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.     

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.     

Buckling of a stiff thin film on a compliant substrate in large deformation

A finite-deformation theory is developed to study the mechanics of thin buckled films on compliant substrates. Perturbation analysis is performed for this highly nonlinear system to obtain the analytical solution. The results agree well with experiments and finite element analysis in wavelength and amplitude. In particular, it is found that the wavelength depends on the strain. Based on the accurate wavelength and amplitude, the membrane and peak strains in thin films, and stretchability and compressibility of the system are also obtained analytically.     

Multi-layer thin films/substrate system subjected to non-uniform misfit strains

Current methodologies used for the inference of thin film stress through curvature measurement are strictly restricted to stress and curvature states that are assumed to remain uniform over the entire film/substrate system. These methodologies have recently been extended to a single layer of thin film deposited on a substrate subjected to the non-uniform misfit strain in the thin film. Such methodologies are further extended to multi-layer thin films deposited on a substrate in the present study. Each thin film may have its own non-uniform misfit strain. We derive relations between the stresses in each thin film and the change of system curvatures due to the deposition of each thin film. The interface shear stresses between the adjacent films and between the thin film and the substrate are also obtained from the system curvatures. This provides the basis for the experimental determination of thin film stresses in multi-layer thin films on a substrate.     

Closed-form solutions for a rectangular layer with central crack under anti-plane shear stress

We consider the problem of determining the stress distributionin a finite rectangular elastic layer containing a Griffithcrack which is opened by internal shear stress acting alongthe length of the crack. The mode III crack is assumed to belocated in the middle plane of the rectangular layer. The followingtwo problems are considered: (A) the central crack is perpendicularto the two fixed lateral surfaces and parallel to the othertwo stress-free surfaces; (B) all the lateral surfaces of therectangular layer are clamped and the central crack is parallelto the two lateral surfaces. By using Fourier transformations,we reduce the solution of each problem to the solution of dualintegral equations with sine kernels and a weight function whichare solved exactly. Finally, we derive closed-form expressionsfor the stress intensity factor at the tip of the crack andthe numerical values for the stress intensity factor at theedges of the cracks are presented in the form of tables.     

An algebra of meromorphic corner symbols

Operators on manifolds with corners that have base configurations with geometric singularities can be analysed in the frame of a conormal symbolic structure which is in spirit similar to the one for conical singularities of Kondrat'ev's work. Solvability of elliptic equations and asymptotics of solutions are determined by meromorphic conormal symbols. We study the case when the base has edge singularities which is a natural assumption in a number of applications. There are new phenomena, caused by a specific kind of higher degeneracy of the underlying symbols. We introduce an algebra of meromorphic edge operators that depend on complex parameters and investigate meromorphic inverses in the parameter-dependent elliptic case. Among the examples are resolvents of elliptic differential operators on manifolds with edges.     

Roles of rhenium diimine complexes as metal‐ion probes and photosensitizers in functional polyurethanes

Polyurethanes incorporated with rhenium diimine complexes were synthesized. The polymers exhibited interesting morphologies and solution properties. Results from gel permeation chromatography suggested the formation of polymer aggregates in solutions. The polymers could act as probes for metal ions. The addition of metal ions to polymer solutions led to significant changes in the electronic absorption properties of the polymer solutions. This was attributed to the interactions between the polyether moieties and metal ions. The metal complexes could also act as efficient photosensitizers. After doping with charge‐transport viologens, the photoconductivity of the polymers was greatly enhanced. The experimental quantum efficiency was simulated with Onsager's theory. The thermalization distances and the primary yields were typically 12–14 Å and 10^?3, respectively. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1708–1715, 2003