This work is concerned with global gradient bounds for a class of divergence-form degenerate elliptic systems with complex-valued coefficients. Notably, the leading coefficients are merely required to be sufficiently small in BMO, which is strictly weaker than the VMO condition. In the complex setting, the well-posedness of this problem was recently investigated in [W. Kim, M. Vestberg, Existence, uniqueness and regularity for elliptic p-Laplace systems with complex coefficients,arXiv:2503.18932], where the authors established a strong accretivity condition on the leading coefficients, and this structural condition allows them to derive Schauder-type estimates for weak solutions. In our study, it has already been observed that gaining existence and uniqueness of weak solutions is possible under a natural and less restrictive assumption on the complex-valued coefficients. Following this direction, we prove a global Caderón-Zygmund-type estimate for weak solutions, from which the Morrey-space regularity follows as a consequence. This paper is a contribution to the better understanding of solution behavior and may be viewed as part of a series of works aimed at extending regularity theory in the complex-valued setting.
Pyridinium alkaloids represent a structurally unique class of nitrogen-containing natural products, primarily obtained from marine sponges. These compounds range from simple mono-substituted derivatives to complex poly-alkylated and a series of unusual oligomeric structures. Additionally, they have also exhibited a wide range of documented biological activities, including cytotoxic, antimicrobial, antifungal, and neuroactive effects. Notably, several compounds, such as coscinoderines and cyclostellettamines, have been explored for their ability to exhibit selective cytotoxicity against nutrient-deprived cancer cells. Polyalkylpyridiniums also represent a promising avenue for drug development due to their potent and diverse biological activities. This is especially the case for halitoxin, a polymeric complex from sponges, which shows high cytotoxicity and strong antibacterial activity, as well as the ability to prevent the onslaught of marine organisms. This review aims to provide a comprehensive overview of 127 pyridinium alkaloid derivatives published in a ranging of 68 years from 1958 to mid-2025, highlighting their sources, structural classes, bioactivities, biosynthetic origins, and synthetic insights. Subsequent assessments and discussions will provide a foundation for further research and development on potential compounds of this class.
We investigate a general class of variational integrals under a structural condition imposed on the double-phase function, recently introduced in . In this setting, the strong Harnack inequality for non-negative local quasi-minimizers is established via an appropriate De Giorgi-type iteration argument. Most notably, the proposed analytical approach in this paper provides a new perspective for deriving Harnack-type inequalities for more general variational functionals under a Muckenhoupt-type structural condition on the double-phase function, without relying on the classical coefficient-freezing strategy based on the Hölder continuity of the modulating coefficient and the balance condition on the growth exponents.
Emotion recognition is pivotal in advancing human-computer interaction, with transformative applications in education, healthcare, and social analysis. Traditional models predominantly rely on facial expressions, often neglecting the critical roles of contextual and bodily cues. In this study, we propose mCFA, a novel context-aware emotion recognition model that integrates facial, body, and contextual cues through a two-level attention mechanism. First, cross-attention modules dynamically learn inter-modality interactions; second, adaptive fusion assigns weights to each modality based on its contribution. Evaluated on the EMOTIC dataset, mCFA achieves a mean Average Precision (mAP) of 28.77
Metal-organic frameworks (MOFs) with a highly porous nature have large surface areas (SSAs), both of which are highly beneficial for gas-sensing studies. Herein, we used a chemical method to synthesize a vanadium-based MOF (V-MOF) and a Cu-doped V-MOF (V-MOF(Cu)) for detecting gaseous ethanol. The morphologies, phases, and chemical compositions of the samples were characterized using various techniques. Notably, V-MOF exhibited a large specific surface area (SSA) of 1405 m2.g-1, while that of V-MOF(Cu) was 1388 m2.g- 1. Gassensing experiments revealed that the V-MOF sensor produced a maximum response of 1.35 toward 10 ppm ethanol gas at 200 degrees C, whereas the V-MOF(Cu) sensor exhibited a 20 % higher response, reaching 1.62 under the same conditions. The underlying ethanol sensing mechanism is attributed to the large SSA of the sensors, the modulation of the width of the hole-accumulation layer in the presence of ethanol, and the high affinity of Cu centers for ethanol adsorption. This study demonstrates the high potential of V-MOF(Cu) for use in gas-sensing devices.
