Phthalic acid esters (PAEs) as common plasticizers, providing convenience to humans. However, they also present a potential threat to ecosystems and human health as emerging contaminants. In this study, co- immobiliza...
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Phthalic acid esters (PAEs) as common plasticizers, providing convenience to humans. However, they also present a potential threat to ecosystems and human health as emerging contaminants. In this study, co- immobilization of nanozyme (PtCo) and laccase (Lac) into dendritic mesoporous silica (DMSN) constitutes nanomaterials (Lac@PtCo@DMSN). PtCo with an atomic ratio of 3:1 has the highest oxidizing activity. DMSN exhibited a maximum Lac loading capacity of 365 mg/g and activity of Lac@PtCo@DMSN exhibits excellent pH, temperature, and storage stability and reusability, and demonstrated greater recoverability. Remarkably, Lac@PtCo@DMSN (50 mg) achieved 81.83% degradation of total PAEs within 72 h and maintained 72.44% degradation of dimethyl phthalate (DMP) in the fifth cycle. Electron transfer between Pt, Co and adsorbed oxygen (O-2ads) in PtCo can generate center dot OH and center dot O-2(-), which were the dominant reactants for PAEs degradation. center dot OH could degrade PAEs to phthalic acid via H-abstration and center dot OH addition. center dot OH effectively enhanced Lac activity, and promoted the synergistic catalytic performance of nanozymes and natural enzymes. The degradation of phthalic acid by Lac accelerated the release of PtCo@DMSN reaction sites, resulting in significantly enhanced PAEs degradation. Thus, artificial/natural enzymes can degrade PAEs without exogenous additives to solve the limitation of Lac application, providing a new strategy for degrading contaminants in water.
We consider the derivation of the defocusing cubic nonlinear Schrodinger equation (NLS) on R-3 from quantum N-body dynamics. We reformat the hierarchy approach with Klainerman-Machedon theory and prove a bi-scattering...
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We consider the derivation of the defocusing cubic nonlinear Schrodinger equation (NLS) on R-3 from quantum N-body dynamics. We reformat the hierarchy approach with Klainerman-Machedon theory and prove a bi-scattering theorem for the NLS to obtain convergence rate estimates under H-1 regularity. The H(1 )convergence rate estimate we obtain is almost optimal for H(1 )datum, and immediately improves if we have any extra regularity on the limiting initial one-particle state.
We consider the T-4 cubic nonlinear Schrodinger equation (NLS), which is energy-critical. We study the unconditional uniqueness of solutions to the NLS via the cubic Gross-Pitaevskii hierarchy, an uncommon method for ...
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We consider the T-4 cubic nonlinear Schrodinger equation (NLS), which is energy-critical. We study the unconditional uniqueness of solutions to the NLS via the cubic Gross-Pitaevskii hierarchy, an uncommon method for NLS analysis which is being explored [24, 35] and does not require the existence of a solution in Strichartz-type spaces. We prove U-V multilinear estimates to replace the previously used Sobolev multilinear estimates. To incorporate the weaker estimates, we work out new combinatorics from scratch and compute, for the first time, the time integration limits, in the recombined Duhamel-Born expansion. The new combinatorics and the U-V estimates then seamlessly conclude the H-1 unconditional uniqueness for the NLS under the infinite-hierarchy framework. This work establishes a unified scheme to prove H-1 uniqueness for the R-3/R-4/T-3/T-4 energy-critical Gross-Pitaevskii hierarchies and thus the corresponding NLS.
We study the mean-field and semiclassical limit of the quantum many-body dynamics with a repulsive δ-type potential N3βV (Nβx) and a Coulomb potential, which leads to a macroscopic fluid equation, the Euler-Poisson...
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We consider the Boltzmann equation with the soft potential and angular cutoff. Inspired by the methods from dispersive PDEs, we establish its sharp local well-posedness and ill-posedness in Hs Sobolev space. We find t...
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We consider the 3D Boltzmann equation for the Maxwellian particle and soft potential with an angular cutoff. We prove sharp global well-posedness with initial data small in the scaling-critical space. The solution als...
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We study the 1D quantum many-body dynamics with a screened Coulomb potential in the mean-field setting. Combining the quantum mean-field, semiclassical, and Debye length limits, we prove the global derivation of the 1...
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We consider the 3D Boltzmann equation with the constant collision kernel. We investigate the well/ill-posedness problem using the methods from nonlinear dispersive PDEs. We construct a family of special solutions, whi...
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We consider the cubic and quintic nonlinear Schrodinger equations (NLS) under the R-d and T-d energy-supercritical setting. Via a newly developed unified scheme, we prove the unconditional uniqueness for solutions to ...
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We consider the cubic and quintic nonlinear Schrodinger equations (NLS) under the R-d and T-d energy-supercritical setting. Via a newly developed unified scheme, we prove the unconditional uniqueness for solutions to NLS at critical regularity for all dimensions. Thus, together with [19, 20], the unconditional uniqueness problems for H-1-critical and H-1-supercritical cubic and quintic NLS are completely and uniformly resolved at critical regularity for these domains. One application of our theorem is to prove that defocusing blowup solutions of the type in [54] is the only possible C([0,T);(H) over dot(sc)) solution if exist in these domains.
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