σ2 Hessian方程的Pogorelov型C2 内估计及应用

提出利用拉格朗日乘子法重新证明σ2算子的最优凹性,并定义了一个凸锥Γ3?=λ=(λ1,λ2,?,λn)∈Rn:σ1(λ)>0,σ2(λ|i)>0,1≤i≤n。利用σ2算子的最优凹性，给出了σ2Hessian方程Pogorelov型C2内估计，进而证明了σ2(D2u(x))=1,x∈Rn的满足二次多项式增长条件的Γ3?-凸整解为二次多项式。     

一致分数阶非线性微分方程的精确解

同时考虑了Kudryashov方法和Khalil一致分数阶变换,构造了求解一致分数阶非线性微分方程精确解的新方法,并将其用于求解时间-空间一致分数阶Whitham-Boroer-Kaup方程,得到了Whitham-Boroer-Kaup方程新的精确解,验证了该方法的有效性和可行性.     

Enhanced CO2 Electrolysis with Metal-oxide Interface Structures

The ever-decreasing fossil fuels and the increasing greenhouse effect have caused substantial concern.Solid oxide electrolyser cell(SOEC)with La_0.75Sr_0.25Cr_(0.5 )Mn_0.5O_3-δ(LSCM)as a cathode was used for CO₂ electrolysis to CO.In this work,the metal-oxide interface was constructed on the LSCM framework by in-situ exsolution and impregnation,and the uniform distribution of metal nanoparticles on the LSCM framework was confirmed by spectroscopy techniques and electron microscopy techniques.The existence of three-phase boundary promoted the absorption and electrolysis of CO₂.(La_0.75 Sr_0.25)0.9(Cr_(0.5 )Mn_0.5)_0.9(Ni_0.5 Cu_0.5)_0.1 O_3-δ(LSCMNC)showed the best electrolytic CO₂ performance at 850℃and exhibited excellent electrocatalytic activity after 100 hours of long-term testing and 8 redox cycles.     

两个基于2,5-二甲氧基对苯二甲酸和咪唑衍生物的超分子钴配位聚合物的结构及光催化反应

本文以咪唑衍生物为配体,通过水热合成法与钴离子制备出两个配位聚合物:{[Co(DTA)(1,4-DIB)(H₂O)]·H₂O}_n(1)和[Co(DTA)(1,3-BMIB)]_n(2)(1,4-DIB=1,4-二(1H-咪唑-1-基)苯; 1,3-BMIB=1,3-二(4-甲基-1H-咪唑-1-基)苯;H₂DTA=2,5-二甲氧基对苯二甲酸)。利用X射线单晶衍射、粉末衍射、热失重、元素分析、红外光谱以及固体紫外-可见光谱等对两个配合物进行了表征。结构分析证实配合物1和2是通过二维结构堆积成的三维超分子化合物。粉末衍射测试则显示两个配合物在水中有很好的稳定性。固体紫外-可见光谱显示两个配合物属半导体材料,对紫外-可见光有很强的吸收作用。在光催化实验中,配合物1和2可加快亚甲基蓝的降解速度。     

Insights into the efficient charge separation over Nb2O5/2D-C3N4 heterostructure for exceptional visible-light driven H2 evolution

Two-dimensional carbon nitride(2 D-C₃ N₄)nanosheets are promising materials in photocatalytic water splitting,but still suffer from easy agglomeration and fast photogene rated electron-hole pairs recombination.To tackle this issue,herein,a hierarchical Nb₂ O₅/2 D-C₃ N₄ heterostructure is precisely constructed and the built-in electric field between Nb₂O₅ and 2 D-C₃ N₄ can provide the driving force to separate/transfer the charge carriers efficiently.Moreover,the strongly Lewis acidic Nb₂O₅ can adsorb TEOA molecules on its surface at locally high concentrations to facilitate the oxidation reaction kinetics under irradiation,resulting in efficient photogene rated electrons-holes separation and exceptional photocatalytic hydrogen evolution.As expected,the champion Nb₂O₅/2 D-C₃N₄ heterostructure achieves an exceptional H2 evolution rate of 31.6 mmol g^-1 h^-1,which is 213.6 times and 4.3 times higher than that of pristine Nb₂O₅ and2 D-C₃N₄,respectively.Moreover,the champion heterostructure possesses a high apparent quantum efficiency(AQE)of 45.08%atλ=405 nm and superior cycling stability.Furthermore,a possible photocatalytic mechanism of the energy band alignment at the hetero-interface is proposed based on the systematical characterizations accompanied by density functional theory(DFT)calculations.This work paves the way for the precise construction of a high-quality heterostructured photocatalyst with efficient charge separation to boost hydrogen production.     

Interface engineering of porous Fe2P-WO2.92 catalyst with oxygen vacancies for highly active and stable large-current oxygen evolution and overall water splitting

Constructing a low cost,and high-efficiency oxygen evolution reaction(OER)electrocatalyst is of great significance for improving the performance of alkaline electrolyzer,which is still suffering from highenergy consumption.Herein,we created a porous iron phosphide and tungsten oxide self-supporting electrocatalyst with oxygen-containing vacancies on foam nickel(Fe₂P-WO_2.92/NF)through a facile insitu growth,etching and phosphating strategies.The sequence-controllable strategy will not only generate oxygen vacancies and improve the charge transfer between Fe₂P and WO_2.92 components,but also improve the catalyst porosity and expose more active sites.Electrochemical studies illustrate that the Fe₂P-WO_2.92/NF catalyst presents good OER activity with a low overpotential of 267 mV at 100 mA cm^-2,a small Tafel slope of 46.3 mV dec^-1,high electrical conductivity,and reliable stability at high current density(100 mA cm^-2 for over 60 h in 1.0 M KOH solution).Most significantly,the operating cell voltage of Fe₂P-WO_2.92/NF‖Pt/C is as low as 1.90 V at 400 mA cm^-2 in alkaline condition,which is one of the lowest reported in the literature.The electrocatalytic mechanism shows that the oxygen vacancies and the synergy between Fe₂P and WO_2.92 can adjust the electronic structure and provide more reaction sites,thereby synergistically increasing OER activity.This work provides a feasible strategy to fabricate high-efficiency and stable non-noble metal OER electrocatalysts on the engineering interface.