On a Result of R. Turner

We study the similarity of perturbed compact operators to operators of block-diagonal structure with respect to some family of orthogonal projection operators, which allows us to refine and essentially strengthen results due to R. Turner. We obtain information about the operator realizing the similarity transformation, present estimates for the eigenvalues and eigenvectors of the perturbed operator, and also study the inverse problem of spectral analysis.     

Unforeseen formation of 2-bromo-3-hydroxybenzaldehyde by bromination of 3-hydroxybenzaldehyde

Contrary to literature reports, bromination of 3-hydroxybenzaldehyde can afford both 2-bromo-5-hydroxybenzaldehyde and 2-bromo-3-hydroxybenzaldehyde, but 4-bromo-3-hydroxybenzaldehyde was not detected. 2-Bromo-3-hydroxybenzaldehyde was converted into 2-(benzyloxy)-1-bromo-5-methoxy-7-methylnaphthalene. X-ray crystallographic analysis supports the identity of 2-bromo-3-hydroxybenzaldehyde.     

Book rewiev

Howard Anton and Robert C. Busby, John Wiley & Sons, Inc., 2002.     

Sensitivity analysis of an optimized bar-spring model with hill-top branching

Summary Characteristics of optimal solutions under nonlinear buckling constraints are investigated by using a bar-spring model. It is demonstrated that optimization under buckling constraints of a symmetric system often leads to a structure with hill-top branching, where a limit point and bifurcation points coincide. A general formulation is derived for imperfection sensitivity of the critical load factor corresponding to a hill-top branching point. It is shown that the critical load is not imperfection-sensitive even for the case where an asymmetric bifurcation point exists at the limit point.     

Estimate for the Best Approximation of Summable Functions of Several Variables with a Certain Symmetry of Fourier Coefficients

An upper bound for the best approximation of summable functions of several variables by trigonometric polynomials in the metric of L is determined in terms of Fourier coefficients. We consider functions representable by trigonometric series with certain symmetry of coefficients satisfying a multiple analog of the Sidon–Telyakovskii conditions.     

O priblizhenii i kharakterizatsii periodicheskikh funktsii mnogikh peremennykh, imeyushchikh mazhorantu smeshannykh modulei nepreryvnosti spetsial'nogo vida

V stat'e izuchayutsya klassy periodicheskikh funktsii mnogikh peremennykh s zadannoi mazhorantoi smeshannykh modulei nepreryvnosti, prichem mazhoranta imeet spetsial'nyi vid. Rassmotreny nailuchshie priblizheniya ukazannykh klassov i vozmozhnost' kharakterizatsii 'etikh klassov cherez nailuchshie priblizheniya.     

Application of a generalized residual model to frequency domain modal parameter estimation

Residuals have long been used in frequency domain parameter estimation methods to model the influence of out-of-band modes but, typically, as a fixed set of no more than two or three terms. Recently, a systematic approach to the use of residual polynomials has led to the development of a generalized residual model. The use of a generalized residual model with rational fraction polynomial frequency domain parameter estimation methods allows the contribution of out-of-band modes to be included without increasing the model order and creating additional computational poles. Of particular interest is the use of the generalized residual for single-degree-of-freedom (s.d.o.f.) techniques, which generally do not consider the residual effects and suffer accordingly. With the use of generalized residuals, it becomes possible to properly account for nearby modes and also extract accurate residues with an s.d.o.f. algorithm. The development of the generalized residual polynomial model is outlined and a new s.d.o.f. frequency domain algorithm with generalized residuals is developed.     

Synthesis of Highly Functionalized Isoxazolinediones from One-pot Reaction of Alkylidene Meldrum ’s Acid with Alkyl Isocyanides in the Presence of Arylhydroxylamines

Alkyl isocyanides undergo a smooth reaction with alkylidene Meldrum’s acids in the presence of arylhydroxylamines to produce N ¹-alkyl-2-(3,5-dioxo-2-aryltetrahydro-4-isoxazolyl)alkanamides in high yields.     

Mechanisms of n‐butanol formation in butyl acrylate latexes

The mechanisms involved in the formation of n‐butanol during the synthesis of butyl acrylate containing latices were investigated. The experimental results showed that neither the hydrolysis of butyl acrylate nor of the ester bond in the butyl acrylate segments of the polymer played a major role in the formation of n‐butanol, which was mainly generated from the polymer backbone, by transfer reactions to polymer chain followed by cyclization. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5838–5846, 2007     

Magnetic poly(N‐isopropylacrylamide) microspheres by dispersion and inverse emulsion polymerization

The aim of this study was to develop novel thermally responsive polymer microspheres with magnetic properties. Dispersion and inverse emulsion copolymerization of N‐isopropylacrylamide (NIPAAm) and N,N′‐methylenebisacrylamide (MBAAm) was investigated in the presence of γ‐Fe₂O₃ nanoparticles. The resulting microspheres were characterized in terms of morphology, size, polydispersity, iron content, and temperature‐dependent swelling using optical microscopy, transmission electron microscopy, scanning electron microscopy, QELS, and AAS. The effects of several variables, such as the concentration of γ‐Fe₂O₃, MBAAm crosslinking agent, Span 80 surfactant, 2,2′‐azobis(2‐methyloctanenitrile) (AMON) initiator, and polymerization temperature on the properties of the microspheres were studied. Swelling and thermoresponsive behavior of the microspheres containing γ‐Fe₂O₃ nanoparticles were also investigated. The microspheres contained about 8 wt % of iron. The presence of magnetic nanoparticles and their concentration changes did not have any significant effect on the temperature sensitivity of the composites. The particles gradually shrink into an increasingly collapsed state when the temperature is raised to 40 °C since the increase in temperature weakens the hydration and PNIPAAm chains gradually become more hydrophobic, which leads to the collapse of the particles. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5884–5898, 2007