2-距离空间中平方型压缩映象的一个新的耦合公共不动点定理

在2-距离空间的框架下, 利用映象对的ω-相容性条件, 建立了一类新的平方型压缩条件, 讨论了此类映象耦合公共不动点的存在性和唯一性.证明了一个新的耦合公共不动点定理, 也提供了一个有效的例子来支持该文的新结果.该文的结果改善了之前文献中的相关结果.     

一类奇异非线性多重调和方程存在正整解的充分必要条件

研究一类奇异非线性多重调和方程?~mu=f(|x|,u,|▽u|)u~(-β),给出了方程存在正的径向对称整体解的充分必要条件和解的性质.     

内蕴平方函数交换子在加权弱Hardy空间上的端点估计

证明了由BMO函数与α阶内蕴面积函数S_α和内蕴g_(λ,α)*函数生成的交换子都是由加权弱Hardy空间WH_(b,ω)~1到加权弱L1空间WL_ω~1上的有界算子.     

可数Sober空间的若干性质北大核心

可数sober空间是sober空间的一种推广.本文讨论了可数sober空间的一些性质,特别地证明了以可数sober空间为对象、以连续映射为态射的范畴CSOB为完备范畴以及从任意空间到可数sober空间的连续映射空间为可数sober空间.     

加权Banach空间中随机指数系完备的若干结论

在允许随机序列上密度无限且减弱权函数是凸函数的条件下,采用新的方法得到C_α中随机指数函数系完备性的充分必要条件,其中C_α是定义在R上的复连续函数构成的加权Banach空间,且要求函数在一致范数下当t→∞时以f(t)exp(-α(t))趋于零.     

循环子空间的进一步应用

以向量的极小多项式作为出发点,深入分析了循环子空间的具体结构,得到了循环子空间进一步的应用.     

例析高考中几何型应用题的解题策略

2017年江苏高考数学应用题延续前几年的命题趋势,即以几何图形为载体,考查解三角、平面解析几何、数列、函数、导数等基础知识,考查考生数学阅读、识图和计算、转化和化归、空间想象力、解决实际问题、数学建模等能力,考查数形结合、转化和化归、函数与方程、分类讨论等数学思想.     

利用空间位阻和氢溢流协同作用促进5-羟甲基糠醛选择性加氢制备5-甲基糠醛

Selective hydrogenation is a vital class of reaction. Various unsaturated functional groups in organic compounds, such as aromatic rings, alkynyl (C≡C), carbonyl (C＝O), nitro (-NO₂), and alkenyl (C＝C) groups, are typical targets in selective hydrogenation. Therefore, selectivity is a key indicator of the efficiency of a designed hydrogenation reaction. 5-(Hydroxymethyl)furfural (HMF) is an important platform compound in the context of biomass conversion, and recently, the hydrogenation of HMF to produce fuels and other valuable chemicals has received significant attention. Controlling the selectivity of HMF hydrogenation is paramount because of the different reducible functional groups (C＝O, C-OH, and C＝C) in HMF. Moreover, the exploration of new routes for hydrogenating HMF to valuable chemicals is becoming attractive. 5-Methylfurfural (MF) is also an important organic compound; thus, the selective hydrogenation of HMF to MF is an essential synthetic route. However, this reaction has challenging thermodynamic and kinetic aspects, making it difficult to realize. Herein, we propose a strategy to design a highly efficient catalytic system for selective hydrogenation by exploiting the synergy between steric hindrance and hydrogen spillover. The design and preparation of the Pt@PVP/Nb₂O₅ catalyst (PVP = polyvinyl pyrrolidone; Nb₂O₅ = niobium(V) oxide) were also conducted. Surprisingly, HMF could be converted to MF with 92% selectivity at 100% HMF conversion. The reaction pathway was revealed through the combination of control experiments and density functional theory calculations. Although PVP blocked HMF from accessing the surface of Pt, hydrogen (H₂) could be activated on the surface of Pt due to its small molecular size, and the activated H₂ could migrate to the surface of Nb₂O₅ through a phenomenon called H₂ spillover. The Lewis acidic surface of Nb₂O₅ could not adsorb the C＝O group but could adsorb and activate the C-OH group of HMF; therefore, when HMF was adsorbed on Nb₂O₅, the C-OH groups were hydrogenated by the spilled over H₂ to form MF. The high selectivity of this reaction was realized because of the unique combination of steric effects, hydrogen spillover, and tuning of the electronic states of the Pt and Nb₂O₅ surfaces. This new route for producing MF has great potential for practical application owing to its discovered advantages. We believe that this novel strategy can be used to design catalysts for other selective hydrogenation reactions. Furthermore, this study demonstrates a significant breakthrough in selective hydrogenation, which will be of interest to researchers working on the utilization of biomass, organic synthesis, catalysis, and other related fields.      

基于H型芴基小分子的双极性有机场效应晶体管存储器

从空间位阻角度出发,设计并合成了H型芴基小分子材料3Ph-TrH,并通过溶液加工方法制备了将其作为电荷捕获层的浮栅型有机场效应晶体管(OFET)存储器.结果表明,该器件的空穴和电子存储窗口分别为31.2和11.6V,实现了基于单个小分子材料的双极性电荷存储.为了提高器件的稳定性,进一步制备了基于3Ph-TrH与聚苯乙烯(PS)掺杂薄膜的浮栅型OFET存储器.测试结果显示,该器件比基于3Ph-TrH作为单组分电荷捕获层的器件具有更高的稳定性和耐受性,在10000s的维持时间测试后,该器件的电流开关比还能维持在1.1×10³.该工作为制备新型双极性电荷存储的OFET存储器提供了一条思路.     

基于高光谱的黑色签字笔墨水种类鉴别方法研究

该文提出了高光谱成像技术结合机器学习快速无损鉴别黑色签字笔墨水种类的新方法。采集36支不同品牌型号的黑色签字笔笔迹的高光谱图像,对每支签字笔笔迹的高光谱图像选取18个感兴趣区域,共提取648个平均光谱作为样本集。对450～950 nm的原始光谱进行Savitzky－Golay平滑、Z－Score标准化和两种组合方法光谱预处理,使用线性判别分析（LDA）和随机子空间－线性判别分析（RSM－LDA）分别构建黑色签字笔墨水种类鉴别模型。实验结果表明：不同预处理方法对RSM－LDA模型的鉴别准确率影响较小,而对于LDA模型,组合预处理具有更优的鉴别准确率;相比LDA模型,RSM－LDA模型分类效果更佳,训练集的平均分类准确率达100%,交叉验证平均分类准确率达99.09%,测试集的平均分类准确率达90.70%,每类样本的准确率、精准率、召回率均高于LDA模型分类结果,模型的接受者操作特征曲线下方面积（AUC值）达0.998 3,模型性能良好。因此,采用高光谱成像技术结合RSM－LDA可实现不同品牌型号黑色签字笔墨水的快速无损鉴别。