多元统计分析中一类矩阵迹函数最小化问题的有效算法

研究来源于多元统计分析中的一类矩阵迹函数最小化问题$\min c+ tr(AX)+\sum\limits_{j=1}^{m}tr(B_j X C_jX^{T}),\ \ {\rm s. t.} \ X^TX=I_p,$其中$c$为常数, $A\in R^{p\times n}\ (n\geq p)$, $B_j\in R^{n\times n}, C_j\in R^{p\times p}$为给定系数矩阵. 数值实验表明已有的Majorization算法虽可行, 但收敛速度缓慢且精度不高. 本文从黎曼流形的角度重新研究该问题, 基于Stiefel流形的几何性质, 构造一类黎曼非单调共轭梯度迭代求解算法, 并给出算法收敛性分析.数值实验和数值比较验证所提出的算法对于问题模型是高效可行的.     

The Synergistic Photocatalytic Effect of H3PW12O40 and Pt Nanoparticles Comodified UiO-66-NH2 on the Reduction of Aqueous Cr(VI) under Original pH

Kinetics and Catalysis - A ternary synergistic photocatalyst H3PW12O40/Pt/UiO-66-NH2 was successfully fabricated for the first time through a simple solvothermal synthetic strategy. We found that...     

In‐Depth Understanding of the Chemical Properties of Rarely Explored Carbide Cluster Metallofullerenes: A Case Study of Sc2C2@C3v(8)‐C82 that Reveals a General Rule

The chemical properties of carbide‐cluster metallofullerenes (CCMFs) remain largely unexplored, although several new members of CCMFs have been discovered recently. Herein, we report the reaction between Sc₂C₂@C_3v(8)‐C₈₂, which is viewed as a prototypical CCMF because of its high abundance, and 3‐triphenylmethyl‐5‐oxazolidinone ( 1 ) to afford the corresponding pyrrolidino derivative Sc₂C₂@C_3v(8)‐C₈₂(CH₂)₂NTrt ( 2 ; Trt=triphenylmethyl). Single‐crystal X‐ray crystallography studies of 2 revealed that the reaction takes place at a [6,6]‐bond junction, which is directly over the encapsulated C₂ unit and is far from either of the two scandium atoms. On the basis of theoretical calculations and by considering previously reports, we have found that a hexagonal carbon ring on the cage of Sc₂C₂@C_3v(8)‐C₈₂ is highly reactive toward different reagents due to the overlap of high p‐orbital axis vector (POAV) angles and large LUMO coefficients. We propose that this highly concentrated area of reactivity is generated by the encapsulation of the Sc₂C₂ cluster because this region is absent from the empty fullerene C_3v(8)‐C₈₂. Moreover, the absorption and electrochemical results confirm that derivative 2 is more stable than pristine Sc₂C₂@C_3v(8)‐C₈₂, thus illuminating its potential applications.     

Synthesis and Photophysical Properties of a Sc3N@C80‐Corrole Electron Donor–Acceptor Conjugate

Embedding endohdedral metallofullerenes (EMFs) into electron donor–acceptor systems is still a challenging task owing to their limited quantities and their still largely unexplored chemical properties. In this study, we have performed a 1,3‐dipolar cycloaddition reaction of a corrole‐based precursor with Sc₃N@C₈₀ to regioselectively form a [5,6]‐adduct ( 1 ). The successful attachment of the corrole moiety was confirmed by mass spectrometry. In the electronic ground state, absorption spectra suggest sizeable electronic communications between the electron acceptor and the electron donor. Moreover, the addition pattern occurring at a [5,6]‐bond junction is firmly proven by NMR spectroscopy and electrochemical investigations performed with 1 . In the electronically excited state, which is probed in photophysical assays with 1 , a fast electron‐transfer yields the radical ion pair state consisting of the one‐electron‐reduced Sc₃N@C₈₀ and of the one‐electron‐oxidized corrole upon its exclusive photoexcitation. As such, our results shed new light on the practical work utilizing EMFs as building blocks in photovoltaics.     

3D Electron Diffraction Unravels the New Zeolite ECNU-23 from the “Pure” Powder Sample of ECNU-21

A novel crystalline high-silica zeolite with 12×8-membered ring (R) channel system is prepared with the aid of the 3D electron diffraction (3D ED) technique. A crystal with the same topology as one of the predicted daughter structures of CIT-13 germanosilicate, named ECNU-23 (East China Normal University 23) was coincidentally detected by the 3D ED investigation during the structure characterization of the “pure” powder sample of existing one-dimension (1D) 10-R ECNU-21. By controlling the alkaline-assisted hydrolysis under moderate conditions, we purified the phase of ECNU-23 by selectively breaking and removing the chemically weak Ge(Si)-O-Ge and metastable Si-O-Si bonds. Its structure was determined based on the 3D ED data, and confirmed by high-resolution TEM images and powder X-ray diffraction (PXRD) data. The aluminosilicate Al-ECNU-23 shows unique catalytic properties in the isomerization/ disproportionation of m-xylene as solid-acid catalyst.     

Topotactic Conversion of Alkali-Treated Intergrown Germanosilicate CIT-13 into Single-Crystalline ECNU-21 Zeolite as Shape-Selective Catalyst for Ethylene Oxide Hydration

The conversion of the alkali-treated intergrowth germanosilicate CIT-13 into the single-crystalline high-silica ECNU-21 (named after East China Normal University) zeolite, with a novel topology and a highly crystalline zeolite framework, has been realized through a creative top-down strategy involving a mild alkaline-induced multistep process consisting of structural degradation and reconstruction. Instead of acid treatment, hydrolysis in aqueous ammonia solution not only readily cleaved the chemically weak Ge(Si)−O−Ge bonds located within the interlayer double four ring (D4R) units of CIT-13, but also cleaved the metastable Si−O−Si bonds therein. This led to extensive removal of the D4R units, and also generated silanol groups on adjacent silica-rich layers, which then condensed to form a novel daughter structure upon calcination. Individual oxygen bridges in the reassembled ECNU-21 replaced the germanium-rich D4R units in CIT-13, thereby eliminating the original intergrowth phenomenon along the b axis. With an ordered crystalline structure of 10-ring (R) channels as well as suitable germanium-related Lewis acid sites, ECNU-21 serves as a stable solid Lewis acid catalyst for the shape-selective hydration of ethylene oxide (EO) to ethylene glycol (EG) at greatly reduced H₂O/EO ratios and reaction temperature in comparison with the noncatalytic industrial process.     

Mesoporous inorganic salts with crystal defects: unusual catalysts and catalyst supports

We proposed a strategy to synthesize mesoporous inorganic salt particles using the special properties of ionic liquid (IL) mixtures, and hollow mesoporous LaF₃, NdF₃, and YF₃ particles were synthesized and characterized using different techniques. The size of the mesopores in the salt particles was about 4 nm, and the materials were full of crystal defects. The LaF₃, NdF₃ and YF₃ particles were used as the catalysts for the cyanosilylation reaction of benzaldehyde using trimethylsilyl cyanide, and Ru/LaF₃ and Ru/NdF₃, in which Ru nanocatalysts were supported on the LaF₃ and NdF₃ particles with mesopores, were used to catalyze hydrogenations of benzene to cyclohexane and levulinic acid (LA) to γ-valerolactone (GVL). It was discovered that the activities of these catalysts were unprecedentedly high for these reactions. Detailed study showed that both the crystal defects and the mesopores in the salt particles played crucial roles for the extremely high catalytic activity.     

AlCl<Subscript>3</Subscript>/amide ionic liquids for electrodeposition of aluminum

AlCl₃/amide (acetamide, propionamide, butyramide) ionic liquids were used as the electrolytes to study the electrodeposition behavior of aluminum on a tungsten electrode. Cyclic voltammograms on the tungsten electrode indicate that Al(III) ions can be reduced to aluminum only within the molar ratio range of 1.1 to 1.5 and the reduction potentials of Al(III) ions strongly depend on the molar ratio of AlCl₃/amide. Raman spectra results reveal that the electroactive specie of AlCl₃/amide ionic liquids is Al₂Cl₇ ^?. Aluminum coatings were prepared at ?0.25 V (vs. Al/Al³⁺) and at 313 K in AlCl₃/amide ionic liquids with the molar ratio of 1.3. The SEM and cross-sectional SEM images show that all the obtained aluminum films are silver-colored, thick, and adherent. The EDS and XRD analysis confirm that the obtained deposits are pure aluminum. The present results can provide a new route for aluminum electrodeposition under ambient conditions.     

应用分区非线性变分原理的杂交薄壳单元

本文讨论了高次杂交壳体元在材料非线性分析中的应用，为了更精确估计单元内各部分应力的不同影响，本文应用了分区非线性变分原理推导出杂交壳元在应力增量下应用初始应力法的失衡节点力，这使得高次杂交元在非线性分析中的优点得以充分的发挥，从而大大提高了计算精度。     

面向仿真数据的电网运行方式可视分析

对真实电网提出故障发生的假设并通过计算检验，观察故障对真实电网的影响。电网仿真能有效发现电网运行中的问题，被广泛应用于电网规划与电网运行方式调整。然而，在实际仿真计算过程中，往往需要依据经验调整电网配置和计算参数，以得到稳定、收敛的电网运行方式。大规模的仿真数据、调整的未知性加之分析的片面性会影响传统人工调整的准确性，为此提出了基于可视化的仿真计算调整方法。分析人员通过与可视分析系统的交互，可以快速认识电网的整体状态，发现问题元件，从而实现高效的仿真调整与计算。最后通过案例分析验证了本可视分析系统的有效性。