Characterization of intrinsic ultracontractivity for one dimensional Schrödinger operators

We consider a Schrödinger operator $L=?d^2/d{x}^2+V(x)$ on $\mathbb{R}$, where V is a real-valued measurable function, and give an explicit and simple characterization of intrinsic ultracontractivity (IU) of the Schrödinger semigroup generated by L for a wide class of potentials. By making use of it, we also give new examples of potentials for which the semigroups satisfy (IU) or non-(IU).     

Amphiphilic liquid‐crystalline 4‐miktoarm star copolymers with a siloxane junction leading to cylindrically nanostructured templates for a siloxane‐based nanodot array

Well‐defined A₃B‐, A₂B₂‐, and AB₃‐type 4‐miktoarm star copolymers (M_n = 10,500–16,200, M_w/M_n = 1.16–1.18) consisting of poly(ethylene oxide) (PEO) and polymethacrylate bearing an azobenzene mesogen (PMA(Az)) as the arms and cyclotetrasiloxane as the core unit were synthesized using a combined route composed of a thiol‐ene click reaction and atom transfer radical polymerization. Microphase‐separated structures of the star copolymers in thin films with a thickness of approximately 100 nm were investigated by GISAXS and TEM. The A₃B‐type star‐(PEO)₃[PMA(Az)]₁ copolymer formed a more highly ordered PEO cylinder array with perpendicular alignment in the PMA(Az) matrix than that of the corresponding linear‐type block copolymer. The center‐to‐center distance of the PEO cylinders and the cylinder diameter were 13 and 4 nm, respectively. The highly ordered star‐(PEO)₃[PMA(Az)]₁ thin film was directly transferred to a siloxane‐based nanodot array by oxygen reactive ion etching. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 1175–1188     

Homo‐double helix formation of an optically active conjugated polymer bearing carboxy groups and amplification of the helicity upon complexation with achiral and chiral amines

An optically active, m‐terphenyl‐based π‐conjugated polymer bearing carboxy groups was synthesized by the copolymerization of the diethynyl monomer bearing a carboxy group with (S,S)‐2,5‐bis(2‐methylbutoxy)‐1,4‐dibromobenzene using Sonogashira reaction. The copolymer showed a weak circular dichroism (CD) in the main‐chain chromophore region due to a homo‐double helix formation with an excess helical handedness biased by the chiral alkoxy substituents through self‐association. However, upon complexation with achiral amines, such as piperidine, the CD intensity of the polymer significantly increased resulting in the formation of a greater excess one‐handed homo‐double helix via hydrogen‐bonded inclusion complexation with the achiral amines between each strand, leading to the amplification of the helicity. A preferred‐handed homo‐double helix was also induced in the polymer in the presence of nonracemic amines. The effect of the achiral and chiral amines on the homo‐double helix formation was investigated by comparing the CD spectra of the polymer to those of its model dimer. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 990–999     

A novel method for determination of inorganic oxyanions by electrospray ionization mass spectrometry using dehydration reactions

Novel methods for the determination of inorganic oxyanions by electrospray (ES) ionization mass spectrometry have been developed using dehydration reactions between oxyanions and carboxylic acids at the ES interface. Twelve oxyanions (VO₃^?, CrO₄^2?, MoO₄^2?, WO₄^2?, BO₃^3?, SiO₃^2?, SiO₄^4?, AsO₄^4?, AsO₂^?, SeO₄^2?, SeO₃^2? and NO₂^?), out of 16 tested, reacted with at least one of four aminopolycarboxylic acids, i.e. iminodiacetic acid (IDA), nitrilotriacetic acid (NTA), trans‐1,2‐diaminocyclohexane‐N,N,N′,N′‐tetraacetic acid and triethylenetetramine‐N,N,N′,N″,N′″,N′″‐hexaacetic acid, at the ES interface to produce the dehydration products that gave intense mass ion responses, sufficient for trace analysis. As examples, trace determinations of Cr^VI and silica in water samples were achieved after online ion exchange chromatography, where the dehydration product of CrO₄^2? and NTA (m/z 290) and that of SiO₄^4? and IDA (m/z 192) were measured. The limits of detection of the respective methods were 17 nM (0.83 ng Cr/ml) for Cr^VI and 0.17 μM (4.8 ng Si/mL) for SiO₄^4?. Copyright © 2016 John Wiley & Sons, Ltd.     

Cross‐Coupling of Organolithium with Ethers or Aryl Ammonium Salts by C−O or C−N Bond Cleavage

Various aryl‐, alkenyl‐, and/or alkyllithium species reacted smoothly with aryl and/or benzyl ethers with cleavage of the inert C?O bond to afford cross‐coupled products, catalyzed by commercially available [Ni(cod)₂] (cod=1,5‐cyclooctadiene) catalysts with N‐heterocyclic carbene (NHC) ligands. Furthermore, the coupling reaction between the aryllithium compounds and aryl ammonium salts proceeded under mild conditions with C?N bond cleavage in the presence of a [Pd(PPh₃)₂Cl₂] catalyst. These methods enable selective sequential functionalizations of arenes having both C?N and C?O bonds in one pot.     

Mechanism of BPh3-Catalyzed N-Methylation of Amines with CO2 and Phenylsilane: Cooperative Activation of Hydrosilane

BPh₃ catalyzes the N-methylation of secondary amines and the C-methylenation (methylene-bridge formation between aromatic rings) of N,N-dimethylanilines or 1-methylindoles in the presence of CO₂ and PhSiH₃; these reactions proceed at 30–40 °C under solvent-free conditions. In contrast, B(C₆F₅)₃ shows little or no activity. ¹¹B NMR spectra suggested the generation of [HBPh₃]⁻. The detailed mechanism of the BPh₃-catalyzed N-methylation of N-methylaniline ( 1 ) with CO₂ and PhSiH₃ was studied by using DFT calculations. BPh₃ promotes the conversion of two substrates (N-methylaniline and CO₂) into a zwitterionic carbamate to give three-component species [Ph(Me)(H)N⁺CO₂⁻⋅⋅⋅BPh₃]. The carbamate and BPh₃ act as the nucleophile and Lewis acid, respectively, for the activation of PhSiH₃ to generate [HBPh₃]⁻, which is used to produce key CO₂-derived species, such as silyl formate and bis(silyl)acetal, essential for the N-methylation of 1 . DFT calculations also suggested other mechanisms involving water for the generation of [HBPh₃]⁻ species.     

Edge proximity and matching extension in projective planar graphs

A graph $G$ with at least $2m+2$ vertices is said to be distance $d$ $m$-extendable if, for any matching $M$ of $G$ with $m$ edges in which the edges lie at distance at least $d$ pairwise, there exists a perfect matching of $G$ containing $M$. In this paper we prove that every 5-connected triangulation on the projective plane of even order is distance 3 7-extendable and distance 4 $m$-extendable for any $m$.