一类Dhombres型函数方程的连续通解

该文研究了一类推广的Dhombrs型函数方程,得到了这个方程的连续通解,并且部分回答了Kahlig P,Matkowska A,Matkowski J等人在1996年提出的一个公开问题.     

IHKp函数及其上算子的刻划

本文借助于ＨＫｐ 空间上的积分,引进了ＩＨＫｐ 函数类的概念,讨论了ＩＨＫｐ函数类的刻划,以及其上算子和有界算子的刻划     

Conditional-quantile screening for ultrahigh-dimensional survival data via martingale difference correlation

Using the so-called martingale difference correlation (MDC), we propose a novel censored-conditional-quantile screening approach for ultrahigh-dimensional survival data with heterogeneity (which is often present in such data). By incorporating a weighting scheme, this method is a natural extension of MDC-based conditional quantile screening, as considered in Shao and Zhang (2014), to handle ultrahigh-dimensional survival data. The proposed screening procedure has a sure-screening property under certain technical conditions and an excellent capability of detecting the nonlinear relationship between independent and censored dependent variables. Both simulation results and an analysis of real data demonstrate the effectiveness of the new censored conditional quantile-screening procedure.     

关于罗尔定理的进一步讨论

对罗尔定理进行深入系统的探讨和研究.给出在更弱条件下的各种区间类型(包括有限区间和无限区间)的罗尔定理的推广形式.     

Catalytic DNA-Assisted Mass Production of Arbitrary Single-Stranded DNA

Synthetic single-stranded (ss) DNA is a cornerstone for life and materials science, yet the purity, quantity, length, and customizability of synthetic DNA are still limiting in various applications. Here, we present PECAN, p aired-e nd c utting a ssisted by DN Azymes (DNA enzymes or deoxyribozymes), which enables mass production of ssDNA of arbitrary sequence (up to 7000 nucleotides, or nt) with single-base precision. At the core of PECAN technique are two newly identified classes of DNAzymes, each robustly self-hydrolyzing with minimal sequence requirement up- or down-stream of its cleavage site. Flanking the target ssDNA with a pair of such DNAzymes generates a precursor ssDNA amplifiable by pseudogene-recombinant bacteriophage, which subsequently releases the target ssDNA in large quantities after efficient auto-processing. PECAN produces ssDNA of virtually any terminal bases and compositions with >98.5 % purity at the milligram-to-gram scale. We demonstrate the feasibility of using PECAN ssDNA for RNA in situ detection, homology-directed genome editing, and DNA-based data storage.     

Photoswitchable Enantioselective and Helix-Sense Controlled Living Polymerization

A pair of enantiomeric photoswitchable Pd^II catalysts, alkyne-Pd^II/ L ^R−azo and alkyne-Pd^II/ L ^S−azo, were prepared via the coordination of alkyne-Pd^II and azobenzene-modified phosphine ligands L ^R−azo and L ^S−azo. Owing to the cis-trans photoisomerization of the azobenzene moiety, alkyne-Pd^II/ L ^R−azo and alkyne-Pd^II/ L ^S−azo exhibited different polymerization activities, helix-sense selectivities, and enantioselectivities during the polymerization of isocyanide monomers under irradiation of different wavelength lights. Furthermore, the achiral isocyanide monomer A- 1 could be polymerized efficiently using alkyne-Pd^II/ L ^R−azo under dark condition in a living/controlled manner. Further, it generated single right-handed helical poly-A- 1 _m( L ^R−azo), confirmed by the circular dichroism spectra and atomic force microscopy images. However, the polymerization of A- 1 almost could not be initiated under 420 nm light in identical conditions of dark condition. Moreover, the photoswitchable catalyst alkyne-Pd^II/ L ^R−azo exhibited high enantioselectivity for the polymerization of the racemates of L- 1 and D- 1 , respectively. D- 1 was polymerized preferentially under dark condition with a D- 1 /L- 1 rate ratio of 70, yielding single right-handed polyisocyanides. Additionally, reversible enantioselectivity was observed under 420 nm light using alkyne-Pd^II/ L ^R−azo, and the calculated polymerization rate ratio of L- 1 /D- 1 was 57 because of the isomerization of the azobenzene moiety of the catalyst. Furthermore, alkyne-Pd^II/ L ^S−azo showed opposite enantioselectivity and helix-sense selectivity during the polymerization of the racemates of L- 1 and D- 1 .     

Reversible Live-Cell Labeling with Retro-engineered HaloTags Enables Long-Term High- and Super-Resolution Imaging

Self-labeling enzymes (SLE) such as the HaloTag have emerged as powerful tools in high and super-resolution fluorescence microscopy. Newly developed fluorogenic SLE substrates enable imaging in the presence of excess dye. To exploit this feature for reversible labeling, we engineered two variants of HaloTag7 with restored dehalogenase activity. Kinetic studies in vitro showed different turnover kinetics for reHaloTagS (≈0.006 s⁻¹) and reHaloTagF (≈0.055 s⁻¹). Imaging by confocal and stimulated emission depletion microscopy yielded 3-5-time enhanced photostability of reHaloTag labeling. Prominently, single molecule imaging with reHaloTags enabled controlled and stable labeling density over extended time periods. By combination with structured illumination, simultaneous visualization of single molecule diffusion and organellar dynamics was achieved. These applications highlight the potential of reHaloTag labeling for pushing the limits of advanced fluorescence microscopy techniques.     

Controlling the Assembly of Cellulose-Based Oligosaccharides through Sequence Modifications

Peptides and nucleic acids with programmable sequences are widely explored for the production of tunable, self-assembling functional materials. Herein we demonstrate that the primary sequence of oligosaccharides can be designed to access materials with tunable shapes and properties. Synthetic cellulose-based oligomers were assembled into 2D or 3D rod-like crystallites. Sequence modifications within the oligosaccharide core influenced the molecular packing and led to the formation of square-like assemblies based on the rare cellulose IV_II allomorph. In contrast, modifications at the termini generated elongated aggregates with tunable surfaces, resulting in self-healing supramolecular hydrogels.     

Enhanced Charging in Common Environments Compared to Independent Environments for Two-Level Systems

The charging process of a quantum battery (i.e., a two-level system) is studied in two scenarios, that is, a quantum battery and a charger are coupled to the common reservoir environments or coupled to their respective independent environments. In the common reservoir scenario, it is shown that the optimal charging process can be realized by increasing the number of environments and setting the same coupling strength between battery-reservoirs and charger-reservoirs. In the independent reservoir scenario, however, it is shown that decreasing either the number of reservoir environments or the coupling strength would enhance the charging performance. These results demonstrate that the charging performance of quantum batteries can be significantly improved by constructing common environments. This may be of help to the realization of the quantum battery with optimal charging performance in multiple environments.