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We study the Cauchy problem for the doubly nonlocal equation where and for some m ∈ ℝ and 0 < α ≤ +∞, here α = +∞ means that J is compactly supported. The problem not only describes nonlocal diffusions and nonlocal interactions, but also it is a nonlocal counterpart of the nonlocal heat equation in [10] where and m > 0. As for the local existence of positive solutions, we find that problem (0.1) is quite different from the nonlocal heat equation. That is, problem (0.1) admits positive solutions if and only if m > n − q(n + α), however the nonlocal heat equation has positive solutions for any m ∈ ℝ. For m ≥ 0 or n(1 − q) < m < 0 with α = +∞, we determine the critical Fujita curve of problem (0.1) as F(p, q, n, m, r, α) := (p − 1)[nq − (n − m)+] − q(β − nr) = 0 with β = min{α, 2}. That is, if F ≤ 0, every positive solution of (0.1) blows up in finite time, whereas if F > 0, there exist both nonglobal solutions and global solutions. In the supercritical case F > 0, we further discuss the second critical exponent which describes the critical decay rate of initial data to distinguish both solutions. Particularly, we find a new phenomenon, namely, if with α = +∞, the second critical exponent is independent of p and r. [ABSTRACT FROM AUTHOR]

To understand complex biological process and disease progression, it is essential to comprehensively track biodynamics across entire organisms. The invaluable tracking tool, photoacoustic computed tomography (PACT), provides insights into structural, functional, and molecular aspects of living tissues. However, current small‐animal PACT systems suffer from low temporal/spatial resolution and a restricted field of view, and they are limited in the biological information they can provide, hindering research on whole‐body biodynamics. Here, it is demonstrated a continuous rotary‐scanning PACT system for rapid monitoring of various parameters within the relatively large torso of a small animal. In this PACT system, a hemispherical transducer array is continuously rotated at high speed, enabling a 3D scan of an entire mouse body in just 54 s, with a spatial resolution of 172–212 µm. The rapid rotary scanning allows us to not only image whole‐body structures but also to monitor pharmacokinetics and changes in hemoglobin oxygen saturation in living animals. This approach holds great promise for advancing the understanding of in vivo biological dynamics, opening up a new avenue of preclinical research in areas such as metabolic diseases and drug delivery. [ABSTRACT FROM AUTHOR]

The massive use of acetaminophen (APAP) poses a potential crisis for humans and the environment. In this paper, the degradation of APAP in aqueous solution was carried out using photocatalytic synergistic persulfate oxidation. To enhance the photocatalytic activity of g-C3N4 and thus activate the persulfate (K2S2O8, PS) more effectively, the heterojunction photocatalyst TiO2/g-C3N4 (TCN) was prepared by a hydrothermal method. The TCN-PS catalytic system showed a high efficiency for APAP degradation. When the amount of TCN and PS added was 0.6 g/L, the degradation rate of APAP at 10 mg/L was 78.3% after 60 min of illumination. Moreover, the TCN-PS catalytic system was effective in removing organic pollutants in acidic, neutral, and weakly alkaline environments. The radical quenching experiment results indicate that both sulfate radicals (SO4−•) and hydroxyl radicals (•OH) are involved in the degradation reaction. After five cycles, the TCN-PS catalytic system still has stable catalytic activity. [ABSTRACT FROM AUTHOR]