BLOW-UP SOLUTIONS OF TWO-COUPLED NONLINEAR SCHR?DINGER EQUATIONS IN THE RADIAL CASE

We consider the blow-up solutions to the following coupled nonlinear Schr¨odinger equations{iu_(t)+Δu+(|u|^(2p)+|u|^(p−1)|v|^(p+1))u=0,iv_(t)+Δv+(|v|^(2p)+|v|^(p−1)|u|^(p+1))v=0,u(0,x)=u0(x),v(0,x)=v0(x),x 2 R N,t0.On the basis of the conservation of mass and energy,we establish two sufficient conditions to obtain the existence of a blow-up for radially symmetric solutions.These results improve the blow-up result of Li and Wu[10]by dropping the hypothesis of finite variance((|x|u_(0),|x|v_(0))∈ L^(2)(R^(N))×L^(2)(R^(N))).

Hydroxylated metal–organic-layer nanocages anchoring single atomic cobalt sites for robust photocatalytic CO_(2) reduction

Assembly of two-dimensional(2D)metal–organic layers(MOLs)based on the hard and soft acid–base theorem represents an exquisite strategy for the construction of photocatalytic platforms in virtue of the highly exposed active sites,much improved mass transport,and greatly elevated stability.Herein,nanocages composed of MOLs are produced for the first time through a cosolvent approach utilizing zirconium-based UiO-66-(OH)2 as the structural precursor.To endow the catalytic activity for CO_(2) conversion,single atomic Co^(2+)sites are appended to the Zr-oxo nodes of the MOL cages,demonstrating a remarkable CO yield of 7.74 mmol·g^(-1)·h^(-1) and operational stability of 97.1%product retention after five repeated cycles.Such an outstanding photocatalytic performance is mainly attributed to the unique nanocage morphology comprising enormous 2D nanosheets for augmented Co^(2+)exposure and the abundant surface hydroxyl groups for local CO_(2) enrichment.This work underlines the tailoring of both metal–organic framework(MOF)morphology and functionality to boost the turnover rate of photocatalytic CO_(2) reduction reaction(CO_(2)RR).

Self-therapeutic metal-based nanoparticles for treating inflammatory diseases

Inflammatory diseases are key contributors to high mortality globally and adversely affect the quality of life.Current treatments include corticosteroids or nonsteroidal anti-inflammatories that may cause systemic toxicity and biologics that may increase the risk of infection.Composite nanoparticles that bear not only the drug payload but also targeting ligands for delivery to inflammation sites at lowered systemic toxicity are established in the nanomedicine field,but their relatively large size often leads to systemic clearance.Metal-based nanoparticles with intrinsic anti-inflammatory properties represent attractive alternatives.They are not only designed to be compact for crossing biological barriers(with the nanoparticle serving as a dual carrier and drug),but also support label-free tracking of their interactions with cells.The review commences with an outline of the common inflammatory diseases,inflammatory pathways involved,and conventional drug-loaded nanoparticles for anti-inflammation.Next,the review features the emerging applications of self-therapeutic metal-based nanoparticles(e.g.,gold,coper oxide,platinum,ceria,and zinc oxide)for managing inflammatory diseases in animals over the past three years,focusing on therapeutic outcomes and anti-inflammatory mechanisms.The review concludes with an outlook on the biodistribution,long-term toxicity,and clinical translation of self-therapeutic metalbased nanoparticles.