We establish sufficient conditions for the existence of ground states of the following normalized nonlinear Schrödinger–Newton system with a point interaction:

\begin{equation*}\begin{cases}- \Delta_\alpha u + \omega u=w u+\beta u |u|^{p - 2}&\text{on} ~ \mathbb{R}^2;\\- \Delta w=2 \pi |u|^2&\text{on} ~ \mathbb{R}^2;\\\|u\|_{L^2}^2 = c,\end{cases}\end{equation*}

where $p \gt 2$; $\alpha, \beta \in \mathbb{R}$; $c \gt 0$ and $- \Delta_\alpha$ denotes the Laplacian of point interaction with s-wave scattering length $(- 2 \pi \alpha)^{- 1}$, the unknowns being $u \colon \mathbb{R}^2 \to \mathbb{C}$, $w \colon \mathbb{R}^2 \to \lbrack0, \infty\lbrack$ and the Lagrange multiplier $\omega \in \mathbb{R}$. Additionally, we show that critical points of the corresponding constrained energy functional are naturally associated with standing waves of the evolution problem

\begin{equation*}\mathrm{i} \psi' (t)=- \Delta_\alpha \psi (t)-(\log |\cdot| \ast |\psi (t)|^2)\psi (t)-\beta\psi (t)|\psi (t)|^{p - 2}.\end{equation*}

Much has been written about women as composers, performers, or teachers around the turn of the twentieth century. Less attention has been paid to how women could build portfolio careers by weaving musical practices together. This article focuses on a group of Scottish women who did not make their names solely as art music composers or stellar performers, and for whom piano teaching was only part of their musical work. Four were related to the Scottish music publishers Mozart Allan, James Kerr, and the Logan brothers; the fifth published with Allan and Kerr, and also self-published. All but one made their careers in Scotland. Their lives and achievements reveal the range of musical occupations open to upper working- or lower middle-class women in this era, and also provide insights into musical scenes beyond the English cities more typically the focus of British music histories.

In [3], Hjorth proved from $ZF + AD + DC$ that there is no sequence of distinct $\boldsymbol {\Sigma ^1_2}$ sets of length $\boldsymbol {\delta ^1_2}$. Sargsyan [11] extends Hjorth’s technique to show there is no sequence of distinct $\boldsymbol {\Sigma ^1_{2n}}$ sets of length $\boldsymbol {\delta ^1_{2n}}$. Sargsyan conjectured an analogous property is true for any regular Suslin pointclass in $L(\mathbb {R})$—i.e., if $\kappa $ is a regular Suslin cardinal in $L(\mathbb {R})$, then there is no sequence of distinct $\kappa $-Suslin sets of length $\kappa ^+$ in $L(\mathbb {R})$. We prove this in the case that the pointclass $S(\kappa )$ is inductive-like.

On 24 May 2024, member states of the World Intellectual Property Organization (WIPO) adopted the Treaty on Intellectual Property, Genetic Resources and Associated Traditional Knowledge. Mandating that contracting parties require that patent applicants disclose any genetic resources or associated traditional knowledge that their invention is based on, the treaty has been hailed as historic triumph. In this article, we analyze whether the treaty is so remarkable in relation to Aotearoa New Zealand’s existing law and practice. Finding that it is not, and that the treaty could place limits on the law, we argue that Aotearoa New Zealand should not sign the Treaty but could learn from it. We conclude that, while Aotearoa New Zealand must continue to partake in any ongoing international negotiations, it should continue to find ways to address the domestic situation.

Both historians of science and Americanists have depicted famed nineteenth-century astronomer and political economist Simon Newcomb as a relatively stern “mugwump,” impressive in his scientific achievement, yet at times stunted by a parochial arrogance. In histories of nineteenth-century liberalism, in particular, Newcomb makes cameos as a stand-in for an economically conservative wing. This article analyzes two facets of Newcomb’s postwar thinking that have been consistently left out: race and nationalism. After the Civil War, Newcomb pushed a nationalist discourse of American scientific progress in The North American Review that at times wavered between cultural and biological determinism. He spoke in terms of national styles and believed that American science, opposed to French, German, or English science, languished. His advocacy for an American science rested upon implicit “ethnoracial” nationalist assumptions. Contrary to his laissez-faire liberalism, it called for a more activist scientific state, and feared a nationalism of apathy that he believed pervaded both American science and politics. This article, moreover, argues that Newcomb’s thought was intimately tied to his experiences in postbellum Washington, suggesting the need for more localist and urban studies of the rise of state science after the Civil War.

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.