Progress in Polyarsolyl Chemistry

The synthesis of heteroatom analogues of the cyclopentadienyl anion Cp^? is a fascinating and challenging field of research. The replacement of methine moieties by phosphorus is well investigated for the synthesis of mono‐, tri‐ and pentaphospholyl ligands. On the other hand, arsenic derivatives are rare and 1,2,4‐triarsolyl and tetraarsolyl salts are unknown. Herein, we report on the synthesis of Cs[E₃C₂(trip)₂] ( 1 a : E=P; 1 b : E=As; trip=2,4,6‐triisopropylphenyl) and Cs[E₄C(trip)] ( 2 a : E=P; 2 b : E=As). Compound 1 b represents the first 1,2,4‐triarsolyl and 2 b the first tetraarsolyl anion. All salts are obtained in one‐pot syntheses using E(SiMe₃)₃, 2,4,6‐triisopropylbenzoyl chloride and CsF. The products 1 a ?2 C₄H₈O₂, 2 a ?Et₂O and 2 b ?3 C₄H₈O₂ were characterized by X‐ray structural analysis, which revealed planar heterocycles. Nucleus‐independent chemical shifts (NICS) confirmed the aromaticity of these anions. Notably, compound 2 a ?Et₂O is only the second tetraphospholyl ligand which is structurally characterized.     

纳米多孔二氧化钛电极辅助光电化学降解乙酰氨基酚及伐昔洛韦

作为一类具有较高生物活性的物质,药物及个人护理品对环境的污染引起人们越来越多的关注.对乙酰氨基酚和伐昔洛韦是两种使用广泛的药物,由于其潜在的对人类健康和生态安全的威胁而逐渐成为研究热点.而电化学辅助光氧化技术因其具备能够高效处理难降解化学品的优点而得到广泛使用.本文合成了纳米多孔二氧化钛电极,研究了电化学还原处理对纳米多孔二氧化钛电极辅助光电化学降解对乙酰氨基酚和伐昔洛韦的影响.使用扫描电镜和色散谱技术对合成的纳米多孔二氧化钛电极的形态和元素组成进行了表征.循环伏安法、莫特-肖特基曲线、紫外-可见分光光度计和总有机碳分析仪被用来研究对乙酰氨基酚和伐昔洛韦的光电化学降解过程.结果显示,对乙酰氨基酚和伐昔洛韦的光化学降解和电化学降解过程非常缓慢,在研究的时间范围内其浓度未见明显变化,因此可以忽略不计.但是对乙酰氨基酚和伐昔洛韦的光电化学降解速度比较快,与未经处理的纳米多孔二氧化钛电极相比,经过电化学还原处理的电极可以使对乙酰氨基酚和伐昔洛韦的光电化学降解分别提高86.96%和53.12%.这可能是由于在电化学还原处理过程中生成了Ti3+, Ti2+和氧空位以及导电性的提高.还研究了温度对对乙酰氨基酚和伐昔洛韦光电化学降解的影响,随着温度升高,对乙酰氨基酚和伐昔洛韦的光电化学降解速率增大.     

Fluctuations in the homogenization of semilinear equations with random potentials

We study the stochastic homogenization and obtain a random fluctuation theory for semilinear elliptic equations with a rapidly varying random potential. To first order, the effective potential is the average potential and the nonlinearity is not affected by the randomness. We then study the limiting distribution of the properly scaled homogenization error (random fluctuations) in the space of square integrable functions, and prove that the limit is a Gaussian distribution characterized by homogenized solution, the Green’s function of the linearized equation around the homogenized solution, and by the integral of the correlation function of the random potential. These results enlarge the scope of the framework that we have developed for linear equations to the class of semilinear equations.     

Homoleptic Phosphaalkyne Complexes of Silver(I)

By employing silver salts with a weakly coordinating anion Ag[A] ([A]=[FAl{OC₁₂F₁₅}₃], [Al{OC(CF₃)₃}₄]), two phosphaalkynes could be coordinated side‐on to a bare silver(I) center to form the unprecedented homoleptic complexes [Ag(η²‐P≡CtBu)₂][FAl{OC₁₂F₁₅}₃] ( 1 ) and [Ag(η²‐P≡CtBu)₂][Al{OC(CF₃)₃}₄] ( 2 ). DFT calculations show that the perpendicular arrangement in 1 is the minimum energy structure of the coordination of the two phosphaalkynes to a silver atom, whereas for 2 a unique square‐planar coordination mode of the phosphaalkynes at Ag⁺ was found. Reactions with donor molecules yield the trigonally planar coordinated silver salts [((CH₃)₂CO)Ag(η²‐P≡CtBu)₂][FAl{OC₁₂F₁₅}₃] ( 3 ) and [(C₇H₈)₂Ag(η²‐P≡CtBu)][FAl{OC₁₂F₁₅}₃] ( 4 ). All of the compounds were comprehensively characterized in solution and in the solid state.     

Online and Quasi-online Colorings of Wedges and Intervals

We consider proper online colorings of hypergraphs defined by geometric regions. We prove that there is an online coloring algorithm that colors N intervals of the real line using \({\Theta }(\log N/k)\) colors such that for every point p, contained in at least k intervals, not all the intervals containing p have the same color. We also prove the corresponding result about online coloring a family of wedges (quadrants) in the plane that are the translates of a given fixed wedge. These results contrast the results of the first and third author showing that in the quasi-online setting 12 colors are enough to color wedges (independent of N and k). We also consider quasi-online coloring of intervals. In all cases we present efficient coloring algorithms.     

Performance of the general amber force field in modeling aqueous POPC membrane bilayers

The aim of this work was to answer the question of whether the general amber force field (GAFF) is good enough to simulate fully hydrated POPC membrane bilayers. The test system contained 128 POPC and 2985 TIP3P water molecules. The equilibration was carried out in a nonarbitrary manner to reach the stable liquid-crystalline phase. The simulations were performed by using particle mesh Ewald electrostatics implemented in molecular dynamics packages Amber8 (NPT ensembles) and NAMD2 (NPgammaT ensembles). The computational results were assessed against the following experimental membrane properties: (i) area per lipid, (ii) area compressibility modulus, (iii) order parameter, (iv) gauche conformations per acyl chain, (v) lateral diffusion coefficients, (vi) electron density profile, and (vii) bound water at the lipid/water interface. The analyses revealed that the tested force field combination approximates the experimental values at an unexpectedly good level when the NPgammaT ensemble is applied with a surface tension of 60 mN m(-1) per bilayer. It is concluded that the GAFF/TIP3P combination can be utilized for aqueous membrane bilayer simulations, as it provides acceptable accuracy for biomolecular modeling.     

Radiative Transport in a Periodic Structure

We derive radiative transport equations for solutions of a Schrödinger equation in a periodic structure with small random inhomogeneities. We use systematically the Wigner transform and the Bloch wave expansion. The streaming part of the radiative transport equations is determined entirely by the Bloch spectrum, and the scattering part by the random fluctuations.     

Study of dielectric behaviour of woven fabric based on two phase models

Dielectric constant of textile fibres plays very important role in electrostatic behavior of textile materials during its processing and use. The effective dielectric constant of textile materials is defined as the ratio of capacitance of a parallel plate capacitor with the textile material to that of the capacitor without the textile material. This paper presents three models considering textile woven fabric as a mixture of air and fibre to relate dielectric constant of fibre material and the effective dielectric constant of fabric. The mathematical models have taken into account measured fabric parameters. Plain woven fabrics of high density polyethylene monofilament yarns were used to do the actual measurement and results of three models based on these fabrics are compared.     

Large antipodal families

A family {A _i | i ∈ I} of sets in ℝ ^d is antipodal if for any distinct i, j ∈ I and any p ∈ A _i , q ∈ A _j , there is a linear functional ϕ:ℝ ^d → ℝ such that ϕ(p) ≠ ϕ(q) and ϕ(p) ≤ ϕ(r) ≤ ϕ(q) for all r ∈ ∪ _i∈I A _i . We study the existence of antipodal families of large finite or infinite sets in ℝ³. The research was supported by the Hungarian-South African Intergovernmental Scientific and Technological Cooperation Programme, NKTH Grant no. ZA-21/2006 and South African National Research Foundation Grant no. UID 61853, as well as Hungarian National Foundation for Scientific Research Grants no. NK 67867, no. T47102, and no. K72537.