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 .

     

Unveiling the Layer‐Dependent Catalytic Activity of PtSe2 Atomic Crystals for the Hydrogen Evolution Reaction

Two‐dimensional (2D) PtSe₂ shows the most prominent layer‐dependent electrical properties among various 2D materials and high catalytic activity for hydrogen evolution reaction (HER), and therefore, it is an ideal material for exploring the structure–activity correlations in 2D systems. Here, starting with the synthesis of single‐crystalline 2D PtSe₂ with a controlled number of layers and probing the HER catalytic activity of individual flakes in micro electrochemical cells, we investigated the layer‐dependent HER catalytic activity of 2D PtSe₂ from both theoretical and experimental perspectives. We clearly demonstrated how the number of layers affects the number of active sites, the electronic structures, and electrical properties of 2D PtSe₂ flakes and thus alters their catalytic performance for HER. Our results also highlight the importance of efficient electron transfer in achieving optimum activity for ultrathin electrocatalysts. Our studies greatly enrich our understanding of the structure–activity correlations for 2D catalysts and provide new insight for the design and synthesis of ultrathin catalysts with high activity.     

Simultaneous determination of major components of Huangqi–Honghua extract in rat plasma using LC–MS/MS and application to a pharmacokinetic study

A sensitive and reliable LC–MS/MS method was developed and validated for simultaneous quantification of the major components of Huangqi–Honghua extact in rat plasma, including hydroxysafflor yellow A (HSYA), astragaloside IV (ASIV), calycosin‐7‐O‐β‐d ‐glucoside (CAG), calycosin, calycosin‐3′‐O‐glucuronide (C‐3′‐G) and calycosin‐3′‐O‐sulfate (C‐3′‐S). After extraction by protein precipitation with acetonitrile and methanol from plasma, the analytes were separated on a Hypersil BDS C₁₈ column by gradient elution with acetonitrile and 5 mM ammonium acetate. The detection was carried out on a triple quadrupole tandem mass spectrometer equipped with electrospray ionization source switched between negative and positive modes. HSYA was monitored in negative ionization mode from 0 to 4.9 min, and ASIV, CAG, calycosin, C‐3′‐G and C‐3′‐S were determined in positive ionization mode from 4.9 to 10 min. The lower limits of quantification of the analytes were 6.25 ng/mL for HSYA, 0.781 ng/mL for CAG and 1.56 ng/mL for ASIV and calycosin. The intra‐ and inter‐assay precision (RSD) values were within 13.43%, and accuracy (RE) ranged from ?8.75 to 9.92%. The validated method was then applied to the pharmacokinetic study of HSYA, ASIV, CAG, calycosin, C‐3′‐G and C‐3′‐S in rat after an oral administration of Huangqi–Honghua extract.     

Miktoarm star‐shaped poly(lactic acid) copolymer: Synthesis and stereocomplex crystallization behavior

The miktoarm star‐shaped poly(lactic acid) (PLA) copolymer, (PLLA)₂‐core‐(PDLA)₂, was synthesized via stepwise ring‐opening polymerization of lactide with dibromoneopentyl glycol as the starting material. ¹H NMR and FTIR spectroscopy proved the feasibility of synthetic route and the successful preparation of star‐shaped PLA copolymers. The results of FTIR spectroscopy and XRD showed that the stereocomplex structure of the copolymer could be more perfect after solvent dissolution treatment. Effect of chain architectures on crystallization was investigated by studying the nonisothermal and isothermal crystallization of the miktoarm star‐shaped PLA copolymer and other stereocomplexes. Nonisothermal differential scanning calorimetry and polarizing optical microscopy tests indicated that (PLLA)₂‐core‐(PDLA)₂ exhibited the fastest formation of a stereocomplex in a dynamic test due to its special structure. In isothermal crystallization tests, the copolymer exhibited the fast crystal growth rate and the most perfect crystal morphology. The results reveal that the unique molecular structure has an important influence on the crystallization of the miktoarm star‐shaped PLA copolymer. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 814–826     

Graphs are (1,Δ+1)-choosable

A graph $G$ is $(k,k^{\prime })$-choosable if the following holds: For any list assignment $L$ which assigns to each vertex $v$ a set $L\left(v\right)$ of $k$ real numbers, and assigns to each edge $e$ a set $L\left(e\right)$ of $k^{\prime }$ real numbers, there is a total weighting $?:V\left(G\right)\cup E\left(G\right)\to R$ such that $?\left(z\right)\in L\left(z\right)$ for $z\in V\cup E$, and ${\sum }_{e\in E\left(u\right)}?\left(e\right)+?\left(u\right)\ne {\sum }_{e\in E\left(v\right)}?\left(e\right)+?\left(v\right)$ for every edge $uv$. This paper proves that if $G$ is a connected graph of maximum degree $\Delta \ge 2$, then $G$ is $(1,\Delta +1)$-choosable.     

A nickel oxide nanoflakes/reduced graphene oxide composite and its high-performance lithium-storage properties

Journal of Solid State Electrochemistry - Since conventional graphite-based anode possesses a low capacity, seeking for high-capacity anode candidates becomes significant for constructing emerging...     

Investigation of mononuclear,dinuclear, and trinuclear transition metal (II) complexes derived from an asymmetric Salamo‐based ligand possessing three different coordination modes

A new asymmetric Salamo‐based ligand H₂L was synthesized using 3‐tert‐butyl‐salicylaldehyde and 6‐methoxy‐2‐[O‐(1‐ethyloxyamide)]‐oxime‐1‐phenol. By adjusting the ratio of the ligand H₂L and Cu (II), Co (II), and Ni (II) ions, mononuclear, dinuclear, and trinuclear transition metal (II) complexes, [Cu(L)], [{Co(L)}₂], and [{Ni(L)(CH₃COO)(CH₃CH₂OH)}₂Ni] with the ligand H₂L possessing completely different coordination modes were obtained, respectively. The optical spectra of ligand H₂L and its Cu (II), Co (II) and Ni (II) complexes were investigated. The Cu (II) complex is a mononuclear structure, and the Cu (II) atom is tetracoordinated to form a planar quadrilateral structure. The Co (II) complex is dinuclear, and the two Co (II) atoms are pentacoordinated and have coordination geometries of distorted triangular bipyramid. The Ni (II) complex is a trinuclear structure, and the terminal and central Ni (II) atoms are all hexacoordinated, forming distorted octahedral geometries. Furthermore, optical properties including UV–Vis, IR, and fluorescence of the Cu (II), Co (II), and Ni (II) complexes were investigated. Finally, the antibacterial activities of the Cu (II), Co (II), and Ni (II) complexes were explored. According to the experimental results, the inhibitory effect was found to be enhanced with increasing concentrations of the Cu (II), Co (II), and Ni (II) complexes.     

细胞松弛素B阻断微核法鉴定男性个体辐射敏感性的方法初探

初步研究了男性个体辐射敏感性的鉴定方法及标准。采集50名男性志愿者的外周血，分别给予不同剂量X射线照射，采用细胞松弛素B阻断双核法测定微核率(MNF)，通过二阶多项拟合法，绘制微核剂量效应选项中心标准曲线，将个人微核剂量效应曲线与标准曲线比对后判断个体辐射敏感性。 $0.0\sim2.5 $ Gy剂量范围内，剂量效应二阶多项拟合的中心方程为(MNF=0.014 7+0.036 2D+0.023 1D 2， r=0.726)。50名志愿者中，辐射敏感的有13人，辐射抗性的有14人，基本符合正态分布。Spearman秩和相关分析结果显示，MNF在各个辐射剂量点与辐射敏感性均存在正相关,与辐射抗性呈负相关,MNF随剂量增加而增加。本研究初步建立了“以线代点”男性个体辐射敏感性鉴定方法,并发现男性外周血淋巴细胞的本底微核率与个体辐射敏感性呈正相关。     

An Upper Bound for the w-Weak Global Dimension of Pullbacks

Let R be a commutative ring with identity and I0 an ideal of R.We introduce and study the c-weak global dimension c-w.gl.dim(R/I0) of the factor ring R/I0.Let T be a w-linked extension of R,and we also introduce the wR-weak global dimension wR-w.gl.dim(T) of T.We show that the ring T with wR-w.gl.dim(T) =0 is exactly a field and the ring T with wR-w.gl.dim(T) ≤ 1 is exactly a PwRMD.As an application,we give an upper bound for the w-weak global dimension of a Cartesian square (RDTF,M).More precisely,if T is w-linked over R,then w-w.gl.dim(R) ≤ max{wR-w.gl.dim(T) + w-fdR T,c-w.gl.dim(D) + w-fdn D}.Furthermore,for a Milnor square (RDTF,M),we obtain w-w.gl.dim(R) ≤ max{wR-w.gl.dim(T) + w-fdR T,w-w.gl.dim(D) + w-fdR D}.