A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Characterization of iron surface modified by 2-mercaptobenzothiazole self-assembled monolayers

A self-assembled monolayer of 2-mercaptobenzothiazole (MBT) adsorbed on the iron surface was prepared. The films were characterized by electrochemical impedance spectroscopy (EIS), X-ray photoelectron spectroscopy (XPS), Fourier transform infrared reflection spectroscopy (FT-IR) and scanning electron microscopy (SEM). Besides, the microcalorimetry method was utilized to study the self-assembled process on iron surface and the adsorption mechanism was discussed from the power-time curve. The results indicated that MBT was able to form a film spontaneously on iron surface and the presence of it could protect iron from corrosion effectively. However, the assembling time and the concentration influence the protection efficiency. Quantum chemical calculations, according to which adsorption mechanism was discussed, could explain the experimental results to some extent.     

Selective dimerization of α-methylstyrene catalyzed by a solid acid

A novel solid acid prepared from concentrated sulfuric, boric and phosphoric acid is a highly selective catalyst for the dimerization of α-methylstyrene at room temperature to generate 4-methyl-2,4-diphenyl-1-pentene.     

Geometry,stability and aromaticity of β-diketiminate-coordinated alkaline-earth compounds

Alkaline-earth (Ae) metals have attracted a wealth of interdependent research from synthetic chemists. In Ae-catalyzed organometallic reactions, β-diketiminate is a typical ligand used to stabilize Ae catalysts by forming six-membered rings comprising Ae metals. Herein, studies focusing on the configuration of β-diketiminate-coordinated Ae compounds observed that the CC and CN bonds are homogeneous and unchanged. Furthermore, energetic studies observed that the formation of the Ae-incorporated six-membered rings results in enhanced stability of >20 kcal/mol. The nucleus-independent chemical shifts, anisotropy of the induced current density, and molecular orbital analyses demonstrated the non-aromaticity of the β-diketiminate-coordinated Ae compounds. The improved stability of these compounds can be explained by the delocalization of the π electrons derived from the β-diketiminate moiety.     

The formation of mesoporous TiO2 spheres via a facile chemical process

The mesoporous TiO(2) solid and hollow spheres have been synthesized via a controllable and simple chemical route. Structural characterization indicates that these TiO(2) mesoporous spheres after calcined at 500 degrees C have an obvious mesoporous structure with the diameters of 200-300 nm for solid spheres and 200-500 nm for hollow spheres. The average pore sizes and BET surface areas of the mesoporous TiO(2) solid and hollow spheres are 6.8, 7.0 nm and 162, 90 m(2)/g, respectively. Optical adsorption investigation shows that TiO(2) solid and hollow spheres possess a direct band gap structure with the optical band gap of 3.68 and 3.75 eV, respectively. A possible formation mechanism for TiO(2) solid and hollow spheres is discussed.     

When does gradient Ricci soliton have one end?

Annals of Global Analysis and Geometry - In this paper, we study a problem of finding compact hypersurfaces of prescribed mean curvature with free boundary in a ball. We transform the problem to an...     

Visually precise,low-damage,single-cell spatial manipulation with single-pixel resolution

The analysis of single living cells, including intracellular delivery and extraction, is essential for monitoring their dynamic biochemical processes and exploring intracellular heterogeneity. However, owing to the 2D view in bright-field microscopy and optical distortions caused by the cell shape and the variation in the refractive index both inside and around the cells, achieving spatially undistorted imaging for high-precision manipulation within a cell is challenging. Here, an accurate and visual system is developed for single-cell spatial manipulation by correcting the aberration for simultaneous bright-field triple-view imaging. Stereo information from the triple view enables higher spatial resolution that facilitates the precise manipulation of single cells. In the bright field, we resolved the spatial locations of subcellular structures of a single cell suspended in a medium and measured the random spatial rotation angle of the cell with a precision of ±5°. Furthermore, we demonstrated the visual manipulation of a probe to an arbitrary spatial point of a cell with an accuracy of <1 pixel. This novel system is more accurate and less destructive for subcellular content extraction and drug delivery.

We achieved the low-damage spatial puncture of single cells at specific visual points with an accuracy of <65 nm.     

Mass spectrometry-based chemical mapping and profiling toward molecular understanding of diseases in precision medicine

Precision medicine has been strongly promoted in recent years. It is used in clinical management for classifying diseases at the molecular level and for selecting the most appropriate drugs or treatments to maximize efficacy and minimize adverse effects. In precision medicine, an in-depth molecular understanding of diseases is of great importance. Therefore, in the last few years, much attention has been given to translating data generated at the molecular level into clinically relevant information. However, current developments in this field lack orderly implementation. For example, high-quality chemical research is not well integrated into clinical practice, especially in the early phase, leading to a lack of understanding in the clinic of the chemistry underlying diseases. In recent years, mass spectrometry (MS) has enabled significant innovations and advances in chemical research. As reported, this technique has shown promise in chemical mapping and profiling for answering “what”, “where”, “how many” and “whose” chemicals underlie the clinical phenotypes, which are assessed by biochemical profiling, MS imaging, molecular targeting and probing, biomarker grading disease classification, etc. These features can potentially enhance the precision of disease diagnosis, monitoring and treatment and thus further transform medicine. For instance, comprehensive MS-based biochemical profiling of ovarian tumors was performed, and the results revealed a number of molecular insights into the pathways and processes that drive ovarian cancer biology and the ways that these pathways are altered in correspondence with clinical phenotypes. Another study demonstrated that quantitative biomarker mapping can be predictive of responses to immunotherapy and of survival in the supposedly homogeneous group of breast cancer patients, allowing for stratification of patients. In this context, our article attempts to provide an overview of MS-based chemical mapping and profiling, and a perspective on their clinical utility to improve the molecular understanding of diseases for advancing precision medicine.

An overview of MS-based chemical mapping and profiling, indicating its contributions to the molecular understanding of diseases in precision medicine by answering "what", "where", "how many" and "whose” chemicals underlying clinical phenotypes.     

Structural and process controls of AIEgens for NIR-II theranostics

Aggregation-induced emission (AIE) is a cutting-edge fluorescence technology, giving highly-efficient solid-state photoluminescence. Particularly, AIE luminogens (AIEgens) with emission in the range of second near-infrared window (NIR-II, 1000–1700 nm) have displayed salient advantages for biomedical imaging and therapy. However, the molecular design strategy and underlying mechanism for regulating the balance between fluorescence (radiative pathway) and photothermal effect (non-radiative pathway) in these narrow bandgap materials remain obscure. In this review, we outline the latest achievements in the molecular guidelines and photophysical process control for developing highly efficient NIR-II emitters or photothermal agents with aggregation-induced emission (AIE) attributes. We provide insights to optimize fluorescence efficiency by regulating multi-hierarchical structures from single molecules (flexibilization) to molecular aggregates (rigidification). We also discuss the crucial role of intramolecular motions in molecular aggregates for balancing the functions of fluorescence imaging and photothermal therapy. The superiority of the NIR-II region is demonstrated by fluorescence/photoacoustic imaging of blood vessels and the brain as well as photothermal ablation of the tumor. Finally, a summary of the challenges and perspectives of NIR-II AIEgens for in vivo theranostics is given.

Structural and process controls of NIR-II AIEgens realize manipulating of radiative (R) and nonradiative (NR) decay for precise theranostics.