A Posteriori Error Estimate of Two Grid Mixed Finite Element Methods for Semilinear Elliptic Equations

In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the mixed method equations. Then, the averaging technique is used to construct the a posteriori error estimates of the two-grid mixed finite element method and theoretical analysis are given for the error estimators. Finally, we give some numerical examples to verify the reliability and efficiency of the a posteriori error estimator.

基于电子给体-受体复合物的脂肪烃碳氢键多样性转化

The ability to selectively introduce diverse functionality onto hydrocarbons is of substantial value in the synthesis of both small molecules and pharmaceuticals.In this endeavour,as a photocatalyst-and metalfree process,the electron donor–acceptor(EDA)strategy has not been well explored.Here we report an approach to aliphatic carbon-hydrogen bond diversification through an EDA complex constituted by HCl and S^(IV)=O groups.As an efficient hydrogen atom transfer(HAT)reagent,chlorine radical can be produced via a proton-coupled electron transfer process in this system.Based on this unusual path,a photopromoted versatile aliphatic C–H functionalization is developed without photo-and metal-catalysts,including thiolation,arylation,alkynylation,and allylation.This conversion has concise and ambient reaction conditions,good functional group tolerance,and substrate diversity,and provides an alternative solution for the high value-added utilization of bulk light alkanes.

A sandwich structure composite wound dressing with firmly anchored silver nanoparticles for severe burn wound healing in a porcine model

Wounds may remain open for a few weeks in severe burns,which provide an entry point for pathogens and microorganisms invading.Thus,wound dressings with long-term antimicrobial activity are crucial for severe burn wound healing.Here,a sandwich structure composite wound dressing anchored with silver nanoparticles(AgNPs)was developed for severe burn wound healing.AgNPs were in situ synthesized on the fibers of chitosan nonwoven fabric(CSNWF)as the interlayer of wound dressing for sustained release of silver ion.The firmly anchored AgNPs could prevent its entry into the body,thereby eliminating the toxicity of nanomaterials.The outer layer was a polyurethane membrane,which has a nanoporous structure that could maintain free transmission of water vapor.Chitosan/collagen sponge was selected as the inner layer because of its excellent biocompatibility and biodegradability.The presence of AgNPs in the CSNWF was fully characterized,and the high antibacterial activity of CSNWF/AgNPs was confirmed by against Escherichia coli,Pseudomonas aeruginosa and Staphylococcus aureus.The superior wound healing effect on deep dermal burns of presented composite wound dressing was demonstrated in a porcine model.Our finding suggested that the prepared AgNPs doped sandwich structure composite wound dressing has great potential application in severe wound care.

Randomized statistical inference:A unified statistical inference frame of frequentist,fiducial,and Bayesian inference

We propose randomized inference(RI),a new statistical inference approach.RI may be realized through a randomized estimate(RE)of a parameter vector,which is a random vector that takes values in the parameter space with a probability density function(PDF)that depends on the sample or sufficient statistics,such as the posterior distributions in Bayesian inference.Based on the PDF of an RE of an unknown parameter,we propose a framework for both the vertical density representation(VDR)test and the construction of a confidence region.This approach is explained with the aid of examples.For the equality hypothesis of multiple normal means without the condition of variance homogeneity,we present an exact VDR test,which is shown as an extension of one-way analysis of variance(ANOVA).In the case of two populations,the PDF of the Welch statistics is given by using the RE.Furthermore,through simulations,we show that the empirical distribution function,the approximated t,and the RE distribution function of Welch statistics are almost equal.The VDR test of the homogeneity of variance is shown to be more efficient than both the Bartlett test and the revised Bartlett test.Finally,we discuss the prospects of RI.