次线性期望下的一般中心极限定理

受Peng-中心极限定理的启发,本文主要应用G-正态分布的概念,放宽Peng-中心极限定理的条件,在次线性期望下得到形式更为一般的中心极限定理.首先,将均值条件E[X_n]=ε[X_n]=0放宽为|E[X_n]|+|ε[X_n]|=O(1/n);其次,应用随机变量截断的方法,放宽随机变量的2阶矩与2+δ阶矩条件;最后,将该定理的Peng-独立性条件进行放宽,得到卷积独立随机变量的中心极限定理.     

Reductions on equivalence relations generated by universal sets

Let X, Y be Polish spaces, , . We say A is universal for Γ provided that each x‐section of A is in Γ and each element of Γ occurs as an x‐section of A. An equivalence relation generated by a set is denoted by , where . The following results are shown:

• (1) If A is a set universal for all nonempty closed subsets of Y, then is a equivalence relation and .
• (2) If A is a set universal for all countable subsets of Y, then is a equivalence relation, and
  • (i) and ;
  • (ii) if , then ;
  • (iii) if every set is Lebesgue measurable or has the Baire property, then .
  • (iv) for , if every set has the Baire property, and E is any equivalence relation, then .

     

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.     

A novel PCR-based technology for rapid and non-sequencing authentication of Bombyx batryticatus using species-specific primers

A novel PCR technology was developed to detect short DNA fragments using species-specific primers for rapid and non-sequencing authentication of Bombyx batryticatus based on differences in the mitochondrial genome. Three specifically designed primer reactions were established to target species for the reliable identification of their commercial products. They were confirmed to have a high inter-species specificity and intra-species stability. The limit of detection was estimated as 1 ng of genomes for Beauveria bassiana and 100 pg for Bombyx mori and Metarhizium anisopliae. Furthermore, validation results demonstrated that raw materials and their processed products can be conveniently authenticated with good sensitivity and precision using this newly proposed approach. In particular, when counterfeits were assayed, these primer sets performed well, whereas COI barcoding technology did not. These could also assist in the discrimination and identification of adulterates of other animal-derived medicines in their pulverized and processed forms and even in complexes.     

An efficient approach to isoquinoline via AgNO3-promoted 6-endo-dig cyclization followed by oxidative elimination of o-alkynylarylaldimines and its application in fluoride recognition

A novel 6-endo-dig cyclization followed by oxidation/elimination of o-alkynylarylaldimines with 4-hydroxybenzylamine was developed for preparation of isoquinolines. The intermediates of this tandem reaction were monitored by mass spectroscopy (MS) to confirm the reaction pathway. This methodology was further applied to the design and synthesis of a novel ratiometric chemosensor for determination of fluoride.     

CH3NH3PbBr3 Nanocrystals Formed in situ in Polystyrene Used for Increasing the Color Rendering Index of White Leds

Theoretical and Experimental Chemistry - A new method is proposed for the formation of MAPbBr3 nanoparticles in situ in a dispersion of polystyrene in toluene in the absence (MAPbBr3@PS) and...     

Synthesis of Tri‐ and Difluoromethoxylated Compounds by Visible‐Light Photoredox Catalysis

Trifluoromethoxy (OCF₃) and difluoromethoxy (OCF₂H) groups are fluorinated structural motifs that exhibit unique physicochemical characteristics. Incorporation of these substituents into organic molecules is a highly desirable approach used in medicinal chemistry and drug discovery processes to alter the properties of a parent compound. Recently, tri‐ and difluoromethyl ethers have received increasing attention and several innovative strategies to access these valuable functional groups have been developed. The focus of this Minireview is the use of visible‐light photoredox catalysis in the synthesis of tri‐ and difluoromethyl ethers. Recent photocatalytic strategies for the formation of O?CF₃, C?OCF_3, O?CF₂H, and C?OCF₂H bonds as well as other transformations leading to the construction of OR_F groups are discussed herein.     

A stable pillared metal–organic framework constructed by H4TCPP ligand as luminescent sensor for selective detection of TNP and Fe3+ ions

A novel luminescent metal–organic framework ( Zn‐TCPP/BPY ) with pillared structure based on 2,3,5,6‐tetrakis(4‐carboxyphenyl)pyrazine (H₄TCPP) and 4,4′‐bipyridine (BPY) has been designed and synthesized through a solvothermal reaction. The [Zn₂(COO)₄] paddlewheel units are linked by TCPP^4? ligands to form two‐dimensional layers and further connected by BPY ligands as pillars to construct the twofold interpenetrating three‐dimensional framework. Interestingly, Zn‐TCPP/BPY possesses outstanding stability in organic solvents and water as well as maintains its structural rigidity in aqueous solutions of different pH values (3–12). After activation, Zn‐TCPP/BPY possesses permanent porosity with Brunauer–Emmett–Teller surface area of 630 m² g^–1. Remarkably, Zn‐TCPP/BPY displays excellent fluorescent property in virtue of the aggregation‐induced emission effect of the H₄TCPP ligand, which can be highly active and quenched by small amounts of 2,4,6‐trinitrophenol (TNP) and Fe³⁺ ions. Furthermore, the detection effect of Zn‐TCPP/BPY remains basically the same even after five cycles. The excellent stability, high sensitivity, and recyclability of Zn‐TCPP/BPY make it an outstanding chemical sensor for detecting TNP and Fe³⁺ ions.     

Metabolomic analysis of raw Pinelliae Rhizoma and its alum‐processed products via UPLC–MS and their cytotoxicity

Alum‐processing is a traditional method to attenuate the toxicity of Pinelliae Rhizoma (tubers of Pinellia ternate, PT). The present study aimed at investigating the chemical and cytotoxic changes during alum processing. Metabolomic profiles of raw and alum‐processed PT were studied based on ultra‐performance liquid chromatography coupled with Orbitrap mass spectrometry. More than 80 chemicals in positive MS mode and 40 chemicals in negative MS mode, such as organic acids, amino acids, glucosides and nucleosides, were identified after multivariate statistical analysis, including principal component analysis and orthogonal partial least‐square discriminant analysis. Almost all of the identified chemical markers were significantly decreased ~10‐ to 100‐fold after alum processing. Meanwhile, the correlations between the chemical markers were assimilated to a positive coefficient from disorderly distribution during the processing. Raw PT extracts could inhibit the proliferation of human carcinoma cells (HCT‐116, HepG2, and A549) at the rate of 40.5, 24.8 and 31.6% more strongly than processed PT. It was concluded that the alum processing of PT could decrease the number of actively water‐soluble principles at the same time as decreasing toxicity. Given the water‐insoluble property of toxic calcium oxalate raphides in PT, we suggest that a more scientific processing method should be sought.     

Polymer nanoparticles with a sensitive CO2‐responsive hydrophilic/hydrophobic surface

Poly(methyl methacrylate) (PMMA) nanoparticles with a sensitive CO₂‐responsive hydrophilic/hydrophobic surface that confers controlled dispersion and aggregation in water were prepared by emulsion polymerization at 50 °C under CO₂ bubbling using amphiphilic diblock copolymers of 2‐dimethylaminoethyl methacrylate (DMAEMA) and N‐isopropyl acrylamide (NIPAAm) as an emulsifier. The amphiphilicity of the hydrophobic–hydrophilic diblock copolymer at 50 °C was triggered by CO₂ bubbling in water and enabled the copolymer to serve as an emulsifier. The resulting PMMA nanoparticles were spherical, approximately 100 nm in diameter and exhibited sensitive CO₂/N₂‐responsive dispersion/aggregation in water. Using copolymers with a longer PNIPAAm block length as an emulsifier resulted in smaller particles. A higher concentration of copolymer emulsifier led to particles with a stickier surface. Given its simple preparation and reversible CO₂‐triggered amphiphilic behavior, this newly developed block copolymer emulsifier offers a highly efficient route toward the fabrication of sensitive CO₂‐stimuli responsive polymeric nanoparticle dispersions. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 2149–2156