Error bound of critical points and KL property of exponent 1/2 for squared F-norm regularized factorization

This paper is concerned with the squared F(robenius)-norm regularized factorization form for noisy low-rank matrix recovery problems. Under a suitable assumption on the restricted condition number of the Hessian matrix of the loss function, we establish an error bound to the true matrix for the non-strict critical points with rank not more than that of the true matrix. Then, for the squared F-norm regularized factorized least squares loss function, we establish its KL property of exponent 1/2 on the global optimal solution set under the noisy and full sample setting, and achieve this property at its certain class of critical points under the noisy and partial sample setting. These theoretical findings are also confirmed by solving the squared F-norm regularized factorization problem with an accelerated alternating minimization method.

     

Equitable Vertex Arboricity Conjecture Holds for Graphs with Low Degeneracy

The equitable tree-coloring can formulate a structure decomposition problem on the communication network with some security considerations. Namely, an equitable tree-k-coloring of a graph is a vertex coloring using k distinct colors such that every color class induces a forest and the sizes of any two color classes differ by at most one. In this paper, we show some theoretical results on the equitable tree-coloring of graphs by proving that every d-degenerate graph with maximum degree at most Δ is equitably tree-k-colorable for every integer k ≥(Δ + 1)/2 provided that Δ≥ 9.818 d,confirming the equitable vertex arboricity conjecture for graphs with low degeneracy.     

Facet effect of single-crystalline Ag3PO4 sub-microcrystals on photocatalytic properties

We recently reported that Ag(3)PO(4) exhibits excellent photooxidative capabilities for O(2) evolution from water and organic dye decomposition under visible-light irradiation. However, very little is known about the shape and facet effects of Ag(3)PO(4) crystals on their photocatalytic properties. Herein we have developed a facile and general route for high-yield fabrication of single-crystalline Ag(3)PO(4) rhombic dodecahedrons with only {110} facets exposed and cubes bounded entirely by {100} facets. Moreover, studies of their photocatalytic performance have indicated that rhombic dodecahedrons exhibit much higher activities than cubes for the degradation of organic contaminants, which may be primarily ascribed to the higher surface energy of {110} facets (1.31 J/m(2)) than of {100} facets (1.12 J/m(2)).     

Hollow Metal–Organic‐Framework‐Mediated In Situ Architecture of Copper Dendrites for Enhanced CO2 Electroreduction

Electrocatalytic reduction of CO₂ to a single product at high current densities and efficiencies remains a challenge. However, the conventional electrode preparation methods, such as drop‐casting, usually suffer from low intrinsic activity. Herein, we report a synthesis strategy for preparing heterogeneous electrocatalyst composed of 3D hierarchical Cu dendrites that derived from an in situ electrosynthesized hollow copper metal–organic framework (MOF), for which the preparation of the Cu‐MOF film took only 5 min. The synthesis strategy preferentially exposes active sites, which favor's the reduction of CO₂ to formate. The current density could be as high as 102.1 mA cm^?2 with a selectivity of 98.2 % in ionic‐liquid‐based electrolyte and a commonly used H‐type cell.     

Direct Observation of Dynamic Bond Evolution in Single‐Atom Pt/C3N4 Catalysts

Single‐atom catalysts are promising platforms for heterogeneous catalysis, especially for clean energy conversion, storage, and utilization. Although great efforts have been made to examine the bonding and oxidation state of single‐atom catalysts before and/or after catalytic reactions, when information about dynamic evolution is not sufficient, the underlying mechanisms are often overlooked. Herein, we report the direct observation of the charge transfer and bond evolution of a single‐atom Pt/C₃N₄ catalyst in photocatalytic water splitting by synchronous illumination X‐ray photoelectron spectroscopy. Specifically, under light excitation, we observed Pt?N bond cleavage to form a Pt⁰ species and the corresponding C=N bond reconstruction; these features could not be detected on the metallic platinum‐decorated C₃N₄ catalyst. As expected, H₂ production activity (14.7 mmol h^?1 g^?1) was enhanced significantly with the single‐atom Pt/C₃N₄ catalyst as compared to metallic Pt‐C₃N₄ (0.74 mmol h^?1 g^?1).     

[3+2] Cycloaddition of Propargylic Alcohols and α‐Oxo Ketene Dithioacetals: Synthesis of Functionalized Cyclopentadienes and Further Application in a Diels–Alder Reaction

Cyclopentadienes are valuable intermediates in organic synthesis and also ubiquitous as the Cp ligands in organometallic chemistry. As part of ongoing efforts to develop novel organic reactions that employ functionalized alkynes, a [3+2] cycloaddition of propargylic alcohols and ketene dithioacetals has been developed, which leads to fully substituted 2,5‐dialkylthio cyclopentadienes in good to excellent yields. In an unusual dethiolating Diels–Alder reaction, the cyclopentadienes were further reacted with maleimides to afford a family of novel fluorescent polycyclic compounds.     

An Aqueous Rechargeable Formate‐Based Hydrogen Battery Driven by Heterogeneous Pd Catalysis

The formate‐based rechargeable hydrogen battery (RHB) promises high reversible capacity to meet the need for safe, reliable, and sustainable H₂ storage used in fuel cell applications. Described herein is an additive‐free RHB which is based on repetitive cycles operated between aqueous formate dehydrogenation (discharging) and bicarbonate hydrogenation (charging). Key to this truly efficient and durable H₂ handling system is the use of highly strained Pd nanoparticles anchored on graphite oxide nanosheets as a robust and efficient solid catalyst, which can facilitate both the discharging and charging processes in a reversible and highly facile manner. Up to six repeated discharging/charging cycles can be performed without noticeable degradation in the storage capacity.     

Gas‐Phase Reaction of CeV2O7+ with C2H4: Activation of CC and CH Bonds

The reactivity of metal oxide clusters toward hydrocarbon molecules can be changed, tuned, or controlled by doping. Cerium‐doped vanadium cluster cations CeV₂O₇⁺ are generated by laser ablation, mass‐selected by a quadrupole mass filter, and then reacted with C₂H₄ in a linear ion trap reactor. The reaction is characterized by a reflectron time‐of‐flight mass spectrometer. Three types of reaction channels are observed: 1) single oxygen‐atom transfer , 2) double oxygen‐atom transfer , and 3) C?C bond cleavage. This study provides the first bimetallic oxide cluster ion, CeV₂O₇⁺, which gives rise to C?C bond cleavage of ethene. Neither Ce_xO_y^± nor V_xO_y^± alone possess the necessary topological and electronic properties to bring about such a reaction.     

Study on effects of carboxymethyl cellulose lithium (CMC-Li) synthesis and electrospinning on high-rate lithium ion batteries

This study, for the first time, synthesized carboxymethyl cellulose lithium (CMC-Li) by a two-step method and applied it to modified electrode material by electrospinning and as a binder on a lithium ion battery. By electrospinning, nano CMC-Li fiber and CMC-Li/9, 10-anthraquinone (AQ) composite fiber were obtained successfully and coated AQ electrode material. AQ was uniformly distributed in fibers, and then CMC-Li/AQ composite fiber was carbonized to obtain the carbon nanofiber/AQ/Li [CAL] composite as lithium battery anode material. Also for the first time we investigated substituting aqueous CMC-Li with different degrees of substitution (DS) for oily polyvinylidene fluoride (PVDF) as a lithium battery binder to assemble the battery with CAL for electrochemical performance tests. Compared with PVDF binder, cells with CMC-Li for a binder have excellent advantages, such as higher discharge capacity (226.4 mAh g^?1), safer cycle performance, lower cost and being more eco-friendly. Furthermore, the cell with CMC-Li with high DS performed better than the cell with low DS. This method also applies to other electrode materials.     

栀子苷在乙腈水体系中诱导相分离分配行为

研究了栀子乙腈水提取液中的栀子苷在诱导相分离后在两相中的分配行为,建立了乙腈/水分相体系分离纯化栀子苷的新方法。 重点考察了能使乙腈/水体系分相的诱导剂的种类,分析了诱导剂的组成比例以及用量、乙腈的体积分数、样品加入量和温度对栀子苷分配行为的影响。 当温度为25 ℃时,栀子的乙腈/水（体积比1∶1）提取液中加入KCl与MgSO4组成的混盐（质量比2∶1）分相诱导剂后,栀子苷的萃取率达到81.63%,含量由分相前的3.05%提高至13.54%。