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...     

Selective Decrosslinking in Liquid Crystal Polymer Actuators for Optical Reconfiguration of Origami and Light‐Fueled Locomotion

The ability to optically reconfigure an existing actuator of a liquid crystal polymer network (LCN) so that it can display a new actuation behavior or function is highly desired in developing materials for soft robotics applications. Demonstrated here is a powerful approach relying on selective polymer chain decrosslinking in a LCN actuator with uniaxial LC alignment. Using an anthracene‐containing LCN, spatially controlled optical decrosslinking can be realized through photocleavage of anthracene dimers under 254 nm UV light, which alters the distribution of actuation (crosslinked) and non‐actuation (decrosslinked) domains and thus determines the actuation behavior upon order‐disorder phase transitions. Based on this mechanism, a single actuator having a flat shape can be reconfigured in an on‐demand manner to exhibit reversible shape transformation such as self‐folding into origami three‐dimensional structures. Moreover, using a dye‐doped LCN actuator, a light‐fueled microwalker can be optically reconfigured to adopt different locomotion behaviors, changing from moving in the laser scanning direction to moving in the opposite direction.     

On the New Shear Constraint for Plane-Stress Orthotropic Plasticity Modeling of Sheet Metals

Experimental Mechanics - A shear constraint was very recently proposed by Abedini et al. (Int. J. Solids and Structures 151: 118–134 2018) to evaluate and calibrate advanced non-quadratic...     

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.     

Tuning Emission Wavelength of Polymorphous Crystal via Controllable Alkyl Chain Stacking and Its Vapor- and Thermo-Responsive Fluorescence

Tuning fluorescence colour of solid-state materials has become a topic of increasing interest for both fundamental mechanism study and practical applications such as sensors, optical recording and security printing. In this work, a fluorescent colour tuneable molecule BA-C16 is rationally designed and facilely synthesized by attaching flexible long alkyl chains to 2-hydroxybenzophenone azine ( BA ), which shows both aggregation-induced emission (AIE) and excited-state intramolecular proton transfer (ESIPT) characteristics. Compared to BA , the simple introduction of long alkyl chains in BA-C16 leads to an emission wavelength redshift from 542 to 558 nm. This strategy of extending emission wavelength is rarely reported, and is ascribed to the enlarged through-space π-conjugation between interplanar molecules in the aggregate of BA-C16 . Three crystals of BA-C16 are obtained with green, yellowish green and yellow emission. According to characterization by X-ray crystallography, X-ray powder diffraction and differential scanning calorimetry, alkyl chains play an important role in inducing different stacking modes of the three crystals, which further leads to polymorph-dependent fluorescence colour. BA-C16 exhibits tuneable solid-state fluorescence upon vapor fumigation, or annealing based on a transition between a “near-monomer” crystalline state and a “dimer” crystalline state. BA-C16 is further applied for rewritable fluorescence printing tuned by vapor- and thermal-treatment.