On the Characterization of the Core of a π-Prefrattini Subgroup of a Finite Soluble Group

Siberian Mathematical Journal - Let π be a set of primes and let H be a π-prefrattini subgroup of a finite soluble group G. We prove that there exist elements x, y, z ∈ G such that...     

Synthesis and Characterization of Phenolphthalein‐Containing Sulfonated Poly(arylene ether phosphine oxide)s by Direct Polycondensation for Proton Exchange Membrane

A series of novel phenolphthalein‐containing sulfonated poly(arylene ether phosphine oxide)s (sPAEPP) with various sulfonation degrees were synthesized by direct polycondensation. The structure of sPAEPP was confirmed by ¹H‐NMR, ¹³C‐NMR, and IR spectroscopy. The high‐molecular weight of these polymers was determined by gel permeation chromatography (GPC). The transparent, tough, and flexible membranes could be achieved by solution casting. The macroscopic properties and microstructure of the obtained membranes were investigated in detail. The results showed that these sPAEPP membranes displayed excellent properties in terms of swelling, proton conductivity, and methanol permeability. For example, sPAEPP‐100 membrane exhibited an appropriate water uptake of 33.1%, a swelling ratio of only 11.7% (lower than 20.1% of Nafion 117), a proton conductivity of 0.11 S cm^?1 (similar to that of Nafion 117) at 80 °C, and a methanol permeability of 4.82 × 10^?7 cm² s^?1. Meanwhile, it also presented outstanding oxidative stability. Atomic force microscope (AFM) micrographs showed that the hydrophilic domains of the sPAEPP‐100 membrane formed connected and narrow ionic channels, which contributed to its high proton conductivity and good dimensional stability. As a result, sPAEPP‐100 membrane displays excellent application prospect for fuel cells. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 1097–1104     

纯奇点范畴中的Buchweitz定理

我们定义纯奇点范畴D_(psg)~b(R)为有界纯导出范畴D_(pur)~b(R)与纯投射模构成的有界同伦范畴K~b(■)的Verdier商,得到了纯奇点范畴D_(psg)~b(R)三角等价于相对纯投射模的Gorenstein范畴的稳定范畴■的一个充分必要条件.同时,还给出三角等价D_(psg)~b(R)≌D_(psg)~b(S)的充分条件,这里R和S都是环.     

Estimation,dependence and stability of solutions of an iterative equation

Aequationes mathematicae - In this paper we study estimation, continuous dependence and Hyers–Ulam stability for continuous solutions of a second order iterative equation. First we give an...     

The catalytic performance study of polymerized ionic liquid synthesized in different conditions on alkylation of o‐Xylene with styrene

In this work, a series of novel acidic polymerized ionic liquids were used as heterogeneous catalyst for alkylation of o‐Xylene with styrene. And the effect of the amount of initiator and the type of acid used for ion exchange on catalyst structure and the catalytic performance of catalysts for alkylation were studied thoroughly. The experiment results show: when the percentage of the amount of initiator in the total material is 3%, the polymerized ionic liquid catalyst MPM‐SO₃H‐[C₃V][SO₃CF₃] has the most uniform with a specific surface area of 97.30 m²/g and a pore volume of 0.35 cm³/g. Benefiting from the unique structure features, MPM‐SO₃H‐[C₃V][SO₃CF₃] manifested an excellent catalytic performance for alkylation of o‐Xylene with styrene, along with the conversion of styrene was 96.8% and the yield of 1‐Phenyl‐1‐ortho‐xylene ethane was 94.7%. Therefore, this work provides a novel reference to the synthesis of polymerized ionic liquids and clearly explains the advantage of novel acidic polymerized ionic liquids on alkylation.     

Tuning Chemical and Physical Properties of Phosphorus Corroles for Advanced Applications

Although the affinity of metallocorroles to axial ligands is quite low, this is not the case when the chelated element is phosphorus. This work is hence focused on the mechanism of ligand exchange of six-coordinate phosphorus corroles as a tool for affecting their chemical and physical properties. These fundamental investigations allowed for the development of facile methodologies for the synthesis of a large series of complexes and the establishment of several new structure/activity profiles that may be used to understand and predict spectroscopic features and for tailor-made modification of photophysical and electrochemical properties. This is exemplified by the facile access to complexes with terminal groups that are of large potential for practical applications based on click chemistry, optical imaging, and surface science.     

Lewis Acid Transition-Metal-Catalyzed Hydrogen Activation: Structures,Mechanisms, and Reactivities

As a new type of bifunctional catalyst, the Lewis acid transition-metal (LA-TM) catalysts have been widely applied for hydrogen activation. This study presents a mechanistic framework to understand the LA-TM-catalyzed H₂ activation through DFT studies. The mer(trans)-homolytic cleavage, the fac(cis)-homolytic cleavage, the synergetic heterolytic cleavage, and the dissociative heterolytic cleavage should be taken as general mechanisms for the field of LA-TM catalysis. Four typical LA-TM catalysts, the Z-type κ⁴-L₃B-Rh complex tri(azaindolyl)borane-Rh, the X-type κ³-L₂B-Co complex bis-phosphino-boryl (PBP)-Co, the η²-BC-type κ³-L₂B-Pd complex diphosphine-borane (DPB)-Pd, and the Z-type κ²-LB-Pt complex (boryl)iminomethane (BIM)-Pt are selected as representative models to systematically illustrate their mechanistic features and explore the influencing factors on mechanistic variations. Our results indicate that the tri(azaindolyl)borane-Rh catalyst favors the synergetic heterolytic mechanism; the PBP-Co catalyst prefers the mer(trans)-homolytic mechanism; the DPB-Pd catalyst operates through the fac(cis)-homolytic mechanism, whereas the BIM-Pt catalyst tends to undergo the dissociative heterolytic mechanism. The mechanistic variations are determined by the coordination geometry, the LA-TM bonding nature, the electronic structure of the TM center, and the flexibility or steric effect of the LA ligands. The presented mechanistic framework should provide helpful guidelines for LA-TM catalyst design and reaction developments.     

Precise Synthesis of Poly(thioester)s with Diverse Structures by Copolymerization of Cyclic Thioanhydrides and Episulfides Mediated by Organic Ammonium Salts

The precise synthesis of poly(thioester)s with diverse structures is still a significant challenge in the polymeric materials field. Herein, we report a novel approach to the synthesis of well‐defined poly(thioester)s by the controlled alternating copolymerization of cyclic thioanhydrides and episulfides induced by simple organic ammonium salts. Both the cation and anion have strong effects on the copolymerization. [PPN]OAc ([PPN]=bis(triphenylphosphine)iminium) with a bulky cation was proven to be efficient in initiating this polymerization, yielding poly(thioester)s with a completely alternating structure, controlled molecular weight, and narrow polydispersity. The poly(thioester) obtained from succinic thioanhydride and propylene sulfide is a typical semicrystalline material, possessing a high refractive index of up to 1.78. Because it uses readily available monomers, this method is expected to open up a new route to poly(thioester)s with diverse structures and properties.     

Control the self-assembly of fluorenone-based polycatenars by tuning chain length

Using Suzuki coupling reactions as key steps, a series of fluorenone-based polycatenars, consisting of a central 2,7-diphenyl-9-fluorenone core connected with the 3,4,5-trialkoxybenzoate unit via –COO- linkage at each side have been synthesized. Upon elongation of the terminal alkyl chain, these compounds self-assembled into mesophase sequence of Col_hex/p6mm - Cub_I/$\mathit{Pm}\overline{3}n$ in solid states as well as organogels with interesting morphologies varied from 3D helical fibers to spherical structures in solvents.     

Brake Orbits of First Order Convex Hamiltonian Systems with Particular Anisotropic Growth

Combining the dual least action principle with Mountain-pass lemma,we obtain the existence of brake orbits for first-order convex Hamiltonian systems with particular anisotropic growth.