On Fermat Diophantine functional equations,little Picard theorem and beyond

Aequationes mathematicae - We discuss equivalence conditions for the non-existence of non-trivial meromorphic solutions to the Fermat Diophantine equation $$f^m(z)+g^n(z)=1$$ with integers $$m,n\ge...     

A Photoactivated Cu–CeO2 Catalyst with Cu-[O]-Ce Active Species Designed through MOF Crystal Engineering

Fully utilizing solar energy for catalysis requires the integration of conversion mechanisms and therefore delicate design of catalyst structures and active species. Herein, a MOF crystal engineering method was developed to controllably synthesize a copper–ceria catalyst with well-dispersed photoactive Cu-[O]-Ce species. Using the preferential oxidation of CO as a model reaction, the catalyst showed remarkably efficient and stable photoactivated catalysis, which found practical application in feed gas treatment for fuel cell gas supply. The coexistence of photochemistry and thermochemistry effects contributes to the high efficiency. Our results demonstrate a catalyst design approach with atomic or molecular precision and a combinatorial photoactivation strategy for solar energy conversion.     

Divergent Synthesis of Oxa-Cyclic Nitrones through Gold(I)-Catalyzed 1,3-Azaprotio Transfer of Propargylic α-Ketocarboxylate Oximes: Experimental and DFT Studies

1,3-Azaprotio transfer of propargylic α-ketocarboxylate oximes, a new type of alkynyl oximes featuring an ester tether, has been explored by taking advantage of gold catalysis. The incorporation of an oxygen atom to the chain of alkynyl oximes led to the formation of two different oxa-cyclic nitrones. It was found that internal alkynyl oximes with an E-configuration deliver five-membered nitrones, whereas terminal alkynyl oximes with an E-configuration afford six-membered nitrones. DFT calculations on four possible pathways supported a stepwise formation of C−N and C−H bonds, in which a 1,3-acyloxy-migration competes with the 1,3-azaprotio-transfer, especially in the case of internal alkynyl oximes. The relative nucleophilic properties of oxygen in the carbonyl group and the nitrogen in the oxime, the electronic effects of alkynes, and the influence of the ring system have been investigated computationally.     

Rational Development of Remote C−H Functionalization of Biphenyl: Experimental and Computational Studies

A simple and efficient nitrile-directed meta-C−H olefination, acetoxylation, and iodination of biaryl compounds is reported. Compared to the previous approach of installing a complex U-shaped template to achieve a molecular U-turn and assemble the large-sized cyclophane transition state for the remote C−H activation, a synthetically useful phenyl nitrile functional group could also direct remote meta-C−H activation. This reaction provides a useful method for the modification of biaryl compounds because the nitrile group can be readily converted to amines, acids, amides, or other heterocycles. Notably, the remote meta-selectivity of biphenylnitriles could not be expected from previous results with a macrocyclophane nitrile template. DFT computational studies show that a ligand-containing Pd–Ag heterodimeric transition state (TS) favors the desired remote meta-selectivity. Control experiments demonstrate the directing effect of the nitrile group and exclude the possibility of non-directed meta-C−H activation. Substituted 2-pyridone ligands were found to be key in assisting the cleavage of the meta-C−H bond in the concerted metalation–deprotonation (CMD) process.     

Multi-stable quantum droplets in optical lattices

Nonlinear Dynamics - We address the nonlinear dynamics of binary Bose-Einstein condensates with mutually symmetric spinor components trapped in an optical lattice. The interaction between the...     

ESTIMATING EXTREME-VALUE INDEX FROM RECORDS

1.IntroductionLet{X.,n21}beasequenceoflidry'swithanondegeneratedistributionfunctionF(x).Supposethereexistsomeconstantsan>0,b.6RandsomeacERsuchthatwhereG.standsforoneoftheextremevaluedistributions:Heretheindex7ERisarealparameter(interpret(1 box)--'/ryase--"for7~0).Theestimationoftheextreme-valueindex7isveryimportantbothintheextremevaluetheoryandinpractice.Manystatistics,suchasHillestimator(forcaseac>0),PickandsestimatorandDekkers-EinmahLdeHaan'smomentestimatorwhicharebasedonafinitesample,…     

聚硅烷研究进展 (1)聚硅烷的合成及应用

聚硅烷的合成及应用因可溶性聚硅烷的发现而成为聚合物研究的又一热点。本文综述了聚硅烷合成与应用的近期发展。     

激光等离子体2660紫外探针及干涉系统

成功地在六路高功率Nd玻璃激光装置上建立了2660紫外激光探针和适合紫外波段的Normaski干涉仪,首次将可见波长的连续激光应用于紫外干涉仪中靶成像调整和光路准直。利用该紫外光干涉仪,在铜柱状靶(φ500μm)上测量了厚等离子体中高达0.6n。的电子密度。     

下料问题的优化模型及其快速算法

结合生产实际中具体的下料问题,本文建立了该类问题的优化模型,并提出下料方式的遴选三准则,即高利用率优先准则,长度优先准则和时间优先准则.运用本文的算法对一维下料的利用率高达99.6%,机器时间4秒.对二维的利用率为98.9%,机器时间约7秒.     

超临界流体触媒作用下石墨-金刚石转变

 研究了超临界流体CO₂在石墨-金刚石转变中的触媒作用。实验中，采用Ag₂O作为流体触媒的先驱材料，在7.7 GPa压力下，Ag₂O在1 200 ℃分解成Ag和O₂，O₂与石墨套管在高温高压下反应形成CO₂超临界流体。研究结果表明，在7.7 GPa和1 500 ℃以上温度条件下，石墨在CO₂流体触媒的作用下可转变为金刚石晶体，在1 500～1 700 ℃温度范围内合成出的金刚石具有完好的八面体形貌，与天然金刚石的生长特征非常相似。