Numerical method and models for anti-plane strain of a system with a thin elastic wedge

The paper presents a general method to find asymptotics for a (multi-)wedge system containing a thin wedge. It employs separation of the symmetric and anti-symmetric parts of the boundary displacements and tractions of the wedge. The method is applicable when the angle of the thin wedge turns to zero. A physical interpretation of the derived equations is obtained by using power expansions of non-polynomial functions, which appear after the Mellin transform. We establish that the first term in the expansion of the symmetric part corresponds to shear, while the first term of the anti-symmetric part describes deflection of the wedge axis. Numerical experiments, performed by using a code developed on the basis of the theory, show that using only the first terms of the expansions insignificantly influence accuracy: the approximate results coincide with the exact values of roots to the third significant digit even for the wedge angle of 30°.     

Living anionic polymerization of N‐methoxymethyl‐N‐isopropylacrylamide: Synthesis of well‐defined poly(N‐isopropylacrylamide) having various stereoregularity

Anionic polymerization of N‐methoxymethyl‐N‐isopropylacrylamide ( 1 ) was carried out with 1,1‐diphenyl‐3‐methylpentyllithium and diphenylmethyllithium, ‐potassium, and ‐cesium in THF at ?78 °C for 2 h in the presence of Et₂Zn. The poly( 1 )s were quantitatively obtained and possessed the predicted molecular weights based on the feed molar ratios between monomer to initiators and narrow molecular weight distributions (M_w/M_n = 1.1). The living character of propagating carbanion of poly( 1 ) either at 0 or ?78 °C was confirmed by the quantitative efficiency of the sequential block copolymerization using N,N‐diethylacrylamide as a second monomer. The methoxymethyl group of the resulting poly( 1 ) was completely removed to give a well‐defined poly(N‐isopropylacrylamide), poly(NIPAM), via the acidic hydrolysis. The racemo diad contents in the poly(NIPAM)s could be widely changed from 15 to 83% by choosing the initiator systems for 1 . The poly(NIPAM)s obtained with Li⁺/Et₂Zn initiator system possessed syndiotactic‐rich configurations (r = 75–83%), while either atactic (r = 50%) or isotactic poly(NIPAM) (r = 15–22%) was generated with K⁺/Et₂Zn or Li⁺/LiCl initiator system, respectively. Atactic and syndiotactic poly(NIPAM)s (42 < r < 83%) were water‐soluble, whereas isotactic‐rich one (r < 31%) was insoluble in water. The cloud points of the aqueous solution of poly(NIPAM)s increased from 32 to 37 °C with the r‐contents. These indicated the significant effect of stereoregularity of the poly(NIPAM) on the water‐solubility and the cloud point in water © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4832–4845, 2006     

Concentrated electrolyte solutions at high temperatures and pressures

A survey is given of recent experimental results obtained from high-temperature, high-pressure investigations with water, aqueous solutions, and ionic fluids. Data on the static dielectric constant of water to 550°C and 5 kbar are given and discussed with respect to their relation to water structure. Infrared and Raman spectra of HDO in pure water have been obtained to 400°C and 4 kbar, which give information on hydrogen bonding. Xe–H₂O and CO₂–H₂O mixtures were investigated in the infrared. Ni(II) and Cu(II) complexes were investigated by absorption spectroscopy in aqueous solutions of high chloride content to 350°C and 2–6 kbar. The gas-liquid critical point of ammonium chloride was found at 880°C and 1635 bars. This fluid appears to be predominantly ionic even in the critical region. The possibility of converting pure polar fluids such as ammonia and water into concentrated ionic solutions by self-ionization at very high pressures is mentioned.This paper was presented at the symposium, The Physical Chemistry of Aqueous Systems, held at the University of Pittsburgh, Pittsburgh, Pennsylvania, June 12–14, 1972, in honor of the 70th birthday of Professor H. S. Frank.     

A “Multiplicative Coboundary” theorem for some sequences of random matrices

Schmidt(¹⁰) showed that if the family of distributions of the partial sums of a strictly stationary random sequence is tight, then that random sequence is a coboundary. Here an analog of that result is proved for some sequences of random matrices, with partial sums replaced by matrix products.     

Cloud point extraction equilibrium of lanthanum(III), europium(III) and lutetium(III) using di(2-ethylhexyl)phosphoric acid and Triton X-100

The cloud point extraction behaviors of lanthanoids(III) (Ln(III) = La(III), Eu(III) and Lu(III)) with and without di(2-ethylhexyl)phosphoric acid (HDEHP) using Triton X-100 were investigated. It was suggested that the extraction of Ln(III) into the surfactant-rich phase without added chelating agent was caused by the impurities contained in Triton X-100. The extraction percentage more than 91% for all Ln(III) metals was obtained using 3.0 × 10⁻⁵ mol dm⁻³ HDEHP and 2.0% (v/v) Triton X-100. From the equilibrium analysis, it was clarified that Ln(III) was extracted as Ln(DEHP)₃ into the surfactant-rich phase. The extraction constant of Ln(III) with HDEHP and 2.0% (v/v) Triton X-100 were also obtained.     

Quantitative separation of zinc traces from cadmium matrices by solid-phase extraction with polyurethane foam

A system for separation of zinc traces from large amounts of cadmium is proposed in this paper. It is based on the solid-phase extraction of the zinc in the form of thiocyanate complexes by the polyurethane foam. The following parameters were studied: effect of pH and of the thiocyanate concentration on the zinc extraction, shaking time required for quantitative extraction, amount of PU foam necessary for complete extraction, conditions for the separation of zinc from cadmium, influence of other cations and anions on the zinc sorption by PU foam, and required conditions for back extraction of zinc from the PU foam. The results show that zinc traces can be separated from large amounts of cadmium at pH 3.0±0.50, with the range of thiocyanate concentration from 0.15 to 0.20 mol l⁻¹, and the shaking time of 5 min. The back extraction of zinc can be done by shaking it with water for 10 min. Calcium, barium, strontium, magnesium, aluminum, nickel and iron(II) are efficiently separated. Iron(III), copper(II) and cobalt(II) are extracted simultaneously with zinc, but the iron reduction with ascorbic acid and the use of citrate to mask copper(II) and cobalt(II) increase the selectivity of the zinc extraction. The anions nitrate, chloride, sulfate, acetate, thiosulphate, tartarate, oxalate, fluoride, citrate, and carbonate do not affect the zinc extraction. Phosphate and EDTA must be absent. The method proposed was applied to determine zinc in cadmium salts using 4-(2-pyridylazo)-resorcinol (PAR) as a spectrophotometric reagent. The result achieved did not show significant difference in the accuracy and precision (95% confidence level) with those obtained by ICP–AES analysis.     

The computation of the representation matrices of the generators of the unitary group

A method is presented for the efficient computation of the representation matrices of the unitary group, U(n) in the Gelfand—Tsetlin basis (corresponding to the usual spin-symmetry adapted basis for an N electron CI). The present scheme is conceptually and computationally attractive in that it is formulated directly in terms of Weyl tableaux and also that it permits simultaneous basis vector generation and matrix element evaluation. In addition the basis vectors are ordered so that subsequent restriction to the three dimensional rotation group is facilitated. An illustrative example is also presented.Taken in part from a thesis submitted to the University of London in partial fulfilment of the requirements for the degree of PhD.     

Catalysis in Organic Solvents with Lipase Immobilized by Sol-Gel Technique

A series of immobilized lipases were obtained by sol-gel process, using silica prepolymers prepared from tetramethoxysilane, methyltrimethoxysilane, propyltrimethoxysilane and (3-aminopropyl)triethoxysilane. The activities of these biocatalysts were compared with the lipase adsorbed on poly(methylhydroxysiloxane) and encapsulated into a silicone rubber, lipase entrapped in nanoporous silica matrix and commercial sol-gel lipase. Model reactions were the esterification of stearic acid and Corey lactone bisalcohol (an intermediate of prostaglandin synthesis). The positive effect of hydrophobic-hydrophilic interface, created by the addition of organosilanes, on the activity of biocatalysts was partially reduced by decreasing specific surface of mesopores. Hydrophobic solvents increased the activity of the lipase entrapped in tetramethoxysilane–methyltrimethoxysilane prepolymer in the sequence acetone < toluene < benzene < decane < hexane. The activity of silicone rubber-encapsulated biocatalysts was proportional to polymer swelling in organic solvents (hexane > toluene > acetone).     

基于激光诱导击穿光谱(LIBS)的煤灰熔点快速检测

炉内结渣是影响火电机组和气化工艺可靠运行的关键因素之一,准确预测灰熔点可以提前调整炉膛出口温度以避免结渣。本论文采用激光诱导击穿光谱（LIBS）采集煤灰样中金属元素的光谱,分别建立煤灰中的金属元素的谱线强度与煤灰熔点的随机森林模型、支持向量机回归模型和线性回归模型,直接预测煤灰熔点温度。采用基于马氏距离(MD)的异常数据剔除算法和基于稀疏矩阵的基线估计与降噪算法（BEADS）,对粉煤灰样的全光谱数据进行了预处理。随机森林模型对粉煤灰熔点的预测平均相对误差（MRE）为54.74%,支持向量机回归模型的预测平均相对误差为60.08%,而线性回归模型的预测平均相对误差达到了9.78%。研究结果表明,线性回归模型对煤灰熔点的预测结果更准确。     

A Note on ＂Global Exponential Convergence Analysis of Hopfield Neural Networks with Continuously Distributed Delays＂

In this note, we would like to point out that （i） of Corollary 1 given by Zhang et al. （cf Commun. Theor. Phys. 39 （2003） 381） is incorrect in general.