关于不定方程x3-1=749y2

利用同余式、平方剩余、Pell方程的解的性质、递归序列证明了:不定方程x³-1=749y²仅有整数解(x,y)=(1,0).     

Melt Crystallization of Poly(butylene 2,6-naphthalate)

Poly(butylene 2,6-naphthalate)(PBN)is a crystallizable linear polyester containing a rigid naphthalene unit and flexible methylene spacer in the chemical repeat unit.Polymeric materials made of PBN exhibit excellent anti-abrasion and low friction properties,superior chemical resista nee,and outstanding gas barrier characteristics.Many of the properties rely on the presence of crystals and the formatio n of a semicrystalline morphology.To develop specific crystal structures and morphologies during cooling the melt,precise information about the melt-crystallization process is required.This review article summarizes the current knowledge about the temperature-controlled crystal polymorphism of PBN.At rather low supercooling of the melt,with decreasi ng crystal I izatio n temperature,0'-and a-crystals grow directly from the melt and organize in largely different spherulitic superstructures.Formation of a-crystals at high supercooling may also proceed via intermediate formation of a transient monotropic liquid crystalline structure,then yielding a non-spherulitic semicrystalline morphology.Crystallization of PBN is rather fast since its suppression requires cooling the melt at a rate higher than 6000 K-s_1.For this reason,investigation of the two-step crystallization process at low temperatu res requires application of sophisticated experimental tools.These in elude temperatureresolved X-ray scattering techniques using fast detectors and synchrotron-based X-rays and fast scanning chip calorimetry.Fast scanning chip calorimetry allows freezi ng the transie nt liquid-crystalline structure before its con version into a-crystals,by fast cooling to below its glass transition temperature.Subsequent an alysis using polarized-light optical microscopy reveals its texture and X-ray scatteri ng con firms the smectic arrangement of the mesogens.The combination of a large variety of experimental techniques allows obtaining a complete picture about crystallization of PBN in the entire range of melt-supercoolings down to the glass transition,including quantitative data about the crystallization kinetics,semicrystalline morphologies at the micrometer length scale,as well as nanoscale X-ray structure information.     

光驱动C1转换到高附加值化学品的研究进展

阐述了光驱动C1化学的最新研究进展, 分别对光驱动费托合成、 水煤气变换、 二氧化碳加氢、 甲烷重整和甲醇重整制氢的研究进行了综述, 提出了当前研究存在的问题及发展方向.     

敏化条件对染料敏化太阳能电池性能的影响

通过实验方案,对影响染料敏化太阳能电池(DSSC)的敏化条件进行了优化设计,在光阳极初始默认的制作条件下,从海带中提取叶绿素,分别对影响DSSC光电性能的敏化染料溶液浓度、pH值、温度、受光时间、敏化时间、对电极背景色等影响因素逐一进行研究,最终确定了光阳极敏化的最优条件:醇水溶液的最佳稀释比为1:2,最佳敏化pH=8,最佳敏化温度为30℃,最佳敏化时间24 h,黑暗环境下敏化效果最好,且对电极采用镜面背景最佳,最终获得光电转换效率0.76;.     

计算代数方程组孤立奇异解的符号数值方法

求解代数方程组是计算代数几何的最基本问题之一,孤立奇异解的计算则是其中最具挑战性的课题之一,在科学与工程计算中有着广泛的应用,如机器人、计算机视觉、机器学习、人工智能、运筹学、密码学和控制论等.本文结合作者的研究成果,综述了符号数值方法在计算代数系统孤立奇异解、特别是近似奇异解精化与验证方面的研究进展,并对未来的研究方向提出了展望.     

In-situ self-templated preparation of porous core-shell Fe1-xS@N,S co-doped carbon architecture for highly efficient oxygen reduction reaction

Transition metal compound(TMC)/carbon hybrids,as prospering electrocatalyst,have attracted great attention in the field of oxygen reduction reaction(ORR).Their morphology,structure and composition often play a crucial role in determining the ORR performance.In this work,we for the first time report the successful fabrication of porous core-shell Fe_1-xS@N,S co-doped carbon(Fe_1-xS@NSC-t,t represents etching time)by a novel in-situ self-template induced strategy using Fe3O4 nanospheres and pyrrole as sacrificial self-template.The post-polymerization of pyrrole can be accomplished by the Fe³⁺released through the etching of Fe₃O₄ by HCl acid.Thus,the etching time has a significant effect on the morphology,structure,composition a nd ORR performance of Fe_1-xS@NSC-t.Based on the cha racterizations,we find Fe_1-xS@NSC-24 can realize effective and balanced combination of Fe_1-xS and NSC,possessing porous core-shell architecture,optimized structure defect,specific surface area and doped heteroatoms configurations(especially for pyridinic N,graphitic N and Fe-N structure).These features thus lead to outstanding catalytic activity and cycling stability towards ORR.Our work provides a good guidance on the design of TMC/carbon-based electrodes with unique stable morphology and optimized structure and composition.     

DMF体系中Cu2O球晶的制备及形貌分析

以N,N-二甲基甲酰胺(DMF)为溶剂,通过改变铜源和表面活性剂,调控反应参数,溶剂热条件下制备了三维十字形、空心及实心的Cu₂O球晶。利用XRD、SEM等表征手段,分析探讨了工艺条件变化对Cu₂O球晶形貌的影响。研究表明,随着DMF浓度的增大,体系的还原能力增强,Cu⁺增多,溶液的过饱和度增大,Cu₂O晶体集合体形态由晶体结构控制的各向异性与对称性的球晶逐渐向各向同性球晶演变。十二烷基硫酸钠(SDS)、十六烷基三甲基溴化铵(CTAB)、聚乙烯吡咯烷酮(PVP)等表面活性剂有助于降低溶液的过饱和度,增加结晶质的表面扩散能力,有利于规则形态Cu₂O晶粒的形成。反应体系中,Cu(Ac)₂·H₂O水解生成的羧基与DMF中的甲酰基在高温下发生脱羧反应产生CO₂气体以及SDS发泡作用产生的气体是形成空心Cu₂O球晶的重要原因。     

基于5-磺基水杨酸的单、双核铜(Ⅱ)三元混配配合物的合成及晶体结构

以5-磺基水杨酸和咪唑衍生物为配体合成了单核、双核结构的三元混配Cu(Ⅱ)配合物:[Cu(H₂biim)(Hssal)(H₂O)₂]·H₂O(1)和{[Cu(MeHbiim)(Hssal)(H₂O)]·0.5H₂O}₂(2)(H₃ssal=5-磺基水杨酸,H₂biim=2,2’-联咪唑,MeHbiim=N-甲基-2,2’-联咪唑),并利用元素分析、红外光谱、紫外-可见光谱、X-射线单晶衍射及热重分析等技术手段对其结构进行了表征。单晶结构解析表明配合物1属于单斜晶系,P2₁／C 空间群,Cu(Ⅱ)离子与1个5-磺基水杨酸根、2个水分子以及1个联咪唑分子形成五配位四角锥构型的单核配合物结构。配合物2属于正交晶系,P2(1)2(1)2(1)空间群,双核Cu(II)离子分别处于五配位四角锥和四配位平面四边形的几何构型的配位环境中,与配合物1不同,5-磺基水杨酸采取μ₂双-单齿配位模式。荧光光谱分析表明配合物2具有较强的荧光性。     

一类非线性发展方程的精确解

利用hirota双线性法,得到(3+1)维孤子方程、(3+1)维KP-Boussinesq方程、(2+1)维修正Caudrey-Dodd-Gibbon-Kotera-S awada方程、Hirota-Satsuma浅水波方程的精确解,并做出一部分解的图形,进一步研究解的结构和性质.     

对氯苯甲酸构筑的铜(Ⅱ)配合物的合成、HSA结合及细胞毒性

本文合成了配合物[Cu(pcba)₂·(phen)(H₂O)] (pcba =对氯苯甲酸,phen = 1,10-邻菲罗啉),该配合物属于三斜晶系,P1空间群,晶胞参数为a=0.790 98(2) nm,b=1.072 40(4) nm,c=1.487 19(6) nm,α=100.613(3)°,β=95.239(3)°,γ=108.334(3)°,Z=2,D_c=1.638 g·cm^-3,F(000)=582,最终结构残差因子R₁=0.035 9,wR₂=0.089 1。采用紫外及荧光研究了配合物和人血清蛋白(HSA)的相互作用方式。结果表明,配合物静态猝灭HSA荧光,可求得配合物与HSA的猝灭常数K_sv=2.35×10⁵ L·mol^-1,猝灭速率常数K_q=2.35×10¹³ L·mol^-1·s^-1,结合常数为K_a=2.14×10¹³ L·mol^-1,结合位点n=2.37。同时,研究了配合物对胃癌细胞A549、宫颈癌细胞Hela和肝癌细胞HepG2的抗增殖能力。