Semiconvergence analysis of the randomized row iterative method and its extended variants

The row iterative method is popular in solving the large‐scale ill‐posed problems due to its simplicity and efficiency. In this work we consider the randomized row iterative (RRI) method to tackle this issue. First, we present the semiconvergence analysis of RRI method for the overdetermined and inconsistent system, and derive upper bounds for the noise error propagation in the iteration vectors. To achieve a least squares solution, we then propose an extended version of the RRI (ERRI) method, which in fact can converge in expectation to the solution of the overdetermined or underdetermined, consistent or inconsistent systems. Finally, some numerical examples are given to demonstrate the convergence behaviors of the RRI and ERRI methods for these types of linear system.     

吸收波长和吸收效率可控的超材料吸收器

为了使超材料完美吸收器(metamaterial perfect absorber,MPA)能够同时实现吸收效率和吸收波长的控制,本文提出利用二氧化钒(VO2)和石墨烯作为MPA的材料,通过对MPA的结构设计,在红外波段实现了高吸收,吸收效率最高可达99%.研究发现通过改变VO2的温度和石墨烯的化学势,可同时实现MPA吸收效率和吸收波长的控制,吸收效率调制深度和吸收波长调谐范围分别可达97.08%和3.2μm.通过对MPA在吸收波长处的磁场分布分析可以得出,MPA能够产生高吸收是由于其形成了法布里-帕罗(Fabry-Pérot,FP)干涉腔共振,研究发现MPA的结构参数对FP腔的共振波长具有显著的影响.     

Crystal phase control in two-dimensional materials

It is the nature of crystals to exist in different polymorphs. The recent emergence of two-dimensional (2D) materials has evoked the discovery of a number of new crystal phases that are different from their bulk structures at ambient conditions, and revealed novel structure-dependent properties, which deserve in-depth understanding and further exploration. In this contribution, we review the recent development of crystal phase control in 2D materials, including group V and VI. transition metal dichalcogenides (TMDs), group IVA metal chalcogenides and noble metals. For each group of materials, we begin with introducing the various existing crystal phases and their structure-related properties, followed by a detailed discussion on factors that influence these crystal structures and thus the possible strategies for phase control. Finally, after summarizing the whole paper, we present the challenges and opportunities in this research direction.     

Piezoelectric Actuator Placement Optimization and Active Vibration Control of a Membrane Structure

The placement optimization of piezoelectric actuators and active vibration control of a membrane structure are studied in this paper. The classical linear quadratic regulator controllers are designed to suppress the unwanted vibration. Simulation results indicate that the optimal locations of piezoelectric actuators are affected deeply by the additional mass and stiffness of actuators, the computational efficiency of particle swarm optimizer is higher than that of genetic algorithm for this particular problem, and the control performance of optimally placed actuators is better than that of non-optimally placed actuators.     

Elucidating Molecule–Plasmon Interactions in Nanocavities with 2 nm Spatial Resolution and at the Single‐Molecule Level

The fundamental understanding of the subtle interactions between molecules and plasmons is of great significance for the development of plasmon‐enhanced spectroscopy (PES) techniques with ultrahigh sensitivity. However, this information has been elusive due to the complex mechanisms and difficulty in reliably constructing and precisely controlling interactions in well‐defined plasmonic systems. Herein, the interactions in plasmonic nanocavities of film‐coupled metallic nanocubes (NCs) are investigated. Through engineering the spacer layer, molecule–plasmon interactions were precisely controlled and resolved within 2 nm. Efficient energy exchange interactions between the NCs and the surface within the 1–2 nm range are demonstrated. Additionally, optical dressed molecular excited states with a huge Lamb shift of ≈7 meV at the single‐molecule (SM) level were observed. This work provides a basis for understanding the underlying molecule–plasmon interaction, paving the way for fully manipulating light–matter interactions at the nanoscale.     

ON THE EXISTENCE WITH EXPONENTIAL DECAY AND THE BLOW-UP OF SOLUTIONS FOR COUPLED SYSTEMS OF SEMI-LINEAR CORNER-DEGENERATE PARABOLIC EQUATIONS WITH SINGULAR POTENTIALS

In this article,we study the initial boundary value problem of coupled semi-linear degenerate parabolic equations with a singular potential term on manifolds with corner singularities.Firstly,we introduce the corner type weighted p-Sobolev spaces and the weighted corner type Sobolev inequality,the Poincare′inequality,and the Hardy inequality.Then,by using the potential well method and the inequality mentioned above,we obtain an existence theorem of global solutions with exponential decay and show the blow-up in finite time of solutions for both cases with low initial energy and critical initial energy.Significantly,the relation between the above two phenomena is derived as a sharp condition.Moreover,we show that the global existence also holds for the case of a potential well family.     

Rapid Detection of AIB1 in Breast Cancer Cells Based on Aptamer-Functionalized Nanomotors

Herein, we report ultrasound-propelled graphene-oxide coated gold nanowire motors, functionalized with fluorescein-labeled DNA aptamers (FAM-AIB1-apt), for qualitative detection of overexpressed AIB1 oncoproteins in MCF-7 breast cancer cells. The movement of nanomotors under the ultrasound field facilitated intracellular uptake and resulted in a faster aptamer binding with the target protein and thus faster fluorescence recovery. The propulsion behavior of the aptamer functionalized nanomotors greatly enhanced the fluorescence intensity compared to static conditions. The new aptamer@nanomotor-based strategy offers considerable potential for further development of sensing methodologies towards diagnosis of breast cancer.     

Synthesis,characterization, and electrochemistry of monophosphine‐containing diiron propane‐1,2‐dithiolate complexes related to the active site of [FeFe]‐hydrogenases

Five monophosphine‐substituted diiron propane‐1,2‐dithiolate complexes as the active site models of [FeFe]‐hydrogenases have been synthesized and characterized. Reactions of complex [Fe₂(CO)₆{μ‐SCH₂CH(CH₃)S}] ( 1 ) with a monophosphine ligand tris(4‐methylphenyl)phosphine, diphenyl‐2‐pyridylphosphine, tris(4‐chlorophenyl)phosphine, triphenylphosphine, or tris(4‐fluorophenyl)phosphine in the presence of the oxidative agent Me₃NO·2H₂O gave the monophosphine‐substituted diiron complexes [Fe₂(CO)₅(L){μ‐SCH₂CH(CH₃)S}] [L = P(4‐C₆H₄CH₃)₃, 2 ; Ph₂P(2‐C₅H₄N), 3 ; P(4‐C₆H₄Cl)₃, 4 ; PPh₃, 5 ; P(4‐C₆H₄F)₃, 6 ] in 81%–94% yields. Complexes 2 – 6 have been characterized by elemental analysis, spectroscopy, and X‐ray crystallography. In addition, electrochemical studies revealed that these complexes can catalyze the reduction of protons to H₂ in the presence of HOAc.     

弹性蛋白酶生物催化酯水解的综合实验设计*

酯的水解是有机化学实验教学中的一个重要化学反应,传统的酯水解实验设计是利用酸性或碱性环境在加热的条件下进行水解,而本实验设计将酯水解与生物催化相结合,利用弹性蛋白酶的水解功能,在常温及中性环境下实现对4-三氟甲基-7-丙酰氧基香豆素的水解。该实验设计创新性地将酯水解和酶催化相结合,有利于拓展学生的知识面,培养化学生物学复合型人才。同时,生物催化反应具有反应温和、环境友好等特点,符合当代绿色化学的需求。