Let T be a bounded linear operator on a separable Banach space that satisfies geometric properties similar to those of $\ell ^p,\, p>1$. We prove that the smallest and the largest norm of weak cluster points of all maximizing sequences for T can only take the values $0$ or $1$. The three classes of bounded linear operators emerging from the dichotomy of these extremal norm values coincide with the partition, created by considering the norm-attaining property and if the essential norm equals the norm.

Contact precaution policies are used to prevent the spread of pathogenic organisms. We aimed to test whether AI-assisted cameras could monitor aspects of compliance with these policies. Testing in both simulated and real patient care settings yielded exceptional sensitivity and good specificity, indicating potential to monitor adherence to contact precautions.

This article examines the sociopolitical evolution of Palenque and the Mensäbäk Basin, focusing on shifting models of organization from the Late Preclassic (300 BC–AD 250) to the Late Postclassic (AD 1250–1525). We argue that changes in access to ritual spaces and landscape-related ceremonies reflected broader transformations in Maya social organization as it made the transition from collective to less collective societies. The transformation from Preclassic to Postclassic occupations in the Mensäbäk Basin provides visible evidence of political and ideological shifts. Findings from Mensäbäk highlight the diversity of governance structures, showing that exclusionary and communal models varied based on spatial and temporal contexts.

This article revisits the history of Muslim Turkish society, questioning its essentialist portrayal as a “religious society,” with religiosity narrowly defined through Sunni Islamic doctrines. It examines the content of Sunni folk Islam through the Mevlid, Karbala, and Ebâ Müslim books published by İstanbul Maarif Kitaphanesi until the 1980s, as well as their political appropriation by elite actors during the early Cold War period. I argue that Sunni and Alevi religiosity shared key elements beyond saint veneration, particularly praising the Prophet through Nur Muhammad, love of Ahl Al-Bayt, and mourning for Karbala. Using these books as religious media through a material approach to religion, I maintain that they made Muhammad and Ahl Al-Bayt “accessible,” “tangible,” and “sense-able” in the world in oral, pictorial, and scriptural forms. Since the publishers, editors, authors, readers, and listeners of these books were descendants of Turkish speakers dating back to the twelfth century, I propose the term “Islam in Turkish” as a conceptual framework to capture these shared elements. I argue that this concept, denoting a vernacular form of religiosity, has the potential to replace the modern category of Turkish folk Islam and contribute to global critical discussions on Islam.

This study is concerned with nonnegative solutions of the no-flux initial-boundary value problem for the doubly degenerate nutrient taxis system with a logistic source, as given by

\begin{align*}\left\{\begin{array}{ll}u_t = \nabla\cdot (uv\nabla u) - \nabla\cdot (u^2 v\nabla v)+ u - u^2,\\[1mm]v_t = \Delta v -uv,\end{array} \right.\end{align*}

$\Omega$

$(u,v)|_{t=0}=(u_0,v_0)$

$v_0 \gt 0$

$\overline{\Omega}$

\begin{align*}\int_\Omega \ln u_0~ \gt ~-\infty,\end{align*}

$t\to\infty$

\begin{align*} u(\cdot,t) \rightharpoonup 1 \quad \text{in } L^1(\Omega) \qquad\text{and}\qquad v(\cdot,t)\to 0 \quad \text{in } L^\infty(\Omega). \end{align*}

In this paper, we are mainly devoted to the limiting behaviour of smooth inertial manifolds for a class of random retarded differential equations with a singular parameter $\delta$ and their Galerkin approximations, which have not been considered before. Under appropriate conditions, we show not only that the inertial manifolds for this class of random retarded equations converge pointwise to those of the corresponding stochastic equations driven by white noise as $\delta\rightarrow 0$, but also that the inertial manifolds of their Galerkin approximations converge pointwise to those of stochastic equations driven by white noise described above under the simultaneous limits $\delta\rightarrow 0$ and $M\rightarrow +\infty$, where $M$ denotes the dimension index of the orthogonal projection operator $P_M$ in the Galerkin scheme.

We use spectral theory and algebraic geometry to establish a higher-degree analogue of a Szemerédi–Trotter-type theorem over finite fields, with an application to polynomial expansion.

Attention-deficit-hyperactivity disorder (ADHD) medication effects and their putative role in shortening the lifespan of adults with ADHD remain unclear. This is largely because ADHD’s diagnostic foundation lacks validity. Thus we argue that, until this is resolved, neither diagnosis nor treatment will serve patients’ needs effectively, and estimates of mortality will remain as conjecture.

This article considers the function of American food and its exchange at the time of the Allied occupation of Italy to revisit the complexity of the encounter with the local population. Through unpublished diaries and confidential reports of the Psychological Warfare Branch, as well as video materials, published interviews and published diaries, the article makes the issues around food central to the understanding of the dynamics of the Italian occupation. While contributing to the growing literature on food availability in the Second World War, the article expands in particular on the historic function of American comfort food and rations, to explore the experience of the Italian occupation through the interactions of gifting, bartering and black market trade. It illuminates the complexity of mutual perceptions shaped by hope, nostalgia, supremacy, and fairness. It concludes with a reading of John Hersey’s A Bell for Adano, which, as a cultural product, brings together and makes valid for future generations, the contrasting image of a benign and a damaging occupation explored in the article.

We consider d-dimensional stochastic differential equations (SDEs) of the form $\textrm{d}U_t = b(U_t)\,\textrm{d}t + \sigma\,\textrm{d}Z_t$. Let $X_t$ denote the solution if the driving noise $Z_t$ is a d-dimensional rotationally symmetric $\alpha$-stable process ($1\lt \alpha\lt 2$), and let $Y_t$ be the solution if the driving noise is a d-dimensional Brownian motion. Continuing the work started in Deng et al. (2025), we derive an estimate of the total variation distance $\|\textrm{law}(X_{t})-\textrm{law}(Y_{t})\|_\textrm{TV}$ for all $t \gt 0$, and we show that the ergodic measures $\mu_\alpha$ and $\mu_2$ of $X_t$ and $Y_t$, respectively, satisfy $\|\mu_\alpha-\mu_2\|_\textrm{TV} \leq {Cd\log(1+d)}(2-\alpha)/({\alpha-1})$. We show that this bound is optimal with respect to $\alpha$ by an Ornstein–Uhlenbeck SDE. Combining this bound with a recent interpolation result from Huang et al. (2023), we can derive a bound in the Wasserstein-p distance ($0 \lt p \lt 1$): $\|\mu_\alpha-\mu_2\|_{W_p} \leq {Cd^{(p+3)/2}\log(1+d)}(2-\alpha)/{\alpha-1}$.