In this paper,we give a locally parabolic version of Tb theorem for a class of vector-valued operators with off-diagonal decay in L^(2) and certain quasi-orthogonality on a subspace of L^(2),in which the testing funct...In this paper,we give a locally parabolic version of Tb theorem for a class of vector-valued operators with off-diagonal decay in L^(2) and certain quasi-orthogonality on a subspace of L^(2),in which the testing functions themselves are also vector-valued.As an application,we establish the boundedness of layer potentials related to parabolic operators in divergence form,defined in the upper half-space Rn+2+:={(x,t,λ)∈R^(n+1)×(0,∞)},with uniformly complex elliptic,L^(∞),t,λ-independent coefficients,and satisfying the De Giorgi/Nash estimates.展开更多
A cake layer is formed by coagulation aggregates under certain transmembrane pressure in the coagulation-microfiltration （MF） process. The characteristics of humic acid aggregates coagulated by different iron-based ...A cake layer is formed by coagulation aggregates under certain transmembrane pressure in the coagulation-microfiltration （MF） process. The characteristics of humic acid aggregates coagulated by different iron-based coagulants, such as charge, size, fractal dimension and compressibility, have an effect on the cake layer structure. At the optimum iron dose of 0.6 to 0.8 mmol/L for ferric chloride （FC） and polymer ferric sulfate （PFS） pre-coagulation, at the point of charge neutralization for near zero zeta potential, the aggregate particles produced possess the greatest size and highest fractal dimension, which contributes to the cake layer being most loose with high porosity and low compressibility. Thus the membrane filterability is better. At a low or high iron dose of FC and PFS, a high negative or positive zeta potential with high charge repulsion results in so many small aggregate particles and low fractal dimension that the cake layer is compact with low porosity and high compressibility. Therefore the membrane fouling is accelerated and MF permeability becomes worse. The variation of cake layer structure as measured by scanning electric microscopy corresponds with the fact that the smaller the coagulation flocs size and fractal dimension are, the lower the porosity and the tighter the cake layer conformation. This also explains the MF membrane flux variation visually and accurately.展开更多
AIM： To detect the relationship between infusion pressure and postoperative ganglion cells function.METHODS： This prospective observational cohort study included sixty-one eyes that underwent uncomplicated cataract ...AIM： To detect the relationship between infusion pressure and postoperative ganglion cells function.METHODS： This prospective observational cohort study included sixty-one eyes that underwent uncomplicated cataract surgery. Patients were divided into two groups according to infusion time（IT） recorded using surgery equipment [Group A： IT〉IT_（mean）（27 eyes）; Group B： IT展开更多
This articles first investigates boundary integral operators for the three-dimensional isotropic linear elasticity of a biphasic model with piecewise constant Lam´e coefficients in the form of a bounded domain of...This articles first investigates boundary integral operators for the three-dimensional isotropic linear elasticity of a biphasic model with piecewise constant Lam´e coefficients in the form of a bounded domain of arbitrary shape surrounded by a background material.In the simple case of a spherical inclusion,the vector spherical harmonics consist of eigenfunctions of the single and double layer boundary operators and we provide their spectra.Further,in the case of many spherical inclusions with isotropic materials,each with its own set of Lam´e parameters,we propose an integral equation and a subsequent Galerkin discretization using the vector spherical harmonics and apply the discretization to several numerical test cases.展开更多
基金Supported by Natural Science Foundation of Jiangsu Province of China(Grant No.BK20220324)Natural Science Research of Jiangsu Higher Education Institutions of China(Grant No.22KJB110016)。
文摘In this paper,we give a locally parabolic version of Tb theorem for a class of vector-valued operators with off-diagonal decay in L^(2) and certain quasi-orthogonality on a subspace of L^(2),in which the testing functions themselves are also vector-valued.As an application,we establish the boundedness of layer potentials related to parabolic operators in divergence form,defined in the upper half-space Rn+2+:={(x,t,λ)∈R^(n+1)×(0,∞)},with uniformly complex elliptic,L^(∞),t,λ-independent coefficients,and satisfying the De Giorgi/Nash estimates.
基金supported by the National Natural Science Foundation of China (No.50978014)the Fundamental Research Funds for the Central Universities (No.2011JBM077)
文摘A cake layer is formed by coagulation aggregates under certain transmembrane pressure in the coagulation-microfiltration （MF） process. The characteristics of humic acid aggregates coagulated by different iron-based coagulants, such as charge, size, fractal dimension and compressibility, have an effect on the cake layer structure. At the optimum iron dose of 0.6 to 0.8 mmol/L for ferric chloride （FC） and polymer ferric sulfate （PFS） pre-coagulation, at the point of charge neutralization for near zero zeta potential, the aggregate particles produced possess the greatest size and highest fractal dimension, which contributes to the cake layer being most loose with high porosity and low compressibility. Thus the membrane filterability is better. At a low or high iron dose of FC and PFS, a high negative or positive zeta potential with high charge repulsion results in so many small aggregate particles and low fractal dimension that the cake layer is compact with low porosity and high compressibility. Therefore the membrane fouling is accelerated and MF permeability becomes worse. The variation of cake layer structure as measured by scanning electric microscopy corresponds with the fact that the smaller the coagulation flocs size and fractal dimension are, the lower the porosity and the tighter the cake layer conformation. This also explains the MF membrane flux variation visually and accurately.
基金Supported by the Beijing Municipal Commission of Science and Technology(No.Z151100004015073)
文摘AIM： To detect the relationship between infusion pressure and postoperative ganglion cells function.METHODS： This prospective observational cohort study included sixty-one eyes that underwent uncomplicated cataract surgery. Patients were divided into two groups according to infusion time（IT） recorded using surgery equipment [Group A： IT〉IT_（mean）（27 eyes）; Group B： IT
基金BS acknowledges the funding from the German Academic Exchange Service(DAAD)from funds of the Bundesministeriums fur Bildung und Forschung(BMBF)for the project Aa-Par-T(Project-ID 57317909)SX acknowledges the funding from the PICSCNRS as well as the PHC PROCOPE 2017(Project N37855ZK).
文摘This articles first investigates boundary integral operators for the three-dimensional isotropic linear elasticity of a biphasic model with piecewise constant Lam´e coefficients in the form of a bounded domain of arbitrary shape surrounded by a background material.In the simple case of a spherical inclusion,the vector spherical harmonics consist of eigenfunctions of the single and double layer boundary operators and we provide their spectra.Further,in the case of many spherical inclusions with isotropic materials,each with its own set of Lam´e parameters,we propose an integral equation and a subsequent Galerkin discretization using the vector spherical harmonics and apply the discretization to several numerical test cases.
