Lehmer's problem for compact Abelian groups

We formulate Lehmer's Problem concerning the Mahler measure of polynomials for general compact abelian groups, introducing a Lehmer constant for each such group. We show that all nontrivial connected compact groups have the same Lehmer constant and conjecture the value of the Lehmer constant for finite cyclic groups. We also show that if a group has infinitely many connected components, then its Lehmer constant vanishes.

     

Water stability of a cheap sol-gel-based adhesive

The humidity and water tolerance of a sol-gel derived binder prepared using a cheap, multicomponent precursor has been studied. The sol was prepared by dissolving the precursor in water under acidic conditions using either formic acid or a mixture of formic acid and citric acid for pH adjustments. It is shown that a post-treatment temperature of 400 °C or higher is needed in order to achieve full binder stability under excess water conditions, as thermal decomposition of metal carboxylates leads to a pronounced decrease in water solubility of the gels. The mesoporous gel can be made hydrophobic by post-treatments with either a silane or an organophosphonate, showing that both silica and metal oxides are exposed on the surface of the binder. Surface functionalization is especially effective for gels heat-treated at higher temperatures where the metal carboxylates have decomposed to the corresponding oxides or carbonates. The results are expected to be of great importance for the use of this cheap binder in large scale industrial applications. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

Preparative and Mössbauer studies of Bi2Sr2Ca n-1Cu n O y compounds withn=2 or 3

The influence of sintering temperatures and nominal starting compositions on the phase contents of polycrystalline Bi₂Sr₂Ca _n-1Cu _n O_4+2n samples are reported. After every sintering the samples were characterized with X-ray diffraction and magnetic AC susceptibility measurements. For Mössbauer studies, in each case also a corresponding specimen containing⁵⁷Fe was synthetized. The identification of various superconducting Bi₂Sr₂Ca _n-1Cu _n O_4+2n phases on the basis of Mössbauer spectra consisting usually of three quadrupole doublets is discussed.     

A sublogarithmic convex hull algorithm

We present a parallel algorithm for finding the convex hull of a sorted set of points in the plane. Our algorithm runs inO(logn/log logn) time usingO(n log logn/logn) processors in theCommon crcw pram computational model, which is shown to be time and cost optimal. The algorithm is based onn ^1/3 divide-and-conquer and uses a simple pointer-based data structure.Part of this work was done when the last three authors were at the Department of Computer and Information Science, Linköping University. The research of the second author was supported by the Academy of Finland.     

Deposition of thin films of organic-inorganic hybrid materials based on aromatic carboxylic acids by atomic layer deposition

Thin films of organic-inorganic hybrid materials have been grown by the atomic layer deposition (ALD) technique, using trimethylaluminium (TMA) and aromatic carboxylic acids such as 1,2-benzene dicarboxylic acid, 1,3-benzene dicarboxylic acid, 1,4-benzene dicarboxylic acid, 1,3,5-benzene tricarboxylic acid, 1,2,4,5-benzene tetracarboxylic acid as precursors. Growth rates as function of temperature show that all systems, with the exception of the benzoic acid-TMA system, possess ALD-windows and provides growth rates in the range of 0.25-1.34 nm/cycle. X-ray diffraction studies of the as-deposited films reveal their amorphous character, which is also supported by very low surface roughness as measured by atomic force microscopy. As-deposited films were investigated by Fourier Transform Infrared Spectroscopy proving that the deposited films are of a hybrid character.     

Synthesis and Self‐Aggregation of Enantiopure and Racemic Molecular Tweezers Based on the Bicyclo[3.3.1]nonane Framework

A pair of molecular tweezers (syn‐ 4 ) that consists of quinoline and pyrazine units fused to a bicyclic framework is presented. The tweezers were synthesised both as a racemic mixture (rac‐ 4 ) and an enantiomerically pure form ((R,R,R,R)‐ 4 ) starting from either racemic or enantiomerically pure bicyclo[3.3.1]nonane‐2,6‐dione ( 3 ). Homochiral dimers were observed in the solid state for rac‐ 4 . The self‐association of both rac‐ 4 and (R,R,R,R)‐ 4 was studied in solution. A weak self‐association constant in CDCl₃ was estimated by ¹H NMR spectroscopic dilution titration experiments in both cases, following several proton resonances. For this purpose, a general normalisation model for the accurate determination of association constants from multiple datasets was developed. In contrast to the solid state, no diastereomeric discrimination was observed for rac‐ 4 in solution.     

珙桐叶总黄酮提取工艺及体外抗氧化性

运用正交试验设计探讨了绵竹白云山珙桐叶黄酮的微波辅助提取工艺条件,并对提取液的抗氧化性能进行了研究。结果表明,珙桐叶总黄酮提取的最佳工艺参数：微波功率700W,料液比（g/mL）1∶40,乙醇质量分数浓度为70%,提取时间为2min,测得每克干叶中总黄酮含量为71.03mg。对提取液的抗氧化性研究表明,珙桐叶总黄酮对超氧阴离子自由基、羟基自由基的清除率较好,在实验所选浓度范围内,总还原能力随浓度增加而增强。