Classification of metal ions according to their complexing properties: a data-driven approach

Factor, cluster and self-organizing map analyses were performed for the stability constants of complexes of 24 metal ions and hydrogen with 3960 ligands (15606 values of log K₁). Five factors reproduce 89% of data variability. Both direct clusterization and clusterization on the basis of factor analysis established the existence of six different classes of similar cations. The similarity series for metal ions and relative similarity of several ions are discussed and the Kohonen two-dimensional map, which visually represents the similarity, is presented.     

On the Order of the Lebesgue Constants for Interpolation by Algebraic Polynomials from Values at Uniform Nodes of a Simplex

For interpolation processes by algebraic polynomials of degree n from values at uniform nodes of an m-simplex, where m ≥ 2, we obtain the order of growth in n of the Lebesgue constants, which coincides with that in the one-dimensional case for which Turetskii obtained an asymptotics earlier.__________Translated from Matematicheskie Zametki, vol. 77, no. 6, 2005, pp. 814–831.Original Russian Text Copyright ©2005 by N. V. Baidakova.     

Elementary reaction analysis of the radical polymerization of α‐ethyl β‐N‐(α′‐methylbenzyl)itaconamates carrying (RS)‐ and (S)‐α‐methylbenzylaminocarbonyl groups

The polymerizations of α‐ethyl β‐N‐(α′‐methylbenzyl)itaconamates carrying (RS)‐ and (S)‐α‐methylbenzylaminocarbonyl groups (RS‐EMBI and S‐EMBI) with dimethyl 2,2′‐azobisisobutyrate (MAIB) were studied in methanol (MeOH) and in benzene kinetically and with electron spin resonance (ESR) spectroscopy. The initial polymerization rate (R_p) at 60 °C was given by R_p = k[MAIB]^{0.58 ± 0.05}[RS‐EMBI]^{2.4 ± 0.l} and R_p = k[MAIB]^{0.61 ± 0.05}[S‐EMBI]^{2.3 ± 0.l} in MeOH and R_p = k[MAIB]^{0.54 ± 0.05}[RS‐EMBI]^{1.7 ± 0.l} in benzene. The rate constants of initiation (k_df), propagation (k_p), and termination (k_t) as elementary reactions were estimated by ESR, where k_d is the rate constant of MAIB decomposition and f is the initiator efficiency. The k_p values of RS‐EMBI (0.50–1.27 L/mol s) and S‐EMBI (0.42–1.32 L/mol s) in MeOH increased with increasing monomer concentrations, whereas the k_t values (0.20?7.78 × 10⁵ L/mol s for RS‐EMBI and 0.18?6.27 × 10⁵ L/mol s for S‐EMBI) decreased with increasing monomer concentrations. Such relations of R_p with k_p and k_t were responsible for the unusually high dependence of R_p on the monomer concentration. The activation energies of the elementary reactions were also determined from the values of k_df, k_p, and k_t at different temperatures. R_p and k_p of RS‐EMBI and S‐EMBI in benzene were considerably higher than those in MeOH. R_p of RS‐EMBI was somewhat higher than that of S‐EMBI in both MeOH and benzene. Such effects of the kinds of solvents and monomers on R_p were explicable in terms of the different monomer associations, as analyzed by ¹H NMR. The copolymerization of RS‐EMBI with styrene was examined at 60 °C in benzene. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1819–1830, 2003     

Existence theory for linearly elastic shells

We review existence and uniqueness results, recently obtained for three of the most important linear two-dimensional shell models: Koiter’s model, the bending model and the membrane model. They rely on a crucial lemma of J L Lions, used in an essential way for establishing in each case a generalized Korn’s inequality, which is then combined with a generalized rigid displacement lemma of a geometrical nature. Dedicated to the memory of Professor K G Ramanathan     

A note on obtaining vibrational mixing parameter from average bending energy criterion

An analytical expression is given for the mixing parameter that characterizes the vibrational eigen vector matrix in the second-order case based on the criterion of minimization of average bending energy of molecular vibration. The expression, which is derived on the assumption that the parameter is small, contains only molecular geometry and the two normal frequencies of the vibrational species. Bent symmetric XY₂ molecular system is treated as an example and the calculated values of the parameter are in good agreement with the standard results.     

Refractive index and nonlinear optical properties of polyaniline derivatives

An investigation of the refractive index and third-order nonlinear optical susceptibility χ⁽³⁾ of two polypernigraniline derivatives, poly (4,4'-diphenylimine methine) (PDPIM) and poly (4,4'-diphenylimine p-heptyloxybenzylidene) (PDPIHB) reveals effects of molecular structure on the linear optical and nonlinear optical properties of conjugated polymers. The χ⁽³⁾ (?3ωω,ω,ω) of PDPIM was found to decrease relative to polypernigraniline, reflecting the observed decrease of the oscillator strength of the 2.2 eV absorption band when a methine carbon replaces one of the nitrogen atoms of pernigraniline repeat unti. The alkoxyphenylene side group substitution at the methine carbon in PDPIHB, however, significantly enhances the nonlinear optical response of PDPIHB while reducing the refractive index compared to PDPIM and polypernigraniline. The present results suggest that structural changes in conjugated polymers can be made in such a way as to enhance the nonlinear optical properties while modulating the linear optical properties. © 1994 John Wiley & Sons, Inc.     

The determination of an equivalent elastic modulus for bodies with cracks by boundary element method

The equivalent elastic modulus of cracked bodies with orderly distributed cracks was computed with the boundary element method. A practical self-consistent scheme has been proposed in consideration of the mutual interaction effects of the cracks. The influence of friction coefficients and orientation of cracks has been investigated. Some computational examples have been given, and the results show that the proposed method is adequate and the scheme is efficient.This project is supported by the National Natural Science Foundation of China.     

The mechanical anisotropy of stratified polyvinyl chloride

The mechanical anisotropy of a material obtained by stratification of oriented polyvinyl chloride (PVC) layers in different ways has been studied. PVC layers, uniaxially oriented by drawing each with a different draw ratio, were stratified in such a way that their draw axes were either parallel or perpendicular. The propagation velocities of ultrasonic pulses were measured in three principal planes defined by draw axes of the stratified material. With an immersion technique, measurements were performed at 2 MHz and 22°C. Experimentally, it was shown that while stratification of layers with draw axes parallel preserves hexagonal symmetry, the stratified material with layers' draw axes perpendicular possesses orthorhombic symmetry. © 1994 John Wiley & Sons, Inc.     

Transmission boundary condition for mixed variable finite-difference method

All kinds of numerical methods based on the discretization of first-order velocity-stress hyperbolic system of elastic wave equations are named mixed variable finite-difference method in this paper, and the transmission boundary condition of artificial boundaries is studied here by the mixed variable finite-difference method. The transmission condition of complex geometrical boundaries of a transversely isotropic medium is presented based on the characteristic variables of wavefields propagating in the normal direction of the boundary. The boundary condition proposed in this paper is a local artificial boundary condition, with which the computation cost is very low. Elastic wave propagations in transversely isotropic medium are modelled by the staggered grid finite-difference method incorporated with the boundary condition presented. Numerical results and analysis of reflection coefficients show that the reflections of incoming waves by artificial boundaries are efficiently reduced.Supported by National Natural Science Foundation and Liaoning Province Science Foundation.