Characterization of Lipschitz spaces via commutators of the Hardy–Littlewood maximal function

Let M be the Hardy–Littlewood maximal function and b be a locally integrable function. Denote by $M_b$ and $[b,M]$ the maximal commutator and the (nonlinear) commutator of M with b. In this paper, the author considers the boundedness of $M_b$ and $[b,M]$ on Lebesgue spaces and Morrey spaces when b belongs to the Lipschitz space, by which some new characterizations of the Lipschitz spaces are given.     

Blow-up of critical norms for the 3-D Navier-Stokes equations

Let u =(uh, u3) be a smooth solution of the 3-D Navier-Stokes equations in R3× [0, T). It was proved that if u3 ∈ L∞(0, T;˙B-1+3/p p,q(R3)) for 3 p, q ∞ and uh∈ L∞(0, T; BMO-1(R3)) with uh(T) ∈ VMO-1(R3), then u can be extended beyond T. This result generalizes the recent result proved by Gallagher et al.(2016), which requires u ∈ L∞(0, T;˙B-1+3/pp,q(R3)). Our proof is based on a new interior regularity criterion in terms of one velocity component, which is independent of interest.     

A mod 2 index theorem for pin<Superscript>−</Superscript> manifolds

We establish a mod 2 index theorem for real vector bundles over 8k + 2 dimensional compact pin^? manifolds. The analytic index is the reduced η invariant of (twisted) Dirac operators and the topological index is defined through KO-theory. Our main result extends the mod 2 index theorem of Atiyah and Singer (1971) to non-orientable manifolds.     

Unsupervised and semi-supervised extreme learning machine with wavelet kernel for high dimensional data

Extreme learning machine (ELM) not only is an effective classifier in supervised learning, but also can be applied on unsupervised learning and semi-supervised learning. The model structure of unsupervised extreme learning machine (US-ELM) and semi-supervised extreme learning machine (SS-ELM) are same as ELM, the difference between them is the cost function. We introduce kernel function to US-ELM and propose unsupervised extreme learning machine with kernel (US-KELM). And SS-KELM has been proposed. Wavelet analysis has the characteristics of multivariate interpolation and sparse change, and Wavelet kernel functions have been widely used in support vector machine. Therefore, to realize a combination of the wavelet kernel function, US-ELM, and SS-ELM, unsupervised extreme learning machine with wavelet kernel function (US-WKELM) and semi-supervised extreme learning machine with wavelet kernel function (SS-WKELM) are proposed in this paper. The experimental results show the feasibility and validity of US-WKELM and SS-WKELM in clustering and classification.     

Lewis酸催化纤维素制乳酸机理研究

Because fossil fuels are continuously depleted, valorization of biomass into valuable liquid products and chemicals is of great significance yet it remains challenging. Among many biomass-derived products, lactic acid is one of the most important renewable monomers for preparing the degradable polymer polylactic acid. The use of raw biomass to produce lactic acid through catalytic conversion is an attractive approach. In this work, the catalytic reaction performance and mechanism of different Lewis acids (Y³⁺, Sc³⁺, and Al³⁺) for the production of lactic acid from cellulose were investigated in detail by isotopic nuclear magnetic resonance (NMR) and mass spectrometry. The production of lactic acid from cellulose includes tandem and competing reactions. The order of catalytic activity for the one-pot conversion of cellulose into lactic acid is as follows: Y³⁺ > Al³⁺ > Sc³⁺. The main tandem reactions involve the hydrolysis of cellulose into glucose, the isomerization of glucose into fructose (the order of catalytic activity, the same below: Y³⁺ > Al³⁺, Y³⁺ > Sc³⁺), the cleavage of fructose via a retro-aldol reaction to glyceraldehyde (GLY) and 1, 3-dihydroxyacetone (DHA) (Sc³⁺ > Y³⁺ > Al³⁺), and the conversion of DHA or GLY to the final product lactic acid (Al³⁺ > Y³⁺ > Sc³⁺). It was found that the process of glucose isomerization to fructose was the key step to the final selectivity of the tandem reaction of cellulose conversion to lactic acid, and it was clarified that the production of lactic acid from DHA underwent a keto-enol (K-E) tautomerization process rather than a classical 1, 2-shift process. First, DHA was transformed into GLY via the isomerization process, then the adjacent hydroxyl group of GLY was removed in the form of water to produce an α, β-unsaturated species. After that, the α, β-unsaturated species underwent K-E tautomerization to generate unsaturated aldehyde-ketone intermediates. Meanwhile, a molecule of water was added to aldehyde-ketone intermediates to obtain a diol product, the hydrogen atom at the methine position was transferred and the lactic acid was finally obtained through the K-E tautomerization process. The in-depth understanding of the reaction mechanism presented in this work will help to design more selective catalysts for cellulose conversion into value-added oxygen-containing small molecule chemicals.      

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.      

原子层沉积构筑Pd/TiO2限域催化剂及其在1,4-丁炔二醇加氢的应用

利用ALD制备了TiO₂限域的Pd催化剂, 研究了限域空间内Pd纳米颗粒与TiO₂的界面作用对1,4-丁炔二醇(BYD)加氢性能的影响. 相比于管外负载型催化剂, 限域催化剂在催化1,4-丁炔二醇选择性加氢反应中体现出非常高的催化活性和1,4-丁烯二醇的选择性. HR-TEM、 EDX-Mapping、 XRD、 XPS和H₂-TPR表征说明, 限域体系中Pd-TiO₂的界面相互作用强于传统TiO₂表面负载型Pd催化剂, 这种强界面作用不仅能够提高BYD的加氢活性, 也可抑制半加氢产物1,4-丁烯二醇的异构化和深度加氢, 提高1,4-丁烯二醇的选择性, 而且限域结构也可阻止管内壁Pd纳米颗粒的脱落, 提高催化剂的稳定性.     

泡沫镍铁合金自支撑NiFeOOH纳米片的制备及析氧性能研究

电催化析氧反应(OER)是电解水制氢的重要半电池反应。然而,OER的缓慢动力学仍需研究高效的电催化剂。在非贵金属催化剂中,NiFe基材料是OER催化剂研究热点。本文通过食人鱼溶液简单一步浸渍刻蚀法将不同Fe含量的泡沫NiFe合金进行氧化,制备了表面具有纳米片形貌的NiFeOOH自支撑电催化剂,并深入研究其电催化析氧性能。通过SEM、XRD、XPS等对电催化剂的形貌结构及成分进行表征,证实了三维多孔基底上NiFeOOH纳米片结构的形成。由于高价镍、铁物种的存在以及二维纳米片结构的生成,NiFeOOH/NF的析氧性能大幅度提高,在10 mA?cm-2的电流密度下过电位仅155.68 mV,Tafel斜率为 88.2 mV?dec-1。这为研制高效、耐用的自支撑非贵金属电极提供了新思路。     

纳米SiC基光催化剂研究进展

Industrialization undoubtedly boosts economic development and improves the standard of living; however, it also leads to some serious problems, including the energy crisis, environmental pollution, and global warming. These problems are associated with or caused by the high carbon dioxide (CO₂) and sulfur dioxide (SO₂) emissions from the burning of fossil fuels such as coal, oil, and gas. Photocatalysis is considered one of the most promising technologies for eliminating these problems because of the possibility of converting CO₂ into hydrocarbon fuels and other valuable chemicals using solar energy, hydrogen (H₂) production from water (H₂O) electrolysis, and degradation of pollutants. Among the various photocatalysts, silicon carbide (SiC) has great potential in the fields of photocatalysis, photoelectrocatalysis, and electrocatalysis because of its good electrical properties and photoelectrochemistry. This review is divided into six sections: introduction, fundamentals of nanostructured SiC, synthesis methods for obtaining nanostructured SiC photocatalysts, strategies for improving the activity of nanostructured SiC photocatalysts, applications of nanostructured SiC photocatalysts, and conclusions and prospects. The fundamentals of nanostructured SiC include its physicochemical characteristics. It possesses a range of unique physical properties, such as extreme hardness, high mechanical stability at high temperatures, a low thermal expansion coefficient, wide bandgap, and superior thermal conductivity. It also possesses exceptional chemical characteristics, such as high oxidation and corrosion resistance. The synthesis methods for obtaining nanostructured SiC have been systematically summarized as follows: Template growth, sol-gel, organic precursor pyrolysis, solvothermal synthesis, arc discharge, carbon thermal reduction, and electrospinning. These synthesis methods require high temperatures, and the reaction mechanism involves SiC formation via the reaction between carbon and silicon oxide. In the section of the review involving the strategies for improving the activity of nanostructured SiC photocatalysts, seven strategies are discussed, viz., element doping, construction of Z-scheme (or S-scheme) systems, supported co-catalysts, visible photosensitization, construction of semiconductor heterojunctions, supported carbon materials, and construction of nanostructures. All of these strategies, except element doping and visible photosensitization, concentrate on enhancing the separation of holes and electrons, while suppressing their recombination, thus improving the photocatalytic performance of the nanostructured SiC photocatalysts. Regarding the element doping and visible photosensitization strategies, element doping can narrow the bandgap of SiC, which generates more holes and electrons to improve photocatalytic activity. On the other hand, the principle of visible photosensitization is that photo-induced electrons move from photosensitizers to the conduction band of SiC to participate in the reaction, thus enhancing the photocatalytic performance. In the section on the applications of nanostructured SiC, photocatalytic H₂ production, pollutant degradation, CO₂ reduction, photoelectrocatalytic, and electrocatalytic applications will be discussed. The mechanism of a photocatalytic reaction requires the SiC photocatalyst to produce photo-induced electrons and holes during irradiation, which participate in the photocatalytic reaction. For example, photo-induced electrons can transform protons into H₂, as well as CO₂ into methane, methanol, or formic acid. Furthermore, photo-induced holes can convert organic waste into H₂O and CO₂. For photoelectrocatalytic and electrocatalytic applications, SiC is used as a catalyst under high temperatures and highly acidic or basic environments because of its remarkable physicochemical characteristics, including low thermal expansion, superior thermal conductivity, and high oxidation and corrosion resistance. The last section of the review will reveal the major obstacles impeding the industrial application of nanostructured SiC photocatalysts, such as insufficient visible absorption, slow reaction kinetics, and hard fabrication, as well as provide some ideas on how to overcome these obstacles.      

多共振热激活延迟荧光过程的理论研究

本工作借助第一性原理和动力学演化,系统地研究了四个叔丁基-咔唑及吩噻嗪取代的硼-氮化合物(BCz-BN、2PTZ-BN、Cz-PTZ-BN和2Cz-PTZ-BN)的多共振热激活延迟荧光的高效发光机制.结果表明上述分子T₁与T₂间的内转换速率远大于其它辐射与非辐射速率,同时T₂到S₁的反向系间窜越速率也高于T₁到S₁的反向系间窜越速率,因此其多共振热激活延迟荧光过程应遵循T₁→T₂→S₁→S₀的路径.进一步动力学演化表明,T₁与T₂之间的内转换主要发生在演化初期,随着时间的推移,能量逐渐由T₂向S₁转移,并最终在S₁完成荧光发射.上述研究揭示了多共振延迟荧光的微观本质,为未来设计及合成新的多共振热激活延迟荧光分子提供了理论依据.