum derived from these equations. As a case study, we applied our throughput analysis on a vertiminal topology in the literature and used our MILP to find the optimal configuration. This dual approach, MILP and throughput analysis, allows for comprehensive capacity analysis without requiring simulations while enabling efficient scheduling through the MILP formulation.