改进的PNC方法及其在非线性偏微分方程多解问题中的应用

2017年，李昭祥等提出了一种偏牛顿-校正法（Partial Newton-Correction Method，简记为PNC方法），并利用它成功地计算出了三类非线性偏微分方程的多重不稳定解.本文在PNC方法的基础上，提出并发展了一种改进的PNC方法.首先，利用Nehari流形$\mathcal{N}$与零平凡解的可分离性，建立并证明了$\mathcal{N}$的某特殊子流形$\mathcal{M}$上的全局分离定理及其推广（即局部分离定理）.全局分离定理只跟非线性偏微分算子或相应的非线性泛函本身有关，而与具体的计算方法无关.对一些典型的非线性偏微分方程多解问题（比如，Henon方程问题），该全局分离定理的分离条件，经验证是成立的.另一个方面，通过修改或补充原辅助变换的定义，去掉了原辅助变换的奇异性；接着建立并证明了某些非线性偏微分方程问题的新未知解与该非线性偏微分算子零核空间的密切关系；在证明中，去掉了在原奇异变换下所需的标准收敛（standard convergence）假设.最后，计算实例与数值结果验证了改进的PNC方法的可行性和有效性；同时表明子流形$\mathcal{M}$与已知解的可分离性是PNC方法和本文新方法能成功找到多解的关键.     

Pd nanoparticles supported on amphiphilic porous organic polymer as an efficient catalyst for aqueous hydrodechlorination and Suzuki-Miyaura coupling reactions

Developing efficient and recyclable heterogeneous catalysts for organic reactions in water is important for the sustainable development of chemical industry. In this work, Pd nanoparticles supported on DABCO-functionalized porous organic polymer was successfully prepared through an easy copolymerization and successive immobilization method. Characterization results indicated that the prepared catalyst featured big surface area, hierarchical porous structure, and excellent surface amphiphilicity. We demonstrated the use of this amphiphilic catalyst in two case reactions, i.e. the aqueous hydrodechlorination and Suzuki-Miyaura coupling reactions. Under mild reaction conditions, the catalyst showed high catalytic activities for the two reactions. In addition, the catalyst could be easily recovered and reused for several times. Also, no obvious Pd leaching and aggregation of Pd nanoparticles occurred up during the consecutive reactions.     

SCR performance enhancement of NiMnTi mixed oxides catalysts by regulating assembling methods of LDHs-Based precursor

A series of NiMnTi mixed metal oxides (Ni/Mn-TiO₂, Mn/NiTi-LDO and TiO₂/NiMn-LDO, NiMnTi-LDO) were synthesized via different assembling methods and evaluated in the selective catalytic reduction of NO_x with NH₃(NH₃-SCR). As the results presented, catalysts via diverse assembling methods of LDHs templates afforded different catalytic denitrification (DeNO_x) performance, which might be related to the exposure degree of active constituents and the interaction intensity between metal components. Noticeably, compared with Ni/Mn-TiO₂, Mn/NiTi-LDO and TiO₂/NiMn-LDO catalysts, the NiMnTi-LDO catalyst deriving from one step in-situ method NiMnTi-LDH precursor template exhibited the most desirable performance at temperature window of 150–360 °C in NH₃-SCR (above 90% NO_x conversion with 95% N₂ selectivity). The specific structure and property of samples were correlated by means of a series of characterizations, where the results indicated that NiMnTi-LDO possessed the highest surface area, the strongest redox ability, the most abundant acid amount and the best dispersion.     

Ce∶LuAG闪烁晶体的生长研究

Ce∶LuAG晶体是一种性能优良的闪烁材料,但采用提拉法生长Ce∶LuAG时,经常出现开裂和包裹物缺陷。本文通过理论与实践相结合的方式分析了温度梯度、提拉速度、晶体旋转速度和热应变等因素对晶体产生缺陷的影响,并提出了解决办法,给出了适合生长优质Ce∶LuAG晶体的工艺参数:熔体上方温度梯度在5 ℃/mm左右,放肩角度在30°~60°,提拉速度1.0~1.5 mm/h,晶体旋转速度15~25 r/min。最后成功生长出直径30 mm、等径长50 mm质量较为完好的Ce∶LuAG单晶,晶体内核心面积小。     

Chitosan hydrogel,as a biological macromolecule-based drug delivery system for exosomes and microvesicles in regenerative medicine: a mini review

Cellulose - Extracellular vesicles are membrane-packed entities that are involved in various physiological and pathological processes. Recently, the role of exosomes and microvesicles in...     

银(I)配位聚合物修饰Preyssler型多金属氧酸盐的高维、高连接结构的组装及性质

以AgNO3、K12.5Na1.5[Na P5W30O110]·15H2O及柔性配体1,1′-双(3,5-二甲基-1H-吡唑)甲烷(H2bdpm)为原料,利用水热合成方法合成了1个新的基于单核银为中心的Preyssler多酸阴离子的有机-无机杂化化合物:[Ag13(H2bdpm)8(H2O)5(HAg P5W30O110)]·2H2O(1),并通过元素分析、红外光谱、热重分析和X-射线单晶衍射等分析手段对化合物1进行了表征.X-射线单晶结构分析表明,该化合物属于三斜晶系,P1空间群,晶胞参数:a=19.135(5),b=20.313(5),c=28.400(5),Z=2,R1=0.0550,w R2=0.1542.化合物1包含罕见的以单核银为中心的Preyssler型多酸阴离子,该阴离子通过金属银连接形成二维无机层.相连的二维层之间通过多种Ag-H2bdpm金属有机亚单元进一步连接形成三维框架.该化合物最大的结构特点在于Preyssler型多酸阴离子的高连接(十八连接)以及Ag(I)离子多样的配位模式.     

Multilayer Porous Vanadium Nitride Microsheets Anodes for Highly Stable Na-ion Batteries

Sodiumion batteries(SIBs)have attracted intensive attention as promising alternative to lithium-ionbatteries(LIBs)for large scale energy storage systems because of low cost of sodium,similar energy storage mechanism and the reasonable performance.However,it is still a great challenge to search and design a robust structure of anode materials with excellent cycling stability and high rate capability for SIBs.Herein,multilayer porous vanadium nitride(VN)microsheets are synthesized through a facile and scalable hydrothermal synthesis-nitrogenization strategy as an effective anode material for SIBs.The multilayer porous VN microsheets not only offer more active sites for fast Na+insertion/extraction process and short diffusion pathway,but also effectively buffer the volume change of anode due to more space in the multilayer porous structure.The large proportions of capacitive behavior imply that the Na+charge storage depends on the intercalation pseudocapacitive mechanism.The multilayer porous VN microsheets electrodes manifest excellent cycling stability and rate capability,delivering a discharge capacity of 156.1 mA·h/g at 200 mA/g after 100 cycles,and a discharge capacity of 111.9 mA·h/g at 1.0 A/g even after 2300 cycles with the Coulombic efficiency of nearly 100%.     

磺酰脲类除草剂分子印迹聚合物制备及应用研究进展

磺酰脲类除草剂本身易降解,在环境和生物样品中痕量存在,其残留分析工作颇具挑战。分子印迹聚合物因其良好的选择性和稳定性已被广泛应用于农药残留分析的分离与富集前处理过程,提高了检测的准确度和精密度。本文从单体、溶剂与致孔剂、聚合方法三个方面概述了近15年来磺酰脲类分子印迹聚合物的制备,并对其在残留检测中的应用方式进行了综述,为磺酰脲类除草剂残留检测技术的进一步开发提供了参考。     

Batch synthesis of polyoxometalate-based phosphonium compounds by one-step room-temperature mechanochemical process,and their morphology-dependent antibacterial activities

Based on the Keggin-type polyoxometalate and quaternary phosphonium salt, the (MePh₃P) _n -POM_Keggin compounds were synthesized via one-step mechanochemical process at room temperature. It showed the advantages of convenient operation, lower cost, less pollution, and mass production. Wonderfully, the morphology of compounds presented a strong dependence on the number of crystal water in the source heteropoly acids. A hypothesis of ‘semi-solid nonlocalized waters’ was brought to discuss the formation mechanism of polyhedrons. Antibacterial experiments indicate that the samples have good antibacterial activities, which resulted from the increase of the positive electrical charge of the phosphonium cation caused by the polarization by POM groups. Additionally, a formula of inhibitory zone per unit surface area was designed to more precisely evaluate the antibacterial activity of the materials. The calculation result indicated that the polyhedral particles give a higher surface antibacterial activity than the grain powder. This work developed an alternative synthesis method for composites from a new perspective, and will promote the research of new type of antibacterial agent.     

Lanthanide-organic frameworks based on terphenyl-tetracarboxylate ligands: syntheses,structures, optical properties and selective sensing of nitro explosives

Three isostructural three-dimensional(3D) lanthanide-based metal-organic frameworks [Ln_2L(H_2L)(NMP)_2].H_2O(Ln=Sm(1), Eu(2), Gd(3); H_4L=1,1′:4′,1″-terphenyl-2′,4,4″,5′-tetracarboxylic acid; NMP=N-methyl-2-pyrrolidone) have been synthesized and structurally characterized. In 1–3, two Ln3+ ions are doubly-bridged by two oxygen atoms of two carboxylate groups to form the dinuclear Ln_2(OCOO–)_2 unit. Each Ln_2(OCOO–)_2 unit links with four H_2L~(2-) ligands and four L4. ligands to lead to the 3D framework,which can be rationalized as a new trinodal 4,4,8-connected(44.62)(45.6)(412.616) topological network by considering the dinuclear Ln_2(OCOO–)_2 units as 8-connected nodes and L~4./H_2L~(2-) ligands as planar 4-connected nodes, respectively. 1 and 3 exhibit blue emission originated from the ligand with the emission maximum at 384 nm, while 2 shows intense characteristic red emission of Eu~(3+) ions and weak ligand-centered emission. Moreover, 2 has fluorescent quenching response towards the aromatic nitro compounds, especially for the 3,4-dinitrotoluene(3,4-DNT) with the linear Stern-Volmer relationship in the concentration range of 0–1 mM and the quenching constant(Ksv) of 2.084×10~3 M~(-1).