After the Supreme Court incorporated the Establishment Clause against the states in Everson v. Board of Education (1947), raucous national debates broke out between Protestants, Catholics, and Jews about the constitutionality of government aid to parochial schools. This article offers the first account of how these interconfessional hostilities shaped the Catholic Church’s parochial school litigation strategy after Everson.

To undercut claims that government aid to parochial schools would perniciously enrich the (Roman) Catholic hierarchy, the Church’s public spokesmen increasingly framed debates about parochial school aid after Everson as implicating the constitutional rights of American parents to direct the religious upbringing of their children. In so doing, these figures eschewed arguments made in the eighteenth and nineteenth centuries that the government has an obligation to fund institutional religion. Moreover, to prevent anti-Catholic prejudice from impacting the disposition of discrete church–state disputes, lawyers associated with the Catholic bishops’ official episcopal organization sometimes refrained from publicly involving themselves in local litigation, all while privately supplying litigants with strategic counsel.

In concluding, this article suggests that the Church’s post-Everson approach to defending the constitutionality of parochial school aid was motivated by a consistent conviction that parents who sent their children to Catholic schools ought to be treated in the same manner as parents who sent their children to other nonpublic (but non-Catholic) schools. When the scope of government aid to nonpublic schools grew in later years, this argument could therefore be invoked to support parochial schools’ equal inclusion in more robust aid programs.

This article argues that weekly “tiny research assignments” in introductory health law courses promote active learning and deepen student engagement. These focused exercises also build foundational research and communication skills by replacing passive lecture with concise, student-driven investigation tied to each week’s topic.

In this note, we offer a cautionary tale on the dangers of drawing inferences from low-quality online survey datasets. We reanalyze and replicate a survey experiment studying the effect of acquiescence bias on estimates of conspiratorial beliefs and political misinformation. Correcting a minor data coding error yields a puzzling result: respondents with a postgraduate education appear to be the most prone to acquiescence bias. We conduct two preregistered replication studies to better understand this finding. In our first replication, conducted using the same survey platform as the original study, we find a nearly identical set of results. But in our second replication, conducted with a larger and higher-quality survey panel, this apparent effect disappears. We conclude that the observed relationship was an artifact of inattentive and fraudulent responses in the original survey panel, and that attention checks alone do not fully resolve the problem. This demonstrates how “survey trolls” and inattentive respondents on low-quality survey platforms can generate spurious and theoretically confusing results.

The primary objective of this paper is to show how the theory of groupoids and their $C^*$-algebras provide new proofs and extensions of Mallat’s famous theorems on the construction of multiresolution analyses that form the basis of wavelet theory. This work was inspired in large part by the research of Iain Raeburn and co-authors.

We investigate uniqueness of solution to the heat equation with a density $\rho$ on complete, non-compact weighted Riemannian manifolds of infinite volume. Our main goal is to identify sufficient conditions under which the solution $u$ vanishes identically, assuming that $u$ belongs to a certain weighted Lebesgue space with exponential or polynomial weight, $L^p_{\phi}$. We distinguish between the cases $p \gt 1$ and $p = 1$ which required stronger assumptions on the manifold and the density function $\rho$. We develop a unified method based on a conformal transformation of the metric, which allows us to reduce the problem to a standard heat equation on a suitably weighted manifold. In addition, we construct explicit counterexamples on model manifolds which demonstrate optimality of our assumptions on the density $\rho$.

Following the pivotal work of Sevastyanov (1957), who considered branching processes with homogeneous Poisson immigration, much has been done to understand the behaviour of such processes under different types of branching and immigration mechanisms. Recently, the case where the times of immigration are generated by a non-homogeneous Poisson process has been considered in depth. In this work, we demonstrate how we can use the framework of point processes in order to go beyond the Poisson process. As an illustration, we show how to transfer techniques from the case of Poisson immigration to the case where it is spanned by a determinantal point process.

This paper introduces an overlapping generations model to explore the interplay between economic growth, the environment, and endogenous technology adoption. Considering an economy with physical capital and publicly funded human capital, the analytical framework extends Prieur and Bréchet (2013, Macroeconomic Dynamics 17, 1135–1157) by incorporating the endogenous technology choice mechanism from Umezuki and Yokoo (2019, Journal of Economic Dynamics & Control 100, 164–175). The analysis focuses on how the choice of capital-intensive technologies impacts environmental dynamics. The model reveals complex equilibrium dynamics, driven by a core trade-off between individuals’ resource allocation on consumption versus environmental protection and firms’ technology decisions.

Constant-force mechanisms (CFMs) are attractive for mechanical energy storage owing to their distinctive force–displacement characteristics, particularly under conditions with limited external load capacity and restricted space. However, conventional CFMs often suffer from short constant-force strokes and inefficient space utilization, which hinder their broader application. To address these limitations, this study exploits the buckling of compliant beams and increases the structural degrees of freedom by adopting a less constrained configuration, which extends the constant-force stroke and space utilization while reducing the required external load, thus improving energy storage efficiency for the same stored elastic energy. A novel catapult was developed through NSGA-II multi-objective optimization, achieving a high energy-to-cost ratio and an extended constant-force stroke. This work presents an effective design approach for motion mechanisms that demand high energy-storage efficiency and high-power output.