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.     

An algorithm to locate perinatal facilities in the municipality of Rio de Janeiro

In order to reduce infant mortality in the municipality of Rio de Janeiro it is desired to encourage all mothers-to-be to attend the appropriate health care facilities. A 3-level hierarchical prenatal–neonatal health care system is described together with a basic model for optimising accessibility to facilities. A genetic algorithm to solve the basic model is developed and some numerical experience reported. Extensions to the basic model and planned future research are briefly indicated.     

Inversion of adjunction for non-degenerate hypersurfaces

 We prove a precise inversion of adjunction formula for the log variety (ℂ ^{d +1},X), where X is a non-degenerate hypersurface. As a corollary, the minimal log discrepancies of non-degenerate normal hypersurface singularities are bounded by dimension. Received: 17 September 2002 / Revised version: 22 November 2002 Published online: 14 February 2003 Current address: DPMMS, CMS, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, England. e-mail: f.ambro@dpmms.cam.ac.uk Mathematics Subject Classification (2000): Primary 14B05; Secondary 14M25, 52B20     

Synthesis and Characterization of Silica@Copper Core–Shell Nanoparticles: Application for Conjugate Addition Reactions

Silica@copper (SiO₂@Cu) core–shell nanoparticles were synthesized and well characterized by XRD, TEM, AFM, XPS, UV/Vis, TGA–MS, and ICP–AES techniques. The synthesized SiO₂@Cu core–shell nanoparticles were employed as catalysts for the conjugate addition of amines to α,β‐unsaturated compounds in water to obtain β‐amino carbonyl compounds in excellent yields in shorter reaction times. Furthermore, the catalyst works well for hetero‐Michael addition reactions of heteroatom nucleophiles such as thiols to α,β‐unsaturated compounds. As the reaction is performed in water, it allows for easy recycling of the catalyst with consistent activity.     

Dislocation model of a nanotwin

We propose a dislocation model of a nanotwin, which is used to calculate the stress fields in the nanotwin. We consider the role of these stresses in the process of interdislocation interaction and nanotwin growth.     

Accuracy analysis of airborne gravimeter calibration using repeated flight paths

Some possible errors in determining the gravity anomalies are discussed. Such errors may be caused by an inaccurate calibration of the gravimeter used in an airborne survey system. An approach based on wavelet decompositions is proposed for its additional calibration with the use of flight data obtained during repeated flights.     

Parametric oscillations and stability of systems with large modulation coefficient

We study parametric oscillations of linear systems with one degree of freedom for large values of the modulation coefficient. We use the classical analytic Lyapunov-Poincaré perturbation methods and an original numerically-analytic method of accelerated convergence to construct periodic solutions and the corresponding eigenvalues. We find the boundaries of stability and instability domains. We use specific models to illustrate the main properties of parametric oscillations of systems with singular character of the perturbation dependence on the modulation coefficient. We consider periodic boundary value problems for the modified Mathieu equation and the Kochin equation modeling crankshaft torsional vibrations and show that there are significant differences between weakly and essentially perturbed periodicmotions both for the lowest and arbitrary oscillation modes. We also describe the unusual properties of the boundaries in the domain of the system determining parameters.