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.     

Spectrum–effect relationship of antioxidant and anti-inflammatory activities of Laportea bulbifera based on multivariate statistical analysis

Laportea bulbifera, named Hong He Ma in Chinese, is a Chinese herbal medicine commonly used by the Miao nationality of China. In this study, 43 batches of L. bulbifera were collected from different origins in China. Ethanol, ethyl acetate and petroleum ether were used to prepare different extracts of the plant. UHPLC technique was used to establish the fingerprints, whereas DPPH assay and RAW264.7 inflammatory cell models were used to evaluate the antioxidant and anti-inflammatory activities, respectively. Moreover, the spectrum–effect relationship between relative peak area of common peaks and efficacy value was set up by multivariate statistical analysis. Furthermore, 10 batches were selected randomly for validation of those models. The results showed that ethyl acetate and petroleum ether extracts possess excellent antioxidant and anti-inflammatory activities, respectively. Peaks A₆ and A₇ demonstrated the greatest antioxidant activity, while peak A₁₇ showed the strongest anti-inflammatory activity. After a verified experiment, the result was obtained and illustrated that the spectrum–effect relationship which we established could reliably infer antioxidant and anti-inflammatory compounds of the Chinese herbal medicine.     

Advantageous Interfacial Effects of AgPd/g-C3N4 for Photocatalytic Hydrogen Evolution: Electronic Structure and H2O Dissociation

Bimetallic AgPd nanoparticles have been synthesized before, but the interfacial electronic effects of AgPd on the photocatalytic performance have been investigated less. In this work, the results of hydrogen evolution suggest that the bimetallic AgPd/g-C₃N₄ sample has superior activity to Ag/g-C₃N₄ and Pd/g-C₃N₄ photocatalysts. The UV/Vis diffuse reflectance spectroscopy, X-ray photoelectron spectroscopy, CO adsorption diffuse reflectance FTIR spectroscopy, and FTIR results demonstrate that in the AgPd/g-C₃N₄, the surface electronic structures of Pd and Ag are changed, which is beneficial for faster photogenerated electron transfer and greater H₂O molecule adsorption. In situ ESR spectra suggest that, under visible light irradiation, there is more H₂O dissociation to radical species on the AgPd/g-C₃N₄ photocatalyst. Furthermore, DFT calculations confirm the interfacial electronic effects of AgPd/g-C₃N₄, that is, Pd^δ−⋅⋅⋅Ag^δ+, and the activation energy of H₂O molecule dissociation on AgPd/g-C₃N₄ is the lowest, which is the main contributor to the enhanced photocatalytic H₂ evolution.     

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.