We establish a new weighted regularity criterion for weak solutions of the 3D Magnetohydro-dynamic (MHD) equations, involving only the gradient of the velocity field. It is proved that a weak solution (u, b) is smooth on R & sup3; x (0, T) provided sup (3)(x0 is an element of R) & Vert;|x - x0|(beta)del u & Vert;L-alpha (0,T ;L gamma (R-3)) < +infinity with 2|alpha + 3|gamma = 2 - beta, 3|2-beta < gamma <= 9 4-3 beta , 3 <= alpha < infinity and - 2 3 <= beta <= 1 3 . Our result improves and known regularity criteria MHD equations, albeit under stronger restrictions on the admissible ranges of a alpha and gamma.
Point cloud completion is a fundamental task in 3D perception and 3D vision. Existing point cloud completion methods typically rely on supervised learning with limited 3D data, resulting in poor generalization and suboptimal recovery in scenarios involving complex shape structures or large missing regions. To overcome these limitations, we propose a novel zero-shot point cloud completion framework (called HybridPC) that achieves high-fidelity 3D reconstruction without any 3D supervision or task-specific training. HybridPC leverages powerful 2D diffusion priors and a progressive implicit-explicit architecture to address severe incompleteness and complex geometries. The framework comprises three key stages: 1) Edge-aware neural field initialization: ControlNet-guided stable diffusion synthesizes multi-view images conditioned on text prompts and orthographic edge projections of the incomplete point cloud, providing strong shape constraints to initialize a coarse NeRF field via Score Distillation Sampling (SDS). 2) Multi-view diffusion collaborative completion: A pre-trained multi-view diffusion model enforces cross-view consistency, collaboratively completing the entire neural radiance field (NeRF) with globally coherent geometry. To reconcile gradient conflicts between ControlNet and multi-view diffusion during joint SDS optimization, a PCGrad-based multi-objective optimization strategy is introduced to balance the structural and semantic guidance, yielding higher-fidelity shape completion. 3) Geometry-aware tetrahedral refinement: The implicit field is converted into a tetrahedral mesh using DMTet, which is further refined via implicit SDS-based normal optimization and explicit geometric constraints on the mesh surface, ensuring structural fidelity to the partial input. Extensive experiments on the ShapeNetPart and Redwood datasets demonstrate that HybridPC outperforms existing supervised and zero-shot methods in both qualitative and quantitative comparisons. Specifically, HybridPC preserves the input structure more faithfully, completes missing regions more accurately, and shows stronger generalization ability, with particularly significant improvements on real-world scans from Redwood dataset. Our results show the strong potential of coupling 2D diffusion priors with 3D geometric modeling for scalable, training-free point cloud completion.
Bacterial infections and rapid degradation remain significant challenges for biodegradable magnesium (Mg) alloy implants. While conventional photothermal antibacterial coatings often rely on exogenous agents, the intrinsic photothermal potential of phosphate materials warrants greater exploration. In this study, amorphous calcium phosphate (CaP), zinc phosphate (ZnP), and magnesium phosphate (MgP) coatings were fabricated on WE43 Mg alloys via a facile chemical deposition method utilizing ultra-low pH solutions. Characterization revealed that these amorphous coatings exhibited exceptional photothermal performance. Upon near-infrared (NIR) irradiation (808 nm) for 240 s, the maximum surface temperature of these amorphous phosphates reached 240.5 °C. The coatings maintained robust photothermal responses in PBS and ex vivo tissue models. Mechanistically, unlike well-crystallized counterparts, the amorphous phosphates possess abundant lattice defects, creating numerous defect energy levels within their bandgaps that facilitate localized photon absorption and phonon-mediated heat generation. Furthermore, the coatings provided substantial corrosion protection for the Mg substrate. This bandgap engineering strategy via structural disorder offers a shift for designing antibiotic-free, smart antibacterial biomaterials with excellent stability and biocompatibility.
The alkali and alkaline earth metals (AAEMs) in biomass ash significantly influence the yield and compositional distribution of bio-oil derived from fast pyrolysis. This study employed corn stover to systematically investigate the selective removal of AAEMs through stepwise demineralization pretreatment (SDP, distilled water, ammonium acetate, and hydrochloric acid) and their impacts on bio-oil composition. Furthermore, the effects of AAEMs-impregnated salts types (K, Ca, Na, Mg), salt concentrations (0.5%, 2.5%, 5%), and different potassium salt anions (Cl-, SO42-, NO3-, CO32-, HCO3-, AC(-) and PO43-) on bio-oil components were comprehensively examined. Results showed that the removal efficiency of AAEMs was enhanced with increasing acidity of demineralizing solutions, and AAEMs in biomass were categorized into three occurrence states: water-soluble metal (K), ion-exchangeable metals (Ca and Mg), and acid-insoluble metal (Na) according to SDP. During subsequent fast pyrolysis, AAEM-impregnated salts acted as catalysts promoting secondary degradation of pyrolytic intermediates (e.g., levoglucosan), leading to the concurrent formation of light oxygenated compounds and hydrocarbons (e.g., furans, ketones, and long-chain alkane). Different potassium salt anions substantially influenced the secondary cracking of anhydrosugars and the cleavage of aryl-ether bonds/phenolic hydroxyl groups in lignin. The proton affinity of anion governed the degradation sequence for anhydrosugars: HCO3- > CO32- > AC(-) > PO43- > Cl- > NO3- > SO42-, while the cleavage efficiency of lignin linkages followed CO32- > Cl- > HCO3- > PO43- approximate to AC(-) > SO42- approximate to NO3-. This work provides fundamental insights for targeted regulation of bio-oil composition through AAEMs management.
Identifying diffusion origins is fundamental to controlling the spread of epidemics and misinformation. Existing sensor-based methods, however, are largely developed for simple networks and are not well suited to higher-order spreading processes. We propose Sensor-based Source Detection in Hypergraphs (SSDH), a framework that integrates sensor deployment with source detection in hypergraph-structured systems. SSDH deploys sensors by maximizing incremental information gain and locates diffusion sources using a path-entropy measure that combines transmission uncertainty with structural proximity. Experiments on hypergraphs ranging from several hundred to more than 5000 nodes show that SSDH consistently outperforms existing methods. Under sensor budgets of 5%-15%, it improves detection accuracy by 5%-30% while reducing detection error. Even with only 10% sensor coverage, SSDH frequently surpasses competing methods operating with twice the sensing budget, indicating that reliable source detection remains possible under highly constrained observations.
